Compare commits

..
49 Commits
Author SHA1 Message Date
seogi_macbook d010886c7e minor fix 2016-06-28 19:16:41 -07:00
seogi_macbook 222035d0b8 Modify testings ... for TDEM 2016-06-28 19:15:20 -07:00
seogi_macbook f4f10ff027 remove temporary print statemement. 2016-06-28 19:01:32 -07:00
seogi_macbook 53adb3abd7 Tracking memory leakages in TDEM code
- make PTv out from the loop
- do not use Data class in the loop for Jv
2016-06-28 19:00:39 -07:00
seogi_macbook 61a1d3207b delete fields_deriv 2016-06-28 11:42:30 -07:00
Lindsey Heagy 875885c684 typo fix 2016-06-28 11:28:44 -07:00
Lindsey Heagy e179b5e71d make sure factors of JtVec get cleaned 2016-06-28 11:25:17 -07:00
seogi_macbook 43d0b0369f Add printing for TDEM fwd problem. 2016-06-28 01:02:03 -07:00
seogi_macbook b7546d332b - Add CircularLoop for TDEM source
- Fix bug for verbose option in Problem_b (TDEM)
2016-06-27 22:59:57 -07:00
Lindsey Heagy 4e02ff3561 Merge branch 'em/dev' into em/ref/tdem 2016-06-20 11:45:44 -07:00
Lindsey Heagy 39ddec8702 Merge pull request #339 from simpeg/em/secondary_Rx
Implementation for Inverting Secondary B field
2016-06-20 12:45:00 -06:00
seogi_macbook e30a657abb update 1D example for simpegEMpaper 2016-06-17 18:22:57 -07:00
seogi_macbook 71213b9f91 Merge branch 'em/secondary_Rx' of https://github.com/simpeg/simpeg into em/ref/tdem 2016-06-17 17:39:01 -07:00
seogi_macbook 2fb0f3fbbb Implementation for Inverting Secondary B field 2016-06-17 07:50:13 -07:00
seogi_macbook fcac3e9bc7 simpegEM paper example 2016-06-12 10:33:42 -07:00
Lindsey Heagy 9c7c89b8ba Merge branch 'em/dev' into em/ref/tdem
# Conflicts:
#	SimPEG/EM/TDEM/SurveyTDEM.py
2016-06-02 07:41:03 -07:00
seogi_macbook 6f8f065643 Update current changes ... about u -> f 2016-06-01 23:45:52 -07:00
seogi_macbook 8e6536b2ed Merge branch 'em/ref/tdem' of https://github.com/simpeg/simpeg into em/ref/tdem
Conflicts:
	SimPEG/EM/FDEM/FieldsFDEM.py
	SimPEG/EM/FDEM/SurveyFDEM.py
2016-06-01 22:11:13 -07:00
Lindsey Heagy 6de786c972 Merge branch 'em/dev' into em/ref/tdem
# Conflicts:
#	SimPEG/EM/FDEM/FDEM.py
#	SimPEG/EM/FDEM/SrcFDEM.py
#	SimPEG/EM/FDEM/SurveyFDEM.py
#	SimPEG/Examples/EM_FDEM_1D_Inversion.py
2016-05-11 09:21:59 -07:00
seogi_macbook 20d75a9704 simple fix for inverting secondary magnetic fields 2016-04-05 09:38:49 -07:00
Lindsey Heagy 1be4082ea3 parse out SrcTDEM 2016-03-20 22:41:40 -07:00
Lindsey Heagy 2d8bbdce45 working to debug JTv for e-formulation... still some work to do 2016-03-20 11:42:31 -07:00
Lindsey Heagy 0be942730a start of Problem_e (e Jvec working) 2016-03-18 15:47:31 -07:00
Lindsey Heagy 74f4705048 cleanup of TDEM example 2016-03-14 13:25:09 -07:00
Lindsey Heagy a9efb2fc8a add dbdt to testing 2016-03-14 13:05:09 -07:00
Lindsey Heagy c91815d14f adjoint hooked up for b formulation 2016-03-14 12:28:05 -07:00
Lindsey Heagy fe91312917 bx, bz running and passing, ey failing adjoint --> I think the initial fields are not being taken care of correctly in the deriv 2016-03-13 14:02:32 -07:00
Lindsey Heagy 605e19eb22 combos will be tested in TDEM_b_DerivAdjoint 2016-03-13 12:35:44 -07:00
Lindsey Heagy f549756208 create only 1 fields object in Jtvec 2016-03-13 12:28:38 -07:00
Lindsey Heagy 576459d17c only save previous tilmestep for back solve (don't need all times) 2016-03-13 12:17:38 -07:00
Lindsey Heagy ea4721a941 first pass at multisrc Jtvec (will be hugely memory inefficient at the moment) 2016-03-13 12:07:26 -07:00
Lindsey Heagy c708ceb53d cleanup and minimal docs for Jvec, JTvec 2016-03-13 11:09:11 -07:00
Lindsey Heagy a1ecef0709 first shot through of passing Jtvec for TDEM problem (code will need to be cleaned up, but it passes!) 2016-03-12 15:13:17 -08:00
Lindsey Heagy fb66acea11 things in the adjoint are the right sizes, but not passing... +1,-1 somewhere?? 2016-03-10 13:08:39 -08:00
Lindsey Heagy 1b401feb54 cleaned up Jvec 2016-03-08 19:56:14 -08:00
Lindsey Heagy ceff861413 forward and Jvec using Adiag, Asubdiag, RHS 2016-03-08 19:38:44 -08:00
Lindsey Heagy 705cdd0c52 jtvec runs, fails 2016-03-08 16:38:45 -08:00
Lindsey Heagy 1d2eac62a3 e hooked up with Jvec 2016-03-06 21:42:30 -08:00
Lindsey Heagy 5cf0acd153 TDEM bderiv from b formulation working 2016-03-06 16:06:14 -08:00
Lindsey Heagy 664adb04ac light notation cleanup in Jvec, testing ADeriv --> passes, Jvec is still first order 2016-03-06 15:10:13 -08:00
Lindsey Heagy 4f31e4e002 tdem deriv runs but is first order at the moment 2016-03-06 11:13:48 -08:00
Lindsey Heagy 0bfc816ecc starting sensitivities 2016-03-04 10:43:19 -08:00
Lindsey Heagy 7ece7c3edb sketching out code 2016-03-04 08:45:36 -08:00
Lindsey Heagy 8bd027c2b2 sketch of derivs 2016-02-24 15:24:56 -08:00
Lindsey Heagy 617241ad4e TDEM forward refactor (no derive yet) 2016-02-22 18:15:29 -08:00
Lindsey Heagy d5967d20b9 forward is running, but not passing 2016-02-22 17:42:22 -08:00
Lindsey Heagy ecbd5c21f5 sketch of sources and waveforms 2016-02-22 15:13:25 -08:00
Lindsey Heagy 341e902469 merged in em/dev 2016-02-22 11:26:30 -08:00
Lindsey Heagy cd51ab8be7 sketching out TDEM problem 2016-02-22 11:04:18 -08:00
130 changed files with 2288 additions and 2168 deletions
+1 -1
View File
@@ -1,4 +1,4 @@
[bumpversion]
current_version = 0.1.12
current_version = 0.1.10
files = setup.py SimPEG/__init__.py docs/conf.py
-2
View File
@@ -39,5 +39,3 @@ nosetests.xml
*.sublime-workspace
docs/_build/
Makefile
docs/warnings.txt
.DS_Store
+4 -26
View File
@@ -24,25 +24,18 @@ env:
- TEST_DIR=tests/examples
- TEST_DIR=tests/em/fdem/inverse/adjoint
- TEST_DIR=tests/em/fdem/forward
- TEST_DIR=tests/docs;
GAE_PYTHONPATH=${HOME}/.cache/google_appengine;
PATH=$PATH:${HOME}/google-cloud-sdk/bin;
PYTHONPATH=${PYTHONPATH}:${GAE_PYTHONPATH};
CLOUDSDK_CORE_DISABLE_PROMPTS=1
# Setup anaconda
before_install:
# Install packages
- if [ ${TRAVIS_PYTHON_VERSION:0:1} == "2" ]; then wget http://repo.continuum.io/miniconda/Miniconda-3.8.3-Linux-x86_64.sh
-O miniconda.sh; else wget http://repo.continuum.io/miniconda/Miniconda3-3.8.3-Linux-x86_64.sh
-O miniconda.sh; fi
- if [ ${TRAVIS_PYTHON_VERSION:0:1} == "2" ]; then wget http://repo.continuum.io/miniconda/Miniconda-3.8.3-Linux-x86_64.sh -O miniconda.sh; else wget http://repo.continuum.io/miniconda/Miniconda3-3.8.3-Linux-x86_64.sh -O miniconda.sh; fi
- chmod +x miniconda.sh
- ./miniconda.sh -b
- export PATH=/home/travis/anaconda/bin:/home/travis/miniconda/bin:$PATH
- conda update --yes conda
# Install packages
install:
- conda install --yes pip python=$TRAVIS_PYTHON_VERSION numpy scipy matplotlib cython ipython nose vtk sphinx
- conda install --yes pip python=$TRAVIS_PYTHON_VERSION numpy scipy matplotlib cython ipython nose vtk
- pip install nose-cov python-coveralls
- git clone https://github.com/rowanc1/pymatsolver.git
@@ -53,26 +46,11 @@ install:
# Run test
script:
# test docs
- nosetests $TEST_DIR --with-cov --cov SimPEG --cov-config .coveragerc -v -s
# Calculate coverage
after_success:
- bash <(curl -s https://codecov.io/bash)
- if [ "$TRAVIS_BRANCH" = "master" -a "$TRAVIS_PULL_REQUEST" = "false" ]; then
if [ ${TEST_DIR} == "tests/docs" ]; then
python scripts/fetch_gae_sdk.py $(dirname "${GAE_PYTHONPATH}");
openssl aes-256-cbc -K $encrypted_93066031461c_key -iv $encrypted_93066031461c_iv
-in docs/credentials.tar.gz.enc -out credentials.tar.gz -d ;
if [ ! -d ${HOME}/google-cloud-sdk ]; then curl https://sdk.cloud.google.com | bash; fi ;
tar -xzf credentials.tar.gz ;
gcloud auth activate-service-account --key-file client-secret.json ;
gcloud config set project simpegdocs;
gcloud -q components update gae-python;
gcloud -q preview app deploy ./docs/app.yaml --version ${TRAVIS_COMMIT} --promote;
fi;
fi
- coveralls --config_file .coveragerc
notifications:
email:
+3 -8
View File
@@ -1,4 +1,4 @@
.. image:: https://raw.github.com/simpeg/simpeg/master/docs/images/simpeg-logo.png
.. image:: https://raw.github.com/simpeg/simpeg/master/docs/simpeg-logo.png
:alt: SimPEG Logo
======
@@ -15,7 +15,7 @@ SimPEG
.. image:: https://img.shields.io/badge/license-MIT-blue.svg
:target: https://github.com/simpeg/simpeg/blob/master/LICENSE
:alt: MIT license
:alt: BSD 3 clause license.
.. image:: https://api.travis-ci.org/simpeg/simpeg.svg?branch=master
:target: https://travis-ci.org/simpeg/simpeg
@@ -28,12 +28,7 @@ SimPEG
.. image:: http://img.shields.io/badge/GITTER-JOIN_CHAT-brightgreen.svg?style=flat-square
:alt: gitter chat room at https://gitter.im/simpeg/simpeg
:target: https://gitter.im/simpeg/simpeg
.. image:: https://codecov.io/gh/simpeg/simpeg/branch/master/graph/badge.svg
:target: https://codecov.io/gh/simpeg/simpeg
:alt: Coverage status
Simulation and Parameter Estimation in Geophysics - A python package for simulation and gradient based parameter estimation in the context of geophysical applications.
The vision is to create a package for finite volume simulation with applications to geophysical imaging and subsurface flow. To enable the understanding of the many different components, this package has the following features:
+2 -2
View File
@@ -162,8 +162,8 @@ class ProblemDC_CC(Problem.BaseProblem):
"""
Makes the matrix A(m) for the DC resistivity problem.
:param numpy.ndarray m: model
:rtype: scipy.sparse.csc_matrix
:param numpy.array m: model
:rtype: scipy.csc_matrix
:return: A(m)
.. math::
+1 -1
View File
@@ -71,7 +71,7 @@ class ProblemIP(Problem.BaseProblem):
Makes the matrix A(m) for the DC resistivity problem.
:param numpy.array m: model
:rtype: scipy.sparse.csc_matrix
:rtype: scipy.csc_matrix
:return: A(m)
.. math::
+17 -30
View File
@@ -167,7 +167,7 @@ class TargetMisfit(InversionDirective):
class SaveEveryIteration(InversionDirective):
class _SaveEveryIteration(InversionDirective):
@property
def name(self):
if getattr(self, '_name', None) is None:
@@ -188,7 +188,7 @@ class SaveEveryIteration(InversionDirective):
self._fileName = value
class SaveModelEveryIteration(SaveEveryIteration):
class SaveModelEveryIteration(_SaveEveryIteration):
"""SaveModelEveryIteration"""
def initialize(self):
@@ -198,7 +198,7 @@ class SaveModelEveryIteration(SaveEveryIteration):
np.save('%03d-%s' % (self.opt.iter, self.fileName), self.opt.xc)
class SaveOutputEveryIteration(SaveEveryIteration):
class SaveOutputEveryIteration(_SaveEveryIteration):
"""SaveModelEveryIteration"""
def initialize(self):
@@ -212,7 +212,7 @@ class SaveOutputEveryIteration(SaveEveryIteration):
f.write(' %3d %1.4e %1.4e %1.4e %1.4e\n'%(self.opt.iter, self.invProb.beta, self.invProb.phi_d, self.invProb.phi_m, self.opt.f))
f.close()
class SaveOutputDictEveryIteration(SaveEveryIteration):
class SaveOutputDictEveryIteration(_SaveEveryIteration):
"""SaveOutputDictEveryIteration"""
def initialize(self):
@@ -253,7 +253,8 @@ class SaveOutputDictEveryIteration(SaveEveryIteration):
class Update_IRLS(InversionDirective):
eps_min = None
eps = None
eps_p = None
eps_q = None
norms = [2.,2.,2.,2.]
factor = None
gamma = None
@@ -262,7 +263,6 @@ class Update_IRLS(InversionDirective):
f_old = None
f_min_change = 1e-2
beta_tol = 5e-2
prctile = 95
# Solving parameter for IRLS (mode:2)
IRLSiter = 0
@@ -297,22 +297,9 @@ class Update_IRLS(InversionDirective):
print "Convergence with smooth l2-norm regularization: Start IRLS steps..."
self.mode = 2
# Either use the supplied epsilon, or fix base on distribution of
# model values
if getattr(self, 'reg.eps', None) is None:
self.reg.eps_p = np.percentile(np.abs(self.invProb.curModel),self.prctile)
else:
self.reg.eps_p = self.eps[0]
if getattr(self, 'reg.eps', None) is None:
self.reg.eps_q = np.percentile(np.abs(self.reg.regmesh.cellDiffxStencil*(self.reg.mapping * self.invProb.curModel)),self.prctile)
else:
self.reg.eps_q = self.eps[1]
print "L[p qx qy qz]-norm : " + str(self.reg.norms)
print "eps_p: " + str(self.reg.eps_p) + " eps_q: " + str(self.reg.eps_q)
print self.eps_p, self.eps_q, self.norms
self.reg.eps_p = self.eps_p
self.reg.eps_q = self.eps_q
self.reg.norms = self.norms
self.coolingFactor = 1.
self.coolingRate = 1
@@ -356,14 +343,14 @@ class Update_IRLS(InversionDirective):
else:
self.f_old = phim_new
# # Cool the threshold parameter if required
# if getattr(self, 'factor', None) is not None:
# eps = self.reg.eps / self.factor
#
# if getattr(self, 'eps_min', None) is not None:
# self.reg.eps = np.max([self.eps_min,eps])
# else:
# self.reg.eps = eps
# Cool the threshold parameter if required
if getattr(self, 'factor', None) is not None:
eps = self.reg.eps / self.factor
if getattr(self, 'eps_min', None) is not None:
self.reg.eps = np.max([self.eps_min,eps])
else:
self.reg.eps = eps
# Get phi_m at the end of current iteration
self.phi_m_last = self.invProb.phi_m_last
-302
View File
@@ -1,302 +0,0 @@
from __future__ import division
import numpy as np
from scipy.constants import mu_0, pi, epsilon_0
from scipy.special import erf
from SimPEG import Utils
omega = lambda f: 2.*np.pi*f
# TODO:
# r = lambda dx, dy, dz: np.sqrt( dx**2. + dy**2. + dz**2.)
# k = lambda f, mu, epsilon, sig: np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
def E_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=0., epsr=1.):
"""
Computing Analytic Electric fields from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
mu = mu_0*(1+kappa)
epsilon = epsilon_0*epsr
sig_hat = sig + 1j*omega(f)*epsilon
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.shape[0] > 1:
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
dx = XYZ[:,0]-srcLoc[0]
dy = XYZ[:,1]-srcLoc[1]
dz = XYZ[:,2]-srcLoc[2]
r = np.sqrt( dx**2. + dy**2. + dz**2.)
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
front = current * length / (4.*np.pi*sig_hat* r**3) * np.exp(-1j*k*r)
mid = -k**2 * r**2 + 3*1j*k*r + 3
if orientation.upper() == 'X':
Ex = front*((dx**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
Ey = front*(dx*dy / r**2)*mid
Ez = front*(dx*dz / r**2)*mid
return Ex, Ey, Ez
elif orientation.upper() == 'Y':
# x--> y, y--> z, z-->x
Ey = front*((dy**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
Ez = front*(dy*dz / r**2)*mid
Ex = front*(dy*dx / r**2)*mid
return Ex, Ey, Ez
elif orientation.upper() == 'Z':
# x --> z, y --> x, z --> y
Ez = front*((dz**2 / r**2)*mid + (k**2 * r**2 -1j*k*r-1.))
Ex = front*(dz*dx / r**2)*mid
Ey = front*(dz*dy / r**2)*mid
return Ex, Ey, Ez
def E_galvanic_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
"""
Computing Galvanic portion of Electric fields from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
mu = mu_0*(1+kappa)
epsilon = epsilon_0*epsr
sig_hat = sig + 1j*omega(f)*epsilon
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.shape[0] > 1:
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
dx = XYZ[:,0]-srcLoc[0]
dy = XYZ[:,1]-srcLoc[1]
dz = XYZ[:,2]-srcLoc[2]
r = np.sqrt( dx**2. + dy**2. + dz**2.)
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
front = current * length / (4.*np.pi*sig_hat* r**3) * np.exp(-1j*k*r)
mid = -k**2 * r**2 + 3*1j*k*r + 3
if orientation.upper() == 'X':
Ex_galvanic = front*((dx**2 / r**2)*mid + (-1j*k*r-1.))
Ey_galvanic = front*(dx*dy / r**2)*mid
Ez_galvanic = front*(dx*dz / r**2)*mid
return Ex_galvanic, Ey_galvanic, Ez_galvanic
elif orientation.upper() == 'Y':
# x--> y, y--> z, z-->x
Ey_galvanic = front*((dy**2 / r**2)*mid + (-1j*k*r-1.))
Ez_galvanic = front*(dy*dz / r**2)*mid
Ex_galvanic = front*(dy*dx / r**2)*mid
return Ex_galvanic, Ey_galvanic, Ez_galvanic
elif orientation.upper() == 'Z':
# x --> z, y --> x, z --> y
Ez_galvanic = front*((dz**2 / r**2)*mid + (-1j*k*r-1.))
Ex_galvanic = front*(dz*dx / r**2)*mid
Ey_galvanic = front*(dz*dy / r**2)*mid
return Ex_galvanic, Ey_galvanic, Ez_galvanic
def E_inductive_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
"""
Computing Inductive portion of Electric fields from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
mu = mu_0*(1+kappa)
epsilon = epsilon_0*epsr
sig_hat = sig + 1j*omega(f)*epsilon
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.shape[0] > 1:
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
dx = XYZ[:,0]-srcLoc[0]
dy = XYZ[:,1]-srcLoc[1]
dz = XYZ[:,2]-srcLoc[2]
r = np.sqrt( dx**2. + dy**2. + dz**2.)
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
front = current * length / (4.*np.pi*sig_hat* r**3) * np.exp(-1j*k*r)
if orientation.upper() == 'X':
Ex_inductive = front*(k**2 * r**2)
Ey_inductive = np.zeros_like(Ex_inductive)
Ez_inductive = np.zeros_like(Ex_inductive)
return Ex_inductive, Ey_inductive, Ez_inductive
elif orientation.upper() == 'Y':
# x--> y, y--> z, z-->x
Ey_inductive = front*(k**2 * r**2)
Ez_inductive = np.zeros_like(Ey_inductive)
Ex_inductive = np.zeros_like(Ey_inductive)
return Ex_inductive, Ey_inductive, Ez_inductive
elif orientation.upper() == 'Z':
# x --> z, y --> x, z --> y
Ez_inductive = front*(k**2 * r**2)
Ex_inductive = np.zeros_like(Ez_inductive)
Ey_inductive = np.zeros_like(Ez_inductive)
return Ex_inductive, Ey_inductive, Ez_inductive
def J_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
"""
Computing Current densities from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
Ex, Ey, Ez = E_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=current, length=length, orientation=orientation, kappa=kappa, epsr=epsr)
Jx = sig*Ex
Jy = sig*Ey
Jz = sig*Ez
return Jx, Jy, Jz
def J_galvanic_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
"""
Computing Galvanic portion of Current densities from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
Ex_galvanic, Ey_galvanic, Ez_galvanic = E_galvanic_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=current, length=length, orientation=orientation, kappa=kappa, epsr=epsr)
Jx_galvanic = sig*Ex_galvanic
Jy_galvanic = sig*Ey_galvanic
Jz_galvanic = sig*Ez_galvanic
return Jx_galvanic, Jy_galvanic, Jz_galvanic
def J_inductive_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
"""
Computing Inductive portion of Current densities from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
Ex_inductive, Ey_inductive, Ez_inductive = E_inductive_from_ElectricDipoleWholeSpaced(XYZ, srcLoc, sig, f, current=current, length=length, orientation=orientation, kappa=kappa, epsr=epsr)
Jx_inductive = sig*Ex_inductive
Jy_inductive = sig*Ey_inductive
Jz_inductive = sig*Ez_inductive
return Jx_inductive, Jy_inductive, Jz_inductive
def H_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
"""
Computing Magnetic fields from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
mu = mu_0*(1+kappa)
epsilon = epsilon_0*epsr
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.shape[0] > 1:
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
dx = XYZ[:,0]-srcLoc[0]
dy = XYZ[:,1]-srcLoc[1]
dz = XYZ[:,2]-srcLoc[2]
r = np.sqrt( dx**2. + dy**2. + dz**2.)
# k = np.sqrt( -1j*2.*np.pi*f*mu*sig )
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
front = current * length / (4.*np.pi* r**2) * (-1j*k*r + 1) * np.exp(-1j*k*r)
if orientation.upper() == 'X':
Hy = front*(-dz / r)
Hz = front*(dy / r)
Hx = np.zeros_like(Hy)
return Hx, Hy, Hz
elif orientation.upper() == 'Y':
Hx = front*(dz / r)
Hz = front*(-dx / r)
Hy = np.zeros_like(Hx)
return Hx, Hy, Hz
elif orientation.upper() == 'Z':
Hx = front*(-dy / r)
Hy = front*(dx / r)
Hz = np.zeros_like(Hx)
return Hx, Hy, Hz
def B_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
"""
Computing Magnetic flux densites from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
Hx, Hy, Hz = H_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=current, length=length, orientation=orientation, kappa=kappa, epsr=epsr)
Bx = mu*Hx
By = mu*Hy
Bz = mu*Hz
return Bx, By, Bz
def A_from_ElectricDipoleWholeSpace(XYZ, srcLoc, sig, f, current=1., length=1., orientation='X', kappa=1., epsr=1.):
"""
Computing Electric vector potentials from Electrical Dipole in a Wholespace
TODO:
Add description of parameters
"""
mu = mu_0*(1+kappa)
epsilon = epsilon_0*epsr
XYZ = Utils.asArray_N_x_Dim(XYZ, 3)
# Check
if XYZ.shape[0] > 1 & f.shape[0] > 1:
raise Exception("I/O type error: For multiple field locations only a single frequency can be specified.")
dx = XYZ[:,0]-srcLoc[0]
dy = XYZ[:,1]-srcLoc[1]
dz = XYZ[:,2]-srcLoc[2]
r = np.sqrt( dx**2. + dy**2. + dz**2.)
k = np.sqrt( omega(f)**2. *mu*epsilon -1j*omega(f)*mu*sig )
front = current * length / (4.*np.pi*r)
if orientation.upper() == 'X':
Ax = front*np.exp(-1j*k*r)
Ay = np.zeros_like(Ax)
Az = np.zeros_like(Ax)
return Ax, Ay, Az
elif orientation.upper() == 'Y':
Ay = front*np.exp(-1j*k*r)
Ax = np.zeros_like(Ay)
Az = np.zeros_like(Ay)
return Ax, Ay, Az
elif orientation.upper() == 'Z':
Az = front*np.exp(-1j*k*r)
Ax = np.zeros_like(Ay)
Ay = np.zeros_like(Ay)
return Ax, Ay, Az
-1
View File
@@ -2,4 +2,3 @@ from TDEM import hzAnalyticDipoleT
from FDEM import hzAnalyticDipoleF
from FDEMcasing import *
from DC import DCAnalyticHalf, DCAnalyticSphere
from FDEMDipolarfields import *
+3 -4
View File
@@ -20,10 +20,10 @@ class BaseEMProblem(Problem.BaseProblem):
Problem.BaseProblem.__init__(self, mesh, **kwargs)
surveyPair = Survey.BaseSurvey #: The survey to pair with.
dataPair = Survey.Data #: The data to pair with.
surveyPair = Survey.BaseSurvey
dataPair = Survey.Data
PropMap = EMPropMap #: The property mapping
PropMap = EMPropMap
Solver = SimpegSolver
solverOpts = {}
@@ -217,7 +217,6 @@ class BaseEMSurvey(Survey.BaseSurvey):
def eval(self, f):
"""
Project fields to receiver locations
:param Fields u: fields object
:rtype: numpy.ndarray
:return: data
+61 -18
View File
