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Merge branch 'master' of https://github.com/simpeg/simpegpf

Browse Source 
Conflicts:
	simpegPF/notebooks/MagInversion.ipynb
	simpegPF/notebooks/tutorials/Tutorial_1_Mag forward modeling.ipynb
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seogi_macbook committed 2016-03-15 00:13:52 -07:00
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commit 241dc83354
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.travis.yml
+2 -1
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@@ -4,7 +4,7 @@ python:
# Setup anaconda
before_install:
- if [ ${TRAVIS_PYTHON_VERSION:0:1} == "2" ]; then wget http://repo.continuum.io/miniconda/Miniconda-3.3.0-Linux-x86_64.sh -O miniconda.sh; else wget http://repo.continuum.io/miniconda/Miniconda3-3.3.0-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
@@ -35,3 +35,4 @@ notifications:
email:
- rowanc1@gmail.com
- sgkang09@gmail.com
- lindseyheagy@gmail.com
simpegPF/BaseMag.py
+357 -6
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@@ -1,6 +1,6 @@
from SimPEG import Maps, Survey, Utils, np, sp
from scipy.constants import mu_0
import re
class BaseMagSurvey(Survey.BaseSurvey):
"""Base Magnetics Survey"""
@@ -132,13 +132,364 @@ class BaseMagMap(Maps.IdentityMap):
class WeightMap(Maps.IdentityMap):
"""Weighted Map for distributed parameters"""
def __init__(self, mesh, weight, **kwargs):
Maps.IdentityMap.__init__(self, mesh)
self.mesh = mesh
def __init__(self, nP, weight, **kwargs):
Maps.IdentityMap.__init__(self, nP)
self.mesh = None
self.weight = weight
def _transform(self, m):
def _transform(self, m):
return m*self.weight
def deriv(self, m):
return Utils.sdiag(self.weight)
return Utils.sdiag(self.weight)
def readUBCmagObs(obs_file):
"""
Read and write UBC mag file format
INPUT:
:param fileName, path to the UBC obs mag file
OUTPUT:
:param dobs, observation in (x y z [data] [wd])
:param B, primary field information (BI, BD, B0)
:param M, magnetization orentiaton (MI, MD)
"""
fid = open(obs_file,'r')
# First line has the inclination,declination and amplitude of B0
line = fid.readline()
B = np.array(line.split(),dtype=float)
# Second line has the magnetization orientation and a flag
line = fid.readline()
M = np.array(line.split(),dtype=float)
# Third line has the number of rows
line = fid.readline()
ndat = np.array(line.split(),dtype=int)
# Pre-allocate space for obsx, obsy, obsz, data, uncert
line = fid.readline()
temp = np.array(line.split(),dtype=float)
dobs = np.zeros((ndat,len(temp)), dtype=float)
for ii in range(ndat):
dobs[ii,:] = np.array(line.split(),dtype=float)
line = fid.readline()
return B, M, dobs
def read_MAGfwr_inp(input_file):
"""Read input files for forward modeling MAG data with integral form
INPUT:
input_file: File name containing the forward parameter
OUTPUT:
mshfile
obsfile
modfile
magfile
topofile
# All files should be in the working directory, otherwise the path must
# be specified.
Created on Jul 17, 2013
@author: dominiquef
"""
fid = open(input_file,'r')
line = fid.readline()
l_input = line.split('!')
mshfile = l_input[0].rstrip()
line = fid.readline()
l_input = line.split('!')
obsfile = l_input[0].rstrip()
line = fid.readline()
l_input = line.split('!')
modfile = l_input[0].rstrip()
line = fid.readline()
l_input = line.split('!')
if l_input=='null':
magfile = []
else:
magfile = l_input[0].rstrip()
line = fid.readline()
l_input = line.split('!')
if l_input=='null':
topofile = []
else:
topofile = l_input[0].rstrip()
return mshfile, obsfile, modfile, magfile, topofile
def read_MAGinv_inp(input_file):
"""Read input files for forward modeling MAG data with integral form
INPUT:
input_file: File name containing the forward parameter
OUTPUT:
mshfile
obsfile
topofile
start model
ref model
mag model
weightfile
chi_target
as, ax ,ay, az
upper, lower bounds
lp, lqx, lqy, lqz
# All files should be in the working directory, otherwise the path must
# be specified.
Created on Dec 21th, 2015
@author: dominiquef
"""
fid = open(input_file,'r')
# Line 1
line = fid.readline()
l_input = line.split('!')
mshfile = l_input[0].rstrip()
# Line 2
line = fid.readline()
l_input = line.split('!')