@@ -6,11 +6,11 @@ from SimPEG.EM.Utils import omega
from SimPEG.Utils import Zero, Identity, sdiag
class FieldsFDEM(SimPEG.Problem.Fields):
class Fields(SimPEG.Problem.Fields):
"""
Fancy Field Storage for a FDEM survey. Only one field type is stored for
each problem, the rest are computed. The fields object acts like an array and is indexed by
each problem, the rest are computed. The fields obejct acts like an array and is indexed by
.. code-block:: python
@@ -60,6 +60,20 @@ class FieldsFDEM(SimPEG.Problem.Fields):
return self._bPrimary(solution, srcList) + self._bSecondary(solution, srcList)
def _bSecondary(self, solution, srcList):
"""
Total magnetic flux density is sum of primary and secondary
:param numpy.ndarray solution: field we solved for
:param list srcList: list of sources
:rtype: numpy.ndarray
:return: total magnetic flux density
"""
if getattr(self, '_bSecondary', None) is None:
raise NotImplementedError ('Getting b from %s is not implemented' %self.knownFields.keys()[0])
return self._bSecondary(solution, srcList)
def _h(self, solution, srcList):
"""
Total magnetic field is sum of primary and secondary
@@ -92,7 +106,7 @@ class FieldsFDEM(SimPEG.Problem.Fields):
"""
Total derivative of e with respect to the inversion model. Returns :math:`d\mathbf{e}/d\mathbf{m}` for forward and (:math:`d\mathbf{e}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: source
:param Src src: sorce
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
@@ -110,7 +124,7 @@ class FieldsFDEM(SimPEG.Problem.Fields):
"""
Total derivative of b with respect to the inversion model. Returns :math:`d\mathbf{b}/d\mathbf{m}` for forward and (:math:`d\mathbf{b}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: source
:param Src src: sorce
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
@@ -124,11 +138,26 @@ class FieldsFDEM(SimPEG.Problem.Fields):
return self._bDeriv_u(src, v, adjoint), self._bDeriv_m(src, v, adjoint)
return np.array(self._bDeriv_u(src, du_dm_v, adjoint) + self._bDeriv_m(src, v, adjoint), dtype = complex)
def _bSecondaryDeriv(self, src, du_dm_v, v, adjoint = False):
"""
Total derivative of b with respect to the inversion model. Returns :math:`d\mathbf{b}/d\mathbf{m}` for forward and (:math:`d\mathbf{b}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param Src src: sorce
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
:return: derivative times a vector (or tuple for adjoint)
"""
# TODO: modify when primary field is dependent on m
return self._bDeriv(src, du_dm_v, v, adjoint = adjoint)
def _hDeriv(self, src, du_dm_v, v, adjoint = False):
"""
Total derivative of h with respect to the inversion model. Returns :math:`d\mathbf{h}/d\mathbf{m}` for forward and (:math:`d\mathbf{h}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: source
:param Src src: sorce
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
@@ -146,7 +175,7 @@ class FieldsFDEM(SimPEG.Problem.Fields):
"""
Total derivative of j with respect to the inversion model. Returns :math:`d\mathbf{j}/d\mathbf{m}` for forward and (:math:`d\mathbf{j}/d\mathbf{u}`, :math:`d\mathb{u}/d\mathbf{m}`) for the adjoint
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: source
:param Src src: sorce
:param numpy.ndarray du_dm_v: derivative of the solution vector with respect to the model times a vector (is None for adjoint)
:param numpy.ndarray v: vector to take sensitivity product with
:param bool adjoint: adjoint?
@@ -160,12 +189,12 @@ class FieldsFDEM(SimPEG.Problem.Fields):
return self._jDeriv_u(src, v, adjoint), self._jDeriv_m(src, v, adjoint)
return np.array(self._jDeriv_u(src, du_dm_v, adjoint) + self._jDeriv_m(src, v, adjoint), dtype = complex)
class Fields3D_e(FieldsFDEM):
class Fields3D_e(Fields):
"""
Fields object for Problem3D_e.
:param BaseMesh mesh: mesh
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'eSolution':'E'}
@@ -180,6 +209,9 @@ class Fields3D_e(FieldsFDEM):
'h' : ['eSolution','CCV','_h'],
}
def __init__(self, mesh, survey, **kwargs):
Fields.__init__(self, mesh, survey, **kwargs)
def startup(self):
self.prob = self.survey.prob
self._edgeCurl = self.survey.prob.mesh.edgeCurl
@@ -423,12 +455,12 @@ class Fields3D_e(FieldsFDEM):
class Fields3D_b(FieldsFDEM):
class Fields3D_b(Fields):
"""
Fields object for Problem3D_b.
:param BaseMesh mesh: mesh
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'bSolution':'F'}
@@ -443,6 +475,9 @@ class Fields3D_b(FieldsFDEM):
'h' : ['bSolution','CCV','_h'],
}
def __init__(self,mesh,survey,**kwargs):
Fields.__init__(self,mesh,survey,**kwargs)
def startup(self):
self.prob = self.survey.prob
self._edgeCurl = self.survey.prob.mesh.edgeCurl
@@ -465,6 +500,8 @@ class Fields3D_b(FieldsFDEM):
return 'E'
elif fieldType == 'b':
return 'F'
elif fieldType == 'bSecondary':
return 'F'
elif (fieldType == 'h') or (fieldType == 'j'):
return'CCV'
else:
@@ -687,12 +724,12 @@ class Fields3D_b(FieldsFDEM):
return Zero()
class Fields3D_j(FieldsFDEM):
class Fields3D_j(Fields):
"""
Fields object for Problem3D_j.
:param BaseMesh mesh: mesh
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'jSolution':'F'}
@@ -707,6 +744,9 @@ class Fields3D_j(FieldsFDEM):
'b' : ['jSolution','CCV','_b'],
}
def __init__(self,mesh,survey,**kwargs):
Fields.__init__(self,mesh,survey,**kwargs)
def startup(self):
self.prob = self.survey.prob
self._edgeCurl = self.survey.prob.mesh.edgeCurl
@@ -979,12 +1019,12 @@ class Fields3D_j(FieldsFDEM):
return 1./(1j * omega(src.freq)) * VI * (self._aveE2CCV * ( s_mDeriv(v) - self._edgeCurl.T * ( self._MfRhoDeriv(jSolution) * v ) ) )
class Fields3D_h(FieldsFDEM):
class Fields3D_h(Fields):
"""
Fields object for Problem3D_h.
:param BaseMesh mesh: mesh
:param SimPEG.EM.FDEM.SurveyFDEM.Survey survey: survey
:param Mesh mesh: mesh
:param Survey survey: survey
"""
knownFields = {'hSolution':'E'}
@@ -999,6 +1039,9 @@ class Fields3D_h(FieldsFDEM):
'b' : ['hSolution','CCV','_b'],
}
def __init__(self,mesh,survey,**kwargs):
Fields.__init__(self,mesh,survey,**kwargs)
def startup(self):
self.prob = self.survey.prob
self._edgeCurl = self.survey.prob.mesh.edgeCurl
+16 -21
View File
@@ -1,7 +1,7 @@
from SimPEG import Problem, Utils, np, sp, Solver as SimpegSolver
from scipy.constants import mu_0
from SurveyFDEM import Survey as SurveyFDEM
from FieldsFDEM import FieldsFDEM, Fields3D_e, Fields3D_b, Fields3D_h, Fields3D_j
from FieldsFDEM import Fields, Fields3D_e, Fields3D_b, Fields3D_h, Fields3D_j
from SimPEG.EM.Base import BaseEMProblem
from SimPEG.EM.Utils import omega
@@ -31,11 +31,10 @@ class BaseFDEMProblem(BaseEMProblem):
if using the H-J formulation (:code:`Problem3D_j` or :code:`Problem3D_h`). Note that here, :math:`\mathbf{s_m}` is an integrated quantity.
The problem performs the elimination so that we are solving the system for \\\(\\\mathbf{e},\\\mathbf{b},\\\mathbf{j} \\\) or \\\(\\\mathbf{h}\\\)
"""
surveyPair = SurveyFDEM
fieldsPair = FieldsFDEM
fieldsPair = Fields
def fields(self, m):
"""
@@ -65,7 +64,7 @@ class BaseFDEMProblem(BaseEMProblem):
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take sensitivity product with (nP,)
:param SimPEG.EM.FDEM.FieldsFDEM.FieldsFDEM u: fields object
:param SimPEG.EM.FDEM.Fields u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
@@ -100,7 +99,7 @@ class BaseFDEMProblem(BaseEMProblem):
:param numpy.array m: inversion model (nP,)
:param numpy.array v: vector which we take adjoint product with (nP,)
:param SimPEG.EM.FDEM.FieldsFDEM.FieldsFDEM u: fields object
:param SimPEG.EM.FDEM.Fields u: fields object
:rtype numpy.array:
:return: Jv (ndata,)
"""
@@ -154,8 +153,8 @@ class BaseFDEMProblem(BaseEMProblem):
Evaluates the sources for a given frequency and puts them in matrix form
:param float freq: Frequency
:rtype: tuple
:return: (s_m, s_e) (nE or nF, nSrc)
:rtype: (numpy.ndarray, numpy.ndarray)
:return: s_m, s_e (nE or nF, nSrc)
"""
Srcs = self.survey.getSrcByFreq(freq)
if self._formulation is 'EB':
@@ -195,7 +194,7 @@ class Problem3D_e(BaseFDEMProblem):
which we solve for :math:`\mathbf{e}`.
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
:param SimPEG.Mesh mesh: mesh
"""
_solutionType = 'eSolution'
@@ -270,7 +269,7 @@ class Problem3D_e(BaseFDEMProblem):
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -306,7 +305,7 @@ class Problem3D_b(BaseFDEMProblem):
.. note ::
The inverse problem will not work with full anisotropy
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
:param SimPEG.Mesh mesh: mesh
"""
_solutionType = 'bSolution'
@@ -401,7 +400,7 @@ class Problem3D_b(BaseFDEMProblem):
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -445,7 +444,6 @@ class Problem3D_j(BaseFDEMProblem):
\mathbf{h} = \\frac{1}{i \omega} \mathbf{M_{\mu}^e}^{-1} \\left(-\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{j} + \mathbf{M^e} \mathbf{s_m} \\right)
and solve for \\\(\\\mathbf{j}\\\) using
.. math ::
@@ -455,7 +453,7 @@ class Problem3D_j(BaseFDEMProblem):
.. note::
This implementation does not yet work with full anisotropy!!
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
:param SimPEG.Mesh mesh: mesh
"""
_solutionType = 'jSolution'
@@ -531,8 +529,8 @@ class Problem3D_j(BaseFDEMProblem):
\mathbf{RHS} = \mathbf{C} \mathbf{M_{\mu}^e}^{-1}\mathbf{s_m} -i\omega \mathbf{s_e}
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS (nE, nSrc)
:rtype: numpy.ndarray (nE, nSrc)
:return: RHS
"""
s_m, s_e = self.getSourceTerm(freq)
@@ -551,7 +549,7 @@ class Problem3D_j(BaseFDEMProblem):
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -593,7 +591,7 @@ class Problem3D_h(BaseFDEMProblem):
\\left(\mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}\\right) \mathbf{h} = \mathbf{M^e} \mathbf{s_m} + \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{s_e}
:param SimPEG.Mesh.BaseMesh.BaseMesh mesh: mesh
:param SimPEG.Mesh mesh: mesh
"""
_solutionType = 'hSolution'
@@ -610,11 +608,9 @@ class Problem3D_h(BaseFDEMProblem):
.. math::
\mathbf{A} = \mathbf{C}^{\\top} \mathbf{M_{\\rho}^f} \mathbf{C} + i \omega \mathbf{M_{\mu}^e}
:param float freq: Frequency
:rtype: scipy.sparse.csr_matrix
:return: A
"""
MeMu = self.MeMu
@@ -657,7 +653,6 @@ class Problem3D_h(BaseFDEMProblem):
:param float freq: Frequency
:rtype: numpy.ndarray
:return: RHS (nE, nSrc)
"""
s_m, s_e = self.getSourceTerm(freq)
@@ -671,7 +666,7 @@ class Problem3D_h(BaseFDEMProblem):
Derivative of the right hand side with respect to the model
:param float freq: frequency
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param SimPEG.EM.FDEM.Src src: FDEM source
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
+18 -5
View File
@@ -25,10 +25,10 @@ class BaseRx(SimPEG.Survey.BaseRx):
def eval(self, src, mesh, f):
"""
Project fields to receivers to get data.
Project fields to recievers to get data.
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param BaseMesh mesh: mesh used
:param Source src: FDEM source
:param Mesh mesh: mesh used
:param Fields f: fields object
:rtype: numpy.ndarray
:return: fields projected to recievers
@@ -44,8 +44,8 @@ class BaseRx(SimPEG.Survey.BaseRx):
"""
Derivative of projected fields with respect to the inversion model times a vector.
:param SimPEG.EM.FDEM.SrcFDEM.BaseSrc src: FDEM source
:param BaseMesh mesh: mesh used
:param Source src: FDEM source
:param Mesh mesh: mesh used
:param Fields f: fields object
:param numpy.ndarray v: vector to multiply
:rtype: numpy.ndarray
@@ -97,6 +97,19 @@ class Point_b(BaseRx):
self.projField = 'b'
super(Point_b, self).__init__(locs, orientation, component)
class Point_bSecondary(BaseRx):
"""
Magnetic flux FDEM receiver
:param numpy.ndarray locs: receiver locations (ie. :code:`np.r_[x,y,z]`)
:param string orientation: receiver orientation 'x', 'y' or 'z'
:param string component: real or imaginary component 'real' or 'imag'
"""
def __init__(self, locs, orientation=None, component=None):
self.projField = 'bSecondary'
super(Point_bSecondary, self).__init__(locs, orientation, component)
class Point_h(BaseRx):
"""
+29 -29
View File
@@ -23,8 +23,8 @@ class BaseSrc(Survey.BaseSrc):
- :math:`s_m` : magnetic source term
- :math:`s_e` : electric source term
:param BaseFDEMProblem prob: FDEM Problem
:rtype: tuple
:param Problem prob: FDEM Problem
:rtype: (numpy.ndarray, numpy.ndarray)
:return: tuple with magnetic source term and electric source term
"""
s_m = self.s_m(prob)
@@ -37,10 +37,10 @@ class BaseSrc(Survey.BaseSrc):
- :code:`s_mDeriv` : derivative of the magnetic source term
- :code:`s_eDeriv` : derivative of the electric source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: tuple
:rtype: (numpy.ndarray, numpy.ndarray)
:return: tuple with magnetic source term and electric source term derivatives times a vector
"""
if v is not None:
@@ -52,7 +52,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Primary magnetic flux density
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary magnetic flux density
"""
@@ -64,7 +64,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Primary magnetic field
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -76,7 +76,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Primary electric field
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary electric field
"""
@@ -88,7 +88,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Primary current density
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: primary current density
"""
@@ -100,7 +100,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Magnetic source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: magnetic source term on mesh
"""
@@ -110,7 +110,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Electric source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: electric source term on mesh
"""
@@ -120,7 +120,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Derivative of magnetic source term with respect to the inversion model
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -133,7 +133,7 @@ class BaseSrc(Survey.BaseSrc):
"""
Derivative of electric source term with respect to the inversion model
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:param numpy.ndarray v: vector to take product with
:param bool adjoint: adjoint?
:rtype: numpy.ndarray
@@ -162,7 +162,7 @@ class RawVec_e(BaseSrc):
"""
Electric source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: electric source term on mesh
"""
@@ -191,7 +191,7 @@ class RawVec_m(BaseSrc):
"""
Magnetic source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: magnetic source term on mesh
"""
@@ -220,7 +220,7 @@ class RawVec(BaseSrc):
"""
Magnetic source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: magnetic source term on mesh
"""
@@ -232,7 +232,7 @@ class RawVec(BaseSrc):
"""
Electric source term
:param BaseFDEMProblem prob: FDEM Problem
:param Problem prob: FDEM Problem
:rtype: numpy.ndarray
:return: electric source term on mesh
"""
@@ -301,7 +301,7 @@ class MagDipole(BaseSrc):
"""
The primary magnetic flux density from a magnetic vector potential
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -339,7 +339,7 @@ class MagDipole(BaseSrc):
"""
The primary magnetic field from a magnetic vector potential
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -350,7 +350,7 @@ class MagDipole(BaseSrc):
"""
The magnetic source term
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -364,7 +364,7 @@ class MagDipole(BaseSrc):
"""
The electric source term
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -416,7 +416,7 @@ class MagDipole_Bfield(BaseSrc):
"""
The primary magnetic flux density from the analytic solution for magnetic fields from a dipole
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -455,7 +455,7 @@ class MagDipole_Bfield(BaseSrc):
"""
The primary magnetic field from a magnetic vector potential
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -466,7 +466,7 @@ class MagDipole_Bfield(BaseSrc):
"""
The magnetic source term
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -479,7 +479,7 @@ class MagDipole_Bfield(BaseSrc):
"""
The electric source term
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -530,7 +530,7 @@ class CircularLoop(BaseSrc):
"""
The primary magnetic flux density from a magnetic vector potential
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -555,7 +555,7 @@ class CircularLoop(BaseSrc):
a = MagneticLoopVectorPotential(self.loc, gridY, 'y', moment=self.radius, mu=self.mu)
else:
srcfct = MagneticDipoleVectorPotential
srcfct = MagneticLoopVectorPotential
ax = srcfct(self.loc, gridX, 'x', self.radius, mu=self.mu)
ay = srcfct(self.loc, gridY, 'y', self.radius, mu=self.mu)
az = srcfct(self.loc, gridZ, 'z', self.radius, mu=self.mu)
@@ -567,7 +567,7 @@ class CircularLoop(BaseSrc):
"""
The primary magnetic field from a magnetic vector potential
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -578,7 +578,7 @@ class CircularLoop(BaseSrc):
"""
The magnetic source term
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
@@ -591,7 +591,7 @@ class CircularLoop(BaseSrc):
"""
The electric source term
:param BaseFDEMProblem prob: FDEM problem
:param Problem prob: FDEM problem
:rtype: numpy.ndarray
:return: primary magnetic field
"""
+142
View File
@@ -0,0 +1,142 @@
import numpy as np
import scipy.sparse as sp
import SimPEG
from SimPEG import Utils
from SimPEG.EM.Utils import omega
from SimPEG.Utils import Zero, Identity
class Fields(SimPEG.Problem.TimeFields):
"""
Fancy Field Storage for a TDEM survey. Only one field type is stored for
each problem, the rest are computed. The fields obejct acts like an array and is indexed by
.. code-block:: python
f = problem.fields(m)
e = f[srcList,'e']
b = f[srcList,'b']
If accessing all sources for a given field, use the :code:`:`
.. code-block:: python
f = problem.fields(m)
e = f[:,'e']
b = f[:,'b']
The array returned will be size (nE or nF, nSrcs :math:`\\times` nFrequencies)
"""
knownFields = {}
dtype = float
def _eDeriv(self, tInd, src, dun_dm_v, v, adjoint=False):
if adjoint is True:
return self._eDeriv_u(tInd, src, v, adjoint), self._eDeriv_m(tInd, src, v, adjoint)
return self._eDeriv_u(tInd, src, dun_dm_v) + self._eDeriv_m(tInd, src, v)
def _bDeriv(self, tInd, src, dun_dm_v, v, adjoint=False):
if adjoint is True:
return self._bDeriv_u(tInd, src, v, adjoint), self._bDeriv_m(tInd, src, v, adjoint)
return self._bDeriv_u(tInd, src, dun_dm_v) + self._bDeriv_m(tInd, src, v)
class Fields_Derivs(Fields):
knownFields = {
'bDeriv': 'F',
'eDeriv': 'E',
'hDeriv': 'E',
'jDeriv': 'F'
}
class Fields_b(Fields):
"""Fancy Field Storage for a TDEM survey."""
knownFields = {'bSolution': 'F'}
aliasFields = {
'b': ['bSolution', 'F', '_b'],
'e': ['bSolution', 'E', '_e'],
}
def startup(self):
self.MeSigmaI = self.survey.prob.MeSigmaI
self.MeSigmaIDeriv = self.survey.prob.MeSigmaIDeriv
self.edgeCurl = self.survey.prob.mesh.edgeCurl
self.MfMui = self.survey.prob.MfMui
def _b(self, bSolution, srcList, tInd):
return bSolution
def _bDeriv_u(self, tInd, src, dun_dm_v, adjoint=False):
return Identity()*dun_dm_v
def _bDeriv_m(self, tInd, src, v, adjoint=False):
return Zero()
# def _bDeriv(self, tInd, src, dun_dm_v, v, adjoint=False):
# if adjoint is True:
# return self._bDeriv_u(tInd, src, v, adjoint), self._bDeriv_m(tInd, src, v, adjoint)
# return self._bDeriv_u(tInd, src, dun_dm_v) + self._bDeriv_m(tInd, src, v)
def _e(self, bSolution, srcList, tInd):
e = self.MeSigmaI * ( self.edgeCurl.T * ( self.MfMui * bSolution ) )
for i, src in enumerate(srcList):
_, S_e = src.eval(self.survey.prob, self.survey.prob.times[tInd])
e[:,i] = e[:,i] - self.MeSigmaI * S_e
return e
def _eDeriv_u(self, tInd, src, dun_dm_v, adjoint = False):
if adjoint is True:
return self.MfMui.T * ( self.edgeCurl * ( self.MeSigmaI.T * dun_dm_v ) )
return self.MeSigmaI * ( self.edgeCurl.T * ( self.MfMui * dun_dm_v ) )
def _eDeriv_m(self, tInd, src, v, adjoint = False):
_, S_e = src.eval(self.survey.prob, self.survey.prob.times[tInd])
bSolution = self[[src],'bSolution',tInd]
_, S_eDeriv = src.evalDeriv(self.survey.prob.times[tInd], self, adjoint=adjoint)
if adjoint is True:
return self.MeSigmaIDeriv(-S_e + self.edgeCurl.T * ( self.MfMui * bSolution ) ).T * v - S_eDeriv(self.MeSigmaI.T * v)
return self.MeSigmaIDeriv(-S_e + self.edgeCurl.T * ( self.MfMui * bSolution)) * v - self.MeSigmaI * S_eDeriv(v)
class Fields_e(Fields):
"""Fancy Field Storage for a TDEM survey."""
knownFields = {'eSolution': 'E'}
aliasFields = {
'e': ['eSolution', 'E', '_e'],
'b': ['eSolution', 'F', '_b'],
}
def startup(self):
self.MeSigmaI = self.survey.prob.MeSigmaI
self.MeSigmaIDeriv = self.survey.prob.MeSigmaIDeriv
self.edgeCurl = self.survey.prob.mesh.edgeCurl
self.MfMui = self.survey.prob.MfMui
def _e(self, eSolution, srcList, tInd):
return eSolution
def _eDeriv_u(self, tInd, src, dun_dm_v, adjoint = False):
return dun_dm_v
def _eDeriv_m(self, tInd, src, v, adjoint = False):
return Zero()
def _b(self, eSolution, srcList, tInd):
raise NotImplementedError
def _bDeriv_u(self, tInd, src, dun_dm_v, adjoint=False):
raise NotImplementedError
def _bDeriv_m(self, tInd, src, v, adjoint=False):
raise NotImplementedError
# def _bDeriv(self, tInd, src, dun_dm_v, v, adjoint=False):
# if adjoint is True:
# return self._bDeriv_u(tInd, src, v, adjoint), self._bDeriv_m(tInd, src, v, adjoint)
# return self._bDeriv_u(tInd, src, dun_dm_v) + self._bDeriv_m(tInd, src, v)
+246
View File
@@ -0,0 +1,246 @@
import SimPEG
from SimPEG import np, Utils
from SimPEG.Utils import Zero, Identity
from scipy.constants import mu_0
from SimPEG.EM.Utils import *
####################################################
# Sources
####################################################
class BaseWaveform(object):
def __init__(self, offTime=0., hasInitialFields=False):
self.offTime = offTime
self.hasInitialFields = hasInitialFields
def _assertMatchesPair(self, pair):
assert (isinstance(self, pair)
), "Waveform object must be an instance of a %s BaseWaveform class."%(pair.__name__)
def eval(self, time):
raise NotImplementedError
def evalDeriv(self, time):
raise NotImplementedError # needed for E-formulation
class StepOffWaveform(BaseWaveform):
def __init__(self, offTime=0.):
BaseWaveform.__init__(self, offTime, hasInitialFields=True)
def eval(self, time):
return 0.
class RawWaveform(BaseWaveform):
def __init__(self, offTime=0.):
BaseWaveform.__init__(self, offTime, hasInitialFields=True)
def eval(self, time):
raise NotImplementedError('RawWaveform has not been implemented, you should write it!')
class TriangularWaveform(BaseWaveform):
def __init__(self, offTime=0.):
BaseWaveform.__init__(self, offTime, hasInitialFields=True)
def eval(self, time):
raise NotImplementedError('TriangularWaveform has not been implemented, you should write it!')
class BaseSrc(SimPEG.Survey.BaseSrc):
# rxPair = Rx
integrate = True
waveformPair = BaseWaveform
@property
def waveform(self):
"A waveform instance is not None"
return getattr(self, '_waveform', None)
@waveform.setter
def waveform(self, val):
if self.waveform is None:
val._assertMatchesPair(self.waveformPair)
self._mapping = val
else:
self._mapping = self.PropMap(val)
def __init__(self, rxList, waveform = StepOffWaveform(), **kwargs):
self.waveform = waveform
SimPEG.Survey.BaseSrc.__init__(self, rxList, **kwargs)
def bInitial(self, prob):
return Zero()
def bInitialDeriv(self, prob, v=None, adjoint=False):
return Zero()
def eInitial(self, prob):
return Zero()
def eInitialDeriv(self, prob, v=None, adjoint=False):
return Zero()
def eval(self, prob, time):
S_m = self.S_m(prob, time)
S_e = self.S_e(prob, time)
return S_m, S_e
def evalDeriv(self, prob, time, v=None, adjoint=False):
if v is not None:
return self.S_mDeriv(prob, time, v, adjoint), self.S_eDeriv(prob, time, v, adjoint)
else:
return lambda v: self.S_mDeriv(prob, time, v, adjoint), lambda v: self.S_eDeriv(prob, time, v, adjoint)
def S_m(self, prob, time):
return Zero()
def S_e(self, prob, time):
return Zero()
def S_mDeriv(self, prob, time, v=None, adjoint=False):
return Zero()
def S_eDeriv(self, prob, time, v=None, adjoint=False):
return Zero()
class MagDipole(BaseSrc):
waveform = None
loc = None
orientation = 'Z'
moment = 1.
mu = mu_0
def __init__(self, rxList, **kwargs):
assert self.orientation in ['X','Y','Z'], "Orientation (right now) doesn't actually do anything! The methods in SrcUtils should take care of this..."
self.integrate = False
BaseSrc.__init__(self, rxList, **kwargs)
def _bfromVectorPotential(self, prob):
if prob._eqLocs is 'FE':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif prob._eqLocs is 'EF':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
a = MagneticDipoleVectorPotential(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
else:
srcfct = MagneticDipoleVectorPotential
ax = srcfct(self.loc, gridX, 'x', mu=self.mu, moment=self.moment)
ay = srcfct(self.loc, gridY, 'y', mu=self.mu, moment=self.moment)
az = srcfct(self.loc, gridZ, 'z', mu=self.mu, moment=self.moment)
a = np.concatenate((ax, ay, az))
return C*a
def bInitial(self, prob):
if self.waveform.hasInitialFields is False:
return Zero()
return self._bfromVectorPotential(prob)
def eInitial(self, prob):
if self.waveform.hasInitialFields is False:
return Zero()
b = self.bInitial(prob)
MeSigmaI = prob.MeSigmaI
MfMui = prob.MfMui
C = prob.mesh.edgeCurl
return MeSigmaI * (C.T * (MfMui * b))
def eInitialDeriv(self, prob, v=None, adjoint=False):
if self.waveform.hasInitialFields is False:
return Zero()
b = self.bInitial(prob)
MeSigmaIDeriv = prob.MeSigmaIDeriv
MfMui = prob.MfMui
C = prob.mesh.edgeCurl
S_e = self.S_e(prob, prob.t0)
# S_e doesn't depend on the model
if adjoint:
return MeSigmaIDeriv( -S_e + C.T * ( MfMui * b ) ).T * v
return MeSigmaIDeriv( -S_e + C.T * ( MfMui * b ) ) * v
def S_m(self, prob, time):
if self.waveform.hasInitialFields is False:
raise NotImplementedError
return Zero()
def S_e(self, prob, time):
if self.waveform.hasInitialFields is False:
raise NotImplementedError
return Zero()
class CircularLoop(MagDipole):
waveform = None
loc = None
orientation = 'Z'
radius = None
mu = mu_0
def __init__(self, rxList, **kwargs):
assert self.orientation in ['X','Y','Z'], "Orientation (right now) doesn't actually do anything! The methods in SrcUtils should take care of this..."
self.integrate = False
BaseSrc.__init__(self, rxList, **kwargs)
def _bfromVectorPotential(self, prob):
if prob._eqLocs is 'FE':
gridX = prob.mesh.gridEx
gridY = prob.mesh.gridEy
gridZ = prob.mesh.gridEz
C = prob.mesh.edgeCurl
elif prob._eqLocs is 'EF':
gridX = prob.mesh.gridFx
gridY = prob.mesh.gridFy
gridZ = prob.mesh.gridFz
C = prob.mesh.edgeCurl.T
if prob.mesh._meshType is 'CYL':
if not prob.mesh.isSymmetric:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
a = MagneticLoopVectorPotential(self.loc, gridY, 'y', radius=self.radius, mu=self.mu)
else:
srcfct = MagneticLoopVectorPotential
ax = srcfct(self.loc, gridX, 'x', mu=self.mu, radius=self.radius)
ay = srcfct(self.loc, gridY, 'y', mu=self.mu, radius=self.radius)
az = srcfct(self.loc, gridZ, 'z', mu=self.mu, radius=self.radius)
a = np.concatenate((ax, ay, az))
return C*a
+45 -123
View File
@@ -1,10 +1,16 @@
from SimPEG import Utils, Survey, np
from SimPEG.Survey import BaseSurvey
import SimPEG
from SimPEG import np, Utils
from SimPEG.Utils import Zero, Identity
from scipy.constants import mu_0
from SimPEG.EM.Utils import *
from BaseTDEM import FieldsTDEM
import SrcTDEM as Src
class RxTDEM(Survey.BaseTimeRx):
####################################################
# Receivers
####################################################
class Rx(SimPEG.Survey.BaseTimeRx):
knownRxTypes = {
'ex':['e', 'Ex', 'N'],
@@ -21,7 +27,7 @@ class RxTDEM(Survey.BaseTimeRx):
}
def __init__(self, locs, times, rxType):
Survey.BaseTimeRx.__init__(self, locs, times, rxType)
SimPEG.Survey.BaseTimeRx.__init__(self, locs, times, rxType)
@property
def projField(self):
@@ -56,144 +62,60 @@ class RxTDEM(Survey.BaseTimeRx):
u_part = Utils.mkvc(u[src, self.projField, :])
return P*u_part
def evalDeriv(self, src, mesh, timeMesh, u, v, adjoint=False):
def evalDeriv(self, src, mesh, timeMesh, v, adjoint=False):
P = self.getP(mesh, timeMesh)
if not adjoint:
return P * Utils.mkvc(v[src, self.projField, :])
return P * v #Utils.mkvc(v[src, self.projField+'Deriv', :])
elif adjoint:
return P.T * v[src, self]
# dP_dF_T = P.T * v #[src, self]
# newshape = (len(dP_dF_T)/timeMesh.nN, timeMesh.nN )
return P.T * v #np.reshape(dP_dF_T, newshape, order='F')
class SrcTDEM(Survey.BaseSrc):
rxPair = RxTDEM
radius = None
####################################################
# Survey
####################################################
def getInitialFields(self, mesh):
F0 = getattr(self, '_getInitialFields_' + self.srcType)(mesh)
return F0
def getJs(self, mesh, time):
return None
class SrcTDEM_VMD_MVP(SrcTDEM):
def __init__(self,rxList,loc,waveformType="STEPOFF"):
self.loc = loc
self.waveformType = waveformType
SrcTDEM.__init__(self,rxList)
def getInitialFields(self, mesh):
"""Vertical magnetic dipole, magnetic vector potential"""
if self.waveformType == "STEPOFF":
print ">> Step waveform: Non-zero initial condition"
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
else:
raise Exception('Unknown mesh for VMD')
return {"b": mesh.edgeCurl*MVP}
elif self.waveformType == "GENERAL":
print ">> General waveform: Zero initial condition"
return {"b": np.zeros(mesh.nF)}
else:
raise NotImplementedError("Only use STEPOFF or GENERAL")
def getMeS(self, mesh, MfMui):
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
else:
raise Exception('Unknown mesh for VMD')
return mesh.edgeCurl.T*MfMui*mesh.edgeCurl*MVP
class SrcTDEM_CircularLoop_MVP(SrcTDEM):
def __init__(self,rxList,loc,radius,waveformType="STEPOFF"):
self.loc = loc
self.radius = radius
self.waveformType = waveformType
SrcTDEM.__init__(self,rxList)
def getInitialFields(self, mesh):
"""Circular Loop, magnetic vector potential"""
if self.waveformType == "STEPOFF":
print ">> Step waveform: Non-zero initial condition"
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticLoopVectorPotential(self.loc, mesh, 'Ey', self.radius)
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticLoopVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'], self.radius)
else:
raise Exception('Unknown mesh for CircularLoop')
return {"b": mesh.edgeCurl*MVP}
elif self.waveformType == "GENERAL":
print ">> General waveform: Zero initial condition"
return {"b": np.zeros(mesh.nF)}
else:
raise NotImplementedError("Only use STEPOFF or GENERAL")
def getMeS(self, mesh, MfMui):
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticLoopVectorPotential(self.loc, mesh, 'Ey', self.radius)
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticLoopVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'], self.radius)
else:
raise Exception('Unknown mesh for CircularLoop')
return mesh.edgeCurl.T*MfMui*mesh.edgeCurl*MVP
class SurveyTDEM(Survey.BaseSurvey):
class Survey(SimPEG.Survey.BaseSurvey):
"""
docstring for SurveyTDEM
Time domain electromagnetic survey
"""
srcPair = SrcTDEM
srcPair = Src.BaseSrc
rxPair = Rx
def __init__(self, srcList, **kwargs):
# Sort these by frequency
self.srcList = srcList
Survey.BaseSurvey.__init__(self, **kwargs)
SimPEG.Survey.BaseSurvey.__init__(self, **kwargs)
def eval(self, u):
data = Survey.Data(self)
data = SimPEG.Survey.Data(self)
for src in self.srcList:
for rx in src.rxList:
data[src, rx] = rx.eval(src, self.mesh, self.prob.timeMesh, u)
return data
def evalDeriv(self, u, v=None, adjoint=False):
assert v is not None, 'v to multiply must be provided.'
raise Exception('Use Receivers to project fields deriv.')
# assert v is not None, 'v to multiply must be provided.'
if not adjoint:
data = Survey.Data(self)
for src in self.srcList:
for rx in src.rxList:
data[src, rx] = rx.evalDeriv(src, self.mesh, self.prob.timeMesh, u, v)
return data
else:
f = FieldsTDEM(self.mesh, self)
for src in self.srcList:
for rx in src.rxList:
Ptv = rx.evalDeriv(src, self.mesh, self.prob.timeMesh, u, v, adjoint=True)
Ptv = Ptv.reshape((-1, self.prob.timeMesh.nN), order='F')
if rx.projField not in f: # first time we are projecting
f[src, rx.projField, :] = Ptv
else: # there are already fields, so let's add to them!
f[src, rx.projField, :] += Ptv
return f
# if not adjoint:
# data = SimPEG.Survey.Data(self)
# for src in self.srcList:
# for rx in src.rxList:
# data[src, rx] = rx.evalDeriv(src, self.mesh, self.prob.timeMesh, u, v)
# return data
# else:
# f = FieldsTDEM(self.mesh, self)
# for src in self.srcList:
# for rx in src.rxList:
# Ptv = rx.evalDeriv(src, self.mesh, self.prob.timeMesh, u, v, adjoint=True)
# Ptv = Ptv.reshape((-1, self.prob.timeMesh.nN), order='F')
# if rx.projField not in f: # first time we are projecting
# f[src, rx.projField, :] = Ptv
# else: # there are already fields, so let's add to them!
# f[src, rx.projField, :] += Ptv
# return f
+553
View File
@@ -0,0 +1,553 @@
from SimPEG import Problem, Utils, np, sp, Solver as SimpegSolver
from SimPEG.EM.Base import BaseEMProblem
from SimPEG.EM.TDEM.SurveyTDEM import Survey as SurveyTDEM
from SimPEG.EM.TDEM.FieldsTDEM import *
from scipy.constants import mu_0
import time
class BaseTDEMProblem(Problem.BaseTimeProblem, BaseEMProblem):
"""
We start with the first order form of Maxwell's equations
"""
surveyPair = SurveyTDEM
fieldsPair = Fields
def __init__(self, mesh, mapping=None, **kwargs):
Problem.BaseTimeProblem.__init__(self, mesh, mapping=mapping, **kwargs)
def fields(self, m):
"""
Solve the forward problem for the fields.
:param numpy.array m: inversion model (nP,)
:rtype numpy.array:
:return F: fields
"""
tic = time.time()
self.curModel = m
F = self.fieldsPair(self.mesh, self.survey)
# set initial fields
F[:,self._fieldType+'Solution',0] = self.getInitialFields()
# timestep to solve forward
if self.verbose: print '%s\nCalculating fields(m)\n%s'%('*'*50,'*'*50)
Ainv = None
for tInd, dt in enumerate(self.timeSteps):
if Ainv is not None and (tInd > 0 and dt != self.timeSteps[tInd - 1]):# keep factors if dt is the same as previous step b/c A will be the same
Ainv.clean()
Ainv = None
if Ainv is None:
A = self.getAdiag(tInd)
if self.verbose: print 'Factoring... (dt = %e)'%dt
Ainv = self.Solver(A, **self.solverOpts)
if self.verbose: print 'Done'
rhs = self.getRHS(tInd+1) # this is on the nodes of the time mesh
Asubdiag = self.getAsubdiag(tInd)
if self.verbose: print (' Solving... (tInd = %i)')% (tInd+1)
sol = Ainv * (rhs - Asubdiag * F[:,self._fieldType+'Solution',tInd]) # taking a step
if self.verbose: print ' Done...'
if sol.ndim == 1:
sol.shape = (sol.size,1)
F[:,self._fieldType+'Solution',tInd+1] = sol
if self.verbose: print '%s\nDone calculating fields(m)\n%s'%('*'*50,'*'*50)
Ainv.clean()
return F
def Jvec(self, m, v, f=None):
"""
Jvec computes the sensitivity times a vector
.. math::
\mathbf{J} \mathbf{v} = \\frac{d\mathbf{P}}{d\mathbf{F}} \left( \\frac{d\mathbf{F}}{d\mathbf{u}} \\frac{d\mathbf{u}}{d\mathbf{m}} + \\frac{\partial\mathbf{F}}{\partial\mathbf{m}} \\right) \mathbf{v}
where
.. math::
\mathbf{A} \\frac{d\mathbf{u}}{d\mathbf{m}} + \\frac{d\mathbf{A}(\mathbf{u})}{d\mathbf{m}} = \\frac{d \mathbf{RHS}}{d \mathbf{m}}
"""
if f is None:
f = self.fields(m)
ftype = self._fieldType + 'Solution' # the thing we solved for
self.curModel = m
# mat to store previous time-step's solution deriv times a vector for each source
# size: nu x nSrc
# this is a bit silly
# if self._fieldType is 'b' or self._fieldType is 'j':
# ifields = np.zeros((self.mesh.nF, len(Srcs)))
# elif self._fieldType is 'e' or self._fieldType is 'h':
# ifields = np.zeros((self.mesh.nE, len(Srcs)))
# for i, src in enumerate(self.survey.srcList):
dun_dm_v = np.hstack([Utils.mkvc(self.getInitialFieldsDeriv(src,v),2) for src in self.survey.srcList]) # can over-write this at each timestep
#
df_dm_v = Fields_Derivs(self.mesh, self.survey) # store the field derivs we need to project to calc full deriv
Adiaginv = None
for tInd, dt in zip(range(self.nT), self.timeSteps):
if Adiaginv is not None and (tInd > 0 and dt != self.timeSteps[tInd - 1]):# keep factors if dt is the same as previous step b/c A will be the same
Adiaginv.clean()
Adiaginv = None
if Adiaginv is None:
A = self.getAdiag(tInd)
Adiaginv = self.Solver(A, **self.solverOpts)
Asubdiag = self.getAsubdiag(tInd)
for i, src in enumerate(self.survey.srcList):
# here, we are lagging by a timestep, so filling in as we go
for projField in set([rx.projField for rx in src.rxList]):
# Seogi: df_duFun?
df_dmFun = getattr(f, '_%sDeriv'%projField, None)
# df_dm_v is dense, but we only need the times at (rx.P.T * ones > 0)
# This should be called rx.footprint
df_dm_v[src, '%sDeriv'%projField , tInd] = df_dmFun(tInd, src, dun_dm_v[:,i], v)
un_src = f[src,ftype,tInd+1]
dA_dm_v = self.getAdiagDeriv(tInd, un_src, v) # cell centered on time mesh
dRHS_dm_v = self.getRHSDeriv(tInd+1, src, v) # on nodes of time mesh
dAsubdiag_dm_v = self.getAsubdiagDeriv(tInd, f[src,ftype,tInd], v)
JRHS = dRHS_dm_v - dAsubdiag_dm_v - dA_dm_v
# step in time and overwrite
if tInd != len(self.timeSteps+1):
dun_dm_v[:,i] = Adiaginv * (JRHS - Asubdiag * dun_dm_v[:,i])
# Seogi: suspcious spot
# Jv = self.dataPair(self.survey)
Jv = []
for src in self.survey.srcList:
for rx in src.rxList:
# Looping over data class append memory as well!!
# Jv[src,rx] = rx.evalDeriv(src, self.mesh, self.timeMesh, Utils.mkvc(df_dm_v[src,'%sDeriv'%rx.projField,:]))
Jv.append(rx.evalDeriv(src, self.mesh, self.timeMesh, Utils.mkvc(df_dm_v[src,'%sDeriv'%rx.projField,:])))
Adiaginv.clean()
# del df_dm_v, dun_dm_v, Asubdiag
# return Utils.mkvc(Jv)
return np.hstack(Jv)
def Jtvec(self, m, v, f=None):
"""
Jvec computes the adjoint of the sensitivity times a vector
.. math::
\mathbf{J}^\\top \mathbf{v} = \left( \\frac{d\mathbf{u}}{d\mathbf{m}} ^ \\top \\frac{d\mathbf{F}}{d\mathbf{u}} ^ \\top + \\frac{\partial\mathbf{F}}{\partial\mathbf{m}} ^ \\top \\right) \\frac{d\mathbf{P}}{d\mathbf{F}} ^ \\top \mathbf{v}
where
.. math::
\\frac{d\mathbf{u}}{d\mathbf{m}} ^\\top \mathbf{A}^\\top + \\frac{d\mathbf{A}(\mathbf{u})}{d\mathbf{m}} ^ \\top = \\frac{d \mathbf{RHS}}{d \mathbf{m}} ^ \\top
"""
if f is None:
f = self.fields(m)
self.curModel = m
ftype = self._fieldType + 'Solution' # the thing we solved for
# Ensure v is a data object.
if not isinstance(v, self.dataPair):
v = self.dataPair(self.survey, v)
df_duT_v = Fields_Derivs(self.mesh, self.survey)
ATinv_df_duT_v = np.zeros((len(self.survey.srcList), len(f[self.survey.srcList[0],ftype,0])), dtype=float) # same size as fields at a single timestep
JTv = np.zeros(m.shape, dtype=float)
# Loop over sources and receivers to create a fields object: PT_v, df_duT_v, df_dmT_v
PT_v = Fields_Derivs(self.mesh, self.survey) # initialize storage for PT_v (don't need to preserve over sources)
for src in self.survey.srcList:
# Looping over initializing field class is appending memory!
# PT_v = Fields_Derivs(self.mesh, self.survey) # initialize storage for PT_v (don't need to preserve over sources)
# initialize size
df_duT_v[src, '%sDeriv'%self._fieldType, :] = np.zeros_like(f[src, self._fieldType, :])
for rx in src.rxList:
print ('_%sDeriv')%(rx.projField)
PT_v[src,'%sDeriv'%rx.projField,:] = rx.evalDeriv(src, self.mesh, self.timeMesh, Utils.mkvc(v[src,rx]), adjoint=True) # this is +=
# PT_v = np.reshape(curPT_v,(len(curPT_v)/self.timeMesh.nN, self.timeMesh.nN), order='F')
df_duTFun = getattr(f, '_%sDeriv'%rx.projField, None)
for tInd in range(self.nT+1):
cur = df_duTFun(tInd, src, None, Utils.mkvc(PT_v[src,'%sDeriv'%rx.projField,tInd]), adjoint=True)
df_duT_v[src, '%sDeriv'%self._fieldType, tInd] = df_duT_v[src, '%sDeriv'%self._fieldType, tInd] + Utils.mkvc(cur[0],2)
JTv = cur[1] + JTv
del PT_v # no longer need this
AdiagTinv = None
# Do the back-solve through time
for tIndP in reversed(range(self.nT + 1)):
tInd = tIndP - 1
if AdiagTinv is not None and (tInd <= self.nT and self.timeSteps[tInd] != self.timeSteps[tInd+1]): # if the previous timestep is the same --> no need to refactor the matrix
AdiagTinv.clean()
AdiagTinv = None
# refactor if we need to
if AdiagTinv is None and tInd > -1:
Adiag = self.getAdiag(tInd)
AdiagTinv = self.Solver(Adiag.T, **self.solverOpts)
dAsubdiag_dm_v = Zero()
if tInd < self.nT - 1:
Asubdiag = self.getAsubdiag(tInd+1)
for isrc, src in enumerate(self.survey.srcList):
# solve against df_duT_v
if tInd >= self.nT-1:
# last timestep (first to be solved)
ATinv_df_duT_v[isrc,:] = AdiagTinv * df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]
elif tInd > -1:
# else:
ATinv_df_duT_v[isrc,:] = AdiagTinv * (Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]) - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]))
else:
# AdiagTinv = I
ATinv_df_duT_v[isrc,:] = Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]) - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:])
# - Utils.mkvc(Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]))
# (Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]) - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]))
if tInd < self.nT - 1:
dAsubdiagT_dm_v = self.getAsubdiagDeriv(tInd+1, f[src,ftype,tInd+1], ATinv_df_duT_v[isrc,:], adjoint = True)
if tInd > -1:
un_src = f[src,ftype,tInd+1]
dAT_dm_v = self.getAdiagDeriv(tInd, un_src, ATinv_df_duT_v[isrc,:], adjoint=True) # cell centered on time mesh
dRHST_dm_v = self.getRHSDeriv(tInd+1, src, ATinv_df_duT_v[isrc,:], adjoint=True) # on nodes of time mesh
JTv = JTv + Utils.mkvc(- dAT_dm_v - dAsubdiag_dm_v + dRHST_dm_v)
else:
# dA_dm_v = self.getInitialFieldsDeriv(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1], adjoint=True)
# print np.linalg.norm(self.getInitialFieldsDeriv(src, df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1], adjoint=True))
# print np.linalg.norm(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1])
# vec = - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]) + Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1])
# dAsubdiagT_dm_v = self.getAsubdiagDeriv(tInd+1, f[src,ftype,tInd+1], Utils.mkvc(ATinv_df_duT_v[isrc,:]), adjoint = True)
dRHST_dm_v = Utils.mkvc(self.getInitialFieldsDeriv(src, Utils.mkvc(ATinv_df_duT_v[isrc,:]) , adjoint=True))
JTv = JTv + Utils.mkvc( -dAsubdiagT_dm_v + dRHST_dm_v) #
# # dAT_dm_v = self.getAdiagDeriv(tInd, un_src, ATinv_df_duT_v[isrc,:], adjoint=True) # cell centered on time mesh
# dRHST_dm_v0 = self.getRHSDeriv(tInd+1, src, ATinv_df_duT_v[isrc,:], adjoint=True) # on nodes of time mesh
# dRHST_dm_v1 = self.getInitialFieldsDeriv( Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]), adjoint=True)
# JTv = JTv + Utils.mkvc(dRHST_dm_v0 + dRHST_dm_v1)
# print 'here'
# inFields = self.getInitialFieldsDeriv(f[src,ftype,tInd+1], Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,tInd+1]), adjoint=True)
# # - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]), adjoint=True)
# print inFields.shape
# JTv = JTv + inFields
# dAsubdiag_dm_v = 0
# Missing the 0 step
# adding du_dm^T * dF_du^T * P^T vfor time 0 (no dRHS_dm_v at time 0)
# Asubdiag = self.getAsubdiag(0)
# for src in self.survey.srcList:
# for projField in set(rx.projField):
# v = AdiagTinv * (Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,0]) - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:]))
# JTv = JTv - Utils.mkvc(self.getAdiagDeriv(0, f[src, ftype, tInd], v, adjoint = True))
# # JTv = JTv + self.getInitialFieldsDeriv(Utils.mkvc(df_duT_v[src,'%sDeriv'%self._fieldType,0] - Asubdiag.T * Utils.mkvc(ATinv_df_duT_v[isrc,:])), adjoint=True)
# del df_duT_v, ATinv_df_duT_v, A, Asubdiag
if AdiagTinv is not None:
AdiagTinv.clean()
return Utils.mkvc(JTv).astype(float)
def getSourceTerm(self, tInd):
Srcs = self.survey.srcList
if self._eqLocs is 'FE':
S_m = np.zeros((self.mesh.nF,len(Srcs)))
S_e = np.zeros((self.mesh.nE,len(Srcs)))
elif self._eqLocs is 'EF':
S_m = np.zeros((self.mesh.nE,len(Srcs)))
S_e = np.zeros((self.mesh.nF,len(Srcs)))
for i, src in enumerate(Srcs):
smi, sei = src.eval(self, self.times[tInd])
S_m[:,i] = S_m[:,i] + smi
S_e[:,i] = S_e[:,i] + sei
return S_m, S_e
def getInitialFields(self):
Srcs = self.survey.srcList
if self._fieldType is 'b' or self._fieldType is 'j':
ifields = np.zeros((self.mesh.nF, len(Srcs)))
elif self._fieldType is 'e' or self._fieldType is 'h':
ifields = np.zeros((self.mesh.nE, len(Srcs)))
for i,src in enumerate(Srcs):
ifields[:,i] = ifields[:,i] + getattr(src, '%sInitial'%self._fieldType, None)(self)
return ifields
def getInitialFieldsDeriv(self, src, v, adjoint=False):
if adjoint is False:
if self._fieldType is 'b' or self._fieldType is 'j':
ifieldsDeriv = np.zeros(self.mesh.nF)
elif self._fieldType is 'e' or self._fieldType is 'h':
ifieldsDeriv = np.zeros(self.mesh.nE)
elif adjoint is True:
ifieldsDeriv = np.zeros(self.mapping.nP)
ifieldsDeriv = Utils.mkvc(getattr(src, '%sInitialDeriv'%self._fieldType, None)(self,v,adjoint)) + ifieldsDeriv
# ifieldsDeriv = Utils.mkvc(getattr(src, '%sInitialDeriv'%self._fieldType, None)(self,v,adjoint)) + ifieldsDeriv
# ifieldsDeriv = self.getAdiagDeriv(None, u, v, adjoint)
# ifieldsDeriv = ifieldsDeriv.sum()
return ifieldsDeriv
##########################################################################################
################################ E-B Formulation #########################################
##########################################################################################
# ------------------------------- Problem_b -------------------------------------------- #
class Problem_b(BaseTDEMProblem):
"""
Starting from the quasi-static E-B formulation of Maxwell's equations (semi-discretized)
.. math::
\mathbf{C} \mathbf{e} + \\frac{\partial \mathbf{b}}{\partial t} = \mathbf{s_m} \\\\
\mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e} \mathbf{e} = \mathbf{s_e}
where :math:`\mathbf{s_e}` is an integrated quantity, we eliminate :math:`\mathbf{e}` using
.. math::
\mathbf{e} = \mathbf{M_{\sigma}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} - \mathbf{M_{\sigma}^e}^{-1} \mathbf{s_e}
to obtain a second order semi-discretized system in :math:`\mathbf{b}`
.. math::
\mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} + \\frac{\partial \mathbf{b}}{\partial t} = \mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{s_e} + \mathbf{s_m}
and moving everything except the time derivative to the rhs gives
.. math::
\\frac{\partial \mathbf{b}}{\partial t} = -\mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b} + \mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{s_e} + \mathbf{s_m}
For the time discretization, we use backward euler. To solve for the :math:`n+1`th time step, we have
.. math::
\\frac{\mathbf{b}^{n+1} - \mathbf{b}^{n}}{\mathbf{dt}} = -\mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f} \mathbf{b}^{n+1} + \mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{s_e}^{n+1} + \mathbf{s_m}^{n+1}
re-arranging to put :math:`\mathbf{b}^{n+1}` on the left hand side gives
.. math::
(\mathbf{I} + \mathbf{dt} \mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f}) \mathbf{b}^{n+1} = \mathbf{b}^{n} + \mathbf{dt}(\mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{s_e}^{n+1} + \mathbf{s_m}^{n+1})
:param Mesh mesh: mesh
:param Mapping mapping: mapping
"""
_fieldType = 'b'
_eqLocs = 'FE'
fieldsPair = Fields_b
surveyPair = SurveyTDEM
def __init__(self, mesh, mapping=None, **kwargs):
BaseTDEMProblem.__init__(self, mesh, mapping=mapping, **kwargs)
def getAdiag(self, tInd):
"""
System matrix at a given time index
.. math::
(\mathbf{I} + \mathbf{dt} \mathbf{C} \mathbf{M_{\sigma}^e}^{-1} \mathbf{C}^{\\top} \mathbf{M_{\mu^{-1}}^f})
"""
assert tInd >= 0 and tInd < self.nT
dt = self.timeSteps[tInd]
C = self.mesh.edgeCurl
MeSigmaI = self.MeSigmaI
MfMui = self.MfMui
I = Utils.speye(self.mesh.nF)
A = 1./dt * I + ( C * ( MeSigmaI * (C.T * MfMui ) ) )
if self._makeASymmetric is True:
return MfMui.T * A
return A
def getAdiagDeriv(self, tInd, u, v, adjoint=False):
C = self.mesh.edgeCurl
MeSigmaIDeriv = lambda x: self.MeSigmaIDeriv(x)
MfMui = self.MfMui
if adjoint:
if self._makeASymmetric is True:
v = MfMui * v
return MeSigmaIDeriv(C.T * ( MfMui * u )).T * ( C.T * v )
ADeriv = ( C * ( MeSigmaIDeriv(C.T * ( MfMui * u )) * v ) )
if self._makeASymmetric is True:
return MfMui.T * ADeriv
return ADeriv
def getAsubdiag(self, tInd):
dt = self.timeSteps[tInd]
MfMui = self.MfMui
Asubdiag = - 1./dt * sp.eye(self.mesh.nF)
if self._makeASymmetric is True:
return MfMui.T * Asubdiag
return Asubdiag
def getAsubdiagDeriv(self, tInd, u, v, adjoint=False):
return Zero() * v
def getRHS(self, tInd):
C = self.mesh.edgeCurl
MeSigmaI = self.MeSigmaI
MfMui = self.MfMui
S_m, S_e = self.getSourceTerm(tInd)
rhs = (C * (MeSigmaI * S_e) + S_m)
if self._makeASymmetric is True:
return MfMui.T * rhs
return rhs
def getRHSDeriv(self, tInd, src, v, adjoint=False):
C = self.mesh.edgeCurl
MeSigmaI = self.MeSigmaI
MeSigmaIDeriv = lambda u: self.MeSigmaIDeriv(u)
MfMui = self.MfMui
_, S_e = src.eval(tInd, self)
S_mDeriv, S_eDeriv = src.evalDeriv(self.times[tInd], self, adjoint=adjoint)
if adjoint:
if self._makeASymmetric is True:
v = self.MfMui * v
if isinstance(S_e, Utils.Zero):
MeSigmaIDerivT_v = Utils.Zero()
else:
MeSigmaIDerivT_v = MeSigmaIDeriv(S_e).T * v
RHSDeriv = MeSigmaIDerivT_v + S_eDeriv( MeSigmaI.T * ( C.T * v ) ) + S_mDeriv(v)
return RHSDeriv
if isinstance(S_e, Utils.Zero):
MeSigmaIDeriv_v = Utils.Zero()
else:
MeSigmaIDeriv_v = MeSigmaIDeriv(S_e) * v
RHSDeriv = (C * (MeSigmaIDeriv_v + MeSigmaI * S_eDeriv(v) + S_mDeriv(v)))
if self._makeASymmetric is True:
return self.MfMui.T * RHSDeriv
return RHSDeriv
# ------------------------------- Problem_e -------------------------------------------- #
class Problem_e(BaseTDEMProblem):
_fieldType = 'e'
_eqLocs = 'FE'
fieldsPair = Fields_e
surveyPair = SurveyTDEM
def __init__(self, mesh, mapping=None, **kwargs):
BaseTDEMProblem.__init__(self, mesh, mapping=mapping, **kwargs)
def getAdiag(self, tInd):
"""
System matrix at a given time index
"""
assert tInd >= 0 and tInd < self.nT
dt = self.timeSteps[tInd]
C = self.mesh.edgeCurl
MfMui = self.MfMui
MeSigma = self.MeSigma
return C.T * ( MfMui * C ) + 1./dt * MeSigma
def getAdiagDeriv(self, tInd, u, v, adjoint=False):
assert tInd >= 0 and tInd < self.nT
dt = self.timeSteps[tInd]
C = self.mesh.edgeCurl
MfMui = self.MfMui
MeSigmaDeriv = self.MeSigmaDeriv(u)
if adjoint:
return 1./dt * MeSigmaDeriv.T * v
return 1./dt * MeSigmaDeriv * v
def getAsubdiag(self, tInd):
assert tInd >= 0 and tInd < self.nT
dt = self.timeSteps[tInd]
return - 1./dt * self.MeSigma
def getAsubdiagDeriv(self, tInd, u, v, adjoint=False):
dt = self.timeSteps[tInd]
if adjoint:
return - 1./dt * self.MeSigmaDeriv(u).T * v
return - 1./dt * self.MeSigmaDeriv(u) * v
def getRHS(self, tInd):
return Zero()
def getRHSDeriv(self, tInd, src, v, adjoint=False):
return Zero()
+3 -3
View File
@@ -1,3 +1,3 @@
from SurveyTDEM import * #SurveyTDEM, RxTDEM, SrcTDEM
from BaseTDEM import BaseTDEMProblem, FieldsTDEM
from TDEM_b import ProblemTDEM_b
from TDEM import BaseTDEMProblem, Problem_b, Problem_e
from FieldsTDEM import Fields, Fields_b
from SurveyTDEM import Survey, Src, Rx
@@ -112,7 +112,7 @@ class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
"""
:param numpy.array m: Conductivity model
:param numpy.ndarray v: vector (model object)
:param FieldsTDEM f: Fields resulting from m
:param simpegEM.TDEM.FieldsTDEM f: Fields resulting from m
:rtype: numpy.ndarray
:return: w (data object)
@@ -136,8 +136,8 @@ class BaseTDEMProblem(BaseTimeProblem, BaseEMProblem):
def Jtvec(self, m, v, f=None):
"""
:param numpy.array m: Conductivity model
:param numpy.ndarray v: vector (or a :class:`SimPEG.Survey.Data` object)
:param FieldsTDEM u: Fields resulting from m
:param numpy.ndarray,SimPEG.Survey.Data v: vector (data object)
:param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
:rtype: numpy.ndarray
:return: w (model object)
+199
View File
@@ -0,0 +1,199 @@
from SimPEG import Utils, Survey, np
from SimPEG.Survey import BaseSurvey
from SimPEG.EM.Utils import *
from BaseTDEM import FieldsTDEM
import SrcTDEM as Src
class RxTDEM(Survey.BaseTimeRx):
knownRxTypes = {
'ex':['e', 'Ex', 'N'],
'ey':['e', 'Ey', 'N'],
'ez':['e', 'Ez', 'N'],
'bx':['b', 'Fx', 'N'],
'by':['b', 'Fy', 'N'],
'bz':['b', 'Fz', 'N'],
'dbxdt':['b', 'Fx', 'CC'],
'dbydt':['b', 'Fy', 'CC'],
'dbzdt':['b', 'Fz', 'CC'],
}
def __init__(self, locs, times, rxType):
Survey.BaseTimeRx.__init__(self, locs, times, rxType)
@property
def projField(self):
"""Field Type projection (e.g. e b ...)"""
return self.knownRxTypes[self.rxType][0]
@property
def projGLoc(self):
"""Grid Location projection (e.g. Ex Fy ...)"""
return self.knownRxTypes[self.rxType][1]
@property
def projTLoc(self):
"""Time Location projection (e.g. CC N)"""
return self.knownRxTypes[self.rxType][2]
def getTimeP(self, timeMesh):
"""
Returns the time projection matrix.
.. note::
This is not stored in memory, but is created on demand.
"""
if self.rxType in ['dbxdt','dbydt','dbzdt']:
return timeMesh.getInterpolationMat(self.times, self.projTLoc)*timeMesh.faceDiv
else:
return timeMesh.getInterpolationMat(self.times, self.projTLoc)
def eval(self, src, mesh, timeMesh, u):
P = self.getP(mesh, timeMesh)
u_part = Utils.mkvc(u[src, self.projField, :])
return P*u_part
def evalDeriv(self, src, mesh, timeMesh, u, v, adjoint=False):
P = self.getP(mesh, timeMesh)
if not adjoint:
return P * Utils.mkvc(v[src, self.projField, :])
elif adjoint:
return P.T * v[src, self]
class SrcTDEM(Survey.BaseSrc):
rxPair = RxTDEM
radius = None
def getInitialFields(self, mesh):
F0 = getattr(self, '_getInitialFields_' + self.srcType)(mesh)
return F0
def getJs(self, mesh, time):
return None
class SrcTDEM_VMD_MVP(SrcTDEM):
def __init__(self,rxList,loc,waveformType="STEPOFF"):
self.loc = loc
self.waveformType = waveformType
SrcTDEM.__init__(self,rxList)
def getInitialFields(self, mesh):
"""Vertical magnetic dipole, magnetic vector potential"""
if self.waveformType == "STEPOFF":
print ">> Step waveform: Non-zero initial condition"
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
else:
raise Exception('Unknown mesh for VMD')
return {"b": mesh.edgeCurl*MVP}
elif self.waveformType == "GENERAL":
print ">> General waveform: Zero initial condition"
return {"b": np.zeros(mesh.nF)}
else:
raise NotImplementedError("Only use STEPOFF or GENERAL")
def getMeS(self, mesh, MfMui):
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticDipoleVectorPotential(self.loc, mesh, 'Ey')
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticDipoleVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'])
else:
raise Exception('Unknown mesh for VMD')
return mesh.edgeCurl.T*MfMui*mesh.edgeCurl*MVP
class SrcTDEM_CircularLoop_MVP(SrcTDEM):
def __init__(self,rxList,loc,radius,waveformType="STEPOFF"):
self.loc = loc
self.radius = radius
self.waveformType = waveformType
SrcTDEM.__init__(self,rxList)
def getInitialFields(self, mesh):
"""Circular Loop, magnetic vector potential"""
if self.waveformType == "STEPOFF":
print ">> Step waveform: Non-zero initial condition"
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticLoopVectorPotential(self.loc, mesh, 'Ey', self.radius)
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticLoopVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'], self.radius)
else:
raise Exception('Unknown mesh for CircularLoop')
return {"b": mesh.edgeCurl*MVP}
elif self.waveformType == "GENERAL":
print ">> General waveform: Zero initial condition"
return {"b": np.zeros(mesh.nF)}
else:
raise NotImplementedError("Only use STEPOFF or GENERAL")
def getMeS(self, mesh, MfMui):
if mesh._meshType is 'CYL':
if mesh.isSymmetric:
MVP = MagneticLoopVectorPotential(self.loc, mesh, 'Ey', self.radius)
else:
raise NotImplementedError('Non-symmetric cyl mesh not implemented yet!')
elif mesh._meshType is 'TENSOR':
MVP = MagneticLoopVectorPotential(self.loc, mesh, ['Ex','Ey','Ez'], self.radius)
else:
raise Exception('Unknown mesh for CircularLoop')
return mesh.edgeCurl.T*MfMui*mesh.edgeCurl*MVP
class SurveyTDEM(Survey.BaseSurvey):
"""
docstring for SurveyTDEM
"""
srcPair = SrcTDEM
def __init__(self, srcList, **kwargs):
# Sort these by frequency
self.srcList = srcList
Survey.BaseSurvey.__init__(self, **kwargs)
def projectFields(self, u):
data = Survey.Data(self)
for src in self.srcList:
for rx in src.rxList:
data[src, rx] = rx.projectFields(src, self.mesh, self.prob.timeMesh, u)
return data
def projectFieldsDeriv(self, u, v=None, adjoint=False):
assert v is not None, 'v to multiply must be provided.'
if not adjoint:
data = Survey.Data(self)
for src in self.srcList:
for rx in src.rxList:
data[src, rx] = rx.projectFieldsDeriv(src, self.mesh, self.prob.timeMesh, u, v)
return data
else:
f = FieldsTDEM(self.mesh, self)
for src in self.srcList:
for rx in src.rxList:
Ptv = rx.projectFieldsDeriv(src, self.mesh, self.prob.timeMesh, u, v, adjoint=True)
Ptv = Ptv.reshape((-1, self.prob.timeMesh.nN), order='F')
if rx.projField not in f: # first time we are projecting
f[src, rx.projField, :] = Ptv
else: # there are already fields, so let's add to them!
f[src, rx.projField, :] += Ptv
return f
@@ -87,8 +87,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
"""
:param numpy.array m: Conductivity model
:param numpy.array vec: vector (like a model)
:param FieldsTDEM u: Fields resulting from m
:rtype: FieldsTDEM
:param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
:rtype: simpegEM.TDEM.FieldsTDEM
:return: f
Multiply G by a vector
@@ -125,9 +125,9 @@ class ProblemTDEM_b(BaseTDEMProblem):
"""
:param numpy.array m: Conductivity model
:param numpy.array vec: vector (like a fields)
:param FieldsTDEM u: Fields resulting from m
:rtype: numpy.ndarray
:return: p (like a model)
:param simpegEM.TDEM.FieldsTDEM u: Fields resulting from m
:rtype: np.ndarray (like a model)
:return: p
Multiply G.T by a vector
"""
@@ -153,8 +153,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
def solveAh(self, m, p):
"""
:param numpy.array m: Conductivity model
:param FieldsTDEM p: Fields object
:rtype: FieldsTDEM
:param simpegEM.TDEM.FieldsTDEM p: Fields object
:rtype: simpegEM.TDEM.FieldsTDEM
:return: y
Solve the block-matrix system \\\(\\\hat{A} \\\hat{y} = \\\hat{p}\\\):
@@ -200,8 +200,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
def solveAht(self, m, p):
"""
:param numpy.array m: Conductivity model
:param FieldsTDEM p: Fields object
:rtype: FieldsTDEM
:param simpegEM.TDEM.FieldsTDEM p: Fields object
:rtype: simpegEM.TDEM.FieldsTDEM
:return: y
Solve the block-matrix system \\\(\\\hat{A}^\\\\top \\\hat{y} = \\\hat{p}\\\):
@@ -270,8 +270,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
def _AhVec(self, m, vec):
"""
:param numpy.array m: Conductivity model
:param FieldsTDEM vec: Fields object
:rtype: FieldsTDEM
:param simpegEM.TDEM.FieldsTDEM vec: Fields object
:rtype: simpegEM.TDEM.FieldsTDEM
:return: f
Multiply the matrix \\\(\\\hat{A}\\\) by a fields vector where
@@ -315,8 +315,8 @@ class ProblemTDEM_b(BaseTDEMProblem):
def _AhtVec(self, m, vec):
"""
:param numpy.array m: Conductivity model
:param FieldsTDEM vec: Fields object
:rtype: FieldsTDEM
:param simpegEM.TDEM.FieldsTDEM vec: Fields object
:rtype: simpegEM.TDEM.FieldsTDEM
:return: f
Multiply the matrix \\\(\\\hat{A}\\\) by a fields vector where
+3
View File
@@ -0,0 +1,3 @@
from SurveyTDEM import * #SurveyTDEM, RxTDEM, SrcTDEM
from BaseTDEM import BaseTDEMProblem, FieldsTDEM
from TDEM_b import ProblemTDEM_b
+7 -7
View File
@@ -1,7 +1,7 @@
from SimPEG import *
import SimPEG.EM.Static.DC as DC
import SimPEG.DCIP as DC
def run(plotIt=True):
def run(plotIt=False):
cs = 25.
hx = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
hy = [(cs,7, -1.3),(cs,21),(cs,7, 1.3)]
@@ -21,10 +21,10 @@ def run(plotIt=True):
# ax.plot(xyz_rxP[:,0],xyz_rxP[:,1], 'w.')
# ax.plot(xyz_rxN[:,0],xyz_rxN[:,1], 'r.', ms = 3)
rx = DC.Rx.Dipole(xyz_rxP, xyz_rxN)
src = DC.Src.Dipole([rx], np.r_[-200, 0, -12.5], np.r_[+200, 0, -12.5])
survey = DC.Survey([src])
problem = DC.Problem3D_CC(mesh)
rx = DC.RxDipole(xyz_rxP, xyz_rxN)
src = DC.SrcDipole([rx], [-200, 0, -12.5], [+200, 0, -12.5])
survey = DC.SurveyDC([src])
problem = DC.ProblemDC_CC(mesh)
problem.pair(survey)
try:
from pymatsolver import MumpsSolver
@@ -65,4 +65,4 @@ def run(plotIt=True):
if __name__ == '__main__':
print run()
print run(plotIt=True)
@@ -19,13 +19,10 @@ def run(plotIt=True):
Morrison Casing Model, and the results are used in a 2016 SEG abstract by
Yang et al.
.. code-block:: text
Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
- Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
The model consists of:
- Air: Conductivity 1e-8 S/m, above z = 0
- Background: conductivity 1e-2 S/m, below z = 0
- Casing: conductivity 1e6 S/m
@@ -218,7 +215,7 @@ def run(plotIt=True):
# ------------ Problem and Survey ---------------
survey = FDEM.Survey(sg_p + dg_p)
mapping = [('sigma', Maps.IdentityMap(mesh))]
problem = FDEM.Problem3D_h(mesh, mapping=mapping, Solver=solver)
problem = FDEM.Problem3D_h(mesh, mapping=mapping)
problem.pair(survey)
# ------------- Solve ---------------------------
+6 -6
View File
@@ -42,10 +42,10 @@ def run(plotIt=True):
rxOffset=1e-3
rx = EM.TDEM.RxTDEM(np.array([[rxOffset, 0., 30]]), np.logspace(-5,-3, 31), 'bz')
src = EM.TDEM.SrcTDEM_VMD_MVP([rx], np.array([0., 0., 80]))
survey = EM.TDEM.SurveyTDEM([src])
prb = EM.TDEM.ProblemTDEM_b(mesh, mapping=mapping)
rx = EM.TDEM.Rx(np.array([[rxOffset, 0., 30]]), np.logspace(-5,-3, 31), 'bz')
src = EM.TDEM.Src.MagDipole([rx], loc=np.array([0., 0., 80]))
survey = EM.TDEM.Survey([src])
prb = EM.TDEM.Problem_b(mesh, mapping=mapping)
prb.Solver = SolverLU
prb.timeSteps = [(1e-06, 20),(1e-05, 20), (0.0001, 20)]
@@ -53,9 +53,9 @@ def run(plotIt=True):
# create observed data
std = 0.05
survey.dobs = survey.makeSyntheticData(mtrue,std)
survey.std = std
survey.std = std
survey.eps = 1e-5*np.linalg.norm(survey.dobs)
if plotIt:
+29 -7
View File
@@ -42,33 +42,55 @@ def run(N=100, plotIt=True):
survey = Survey.LinearSurvey()
survey.pair(prob)
survey.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk)
#survey.makeSyntheticData(mtrue, std=std_noise)
wd = np.ones(nk) * std_noise
#print survey.std[0]
#M = prob.mesh
# Distance weighting
wr = np.sum(prob.G**2.,axis=0)**0.5
wr = ( wr/np.max(wr) )
# reg = Regularization.Simple(mesh)
# reg.mref = mref
# reg.cell_weights = wr
#
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = 1./wd
#
# opt = Optimization.ProjectedGNCG(maxIter=20,lower=-2.,upper=2., maxIterCG= 10, tolCG = 1e-4)
# invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
# invProb.curModel = m0
#
# beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)
# target = Directives.TargetMisfit()
#
betaest = Directives.BetaEstimate_ByEig()
# inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest, target])
#
#
# mrec = inv.run(m0)
# ml2 = mrec
# print "Final misfit:" + str(invProb.dmisfit.eval(mrec))
#
# # Switch regularization to sparse
# phim = invProb.phi_m_last
# phid = invProb.phi_d
reg = Regularization.Sparse(mesh)
reg.mref = mref
reg.cell_weights = wr
reg.mref = np.zeros(mesh.nC)
eps_p = 5e-2
eps_q = 5e-2
norms = [0., 0., 2., 2.]
opt = Optimization.ProjectedGNCG(maxIter=100 ,lower=-2.,upper=2., maxIterLS = 20, maxIterCG= 10, tolCG = 1e-3)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt)
update_Jacobi = Directives.Update_lin_PreCond()
# Set the IRLS directive, penalize the lowest 25 percentile of model values
# Start with an l2-l2, then switch to lp-norms
norms = [0., 0., 2., 2.]
IRLS = Directives.Update_IRLS( norms=norms, prctile = 25, maxIRLSiter = 15, minGNiter=3)
IRLS = Directives.Update_IRLS( norms=norms, eps_p=eps_p, eps_q=eps_q)
inv = Inversion.BaseInversion(invProb, directiveList=[IRLS,betaest,update_Jacobi])
+3 -3
View File
@@ -7,7 +7,7 @@ import matplotlib.pyplot as plt
def run(plotIt=True):
"""
MT: 1D: Inversion
=================
=======================
Forward model 1D MT data.
Setup and run a MT 1D inversion.
@@ -50,7 +50,7 @@ def run(plotIt=True):
m_0 = np.log(sigma_0[active])
# Set the mapping
actMap = simpeg.Maps.InjectActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
actMap = simpeg.Maps.ActiveCells(m1d, active, np.log(1e-8), nC=m1d.nCx)
mappingExpAct = simpeg.Maps.ExpMap(m1d) * actMap
## Setup the layout of the survey, set the sources and the connected receivers
@@ -76,7 +76,7 @@ def run(plotIt=True):
survey.dobs = survey.dtrue + 0.025*abs(survey.dtrue)*np.random.randn(*survey.dtrue.shape)
if plotIt:
fig = MT.Utils.dataUtils.plotMT1DModelData(problem, [m_0])
fig = MT.Utils.dataUtils.plotMT1DModelData(problem)
fig.suptitle('Target - smooth true')
+4 -3
View File
@@ -12,7 +12,7 @@ except:
def run(plotIt=True, nFreq=1):
"""
MT: 3D: Forward
===============
=======================
Forward model 3D MT data.
@@ -46,15 +46,16 @@ def run(plotIt=True, nFreq=1):
survey = MT.Survey(srcList)
## Setup the problem object
problem = MT.Problem3D.eForm_ps(M, sigmaPrimary=sigBG, Solver=Solver)
problem = MT.Problem3D.eForm_ps(M, sigmaPrimary=sigBG)
problem.pair(survey)
problem.Solver = Solver
# Calculate the data
fields = problem.fields(sig)
dataVec = survey.eval(fields)
# Make the data
mtData = MT.Data(survey, dataVec)
mtData = MT.Data(survey,dataVec)
# Add plots
if plotIt:
pass
-62
View File
@@ -1,62 +0,0 @@
from SimPEG import Mesh, Maps, np
def run(plotIt=True):
"""
Maps: ComboMaps
===============
We will use an example where we want a 1D layered earth as
our model, but we want to map this to a 2D discretization to do our forward
modeling. We will also assume that we are working in log conductivity still,
so after the transformation we want to map to conductivity space.
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
which does the first part of what we just described. The second part will be
done by the :class:`SimPEG.Maps.ExpMap` described above.
.. code-block:: python
:linenos:
M = Mesh.TensorMesh([7,5])
v1dMap = Maps.SurjectVertical1D(M)
expMap = Maps.ExpMap(M)
myMap = expMap * v1dMap
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
sig = myMap * m
If you noticed, it was pretty easy to combine maps. What is even cooler is
that the derivatives also are made for you (if everything goes right).
Just to be sure that the derivative is correct, you should always run the test
on the mapping that you create.
"""
M = Mesh.TensorMesh([7,5])
v1dMap = Maps.SurjectVertical1D(M)
expMap = Maps.ExpMap(M)
myMap = expMap * v1dMap
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
sig = myMap * m
if not plotIt: return
import matplotlib.pyplot as plt
figs, axs = plt.subplots(1,2)
axs[0].plot(m, M.vectorCCy, 'b-o')
axs[0].set_title('Model')
axs[0].set_ylabel('Depth, y')
axs[0].set_xlabel('Value, $m_i$')
axs[0].set_xlim(0,3)
axs[0].set_ylim(0,1)
clbar = plt.colorbar(M.plotImage(sig,ax=axs[1],grid=True,gridOpts=dict(color='grey'))[0])
axs[1].set_title('Physical Property')
axs[1].set_ylabel('Depth, y')
clbar.set_label('$\sigma = \exp(\mathbf{P}m)$')
plt.tight_layout()
plt.show()
if __name__ == '__main__':
run()
-41
View File
@@ -1,41 +0,0 @@
from SimPEG import Mesh, Maps, Utils
def run(plotIt=True):
"""
Maps: Mesh2Mesh
===============
This mapping allows you to go from one mesh to another.
"""
M = Mesh.TensorMesh([100,100])
h1 = Utils.meshTensor([(6,7,-1.5),(6,10),(6,7,1.5)])
h1 = h1/h1.sum()
M2 = Mesh.TensorMesh([h1,h1])
V = Utils.ModelBuilder.randomModel(M.vnC, seed=79, its=50)
v = Utils.mkvc(V)
modh = Maps.Mesh2Mesh([M,M2])
modH = Maps.Mesh2Mesh([M2,M])
H = modH * v
h = modh * H
if not plotIt: return
import matplotlib.pyplot as plt
ax = plt.subplot(131)
M.plotImage(v, ax=ax)
ax.set_title('Fine Mesh (Original)')
ax = plt.subplot(132)
M2.plotImage(H,clim=[0,1],ax=ax)
ax.set_title('Course Mesh')
ax = plt.subplot(133)
M.plotImage(h,clim=[0,1],ax=ax)
ax.set_title('Fine Mesh (Interpolated)')
plt.show()
if __name__ == '__main__':
run()
+7 -9
View File
@@ -2,12 +2,8 @@ from SimPEG import *
from SimPEG.Utils import surface2ind_topo
def run(plotIt=True, nx=5, ny=5):
def run(plotIt=False, nx = 5, ny = 5):
"""
Utils: surface2ind_topo
=======================
Here we show how to use :code:`Utils.surface2ind_topo` to identify cells below
a topographic surface.
@@ -17,25 +13,27 @@ def run(plotIt=True, nx=5, ny=5):
xtopo = np.linspace(mesh.gridN[:,0].min(), mesh.gridN[:,0].max())
topo = 0.4*np.sin(xtopo*5) # define a topographic surface
Topo = np.hstack([Utils.mkvc(xtopo,2), Utils.mkvc(topo,2)]) #make it an array
Topo = np.hstack([Utils.mkvc(xtopo,2),Utils.mkvc(topo,2)]) #make it an array
indcc = surface2ind_topo(mesh, Topo, 'CC')
indcc = surface2ind_topo(mesh, Topo,'CC')
if plotIt:
from matplotlib.pylab import plt
from scipy.interpolate import interp1d
fig, ax = plt.subplots(1,1, figsize=(6,6))
fig, ax = plt.subplots(1,1,figsize=(6,6))
mesh.plotGrid(ax=ax, nodes=True, centers=True)
ax.plot(xtopo,topo,'k',linewidth=1)
# ax.plot(mesh.vectorNx, interp1d(xtopo,topo)(mesh.vectorNx),'--k',linewidth=3)
ax.plot(mesh.vectorCCx, interp1d(xtopo,topo)(mesh.vectorCCx),'--k',linewidth=3)
aveN2CC = Utils.sdiag(mesh.aveN2CC.T.sum(1))*mesh.aveN2CC.T
a = aveN2CC * indcc
a[a > 0] = 1.
a[a < 0.25] = np.nan
a = a.reshape(mesh.vnN, order='F')
masked_array = np.ma.array(a, mask=np.isnan(a))
ax.pcolor(mesh.vectorNx,mesh.vectorNy,masked_array.T, cmap=plt.cm.gray, alpha=0.2)
ax.pcolor(mesh.vectorNx,mesh.vectorNy,masked_array.T, cmap = plt.cm.gray,alpha=0.2)
plt.show()
+4 -6
View File
@@ -10,8 +10,6 @@ import EM_TDEM_1D_Inversion
import FLOW_Richards_1D_Celia1990
import Inversion_IRLS
import Inversion_Linear
import Maps_ComboMaps
import Maps_Mesh2Mesh
import Mesh_Basic_ForwardDC
import Mesh_Basic_PlotImage
import Mesh_Basic_Types
@@ -24,7 +22,7 @@ import MT_1D_ForwardAndInversion
import MT_3D_Foward
import Utils_surface2ind_topo
__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_Schenkel_Morrison_Casing", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Inversion_IRLS", "Inversion_Linear", "Maps_ComboMaps", "Maps_Mesh2Mesh", "Mesh_Basic_ForwardDC", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_ForwardAndInversion", "MT_3D_Foward", "Utils_surface2ind_topo"]
__examples__ = ["DC_Analytic_Dipole", "DC_Forward_PseudoSection", "EM_FDEM_1D_Inversion", "EM_FDEM_Analytic_MagDipoleWholespace", "EM_Schenkel_Morrison_Casing", "EM_TDEM_1D_Inversion", "FLOW_Richards_1D_Celia1990", "Inversion_IRLS", "Inversion_Linear", "Mesh_Basic_ForwardDC", "Mesh_Basic_PlotImage", "Mesh_Basic_Types", "Mesh_Operators_CahnHilliard", "Mesh_QuadTree_Creation", "Mesh_QuadTree_FaceDiv", "Mesh_QuadTree_HangingNodes", "Mesh_Tensor_Creation", "MT_1D_ForwardAndInversion", "MT_3D_Foward", "Utils_surface2ind_topo"]
##### AUTOIMPORTS #####
@@ -40,7 +38,7 @@ if __name__ == '__main__':
# Create the examples dir in the docs folder.
fName = os.path.realpath(__file__)
docExamplesDir = os.path.sep.join(fName.split(os.path.sep)[:-3] + ['docs', 'content', 'examples'])
docExamplesDir = os.path.sep.join(fName.split(os.path.sep)[:-3] + ['docs', 'examples'])
shutil.rmtree(docExamplesDir)
os.makedirs(docExamplesDir)
@@ -97,12 +95,12 @@ if __name__ == '__main__':
from SimPEG import Examples
Examples.%s.run()
.. literalinclude:: ../../../SimPEG/Examples/%s.py
.. literalinclude:: ../../SimPEG/Examples/%s.py
:language: python
:linenos:
"""%(name,doc,name,name)
rst = os.path.sep.join((filePath.split(os.path.sep)[:-3] + ['docs', 'content', 'examples', name + '.rst']))
rst = os.path.sep.join((filePath.split(os.path.sep)[:-3] + ['docs', 'examples', name + '.rst']))
print 'Creating: %s.rst'%name
f = open(rst, 'w')
+157
View File
@@ -0,0 +1,157 @@
from SimPEG import np, Mesh, Maps, Utils, DataMisfit, Regularization, Optimization, Inversion, InvProblem, Directives
from SimPEG import SolverLU
from SimPEG.EM import FDEM, TDEM, mu_0
import matplotlib.pyplot as plt
import matplotlib
matplotlib.rcParams['font.size'] = 14
def run(plotIt=True):
# Set up cylindrically symmeric mesh
cs, ncx, ncz, npad = 10., 15, 25, 13 # padded cyl mesh
hx = [(cs,ncx), (cs,npad,1.3)]
hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
mesh = Mesh.CylMesh([hx,1,hz], '00C')
# Conductivity model
layerz = np.r_[-200., -100.]
layer = (mesh.vectorCCz>=layerz[0]) & (mesh.vectorCCz<=layerz[1])
active = mesh.vectorCCz<0.
sig_half = 1e-2 # Half-space conductivity
sig_air = 1e-8 # Air conductivity
sig_layer = 5e-2 # Layer conductivity
sigma = np.ones(mesh.nCz)*sig_air
sigma[active] = sig_half
sigma[layer] = sig_layer
# Mapping
actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap
mtrue = np.log(sigma[active])
# FDEM problem & survey
rxlocs = Utils.ndgrid([np.r_[50.], np.r_[0], np.r_[0.]])
bzi = FDEM.Rx.Point_bSecondary(rxlocs, 'z', 'real')
bzr = FDEM.Rx.Point_bSecondary(rxlocs, 'z', 'imag')
freqs = np.logspace(2, 3, 5)
srcLoc = np.array([0., 0., 0.])
print 'min skin depth = ', 500./np.sqrt(freqs.max() * sig_half), 'max skin depth = ', 500./np.sqrt(freqs.min() * sig_half)
print 'max x ', mesh.vectorCCx.max(), 'min z ', mesh.vectorCCz.min(), 'max z ', mesh.vectorCCz.max()
srcList = []
[srcList.append(FDEM.Src.MagDipole([bzr, bzi],freq, srcLoc,orientation='Z')) for freq in freqs]
surveyFD = FDEM.Survey(srcList)
prbFD = FDEM.Problem3D_b(mesh, mapping=mapping)
prbFD.pair(surveyFD)
std = 0.03
surveyFD.makeSyntheticData(mtrue, std)
surveyFD.eps = np.linalg.norm(surveyFD.dtrue)*1e-5
# FDEM inversion
np.random.seed(1)
dmisfit = DataMisfit.l2_DataMisfit(surveyFD)
regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]])
reg = Regularization.Simple(regMesh)
opt = Optimization.InexactGaussNewton(maxIterCG=10, maxIter=4)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
# Inversion Directives
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=3)
# betaest = Directives.BetaEstimate_ByEig(beta0_ratio=10.)
invProb.beta = 1.
target = Directives.TargetMisfit()
inv = Inversion.BaseInversion(invProb, directiveList=[beta,target])
m0 = np.log(np.ones(mtrue.size)*sig_half)
reg.alpha_s = 5e-1
reg.alpha_x = 1.
prbFD.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.tolG = 1e-10
opt.eps = 1e-10
opt.remember('xc')
moptFD = inv.run(m0)
# TDEM problem
times = np.logspace(-4, np.log10(2e-3), 10)
print 'min diffusion distance ', 1.28*np.sqrt(times.min()/(sig_half*mu_0)), 'max diffusion distance ', 1.28*np.sqrt(times.max()/(sig_half*mu_0))
rx = TDEM.Rx(rxlocs, times, 'bz')
src = TDEM.Src.MagDipole([rx], waveform=TDEM.Src.StepOffWaveform(), loc=srcLoc) # same src location as FDEM problem
surveyTD = TDEM.Survey([src])
prbTD = TDEM.Problem_b(mesh, mapping=mapping)
prbTD.timeSteps = [(5e-5, 10),(1e-4, 10),(5e-4, 10)]
prbTD.pair(surveyTD)
prbTD.Solver = SolverLU
std = 0.03
surveyTD.makeSyntheticData(mtrue, std)
surveyTD.std = std
surveyTD.eps = np.linalg.norm(surveyTD.dtrue)*1e-5
# TDEM inversion
dmisfit = DataMisfit.l2_DataMisfit(surveyTD)
regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]])
reg = Regularization.Simple(regMesh)
opt = Optimization.InexactGaussNewton(maxIterCG=10, maxIter=4)
invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
# Inversion Directives
beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=3)
invProb.beta = 1.
# betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1.)
target = Directives.TargetMisfit()
inv = Inversion.BaseInversion(invProb, directiveList=[beta, target])
m0 = np.log(np.ones(mtrue.size)*sig_half)
reg.alpha_s = 5e-1
reg.alpha_x = 1.
prbTD.counter = opt.counter = Utils.Counter()
opt.LSshorten = 0.5
opt.remember('xc')
moptTD = inv.run(m0)
if plotIt:
fig, ax = plt.subplots(1,1, figsize = (4, 6))
plt.semilogx(sigma[active], mesh.vectorCCz[active], 'k-', lw=2)
plt.semilogx(np.exp(moptFD), mesh.vectorCCz[active], 'ko', ms=3)
plt.semilogx(np.exp(moptTD), mesh.vectorCCz[active], 'k*')
ax.set_ylim(-1000, 0)
ax.set_xlim(5e-3, 1e-1)
ax.set_xlabel('Conductivity (S/m)', fontsize = 14)
ax.set_ylabel('Depth (m)', fontsize = 14)
ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
plt.legend(['True', 'Pred (FD)', 'Pred (TD)'], fontsize=13, loc=4)
plt.show()
fig = plt.figure(figsize = (10*1.3, 5*1.3))
ax2 = plt.subplot(122)
ax2.plot(times, surveyTD.dobs, 'k-', lw=2)
ax2.plot(times, surveyTD.dpred(moptTD), 'ko', ms=4)
ax2.set_xscale('log')
ax2.set_yscale('log')
ax2.set_xlim(times.min(), times.max())
ax1 = plt.subplot(121)
ax1.plot(freqs, -surveyFD.dobs[::2], 'k-', lw=2)
ax1.plot(freqs, -surveyFD.dobs[1::2], 'k--', lw=2)
dpredFD = surveyFD.dpred(moptTD)
ax1.plot(freqs, -dpredFD[::2], 'ko', ms=4)
ax1.plot(freqs, -dpredFD[1::2], 'k+', markeredgewidth=2., ms=10)
ax1.set_xscale('log')
ax1.set_yscale('log')
ax2.set_xlabel('Time (s)', fontsize = 14)
ax1.set_xlabel('Frequency (Hz)', fontsize = 14)
ax1.set_ylabel('Vertical magnetic field (T)', fontsize = 14)
ax2.grid(True,which='minor')
ax1.grid(True,which='minor')
ax2.set_title("(b) TD observed vs. predicted", fontsize = 14)
ax1.set_title("(a) FD observed vs. predicted", fontsize = 14)
ax2.legend(("Obs", "Pred"), fontsize = 12)
ax1.legend(("Obs", "Pred (real)", "Pred (imag)"), fontsize = 12, loc=3)
ax1.set_xlim(freqs.max(), freqs.min())
plt.show()
if __name__ == '__main__':
run()
+2 -2
View File
@@ -31,7 +31,7 @@ class NonLinearMap(object):
"""
:param numpy.array u: fields
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
The *transform* changes the model into the physical property.
@@ -44,7 +44,7 @@ class NonLinearMap(object):
"""
:param numpy.array u: fields
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
The *transform* changes the model into the physical property.
+2 -2
View File
@@ -86,7 +86,7 @@ class polxy_1Dprimary(BaseMTSrc):
Get the electrical field source
"""
e_p = self.ePrimary(problem)
Map_sigma_p = Maps.SurjectVertical1D(problem.mesh)
Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
sigma_p = Map_sigma_p._transform(self.sigma1d)
# Make mass matrix
# Note: M(sig) - M(sig_p) = M(sig - sig_p)
@@ -163,7 +163,7 @@ class polxy_3Dprimary(BaseMTSrc):
Get the electrical field source
"""
e_p = self.ePrimary(problem)
Map_sigma_p = Maps.SurjectVertical1D(problem.mesh)
Map_sigma_p = Maps.Vertical1DMap(problem.mesh)
sigma_p = Map_sigma_p._transform(self.sigma1d)
# Make mass matrix
# Note: M(sig) - M(sig_p) = M(sig - sig_p)
+6 -6
View File
@@ -19,7 +19,7 @@ def getAppRes(MTdata):
zList.append(zc)
return [appResPhs(zList[i][0],np.sum(zList[i][1:3])) for i in np.arange(len(zList))]
def rotateData(MTdata, rotAngle):
def rotateData(MTdata,rotAngle):
'''
Function that rotates clockwist by rotAngle (- negative for a counter-clockwise rotation)
'''
@@ -44,19 +44,19 @@ def rotateData(MTdata, rotAngle):
return MT.Data.fromRecArray(outRec)
def appResPhs(freq, z):
def appResPhs(freq,z):
app_res = ((1./(8e-7*np.pi**2))/freq)*np.abs(z)**2
app_phs = np.arctan2(z.imag,z.real)*(180/np.pi)
return app_res, app_phs
def skindepth(rho, freq):
def skindepth(rho,freq):
''' Function to calculate the skindepth of EM waves'''
return np.sqrt( (rho*((1/(freq * mu_0 * np.pi )))))
def rec2ndarr(x, dt=float):
def rec2ndarr(x,dt=float):
return x.view((dt, len(x.dtype.names)))
def makeAnalyticSolution(mesh, model, elev, freqs):
def makeAnalyticSolution(mesh,model,elev,freqs):
from SimPEG import MT
data1D = []
for freq in freqs:
@@ -70,7 +70,7 @@ def makeAnalyticSolution(mesh, model, elev, freqs):
dataRec = np.array(data1D,dtype=[('freq',float),('x',float),('y',float),('z',float),('zyx',complex)])
return dataRec
def plotMT1DModelData(problem, models, symList=None):
def plotMT1DModelData(problem,models,symList=None):
from SimPEG import MT
# Setup the figure
fontSize = 15
+7 -9
View File
@@ -41,8 +41,8 @@ class IdentityMap(object):
If this is a meshless mapping (i.e. nP is defined independently)
the shape will be the the shape (nP,nP).
:rtype: tuple
:return: shape of the operator as a tuple (int,int)
:rtype: (int,int)
:return: shape of the operator as a tuple
"""
if self._nP is not None:
return (self.nP, self.nP)
@@ -86,7 +86,7 @@ class IdentityMap(object):
The derivative of the transformation.
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
"""
@@ -216,7 +216,7 @@ class ExpMap(IdentityMap):
def deriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
The *transform* changes the model into the physical property.
@@ -366,7 +366,7 @@ class SurjectVertical1D(IdentityMap):
def deriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
"""
repNum = self.mesh.vnC[:self.mesh.dim-1].prod()
@@ -427,7 +427,7 @@ class Surject2Dto3D(IdentityMap):
def deriv(self, m):
"""
:param numpy.array m: model
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: derivative of transformed model
"""
inds = self * np.arange(self.nP)
@@ -502,9 +502,7 @@ class InjectActiveCells(IdentityMap):
if Utils.isScalar(valInactive):
self.valInactive = np.ones(self.nC)*float(valInactive)
else:
self.valInactive = np.ones(self.nC)
self.valInactive[self.indInactive] = valInactive.copy()
self.valInactive = valInactive.copy()
self.valInactive[self.indActive] = 0
inds = np.nonzero(self.indActive)[0]
+24 -26
View File
@@ -7,8 +7,8 @@ class BaseMesh(object):
BaseMesh does all the counting you don't want to do.
BaseMesh should be inherited by meshes with a regular structure.
:param numpy.array n: (or list) number of cells in each direction (dim, )
:param numpy.array x0: (or list) Origin of the mesh (dim, )
:param numpy.array,list n: number of cells in each direction (dim, )
:param numpy.array,list x0: Origin of the mesh (dim, )
"""
@@ -34,8 +34,8 @@ class BaseMesh(object):
"""
Origin of the mesh
:rtype: numpy.array
:return: x0, (dim, )
:rtype: numpy.array (dim, )
:return: x0
"""
return self._x0
@@ -116,8 +116,8 @@ class BaseMesh(object):
"""
Total number of edges in each direction
:rtype: numpy.array
:return: [nEx, nEy, nEz], (dim, )
:rtype: numpy.array (dim, )
:return: [nEx, nEy, nEz]
.. plot::
:include-source:
@@ -173,8 +173,8 @@ class BaseMesh(object):
"""
Total number of faces in each direction
:rtype: numpy.array
:return: [nFx, nFy, nFz], (dim, )
:rtype: numpy.array (dim, )
:return: [nFx, nFy, nFz]
.. plot::
:include-source:
@@ -200,8 +200,8 @@ class BaseMesh(object):
"""
Face Normals
:rtype: numpy.array
:return: normals, (sum(nF), dim)
:rtype: numpy.array (sum(nF), dim)
:return: normals
"""
if self.dim == 2:
nX = np.c_[np.ones(self.nFx), np.zeros(self.nFx)]
@@ -218,8 +218,8 @@ class BaseMesh(object):
"""
Edge Tangents
:rtype: numpy.array
:return: normals, (sum(nE), dim)
:rtype: numpy.array (sum(nE), dim)
:return: normals
"""
if self.dim == 2:
tX = np.c_[np.ones(self.nEx), np.zeros(self.nEx)]
@@ -236,9 +236,8 @@ class BaseMesh(object):
Given a vector, fV, in cartesian coordinates, this will project it onto the mesh using the normals
:param numpy.array fV: face vector with shape (nF, dim)
:rtype: numpy.array
:return: projected face vector, (nF, )
:rtype: numpy.array with shape (nF, )
:return: projected face vector
"""
assert isinstance(fV, np.ndarray), 'fV must be an ndarray'
assert len(fV.shape) == 2 and fV.shape[0] == self.nF and fV.shape[1] == self.dim, 'fV must be an ndarray of shape (nF x dim)'
@@ -249,9 +248,8 @@ class BaseMesh(object):
Given a vector, eV, in cartesian coordinates, this will project it onto the mesh using the tangents
:param numpy.array eV: edge vector with shape (nE, dim)
:rtype: numpy.array
:return: projected edge vector, (nE, )
:rtype: numpy.array with shape (nE, )
:return: projected edge vector
"""
assert isinstance(eV, np.ndarray), 'eV must be an ndarray'
assert len(eV.shape) == 2 and eV.shape[0] == self.nE and eV.shape[1] == self.dim, 'eV must be an ndarray of shape (nE x dim)'
@@ -297,7 +295,7 @@ class BaseRectangularMesh(BaseMesh):
"""
Total number of cells in each direction
:rtype: numpy.array
:rtype: numpy.array (dim, )
:return: [nCx, nCy, nCz]
"""
return np.array([x for x in [self.nCx, self.nCy, self.nCz] if not x is None])
@@ -337,7 +335,7 @@ class BaseRectangularMesh(BaseMesh):
"""
Total number of nodes in each direction
:rtype: numpy.array
:rtype: numpy.array (dim, )
:return: [nNx, nNy, nNz]
"""
return np.array([x for x in [self.nNx, self.nNy, self.nNz] if not x is None])
@@ -347,7 +345,7 @@ class BaseRectangularMesh(BaseMesh):
"""
Number of x-edges in each direction
:rtype: numpy.array
:rtype: numpy.array (dim, )
:return: vnEx
"""
return np.array([x for x in [self.nCx, self.nNy, self.nNz] if not x is None])
@@ -357,7 +355,7 @@ class BaseRectangularMesh(BaseMesh):
"""
Number of y-edges in each direction
:rtype: numpy.array
:rtype: numpy.array (dim, )
:return: vnEy or None if dim < 2
"""
return None if self.dim < 2 else np.array([x for x in [self.nNx, self.nCy, self.nNz] if not x is None])
@@ -367,7 +365,7 @@ class BaseRectangularMesh(BaseMesh):
"""
Number of z-edges in each direction
:rtype: numpy.array
:rtype: numpy.array (dim, )
:return: vnEz or None if dim < 3
"""
return None if self.dim < 3 else np.array([x for x in [self.nNx, self.nNy, self.nCz] if not x is None])
@@ -377,7 +375,7 @@ class BaseRectangularMesh(BaseMesh):
"""
Number of x-faces in each direction
:rtype: numpy.array
:rtype: numpy.array (dim, )
:return: vnFx
"""
return np.array([x for x in [self.nNx, self.nCy, self.nCz] if not x is None])
@@ -387,7 +385,7 @@ class BaseRectangularMesh(BaseMesh):
"""
Number of y-faces in each direction
:rtype: numpy.array
:rtype: numpy.array (dim, )
:return: vnFy or None if dim < 2
"""
return None if self.dim < 2 else np.array([x for x in [self.nCx, self.nNy, self.nCz] if not x is None])
@@ -397,7 +395,7 @@ class BaseRectangularMesh(BaseMesh):
"""
Number of z-faces in each direction
:rtype: numpy.array
:rtype: numpy.array (dim, )
:return: vnFz or None if dim < 3
"""
return None if self.dim < 3 else np.array([x for x in [self.nCx, self.nCy, self.nNz] if not x is None])
+6 -6
View File
@@ -68,8 +68,8 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
"""
Number of x-faces in each direction
:rtype: numpy.array
:return: vnFx, (dim, )
:rtype: numpy.array (dim, )
:return: vnFx
"""
return self.vnC
@@ -78,8 +78,8 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
"""
Number of y-edges in each direction
:rtype: numpy.array
:return: vnEy or None if dim < 2, (dim, )
:rtype: numpy.array (dim, )
:return: vnEy or None if dim < 2
"""
nNx = self.nNx if self.isSymmetric else self.nNx - 1
return np.r_[nNx, self.nCy, self.nNz]
@@ -89,8 +89,8 @@ class CylMesh(BaseTensorMesh, BaseRectangularMesh, InnerProducts, CylView):
"""
Number of z-edges in each direction
:rtype: numpy.array
:return: vnEz or None if nCy > 1, (dim, )
:rtype: numpy.array (dim, )
:return: vnEz or None if nCy > 1
"""
if self.isSymmetric:
return np.r_[self.nNx, self.nNy, self.nCz]
+9 -8
View File
@@ -16,7 +16,7 @@ class InnerProducts(object):
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:param bool doFast: do a faster implementation if available.
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
return self._getInnerProduct('F', prop=prop, invProp=invProp, invMat=invMat, doFast=doFast)
@@ -27,7 +27,7 @@ class InnerProducts(object):
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:param bool doFast: do a faster implementation if available.
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: M, the inner product matrix (nE, nE)
"""
return self._getInnerProduct('E', prop=prop, invProp=invProp, invMat=invMat, doFast=doFast)
@@ -39,7 +39,7 @@ class InnerProducts(object):
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:param bool doFast: do a faster implementation if available.
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: M, the inner product matrix (nE, nE)
"""
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
@@ -115,12 +115,13 @@ class InnerProducts(object):
:param bool doFast: do a faster implementation if available.
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: function
:return: dMdmu(u), the derivative of the inner product matrix (u)
Given u, dMdmu returns (nF, nC*nA)
:param numpy.ndarray u: vector that multiplies dMdmu
:rtype: scipy.sparse.csr_matrix
:param np.ndarray u: vector that multiplies dMdmu
:rtype: scipy.csr_matrix
:return: dMdmu, the derivative of the inner product matrix for a certain u
"""
return self._getInnerProductDeriv(prop, 'F', doFast=doFast, invProp=invProp, invMat=invMat)
@@ -132,7 +133,7 @@ class InnerProducts(object):
:param bool doFast: do a faster implementation if available.
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: dMdm, the derivative of the inner product matrix (nE, nC*nA)
"""
return self._getInnerProductDeriv(prop, 'E', doFast=doFast, invProp=invProp, invMat=invMat)
@@ -144,7 +145,7 @@ class InnerProducts(object):
:param bool doFast: do a faster implementation if available.
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: dMdm, the derivative of the inner product matrix (nE, nC*nA)
"""
fast = None
@@ -168,7 +169,7 @@ class InnerProducts(object):
:param numpy.array v: vector to multiply (required in the general implementation)
:param list P: list of projection matrices
:param str projType: 'F' for faces 'E' for edges
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: dMdm, the derivative of the inner product matrix (n, nC*nA)
"""
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
+35 -22
View File
@@ -6,11 +6,13 @@ class TensorMeshIO(object):
@classmethod
def readUBC(TensorMesh, fileName):
"""
Read UBC GIF 3D tensor mesh and generate 3D TensorMesh in SimPEG.
Read UBC GIF 3DTensor mesh and generate 3D Tensor mesh in simpegTD
:param string fileName: path to the UBC GIF mesh file
:rtype: TensorMesh
:return: The tensor mesh for the fileName.
Input:
:param fileName, path to the UBC GIF mesh file
Output:
:param SimPEG TensorMesh object
"""
# Interal function to read cell size lines for the UBC mesh files.
@@ -46,9 +48,11 @@ class TensorMeshIO(object):
Read VTK Rectilinear (vtr xml file) and return SimPEG Tensor mesh and model
Input:
:param string fileName: path to the vtr model file to read
:rtype: tuple
:return: (TensorMesh, modelDictionary)
:param vtrFileName, path to the vtr model file to write to
Output:
:return SimPEG TensorMesh object
:return SimPEG model dictionary
"""
# Import
@@ -98,8 +102,9 @@ class TensorMeshIO(object):
Makes and saves a VTK rectilinear file (vtr) for a simpeg Tensor mesh and model.
Input:
:param string fileName: path to the output vtk file
:param dict models: dictionary of numpy.array - Name('s) and array('s). Match number of cells
:param str, path to the output vtk file
:param mesh, SimPEG TensorMesh object - mesh to be transfer to VTK
:param models, dictionary of numpy.array - Name('s) and array('s). Match number of cells
"""
# Import
@@ -157,9 +162,12 @@ class TensorMeshIO(object):
"""
Read UBC 3DTensor mesh model and generate 3D Tensor mesh model in simpeg
:param string fileName: path to the UBC GIF mesh file to read
:rtype: numpy.ndarray
:return: model with TensorMesh ordered
Input:
:param fileName, path to the UBC GIF mesh file to read
:param mesh, TensorMesh object, mesh that coresponds to the model
Output:
:return numpy array, model with TensorMesh ordered
"""
f = open(fileName, 'r')
model = np.array(map(float, f.readlines()))
@@ -175,7 +183,8 @@ class TensorMeshIO(object):
Writes a model associated with a SimPEG TensorMesh
to a UBC-GIF format model file.
:param string fileName: File to write to
:param str fileName: File to write to
:param simpeg.Mesh.TensorMesh mesh: The mesh
:param numpy.ndarray model: The model
"""
@@ -192,8 +201,8 @@ class TensorMeshIO(object):
"""
Writes a SimPEG TensorMesh to a UBC-GIF format mesh file.
:param string fileName: File to write to
:param dict models: A dictionary of the models
:param str fileName: File to write to
:param simpeg.Mesh.TensorMesh mesh: The mesh
"""
assert mesh.dim == 3
@@ -222,8 +231,9 @@ class TreeMeshIO(object):
"""
Write UBC ocTree mesh and model files from a simpeg ocTree mesh and model.
:param string fileName: File to write to
:param dict models: The models in a dictionary, where the keys is the name of the of the model file
:param str fileName: File to write to
:param simpeg.Mesh.TreeMesh mesh: The mesh
:param dictionary models: The models in a dictionary, where the keys is the name of the of the model file
"""
# Calculate information to write in the file.
@@ -276,9 +286,10 @@ class TreeMeshIO(object):
Input:
:param str meshFile: path to the UBC GIF OcTree mesh file to read
:rtype: SimPEG.Mesh.TreeMesh
:return: The octree mesh
Output:
:return SimPEG.Mesh.TreeMesh mesh: The octree mesh
:return list of ndarray's: models as a list of numpy array's
"""
## Read the file lines
@@ -324,9 +335,11 @@ class TreeMeshIO(object):
"""
Read UBC OcTree model and get vector
:param string fileName: path to the UBC GIF model file to read
:rtype: numpy.ndarray
:return: OcTree model
Input:
:param fileName, path to the UBC GIF model file to read
Output:
:return numpy array, OcTree model
"""
if type(fileName) is list:
+4 -4
View File
@@ -198,8 +198,8 @@ class BaseTensorMesh(BaseMesh):
Determines if a set of points are inside a mesh.
:param numpy.ndarray pts: Location of points to test
:rtype numpy.ndarray:
:return: inside, numpy array of booleans
:rtype numpy.ndarray
:return inside, numpy array of booleans
"""
pts = Utils.asArray_N_x_Dim(pts, self.dim)
@@ -221,7 +221,7 @@ class BaseTensorMesh(BaseMesh):
:param numpy.ndarray loc: Location of points to interpolate to
:param str locType: What to interpolate (see below)
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.sparse.csr.csr_matrix
:return: M, the interpolation matrix
locType can be::
@@ -289,7 +289,7 @@ class BaseTensorMesh(BaseMesh):
:param bool returnP: returns the projection matrices
:param bool invProp: inverts the material property
:param bool invMat: inverts the matrix
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.csr_matrix
:return: M, the inner product matrix (nF, nF)
"""
assert projType in ['F', 'E'], "projType must be 'F' for faces or 'E' for edges"
+1 -1
View File
@@ -1875,7 +1875,7 @@ class TreeMesh(BaseTensorMesh, InnerProducts, TreeMeshIO):
:param numpy.ndarray locs: Location of points to interpolate to
:param str locType: What to interpolate (see below)
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.sparse.csr.csr_matrix
:return: M, the interpolation matrix
locType can be::
+5 -5
View File
@@ -131,7 +131,7 @@ class Minimize(object):
Minimizes the function (evalFunction) starting at the location x0.
:param callable evalFunction: function handle that evaluates: f, g, H = F(x)
:param def evalFunction: function handle that evaluates: f, g, H = F(x)
:param numpy.ndarray x0: starting location
:rtype: numpy.ndarray
:return: x, the last iterate of the optimization algorithm
@@ -372,8 +372,8 @@ class Minimize(object):
Else, a modifySearchDirectionBreak call is preformed.
:param numpy.ndarray p: searchDirection
:rtype: tuple
:return: (xt, passLS) numpy.ndarray, bool
:rtype: numpy.ndarray,bool
:return: (xt, passLS)
"""
# Projected Armijo linesearch
self._LS_t = 1
@@ -408,8 +408,8 @@ class Minimize(object):
evalFunction returns a False indicating the break was not caught.
:param numpy.ndarray p: searchDirection
:rtype: tuple
:return: (xt, breakCaught) numpy.ndarray, bool
:rtype: numpy.ndarray,bool
:return: (xt, breakCaught)
"""
self.printDone(inLS=True)
print 'The linesearch got broken. Boo.'
+1 -1
View File
@@ -187,7 +187,7 @@ class _PropMapMetaClass(type):
attrs[attr + 'Model'] = prop._getModelProperty()
attrs[attr + 'Deriv'] = prop._getModelDerivProperty()
return type('PropModel', (PropModel, ), attrs)
return type(name.replace('PropMap', 'PropModel'), (PropModel, ), attrs)
class PropMap(object):
+6 -6
View File
@@ -10,7 +10,7 @@ class RegularizationMesh(object):
are not necessarily true differential operators, but are constructed from
a SimPEG Mesh.
:param BaseMesh mesh: problem mesh
:param Mesh mesh: problem mesh
:param numpy.array indActive: bool array, size nC, that is True where we have active cells. Used to reduce the operators so we regularize only on active cells
"""
@@ -383,8 +383,8 @@ class BaseRegularization(object):
:param numpy.array m: geophysical model
:param numpy.array v: vector to multiply
:rtype: scipy.sparse.csr_matrix
:return: WtW, or if v is supplied WtW*v (numpy.ndarray)
:rtype: scipy.sparse.csr_matrix or numpy.ndarray
:return: WtW or WtW*v
The regularization is:
@@ -650,8 +650,8 @@ class Tikhonov(Simple):
Note if the key word argument `mrefInSmooth` is False, then mref is not
included in the smoothness contribution.
:param BaseMesh mesh: SimPEG mesh
:param IdentityMap mapping: regularization mapping, takes the model from model space to the thing you want to regularize
:param Mesh mesh: SimPEG mesh
:param Maps mapping: regularization mapping, takes the model from model space to the thing you want to regularize
:param numpy.ndarray indActive: active cell indices for reducing the size of differential operators in the definition of a regularization mesh
:param bool mrefInSmooth: (default = False) put mref in the smoothness component?
:param float alpha_s: (default 1e-6) smallness weight
@@ -671,7 +671,7 @@ class Tikhonov(Simple):
alpha_yy = Utils.dependentProperty('_alpha_yy', 0.0, ['_W', '_Wyy'], "Weight for the second derivative in the y direction")
alpha_zz = Utils.dependentProperty('_alpha_zz', 0.0, ['_W', '_Wzz'], "Weight for the second derivative in the z direction")
def __init__(self, mesh, mapping=None, indActive=None, **kwargs):
def __init__(self, mesh, mapping=None, indActive = None, **kwargs):
BaseRegularization.__init__(self, mesh, mapping=mapping, indActive=indActive, **kwargs)
@property
+4 -2
View File
@@ -1,4 +1,5 @@
import Utils, numpy as np, scipy.sparse as sp, uuid
import gc
class BaseRx(object):
"""SimPEG Receiver Object"""
@@ -311,6 +312,7 @@ class BaseSurvey(object):
if f is None: f = self.prob.fields(m)
return Utils.mkvc(self.eval(f))
@Utils.count
def eval(self, f):
"""eval(f)
@@ -321,7 +323,7 @@ class BaseSurvey(object):
d_\\text{pred} = \mathbf{P} f(m)
"""
raise NotImplementedError('eval is not yet implemented.')
raise NotImplemented('eval is not yet implemented.')
@Utils.count
def evalDeriv(self, f):
@@ -333,7 +335,7 @@ class BaseSurvey(object):
\\frac{\partial d_\\text{pred}}{\partial u} = \mathbf{P}
"""
raise NotImplementedError('eval is not yet implemented.')
raise NotImplemented('eval is not yet implemented.')
@Utils.count
def residual(self, m, f=None):
+1 -1
View File
@@ -237,7 +237,7 @@ def checkDerivative(fctn, x0, num=7, plotIt=True, dx=None, expectedOrder=2, tole
Compares error decay of 0th and 1st order Taylor approximation at point
x0 for a randomized search direction.
:param callable fctn: function handle
:param lambda fctn: function handle
:param numpy.array x0: point at which to check derivative
:param int num: number of times to reduce step length, h
:param bool plotIt: if you would like to plot
+13 -13
View File
@@ -7,11 +7,11 @@ def addBlock(gridCC, modelCC, p0, p1, blockProp):
"""
Add a block to an exsisting cell centered model, modelCC
:param numpy.array gridCC: mesh.gridCC is the cell centered grid
:param numpy.array modelCC: cell centered model
:param numpy.array p0: bottom, southwest corner of block
:param numpy.array p1: top, northeast corner of block
:blockProp float blockProp: property to assign to the model
:param numpy.array, gridCC: mesh.gridCC is the cell centered grid
:param numpy.array, modelCC: cell centered model
:param numpy.array, p0: bottom, southwest corner of block
:param numpy.array, p1: top, northeast corner of block
:blockProp float, blockProp: property to assign to the model
:return numpy.array, modelBlock: model with block
"""
@@ -147,7 +147,7 @@ def getIndicesSphere(center,radius,ccMesh):
if dimMesh == 1:
# Define the reference points
ind = np.abs(center[0] - ccMesh[:,0]) < radius
elif dimMesh == 2:
@@ -222,14 +222,14 @@ def layeredModel(ccMesh, layerTops, layerValues):
:param numpy.array ccMesh: cell-centered mesh
:param numpy.array layerTops: z-locations of the tops of each layer
:param numpy.array layerValue: values of the property to assign for each layer (starting at the top)
:param numpy.array layerValue: values of the property to assign for each layer (starting at the top)
:rtype: numpy.array
:return: M, layered model on the mesh
:return: M, layered model on the mesh
"""
descending = np.linalg.norm(sorted(layerTops, reverse=True) - layerTops) < 1e-20
# TODO: put an error check to make sure that there is an ordering... needs to work with inf elts
# TODO: put an error check to make sure that there is an ordering... needs to work with inf elts
# assert ascending or descending, "Layers must be listed in either ascending or descending order"
# start from bottom up
@@ -253,10 +253,10 @@ def layeredModel(ccMesh, layerTops, layerValues):
model = np.zeros(ccMesh.shape[0])
for i, top in enumerate(layerTops):
zind = z <= top
zind = z <= top
model[zind] = layerValues[i]
return model
return model
@@ -265,9 +265,9 @@ def randomModel(shape, seed=None, anisotropy=None, its=100, bounds=None):
Create a random model by convolving a kernel with a
uniformly distributed model.
:param tuple shape: shape of the model.
:param int,tuple shape: shape of the model.
:param int seed: pick which model to produce, prints the seed if you don't choose.
:param numpy.ndarray anisotropy: this is the (3 x n) blurring kernel that is used.
:param numpy.ndarray,list anisotropy: this is the (3 x n) blurring kernel that is used.
:param int its: number of smoothing iterations
:param list bounds: bounds on the model, len(list) == 2
:rtype: numpy.ndarray
+7 -7
View File
@@ -13,7 +13,7 @@ def _checkAccuracy(A, b, X, accuracyTol):
warnings.warn(msg, RuntimeWarning)
def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6, name=None):
def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6):
"""
Wraps a direct Solver.
@@ -72,11 +72,11 @@ def SolverWrapD(fun, factorize=True, checkAccuracy=True, accuracyTol=1e-6, name=
if factorize and hasattr(self.solver, 'clean'):
return self.solver.clean()
return type(name if name is not None else fun.__name__, (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
return type(fun.__name__+'_Wrapped', (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5, name=None):
def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5):
"""
Wraps an iterative Solver.
@@ -128,13 +128,13 @@ def SolverWrapI(fun, checkAccuracy=True, accuracyTol=1e-5, name=None):
def clean(self):
pass
return type(name if name is not None else fun.__name__, (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
return type(fun.__name__+'_Wrapped', (object,), {"__init__": __init__, "clean": clean, "__mul__": __mul__})
from scipy.sparse import linalg
Solver = SolverWrapD(linalg.spsolve, factorize=False, name="Solver")
SolverLU = SolverWrapD(linalg.splu, factorize=True, name="SolverLU")
SolverCG = SolverWrapI(linalg.cg, name="SolverCG")
Solver = SolverWrapD(linalg.spsolve, factorize=False)
SolverLU = SolverWrapD(linalg.splu, factorize=True)
SolverCG = SolverWrapI(linalg.cg)
class SolverDiag(object):
+1 -1
View File
@@ -25,7 +25,7 @@ def interpmat(locs, x, y=None, z=None):
:param numpy.ndarray x: Tensor vector of 1st dimension of grid.
:param numpy.ndarray y: Tensor vector of 2nd dimension of grid. None by default.
:param numpy.ndarray z: Tensor vector of 3rd dimension of grid. None by default.
:rtype: scipy.sparse.csr_matrix
:rtype: scipy.sparse.csr.csr_matrix
:return: Interpolation matrix
.. plot::
+6 -6
View File
@@ -27,7 +27,7 @@ def mkvc(x, numDims=1):
if isinstance(x, Zero):
return x
assert isinstance(x, np.ndarray), "Vector must be a numpy array"
if numDims == 1:
@@ -355,9 +355,9 @@ def diagEst(matFun, n, k=None, approach='Probing'):
2. Ones : random +/- 1 entries
3. Random : random vectors
:param callable matFun: takes a (numpy.array) and multiplies it by a matrix to estimate the diagonal
:param int n: size of the vector that should be used to compute matFun(v)
:param int k: number of vectors to be used to estimate the diagonal
:param lambda (numpy.array) matFun: matrix to estimate the diagonal of
:param int64 n: size of the vector that should be used to compute matFun(v)
:param int64 k: number of vectors to be used to estimate the diagonal
:param str approach: approach to be used for getting vectors
:rtype: numpy.array
:return: est_diag(A)
@@ -422,9 +422,9 @@ class Zero(object):
def __ge__(self, v):return 0 >= v
def __gt__(self, v):return 0 > v
@property
@property
def transpose(self): return Zero()
@property
def T(self): return Zero()
+14 -18
View File
@@ -83,7 +83,7 @@ def closestPoints(mesh, pts, gridLoc='CC'):
"""
Move a list of points to the closest points on a grid.
:param BaseMesh mesh: The mesh
:param simpeg.Mesh.BaseMesh mesh: The mesh
:param numpy.ndarray pts: Points to move
:param string gridLoc: ['CC', 'N', 'Fx', 'Fy', 'Fz', 'Ex', 'Ex', 'Ey', 'Ez']
:rtype: numpy.ndarray
@@ -104,20 +104,16 @@ def closestPoints(mesh, pts, gridLoc='CC'):
def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
"""
Extracts Core Mesh from Global mesh
:param numpy.ndarray xyzlim: 2D array [ndim x 2]
:param BaseMesh mesh: The mesh
This function ouputs::
- actind: corresponding boolean index from global to core
- meshcore: core SimPEG mesh
Warning: 1D and 2D has not been tested
Extracts Core Mesh from Global mesh
xyzlim: 2D array [ndim x 2]
mesh: SimPEG mesh
This function ouputs:
- actind: corresponding boolean index from global to core
- meshcore: core SimPEG mesh
Warning: 1D and 2D has not been tested
"""
from SimPEG import Mesh
if mesh.dim == 1:
if mesh.dim ==1:
xyzlim = xyzlim.flatten()
xmin, xmax = xyzlim[0], xyzlim[1]
@@ -129,11 +125,11 @@ def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5]
meshCore = Mesh.TensorMesh([hx, hy], x0=x0)
meshCore = Mesh.TensorMesh([hx, hy] ,x0=x0)
actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax)
elif mesh.dim == 2:
elif mesh.dim ==2:
xmin, xmax = xyzlim[0,0], xyzlim[0,1]
ymin, ymax = xyzlim[1,0], xyzlim[1,1]
@@ -148,12 +144,12 @@ def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5]
meshCore = Mesh.TensorMesh([hx, hy], x0=x0)
meshCore = Mesh.TensorMesh([hx, hy] ,x0=x0)
actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax) \
& (mesh.gridCC[:,1]>ymin) & (mesh.gridCC[:,1]<ymax) \
elif mesh.dim == 3:
elif mesh.dim==3:
xmin, xmax = xyzlim[0,0], xyzlim[0,1]
ymin, ymax = xyzlim[1,0], xyzlim[1,1]
zmin, zmax = xyzlim[2,0], xyzlim[2,1]
@@ -172,7 +168,7 @@ def ExtractCoreMesh(xyzlim, mesh, meshType='tensor'):
x0 = [xc[0]-hx[0]*0.5, yc[0]-hy[0]*0.5, zc[0]-hz[0]*0.5]
meshCore = Mesh.TensorMesh([hx, hy, hz], x0=x0)
meshCore = Mesh.TensorMesh([hx, hy, hz] ,x0=x0)
actind = (mesh.gridCC[:,0]>xmin) & (mesh.gridCC[:,0]<xmax) \
& (mesh.gridCC[:,1]>ymin) & (mesh.gridCC[:,1]<ymax) \
+1 -1
View File
@@ -15,7 +15,7 @@ import Directives
import Inversion
import Tests
__version__ = '0.1.12'
__version__ = '0.1.10'
__author__ = 'Rowan Cockett'
__license__ = 'MIT'
__copyright__ = 'Copyright 2014 Rowan Cockett'

Before

Width:  |  Height:  |  Size: 49 KiB

After

Width:  |  Height:  |  Size: 49 KiB

Before

Width:  |  Height:  |  Size: 58 KiB

After

Width:  |  Height:  |  Size: 58 KiB

+1 -1
View File
@@ -2,7 +2,7 @@
#
# You can set these variables from the command line.
SPHINXOPTS = -n -w warnings.txt
SPHINXOPTS =
SPHINXBUILD = sphinx-build
PAPER =
BUILDDIR = _build

Before

Width:  |  Height:  |  Size: 30 KiB

After

Width:  |  Height:  |  Size: 30 KiB

-22
View File
@@ -1,22 +0,0 @@
{# Import the theme's layout. #}
{% extends "!layout.html" %}
{% block extrahead %}
{{ super() }}
<meta name="description" content="Simulation and Parameter Estimation in Geophysics">
<meta name="author" content="SimPEG Developers">
<meta name="keywords" content="python, geophysics, inversion, electromagnetics, magnetotellurics, magnetics, gravity, DC, flow inverse problems, open source, finite volume">
<script>
(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){
(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),
m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)
})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');
ga('create', 'UA-45185336-1', 'auto');
ga('send', 'pageview');
</script>
{% endblock %}
+9 -16
View File
@@ -1,3 +1,5 @@
.. _api_DC:
.. math::
\renewcommand{\div}{\nabla\cdot\,}
@@ -36,16 +38,8 @@
\renewcommand {\u} { {\vec u} }
\newcommand{\I}{\vec{I}}
Direct Current Resistivity
**************************
`SimPEG.DCIP` uses SimPEG as the framework for the forward and inverse
direct current (DC) resistivity and induced polarization (IP) geophysical problems.
DC resistivity survey
=====================
*********************
Electrical resistivity of subsurface materials is measured by causing an electrical current to flow in the earth between one pair of electrodes while the voltage across a second pair of electrodes is measured. The result is an "apparent" resistivity which is a value representing the weighted average resistivity over a volume of the earth. Variations in this measurement are caused by variations in the soil, rock, and pore fluid electrical resistivity. Surveys require contact with the ground, so they can be labour intensive. Results are sometimes interpreted directly, but more commonly, 1D, 2D or 3D models are estimated using inversion procedures (`GPG <http://www.eos.ubc.ca/courses/eosc350/content/>`_).
@@ -61,7 +55,7 @@ As direct current (DC) implies, in DC resistivity survey, we assume steady-state
\curl \e = 0
Then by taking \\(\\div\\) of the first equation, we have
Then by taking \\(\\curl\\) for the first equation, we have
.. math::
@@ -143,14 +137,13 @@ Comparing to the analytic function:
.. plot::
from SimPEG import Examples
Examples.DC_Analytic_Dipole.run(plotIt=True)
import simpegDC as DC
DC.Examples.Verification.run(plotIt=True)
API
===
API for DC codes
================
.. automodule:: SimPEG.DCIP.BaseDC
.. automodule:: simpegDC.BaseDC
:show-inheritance:
:members:
:undoc-members:
@@ -7,7 +7,7 @@ Examples
:maxdepth: 1
:glob:
../examples/*
examples/*
External Notebooks
+19
View File
@@ -0,0 +1,19 @@
.. _api_FiniteVolume:
Finite Volume
*************
Any numerical implementation requires the discretization of continuous functions into discrete approximations. These approximations are typically organized in a mesh, which defines boundaries, locations, and connectivity. Of specific interest to geophysical simulations, we require that averaging, interpolation and differential operators be defined for any mesh. In SimPEG, we have implemented a staggered mimetic finite volume approach (`Hyman and Shashkov, 1999 <http://math.lanl.gov/~mac/papers/numerics/HS99B.pdf>`_). This approach requires the definitions of variables at either cell-centers, nodes, faces, or edges as seen in the figure below.
.. image:: images/finitevolrealestate.png
:width: 400 px
:alt: FiniteVolume
:align: center
.. toctree::
:maxdepth: 2
api_Mesh
api_DiffOps
api_InnerProducts
@@ -52,15 +52,13 @@ We can take the derivative of the PDE:
\nabla_m c(m, u) \partial m + \nabla_u c(m, u) \partial u = 0
If the forward problem is invertible, then we can rearrange for
\\(\\frac{\\partial u}{\\partial m}\\):
If the forward problem is invertible, then we can rearrange for \\(\\frac{\\partial u}{\\partial m}\\):
.. math::
J = - P \left( \nabla_u c(m, u) \right)^{-1} \nabla_m c(m, u)
This can often be computed given a vector (i.e. \\(J(v)\\)) rather than
stored, as \\(J\\) is a large dense matrix.
This can often be computed given a vector (i.e. \\(J(v)\\)) rather than stored, as \\(J\\) is a large dense matrix.
@@ -69,45 +67,13 @@ The API
Problem
-------
.. autoclass:: SimPEG.Problem.BaseProblem
:members:
:undoc-members:
.. autoclass:: SimPEG.Problem.BaseTimeProblem
:members:
:undoc-members:
Fields
------
.. autoclass:: SimPEG.Fields.Fields
:members:
:undoc-members:
.. autoclass:: SimPEG.Fields.TimeFields
.. automodule:: SimPEG.Problem
:members:
:undoc-members:
Survey
------
.. autoclass:: SimPEG.Survey.BaseSurvey
.. automodule:: SimPEG.Survey
:members:
:undoc-members:
.. autoclass:: SimPEG.Survey.BaseSrc
:members:
:undoc-members:
.. autoclass:: SimPEG.Survey.BaseRx
:members:
:undoc-members:
.. autoclass:: SimPEG.Survey.BaseTimeRx
:members:
:undoc-members:
.. autoclass:: SimPEG.Survey.Data
:members:
:undoc-members:
@@ -4,10 +4,7 @@
Inner Products
**************
By using the weak formulation of many of the PDEs in geophysical applications,
we can rapidly develop discretizations. Much of this work, however, needs a
good understanding of how to approximate inner products on our discretized
meshes. We will define the inner product as:
By using the weak formulation of many of the PDEs in geophysical applications, we can rapidly develop discretizations. Much of this work, however, needs a good understanding of how to approximate inner products on our discretized meshes. We will define the inner product as:
.. math::
@@ -17,15 +14,12 @@ where a and b are either scalars or vectors.
.. note::
The InnerProducts class is a base class providing inner product matrices
for meshes and cannot run on its own.
The InnerProducts class is a base class providing inner product matrices for meshes and cannot run on its own.
Example problem for DC resistivity
----------------------------------
We will start with the formulation of the Direct Current (DC) resistivity
problem in geophysics.
We will start with the formulation of the Direct Current (DC) resistivity problem in geophysics.
.. math::
@@ -34,13 +28,12 @@ problem in geophysics.
\nabla\cdot \vec{j} = q
In the following discretization, :math:`\sigma` and :math:`\phi`
will be discretized on the cell-centers and the flux, :math:`\vec{j}`,
In the following discretization, \\\( \\sigma \\\) and \\\( \\phi \\\)
will be discretized on the cell-centers and the flux, \\\(\\vec{j}\\\),
will be on the faces. We will use the weak formulation to discretize
the DC resistivity equation.
We can define in weak form by integrating with a general face function
:math:`\vec{f}`:
We can define in weak form by integrating with a general face function \\\(\\vec{f}\\\):
.. math::
@@ -68,16 +61,9 @@ We can then discretize for every cell:
.. note::
We have discretized the dot product above, but remember that we do not
really have a single vector :math:`\mathbf{J}`, but approximations of
:math:`\vec{j}` on each face of our cell. In 2D that means 2
approximations of :math:`\mathbf{J}_x` and 2 approximations of
:math:`\mathbf{J}_y`. In 3D we also have 2 approximations of
:math:`\mathbf{J}_z`.
We have discretized the dot product above, but remember that we do not really have a single vector \\\(\\mathbf{J}\\\), but approximations of \\\(\\vec{j}\\\) on each face of our cell. In 2D that means 2 approximations of \\\(\\mathbf{J}_x\\\) and 2 approximations of \\\(\\mathbf{J}_y\\\). In 3D we also have 2 approximations of \\\(\\mathbf{J}_z\\\).
Regardless of how we choose to approximate this dot product, we can represent
this in vector form (again this is for every cell), and will generalize for
the case of anisotropic (tensor) sigma.
Regardless of how we choose to approximate this dot product, we can represent this in vector form (again this is for every cell), and will generalize for the case of anisotropic (tensor) sigma.
.. math::
@@ -85,17 +71,14 @@ the case of anisotropic (tensor) sigma.
-\phi^{\top} v_{\text{cell}} \mathbf{D}_{\text{cell}} \mathbf{F})
+ \text{BC}
We multiply by square-root of volume on each side of the tensor conductivity
to keep symmetry in the system. Here :math:`\mathbf{J}_c` is the Cartesian
:math:`\mathbf{J}` (on the faces that we choose to use in our approximation)
and must be calculated differently depending on the mesh:
We multiply by square-root of volume on each side of the tensor conductivity to keep symmetry in the system. Here \\\(\\mathbf{J}_c\\\) is the Cartesian \\\(\\mathbf{J}\\\) (on the faces that we choose to use in our approximation) and must be calculated differently depending on the mesh:
.. math::
\mathbf{J}_c = \mathbf{Q}_{(i)}\mathbf{J}_\text{TENSOR} \\
\mathbf{J}_c = \mathbf{N}_{(i)}^{-1}\mathbf{Q}_{(i)}\mathbf{J}_\text{Curv}
Here the :math:`i` index refers to where we choose to approximate this integral, as discussed in the note above.
We will approximate this integral by taking the fluxes clustered around every node of the cell, there are 8 combinations in 3D, and 4 in 2D. We will use a projection matrix :math:`\mathbf{Q}_{(i)}` to pick the appropriate fluxes. So, now that we have 8 approximations of this integral, we will just take the average. For the TensorMesh, this looks like:
Here the \\\(i\\\) index refers to where we choose to approximate this integral, as discussed in the note above.
We will approximate this integral by taking the fluxes clustered around every node of the cell, there are 8 combinations in 3D, and 4 in 2D. We will use a projection matrix \\\( \\mathbf{Q}_{(i)} \\\) to pick the appropriate fluxes. So, now that we have 8 approximations of this integral, we will just take the average. For the TensorMesh, this looks like:
.. math::
@@ -124,12 +107,10 @@ By defining the faceInnerProduct (8 combinations of fluxes in 3D, 4 in 2D, 2 in
\sum_{i=1}^{2^d}
\mathbf{P}_{(i)}^{\top} \Sigma^{-1} \mathbf{P}_{(i)}
Where :math:`d` is the dimension of the mesh.
The :math:`\mathbf{M}^f` is returned when given the input of :math:`\Sigma^{-1}`.
Where \\\(d\\\) is the dimension of the mesh.
The \\\( \\mathbf{M}^f \\\) is returned when given the input of \\\( \\Sigma^{-1} \\\).
Here each :math:`\mathbf{P} ~ \in ~ \mathbb{R}^{(d*nC, nF)}` is a combination
of the projection, volume, and any normalization to Cartesian coordinates
(where the dot product is well defined):
Here each \\( \\mathbf{P} \\in \\mathbb{R}^{(d*nC, nF)} \\\) is a combination of the projection, volume, and any normalization to Cartesian coordinates (where the dot product is well defined):
.. math::
@@ -148,10 +129,7 @@ If ``returnP=True`` is requested in any of these methods the projection matrices
# In 1D
P = [P0, P1]
The derivation for ``edgeInnerProducts`` is exactly the same, however, when we
approximate the integral using the fields around each node, the projection
matrices look a bit different because we have 12 edges in 3D instead of just 6
faces. The interface to the code is exactly the same.
The derivation for ``edgeInnerProducts`` is exactly the same, however, when we approximate the integral using the fields around each node, the projection matrices look a bit different because we have 12 edges in 3D instead of just 6 faces. The interface to the code is exactly the same.
Defining Tensor Properties
@@ -159,8 +137,7 @@ Defining Tensor Properties
**For 3D:**
Depending on the number of columns (either 1, 3, or 6) of mu, the material
property is interpreted as follows:
Depending on the number of columns (either 1, 3, or 6) of mu, the material property is interpreted as follows:
.. math::
@@ -211,16 +188,13 @@ Which is nice and easy to invert if necessary, however, in the fully anisotropic
Taking Derivatives
------------------
We will take the derivative of the fully anisotropic tensor for a 3D mesh, the
other cases are easier and will not be discussed here. Let us start with one
part of the sum which makes up :math:`\mathbf{M}^f_\Sigma` and take the
derivative when this is multiplied by some vector :math:`\mathbf{v}`:
We will take the derivative of the fully anisotropic tensor for a 3D mesh, the other cases are easier and will not be discussed here. Let us start with one part of the sum which makes up \\\(\\mathbf{M}^f_\\Sigma\\\) and take the derivative when this is multiplied by some vector \\\(\\mathbf{v}\\\):
.. math::
\mathbf{P}^\top \boldsymbol{\Sigma} \mathbf{Pv}
Here we will let :math:`\mathbf{Pv} = \mathbf{y}` and :math:`\mathbf{y}` will have the form:
Here we will let \\\( \\mathbf{Pv} = \\mathbf{y} \\\) and \\\(\\mathbf{y}\\\) will have the form:
.. math::
@@ -259,9 +233,7 @@ Here we will let :math:`\mathbf{Pv} = \mathbf{y}` and :math:`\mathbf{y}` will ha
\end{matrix}
\right]
Now it is easy to take the derivative with respect to any one of the
parameters, for example,
:math:`\frac{\partial}{\partial\boldsymbol{\sigma}_1}`
Now it is easy to take the derivative with respect to any one of the parameters, for example, \\\(\\frac{\\partial}{\\partial\\boldsymbol{\\sigma}_1}\\\)
.. math::
\frac{\partial}{\partial \boldsymbol{\sigma}_1}\left(\mathbf{P}^\top\Sigma\mathbf{y}\right)
@@ -275,8 +247,7 @@ parameters, for example,
\end{matrix}
\right]
Whereas :math:`\frac{\partial}{\partial\boldsymbol{\sigma}_4}`, for
example, is:
Whereas \\\(\\frac{\\partial}{\\partial\\boldsymbol{\\sigma}_4}\\\), for example, is:
.. math::
\frac{\partial}{\partial \boldsymbol{\sigma}_4}\left(\mathbf{P}^\top\Sigma\mathbf{y}\right)
@@ -290,12 +261,11 @@ example, is:
\end{matrix}
\right]
These are computed for each of the 8 projections, horizontally concatenated,
and returned.
These are computed for each of the 8 projections, horizontally concatenated, and returned.
The API
-------
.. autoclass:: SimPEG.Mesh.InnerProducts.InnerProducts
.. automodule:: SimPEG.Mesh.InnerProducts
:members:
:undoc-members:
@@ -3,7 +3,7 @@
InvProblem
**********
.. autoclass:: SimPEG.InvProblem.BaseInvProblem
.. automodule:: SimPEG.InvProblem
:show-inheritance:
:members:
:undoc-members:
@@ -12,7 +12,7 @@ InvProblem
Inversion
*********
.. autoclass:: SimPEG.Inversion.BaseInversion
.. automodule:: SimPEG.Inversion
:show-inheritance:
:members:
:undoc-members:
@@ -27,8 +27,7 @@ back to conductivity. This is a relatively trivial example (we are just taking
the exponential!) but by defining maps we can start to combine and manipulate
exactly what we think about as our model, \\\(m\\\). In code, this looks like
.. code-block:: python
:linenos:
::
M = Mesh.TensorMesh([100]) # Create a mesh
expMap = Maps.ExpMap(M) # Create a mapping
@@ -47,15 +46,14 @@ We will use an example where we want a 1D layered earth as
our model, but we want to map this to a 2D discretization to do our forward
modeling. We will also assume that we are working in log conductivity still,
so after the transformation we want to map to conductivity space.
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.Vertical1DMap`),
which does the first part of what we just described. The second part will be
done by the :class:`SimPEG.Maps.ExpMap` described above.
.. code-block:: python
:linenos:
::
M = Mesh.TensorMesh([7,5])
v1dMap = Maps.SurjectVertical1D(M)
v1dMap = Maps.Vertical1DMap(M)
expMap = Maps.ExpMap(M)
myMap = expMap * v1dMap
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
@@ -63,8 +61,26 @@ done by the :class:`SimPEG.Maps.ExpMap` described above.
.. plot::
from SimPEG import Examples
Examples.Maps_ComboMaps.run()
from SimPEG import *
import matplotlib.pyplot as plt
M = Mesh.TensorMesh([7,5])
v1dMap = Maps.Vertical1DMap(M)
expMap = Maps.ExpMap(M)
myMap = expMap * v1dMap
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
sig = myMap * m
figs, axs = plt.subplots(1,2)
axs[0].plot(m, M.vectorCCy, 'b-o')
axs[0].set_title('Model')
axs[0].set_ylabel('Depth, y')
axs[0].set_xlabel('Value, $m_i$')
axs[0].set_xlim(0,3)
axs[0].set_ylim(0,1)
clbar = plt.colorbar(M.plotImage(sig,ax=axs[1],grid=True,gridOpts=dict(color='grey'))[0])
axs[1].set_title('Physical Property')
axs[1].set_ylabel('Depth, y')
clbar.set_label('$\sigma = \exp(\mathbf{P}m)$')
plt.tight_layout()
If you noticed, it was pretty easy to combine maps. What is even cooler is
that the derivatives also are made for you (if everything goes right).
@@ -106,8 +122,6 @@ When these are used in the inverse problem, this is extremely important!!
The API
=======
The :code:`IdentityMap` is the base class for all mappings, and it does absolutely nothing.
.. autoclass:: SimPEG.Maps.IdentityMap
:members:
:undoc-members:
@@ -116,6 +130,7 @@ The :code:`IdentityMap` is the base class for all mappings, and it does absolute
Common Maps
===========
Exponential Map
---------------
@@ -133,7 +148,7 @@ lives (i.e. it varies logarithmically).
Vertical 1D Map
---------------
.. autoclass:: SimPEG.Maps.SurjectVertical1D
.. autoclass:: SimPEG.Maps.Vertical1DMap
:members:
:undoc-members:
@@ -149,10 +164,31 @@ Map 2D Cross-Section to 3D Model
Mesh to Mesh Map
----------------
.. plot::
from SimPEG import Examples
Examples.Maps_Mesh2Mesh.run()
from SimPEG import *
import matplotlib.pyplot as plt
M = Mesh.TensorMesh([100,100])
h1 = Utils.meshTensor([(6,7,-1.5),(6,10),(6,7,1.5)])
h1 = h1/h1.sum()
M2 = Mesh.TensorMesh([h1,h1])
V = Utils.ModelBuilder.randomModel(M.vnC, seed=79, its=50)
v = Utils.mkvc(V)
modh = Maps.Mesh2Mesh([M,M2])
modH = Maps.Mesh2Mesh([M2,M])
H = modH * v
h = modh * H
ax = plt.subplot(131)
M.plotImage(v, ax=ax)
ax.set_title('Fine Mesh (Original)')
ax = plt.subplot(132)
M2.plotImage(H,clim=[0,1],ax=ax)
ax.set_title('Course Mesh')
ax = plt.subplot(133)
M.plotImage(h,clim=[0,1],ax=ax)
ax.set_title('Fine Mesh (Interpolated)')
plt.show()
.. autoclass:: SimPEG.Maps.Mesh2Mesh
@@ -160,8 +196,8 @@ Mesh to Mesh Map
:undoc-members:
Under the Hood
==============
Some Extras
===========
Combo Map
---------
@@ -188,6 +188,6 @@ other types of meshes in this SimPEG framework.
The API
=======
.. autoclass:: SimPEG.Mesh.BaseMesh.BaseMesh
.. automodule:: SimPEG.Mesh.BaseMesh
:members:
:undoc-members:
+36
View File
@@ -0,0 +1,36 @@
.. _api_MeshCode:
Tensor Mesh
===========
.. automodule:: SimPEG.Mesh.TensorMesh
:show-inheritance:
:members:
:undoc-members:
Cylindrical Mesh
================
.. automodule:: SimPEG.Mesh.CylMesh
:show-inheritance:
:members:
:undoc-members:
Tree Mesh
=========
.. autoclass:: SimPEG.Mesh.TreeMesh.TreeMesh
:show-inheritance:
:members:
:undoc-members:
Curvilinear Mesh
================
.. automodule:: SimPEG.Mesh.CurvilinearMesh
:show-inheritance:
:members:
:undoc-members:
@@ -91,21 +91,10 @@ The API
:members:
:undoc-members:
.. autoclass:: SimPEG.Regularization.Simple
:show-inheritance:
:members:
.. autoclass:: SimPEG.Regularization.Tikhonov
:show-inheritance:
:members:
.. autoclass:: SimPEG.Regularization.Sparse
:show-inheritance:
:members:
.. autoclass:: SimPEG.Regularization.RegularizationMesh
:show-inheritance:
:members:
@@ -46,8 +46,6 @@ The API
=======
.. autofunction:: SimPEG.Utils.SolverUtils.SolverWrapD
:noindex:
.. autofunction:: SimPEG.Utils.SolverUtils.SolverWrapI
:noindex:
@@ -6,6 +6,5 @@ Utilities
api_Solver
api_Maps
api_PropMaps
api_Utils
api_Tests
@@ -21,7 +21,7 @@ Solver Utilities
:undoc-members:
Curv Utilities
==============
=============
.. automodule:: SimPEG.Utils.curvutils
:members:
@@ -51,9 +51,7 @@ Interpolation Utilities
Counter Utilities
=================
.. code-block:: python
:linenos:
::
class MyClass(object):
def __init__(self, url):
self.counter = Counter()
@@ -71,9 +69,7 @@ Counter Utilities
for i in range(300): c.MySecondMethod()
c.counter.summary()
.. code-block:: text
:linenos:
::
Counters:
MyClass.MyMethod : 100
@@ -81,8 +77,6 @@ Counter Utilities
Times: mean sum
MyClass.MySecondMethod : 1.70e-06, 5.10e-04, 300x
The API
-------
@@ -35,7 +35,7 @@ The Big Picture
Defining a well-posed inverse problem and solving it is a complex task that requires many components that must interact. It is helpful
to view this task as a workflow in which various elements are explicitly identified and integrated. The figure below outlines the inversion components that consists of inputs, implementation, and evaluation. The inputs are composed of the geophysical data, the equations which are a mathematical description of the governing physics, and prior knowledge or assumptions about the setting. The implementation consists of two broad categories: the forward simulation and the inversion. The **forward simulation** is the means by which we solve the governing equations given a model and the **inversion components** evaluate and update this model. We are considering a gradient based approach, which updates the model through an optimization routine. The output of this implementation is a model, which, prior to interpretation, must be evaluated. This requires considering, and often re-assessing, the choices and assumptions made in both the input and implementation stages.
.. image:: ../../images/InversionWorkflow-PreSimPEG.png
.. image:: InversionWorkflow-PreSimPEG.png
:width: 400 px
:alt: Components
:align: center
@@ -46,24 +46,24 @@ A Comprehensive Framework
There are an overwhelming amount of choices to be made as one works through the forward modeling and inversion process (see figure above). As a result, software implementations of this workflow often become complex and highly interdependent, making it difficult to interact with and to ask other scientists to pick up and change. Our approach to handling this complexity is to propose a framework, (see below), that compartmentalizes the implementation of inversions into various units. We present it in this specific modular style, as each unit contains a targeted subset of choices crucial to the inversion process.
.. image:: ../../images/InversionWorkflow.png
.. image:: InversionWorkflow.png
:width: 400 px
:alt: Framework
:align: center
The process of obtaining an acceptable model from an inversion generally requires the geophysicist to perform several iterations of the inversion workflow, rethinking and redesigning each piece of the framework to ensure it is appropriate in the current context. Inversions are experimental and empirical by nature and our software package is designed to facilitate this iterative process. To accomplish this, we have divided the inversion methodology into eight major components (See figure above). The :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class handles the discretization of the earth and also provides numerical operators. The forward simulation is split into two classes, the :class:`SimPEG.Survey.BaseSurvey` and the :class:`SimPEG.Problem.BaseProblem`. The :class:`SimPEG.Survey.BaseSurvey` class handles the geometry of a geophysical problem as well as sources. The :class:`SimPEG.Problem.BaseProblem` class handles the simulation of the physics for the geophysical problem of interest. Although created independently, these two classes must be paired to form all of the components necessary for a geophysical forward simulation and calculation of the sensitivity. The :class:`SimPEG.Problem.BaseProblem` creates geophysical fields given a source from the :class:`SimPEG.Survey.BaseSurvey`. The :class:`SimPEG.Survey.BaseSurvey` interpolates these fields to the receiver locations and converts them to the appropriate data type, for example, by selecting only the measured components of the field. Each of these operations may have associated derivatives with respect to the model and the computed field; these are included in the calculation of the sensitivity. For the inversion, a :class:`SimPEG.DataMisfit.BaseDataMisfit` is chosen to capture the goodness of fit of the predicted data and a :class:`SimPEG.Regularization.BaseRegularization` is chosen to handle the non-uniqueness. These inversion elements and an Optimization routine are combined into an inverse problem class :class:`SimPEG.InvProblem.BaseInvProblem`. :class:`SimPEG.InvProblem.BaseInvProblem` is the mathematical statement that will be numerically solved by running an Inversion. The :class:`SimPEG.Inversion.BaseInversion` class handles organization and dispatch of directives between all of the various pieces of the framework.
The process of obtaining an acceptable model from an inversion generally requires the geophysicist to perform several iterations of the inversion workflow, rethinking and redesigning each piece of the framework to ensure it is appropriate in the current context. Inversions are experimental and empirical by nature and our software package is designed to facilitate this iterative process. To accomplish this, we have divided the inversion methodology into eight major components (See figure above). The (:class:`SimPEG.Mesh.BaseMesh`) class handles the discretization of the earth and also provides numerical operators. The forward simulation is split into two classes, the (:class:`SimPEG.Survey.BaseSurvey`) and the (:class:`SimPEG.Problem.BaseProblem`). The (:class:`SimPEG.Survey.BaseSurvey`) class handles the geometry of a geophysical problem as well as sources. The (:class:`SimPEG.Problem.BaseProblem`) class handles the simulation of the physics for the geophysical problem of interest. Although created independently, these two classes must be paired to form all of the components necessary for a geophysical forward simulation and calculation of the sensitivity. The (:class:`SimPEG.Problem.BaseProblem`) creates geophysical fields given a source from the (:class:`SimPEG.Survey.BaseSurvey`). The (:class:`SimPEG.Survey.BaseSurvey`) interpolates these fields to the receiver locations and converts them to the appropriate data type, for example, by selecting only the measured components of the field. Each of these operations may have associated derivatives with respect to the model and the computed field; these are included in the calculation of the sensitivity. For the inversion, a (:class:`SimPEG.DataMisfit.BaseDataMisfit`) is chosen to capture the goodness of fit of the predicted data and a (:class:`SimPEG.Regularization.BaseRegularization`) is chosen to handle the non-uniqueness. These inversion elements and an Optimization routine are combined into an inverse problem class (:class:`SimPEG.InvProblem.BaseInvProblem`). (:class:`SimPEG.InvProblem.BaseInvProblem`) is the mathematical statement that will be numerically solved by running an Inversion. The (:class:`SimPEG.Inversion.BaseInversion`) class handles organization and dispatch of directives between all of the various pieces of the framework.
The arrows in the figure above indicate what each class takes as a primary argument. For example, both the :class:`SimPEG.Problem.BaseProblem` and :class:`SimPEG.Regularization.BaseRegularization` classes take a :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class as an argument. The diagram does not show class inheritance, as each of the base classes outlined have many subtypes that can be interchanged. The :class:`SimPEG.Mesh.BaseMesh.BaseMesh` class, for example, could be a regular Cartesian mesh :class:`SimPEG.Mesh.TensorMesh` or a cylindrical coordinate mesh :class:`SimPEG.Mesh.CylMesh`, which have many properties in common. These common features, such as both meshes being created from tensor products, can be exploited through inheritance of base classes, and differences can be expressed through subtype polymorphism. Please look at the documentation here for more in-depth information.
The arrows in the figure above indicate what each class takes as a primary argument. For example, both the (:class:`SimPEG.Problem.BaseProblem`) and (:class:`SimPEG.Regularization.BaseRegularization`) classes take a (:class:`SimPEG.Mesh.BaseMesh`) class as an argument. The diagram does not show class inheritance, as each of the base classes outlined have many subtypes that can be interchanged. The (:class:`SimPEG.Mesh.BaseMesh`) class, for example, could be a regular Cartesian mesh (:class:`SimPEG.Mesh.TensorMesh`) or a cylindrical coordinate mesh (:class:`SimPEG.Mesh.CylMesh`), which have many properties in common. These common features, such as both meshes being created from tensor products, can be exploited through inheritance of base classes, and differences can be expressed through subtype polymorphism. Please look at the documentation here for more in-depth information.
.. include:: ../../../CITATION.rst
.. include:: ../CITATION.rst
Authors
-------
.. include:: ../../../AUTHORS.rst
.. include:: ../AUTHORS.rst
License
-------
.. include:: ../../../LICENSE
.. include:: ../LICENSE
-95
View File
@@ -1,95 +0,0 @@
# application: simpegdocs
# version: 1
runtime: python27
api_version: 1
threadsafe: yes
handlers:
# favicon
- url: /images/logo-block\.ico
static_files: /images/logo-block.ico
upload: /images/logo-block\.ico
# all css
- url: /(.*\.css)
mime_type: text/css
static_files: _build/html/\1
upload: _build/html/(.*\.css)
# webfonts
- url: /(.*\.(eot|svg|ttf|woff|woff2|otf))
static_files: _build/html/\1
upload: _build/html/(.*\.(eot|svg|ttf|woff|woff2|otf))
# javascript
- url: /(.*\.js)
mime_type: text/javascript
static_files: _build/html/\1
upload: _build/html/(.*\.js)
# plain text source
- url: /(.*\.txt)
mime_type: text/plain
static_files: _build/html/\1
upload: _build/html/(.*\.txt)
# images
- url: /_images/(.*\.(gif|png|jpg|ico))
static_files: _build/html/_images/\1
upload: _build/html/_images/(.*\.(gif|png|jpg|ico))
# redirect en/latest traffic
- url: /en/latest/(.*\.html)
script: simpegdocs.app
# raw html
- url: /(.*\.html)
mime_type: text/html
static_files: _build/html/\1
upload: _build/html/(.*\.html)
# serve index files
- url: /(.+)/
static_files: _build/html/\1/index.html
upload: _build/html/(.+)/index.html
- url: /(.+)
static_files: _build/html/\1/index.html
upload: _build/html/(.+)/index.html
- url: /
static_files: _build/html/index.html
upload: _build/html/index.html
- url: .*
script: simpegdocs.app
# Recommended file skipping declaration from the GAE tutorials
skip_files:
- ^(.*/)?app\.yaml
- ^(.*/)?app\.yml
- ^(.*/)?#.*#
- ^(.*/)?.*~
- ^(.*/)?.*\.py[co]
- ^(.*/)?.*/RCS/.*
- ^(.*/)?\..*
- ^(.*/)?tests$
- ^(.*/)?test$
- ^test/(.*/)?
- ^COPYING.LESSER
- ^README\..*
- \.gitignore
- ^\.git/.*
- \.*\.lint$
- ^(.*/)?.*\.doctree$
libraries:
- name: webapp2
version: "2.5.2"
- name: PIL
version: "1.1.7"
- name: numpy
version: "latest"
- name: jinja2
version: "latest"
+6 -45
View File
@@ -28,7 +28,7 @@ sys.path.append('../')
# Add any Sphinx extension module names here, as strings. They can be extensions
# coming with Sphinx (named 'sphinx.ext.*') or your custom ones.
extensions = ['sphinx.ext.todo', 'sphinx.ext.mathjax', 'sphinx.ext.viewcode', 'sphinx.ext.autodoc', 'sphinx.ext.intersphinx', 'matplotlib.sphinxext.plot_directive']
extensions = ['sphinx.ext.todo', 'sphinx.ext.mathjax', 'sphinx.ext.viewcode', 'sphinx.ext.autodoc', 'matplotlib.sphinxext.plot_directive']
# Add any paths that contain templates here, relative to this directory.
templates_path = ['_templates']
@@ -44,16 +44,16 @@ master_doc = 'index'
# General information about the project.
project = u'SimPEG'
copyright = u'2013 - 2016, SimPEG Developers'
copyright = u'2013, SimPEG Developers'
# The version info for the project you're documenting, acts as replacement for
# |version| and |release|, also used in various other places throughout the
# built documents.
#
# The short X.Y version.
version = '0.1.12'
version = '0.1.10'
# The full version, including alpha/beta/rc tags.
release = '0.1.12'
release = '0.1.10'
# The language for content autogenerated by Sphinx. Refer to documentation
# for a list of supported languages.
@@ -124,12 +124,12 @@ except Exception, e:
# The name of an image file (within the static path) to use as favicon of the
# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
# pixels large.
html_favicon = './images/logo-block.ico'
#html_favicon = None
# Add any paths that contain custom static files (such as style sheets) here,
# relative to this directory. They are copied after the builtin static files,
# so a file named "default.css" will overwrite the builtin "default.css".
html_static_path = []
html_static_path = ['_static']
# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
# using the given strftime format.
@@ -229,12 +229,6 @@ man_pages = [
# If true, show URL addresses after external links.
#man_show_urls = False
# Intersphinx
intersphinx_mapping = {'python': ('http://docs.python.org/2', None),
'numpy': ('http://docs.scipy.org/doc/numpy/', None),
'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None),
'matplotlib': ('http://matplotlib.sourceforge.net/', None)}
# -- Options for Texinfo output ------------------------------------------------
@@ -257,36 +251,3 @@ texinfo_documents = [
#texinfo_show_urls = 'footnote'
autodoc_member_order = 'bysource'
def supress_nonlocal_image_warn():
import sphinx.environment
sphinx.environment.BuildEnvironment.warn_node = _supress_nonlocal_image_warn
def _supress_nonlocal_image_warn(self, msg, node):
from docutils.utils import get_source_line
if not msg.startswith('nonlocal image URI found:'):
self._warnfunc(msg, '%s:%s' % get_source_line(node))
supress_nonlocal_image_warn()
nitpick_ignore = [
('py:class', 'IdentityMap'),
('py:class', 'BaseSurvey'),
('py:class', 'BaseSrc'),
('py:class', 'BaseRx'),
('py:class', 'Survey'),
('py:class', 'FieldsFDEM'),
('py:class', 'Fields3D_e'),
('py:class', 'Fields3D_b'),
('py:class', 'Fields3D_j'),
('py:class', 'Fields3D_h'),
('py:class', 'SurveyTDEM'),
('py:class', 'SrcTDEM'),
('py:class', 'EMPropMap'),
('py:class', 'Data'),
('py:class', 'SurveyDC'),
('py:class', 'BaseMTFields'),
('py:class', 'SolverLU'),
]
@@ -1,27 +0,0 @@
.. _api_FiniteVolume:
Finite Volume
*************
Any numerical implementation requires the discretization of continuous
functions into discrete approximations. These approximations are typically
organized in a mesh, which defines boundaries, locations, and connectivity. Of
specific interest to geophysical simulations, we require that averaging,
interpolation and differential operators be defined for any mesh. In SimPEG,
we have implemented a staggered mimetic finite volume approach (`Hyman and
Shashkov, 1999 <http://math.lanl.gov/~mac/papers/numerics/HS99B.pdf>`_). This
approach requires the definitions of variables at either cell-centers, nodes,
faces, or edges as seen in the figure below.
.. image:: ../../images/finitevolrealestate.png
:width: 400 px
:alt: FiniteVolume
:align: center
.. toctree::
:maxdepth: 2
api_Mesh
api_DiffOps
api_InnerProducts
-68
View File
@@ -1,68 +0,0 @@
.. _api_MeshCode:
Tensor Mesh
===========
.. autoclass:: SimPEG.Mesh.TensorMesh
:members:
:undoc-members:
:show-inheritance:
Cylindrical Mesh
================
.. autoclass:: SimPEG.Mesh.CylMesh
:members:
:undoc-members:
:show-inheritance:
Tree Mesh
=========
.. autoclass:: SimPEG.Mesh.TreeMesh
:members:
:undoc-members:
:show-inheritance:
Curvilinear Mesh
================
.. autoclass:: SimPEG.Mesh.CurvilinearMesh
:members:
:undoc-members:
:show-inheritance:
Base Rectangular Mesh
=====================
.. autoclass:: SimPEG.Mesh.BaseMesh.BaseRectangularMesh
:members:
:undoc-members:
:show-inheritance:
Base Tensor Mesh
================
.. autoclass:: SimPEG.Mesh.TensorMesh.BaseTensorMesh
:members:
:undoc-members:
:show-inheritance:
Mesh IO
=======
.. automodule:: SimPEG.Mesh.MeshIO
:members:
:undoc-members:
:show-inheritance:
Mesh Viewing
============
.. automodule:: SimPEG.Mesh.View
:members:
:undoc-members:
:show-inheritance:
-29
View File
@@ -1,29 +0,0 @@
SimPEG PropMaps
***************
The API
=======
Property
--------
.. autoclass:: SimPEG.PropMaps.Property
:members:
:undoc-members:
PropMap
-------
.. autoclass:: SimPEG.PropMaps.PropMap
:members:
:undoc-members:
PropModel
---------
.. autoclass:: SimPEG.PropMaps.PropModel
:members:
:undoc-members:
-33
View File
@@ -1,33 +0,0 @@
Overview of Electromagnetics in SimPEG
**************************************
The API
=======
Physical Properties
-------------------
.. autoclass:: SimPEG.EM.Base.EMPropMap
:show-inheritance:
:members:
:undoc-members:
Problem
-------
.. autoclass:: SimPEG.EM.Base.BaseEMProblem
:show-inheritance:
:members:
:undoc-members:
Survey
------
.. autoclass:: SimPEG.EM.Base.BaseEMSurvey
:show-inheritance:
:members:
:undoc-members:
-48
View File
@@ -1,48 +0,0 @@
.. _examples_Maps_ComboMaps:
.. --------------------------------- ..
.. ..
.. THIS FILE IS AUTO GENEREATED ..
.. ..
.. SimPEG/Examples/__init__.py ..
.. ..
.. --------------------------------- ..
Maps: ComboMaps
===============
We will use an example where we want a 1D layered earth as
our model, but we want to map this to a 2D discretization to do our forward
modeling. We will also assume that we are working in log conductivity still,
so after the transformation we want to map to conductivity space.
To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
which does the first part of what we just described. The second part will be
done by the :class:`SimPEG.Maps.ExpMap` described above.
.. code-block:: python
:linenos:
M = Mesh.TensorMesh([7,5])
v1dMap = Maps.SurjectVertical1D(M)
expMap = Maps.ExpMap(M)
myMap = expMap * v1dMap
m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
sig = myMap * m
If you noticed, it was pretty easy to combine maps. What is even cooler is
that the derivatives also are made for you (if everything goes right).
Just to be sure that the derivative is correct, you should always run the test
on the mapping that you create.
.. plot::
from SimPEG import Examples
Examples.Maps_ComboMaps.run()
.. literalinclude:: ../../../SimPEG/Examples/Maps_ComboMaps.py
:language: python
:linenos:
-27
View File
@@ -1,27 +0,0 @@
.. _examples_Maps_Mesh2Mesh:
.. --------------------------------- ..
.. ..
.. THIS FILE IS AUTO GENEREATED ..
.. ..
.. SimPEG/Examples/__init__.py ..
.. ..
.. --------------------------------- ..
Maps: Mesh2Mesh
===============
This mapping allows you to go from one mesh to another.
.. plot::
from SimPEG import Examples
Examples.Maps_Mesh2Mesh.run()
.. literalinclude:: ../../../SimPEG/Examples/Maps_Mesh2Mesh.py
:language: python
:linenos:
-14
View File
@@ -1,14 +0,0 @@
Induced Polarization
********************
Todo: docs for IP!
API for IP codes
================
.. automodule:: SimPEG.DCIP.BaseIP
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
Binary file not shown.
@@ -9,28 +9,17 @@
Frequency Domain Electromagnetics
*********************************
Electromagnetic (EM) geophysical methods are used in a variety of applications
from resource exploration, including for hydrocarbons and minerals, to
environmental applications, such as groundwater monitoring. The primary
physical property of interest in EM is electrical conductivity, which
describes the ease with which electric current flows through a material.
Electromagnetic (EM) geophysical methods are used in a variety of applications from resource exploration, including for hydrocarbons and minerals, to environmental applications, such as groundwater monitoring. The primary physical property of interest in EM is electrical conductivity, which describes the ease with which electric current flows through a material.
Background
==========
Electromagnetic phenomena are governed by Maxwell's equations. They describe
the behavior of EM fields and fluxes. Electromagnetic theory for geophysical
applications by Ward and Hohmann (1988) is a highly recommended resource on
this topic.
Electromagnetic phenomena are governed by Maxwell's equations. They describe the behavior of EM fields and fluxes. Electromagnetic theory for geophysical applications by Ward and Hohmann (1988) is a highly recommended resource on this topic.
Fourier Transform Convention
----------------------------
In order to examine Maxwell's equations in the frequency domain, we must first
define our choice of harmonic time-dependence by choosing a Fourier transform
convention. We use the :math:`e^{i \omega t}` convention, so we define our
Fourier Transform pair as
In order to examine Maxwell's equations in the frequency domain, we must first define our choice of harmonic time-dependence by choosing a Fourier transform convention. We use the :math:`e^{i \omega t}` convention, so we define our Fourier Transform pair as
.. math ::
F(\omega) = \int_{-\infty}^{\infty} f(t) e^{- i \omega t} dt \\
@@ -42,7 +31,6 @@ where :math:`\omega` is angular frequency, :math:`t` is time, :math:`F(\omega)`
Maxwell's Equations
===================
In the frequency domain, Maxwell's equations are given by
.. math ::
@@ -116,20 +104,19 @@ The H-J formulation is in terms of the current density and the magnetic field:
Discretizing
------------
For both formulations, we use a finite volume discretization
and discretize fields on cell edges, fluxes on cell faces and
physical properties in cell centers. This is particularly
important when using symmetry to reduce the dimensionality of a problem
(for instance on a 2D CylMesh, there are :math:`r`, :math:`z` faces and :math:`\theta` edges)
.. figure:: ../../images/finitevolrealestate.png
.. figure:: ../images/finitevolrealestate.png
:align: center
:scale: 60 %
For the two formulations, the discretization of the physical properties, fields and fluxes are summarized below.
.. figure:: ../../images/ebjhdiscretizations.png
.. figure:: ../images/ebjhdiscretizations.png
:align: center
:scale: 60 %
@@ -163,7 +150,7 @@ API
FDEM Problem
------------
.. automodule:: SimPEG.EM.FDEM.ProblemFDEM
.. automodule:: SimPEG.EM.FDEM.FDEM
:show-inheritance:
:members:
:undoc-members:
@@ -182,11 +169,6 @@ FDEM Survey
:members:
:undoc-members:
.. automodule:: SimPEG.EM.FDEM.RxFDEM
:show-inheritance:
:members:
:undoc-members:
FDEM Fields
-----------
@@ -347,10 +347,10 @@ and
TDEM - B formulation
====================
TDEM Problem
============
.. automodule:: SimPEG.EM.TDEM.TDEM_b
.. automodule:: SimPEG.EM.TDEM.TDEM
:show-inheritance:
:members:
:undoc-members:
@@ -359,7 +359,7 @@ TDEM - B formulation
Field Storage
=============
.. autoclass:: SimPEG.EM.TDEM.BaseTDEM.FieldsTDEM
.. autoclass:: SimPEG.EM.TDEM.SurveyTDEM.Fields
:show-inheritance:
:members:
:undoc-members:
@@ -369,19 +369,19 @@ Field Storage
TDEM Survey Classes
===================
.. autoclass:: SimPEG.EM.TDEM.SurveyTDEM.SurveyTDEM
.. autoclass:: SimPEG.EM.TDEM.SurveyTDEM.Survey
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
Base Classes
============
.. Base Classes
.. ============
.. automodule:: SimPEG.EM.TDEM.BaseTDEM
:show-inheritance:
:members:
:undoc-members:
:inherited-members:
.. .. automodule:: SimPEG.EM.TDEM.BaseTDEM
.. :show-inheritance:
.. :members:
.. :undoc-members:
.. :inherited-members:
@@ -3,23 +3,22 @@ Electromagnetics
================
`SimPEG.EM` uses SimPEG as the framework for the forward and inverse
electromagnetics geophysical problems.
electromagnetics geophysical problems.
To solve for predicted data, we follow the framework shown below. The model is
what we invert for. This is mapped to a physical property on the simulation
mesh. A source which is used to excite the system is specified. Having a model
and a source, we can solve Maxwell's equations for fields. We sample these
fields with recievers to give us predicted data.
fields with recievers to give us predicted data.
.. image:: ../../images/simpegEM_noMath.png
.. image:: ../images/simpegEM_noMath.png
:scale: 50%
.. toctree::
:maxdepth: 2
api_basic
api_FDEM
api_TDEM
api_Utils
@@ -16,6 +16,6 @@ DC Analytic Dipole
from SimPEG import Examples
Examples.DC_Analytic_Dipole.run()
.. literalinclude:: ../../../SimPEG/Examples/DC_Analytic_Dipole.py
.. literalinclude:: ../../SimPEG/Examples/DC_Analytic_Dipole.py
:language: python
:linenos:
@@ -31,6 +31,6 @@ Created by @fourndo
from SimPEG import Examples
Examples.DC_Forward_PseudoSection.run()
.. literalinclude:: ../../../SimPEG/Examples/DC_Forward_PseudoSection.py
.. literalinclude:: ../../SimPEG/Examples/DC_Forward_PseudoSection.py
:language: python
:linenos:
@@ -21,6 +21,6 @@ Here we will create and run a FDEM 1D inversion.
from SimPEG import Examples
Examples.EM_FDEM_1D_Inversion.run()
.. literalinclude:: ../../../SimPEG/Examples/EM_FDEM_1D_Inversion.py
.. literalinclude:: ../../SimPEG/Examples/EM_FDEM_1D_Inversion.py
:language: python
:linenos:
@@ -21,6 +21,6 @@ Here we plot the magnetic flux density from a harmonic dipole in a wholespace.
from SimPEG import Examples
Examples.EM_FDEM_Analytic_MagDipoleWholespace.run()
.. literalinclude:: ../../../SimPEG/Examples/EM_FDEM_Analytic_MagDipoleWholespace.py
.. literalinclude:: ../../SimPEG/Examples/EM_FDEM_Analytic_MagDipoleWholespace.py
:language: python
:linenos:
@@ -17,13 +17,10 @@ current inside a steel-cased. The model is based on the Schenkel and
Morrison Casing Model, and the results are used in a 2016 SEG abstract by
Yang et al.
.. code-block:: text
Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
- Schenkel, C.J., and H.F. Morrison, 1990, Effects of well casing on potential field measurements using downhole current sources: Geophysical prospecting, 38, 663-686.
The model consists of:
- Air: Conductivity 1e-8 S/m, above z = 0
- Background: conductivity 1e-2 S/m, below z = 0
- Casing: conductivity 1e6 S/m
@@ -56,6 +53,6 @@ citation would be much appreciated!
from SimPEG import Examples
Examples.EM_Schenkel_Morrison_Casing.run()
.. literalinclude:: ../../../SimPEG/Examples/EM_Schenkel_Morrison_Casing.py
.. literalinclude:: ../../SimPEG/Examples/EM_Schenkel_Morrison_Casing.py
:language: python
:linenos:
@@ -21,6 +21,6 @@ Here we will create and run a TDEM 1D inversion.
from SimPEG import Examples
Examples.EM_TDEM_1D_Inversion.run()
.. literalinclude:: ../../../SimPEG/Examples/EM_TDEM_1D_Inversion.py
.. literalinclude:: ../../SimPEG/Examples/EM_TDEM_1D_Inversion.py
:language: python
:linenos:

Some files were not shown because too many files have changed in this diff Show More