obsfile = l_input[0].rstrip()
# Line 3
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input=='null':
topofile = []
else:
topofile = l_input[0].rstrip()
# Line 4
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
mstart = float(l_input[1])
else:
mstart = l_input[0].rstrip()
# Line 5
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
mref = float(l_input[1])
else:
mref = l_input[0].rstrip()
# Line 6
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input=='DEFAULT':
magfile = []
else:
magfile = l_input[0].rstrip()
# Line 7
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input=='DEFAULT':
wgtfile = []
else:
wgtfile = l_input[0].rstrip()
# Line 8
line = fid.readline()
l_input = re.split('[!\s]',line)
chi = float(l_input[0])
# Line 9
line = fid.readline()
l_input = re.split('[!\s]',line)
val = np.array(l_input[0:4])
alphas = val.astype(np.float)
# Line 10
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:3])
bounds = val.astype(np.float)
else:
bounds = l_input[0].rstrip()
# Line 11
line = fid.readline()
l_input = re.split('[!\s]',line)
if l_input[0]=='VALUE':
val = np.array(l_input[1:6])
lpnorms = val.astype(np.float)
else:
lpnorms = l_input[0].rstrip()
return mshfile, obsfile, topofile, mstart, mref, magfile, wgtfile, chi, alphas, bounds, lpnorms
def read_GOCAD_ts(tsfile):
"""Read GOCAD triangulated surface (*.ts) file
INPUT:
tsfile: Triangulated surface
OUTPUT:
vrts : Array of vertices in XYZ coordinates [n x 3]
trgl : Array of index for triangles [m x 3]. The order of the vertices
is important and describes the normal
n = cross( (P2 - P1 ) , (P3 - P1) )
Created on Jan 13th, 2016
Author: @fourndo
"""
fid = open(tsfile,'r')
line = fid.readline()
# Skip all the lines until the vertices
while re.match('TFACE',line)==None:
line = fid.readline()
line = fid.readline()
vrtx = []
# Run down all the vertices and save in array
while re.match('VRTX',line):
l_input = re.split('[\s*]',line)
temp = np.array(l_input[2:5])
vrtx.append(temp.astype(np.float))
# Read next line
line = fid.readline()
vrtx = np.asarray(vrtx)
# Skip lines to the triangles
while re.match('TRGL',line)==None:
line = fid.readline()
# Run down the list of triangles
trgl = []
# Run down all the vertices and save in array
while re.match('TRGL',line):
l_input = re.split('[\s*]',line)
temp = np.array(l_input[1:4])
trgl.append(temp.astype(np.int))
# Read next line
line = fid.readline()
trgl = np.asarray(trgl)
return vrtx, trgl
def gocad2vtk(gcFile,mesh,bcflag,inflag):
""""
Function to read gocad polystructure file and output indexes of mesh with in the structure.
"""
import vtk, vtk.util.numpy_support as npsup
print "Reading GOCAD ts file..."
vrtx, trgl = read_GOCAD_ts(gcFile)
# Adjust the index
trgl = trgl - 1
# Make vtk pts
ptsvtk = vtk.vtkPoints()
ptsvtk.SetData(npsup.numpy_to_vtk(vrtx,deep=1))
# Make the polygon connection
polys = vtk.vtkCellArray()
for face in trgl:
poly = vtk.vtkPolygon()
poly.GetPointIds().SetNumberOfIds(len(face))
for nrv, vert in enumerate(face):
poly.GetPointIds().SetId(nrv,vert)
polys.InsertNextCell(poly)
# Make the polydata, structure of connections and vrtx
polyData = vtk.vtkPolyData()
polyData.SetPoints(ptsvtk)
polyData.SetPolys(polys)
# Make implicit func
ImpDistFunc = vtk.vtkImplicitPolyDataDistance()
ImpDistFunc.SetInput(polyData)
# Convert the mesh
vtkMesh = vtk.vtkRectilinearGrid()
vtkMesh.SetDimensions(mesh.nNx,mesh.nNy,mesh.nNz)
vtkMesh.SetXCoordinates(npsup.numpy_to_vtk(mesh.vectorNx,deep=1))
vtkMesh.SetYCoordinates(npsup.numpy_to_vtk(mesh.vectorNy,deep=1))
vtkMesh.SetZCoordinates(npsup.numpy_to_vtk(mesh.vectorNz,deep=1))
# Add indexes
vtkInd = npsup.numpy_to_vtk(np.arange(mesh.nC),deep=1)
vtkInd.SetName('Index')
vtkMesh.GetCellData().AddArray(vtkInd)
extractImpDistRectGridFilt = vtk.vtkExtractGeometry() # Object constructor
extractImpDistRectGridFilt.SetImplicitFunction(ImpDistFunc) #
extractImpDistRectGridFilt.SetInputData(vtkMesh)
if bcflag is True:
extractImpDistRectGridFilt.ExtractBoundaryCellsOn()
else:
extractImpDistRectGridFilt.ExtractBoundaryCellsOff()
if inflag is True:
extractImpDistRectGridFilt.ExtractInsideOn()
else:
extractImpDistRectGridFilt.ExtractInsideOff()
print "Extracting indices from grid..."
# Executing the pipe
extractImpDistRectGridFilt.Update()
# Get index inside
insideGrid = extractImpDistRectGridFilt.GetOutput()
insideGrid = npsup.vtk_to_numpy(insideGrid.GetCellData().GetArray('Index'))
# Return the indexes inside
return insideGrid
simpegPF/Dev/Archives/fwr_MAG_data.py
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@@ -0,0 +1,95 @@
def fwr_MAG_data(mesh,B,M,rxLoc,model,flag):
"""
Forward model magnetic data using integral equation
INPUT:
xn, yn, zn = Mesh nodes location
B = Inducing field parameter [Binc, Bdecl, B0]
M = Magnetization matrix [Minc, Mdecl]
rxLox = Observation location informat [obsx, obsy, obsz]
model = Model associated with mesh
OUTPUT:
dobs =Observation array in format [obsx, obsy, obsz, data]
Created on Oct 7, 2015
@author: dominiquef
"""
#%%
from SimPEG import np, Utils, sp, mkvc
from get_T_mat import get_T_mat
xn = mesh.vectorNx;
yn = mesh.vectorNy;
zn = mesh.vectorNz;
mcell = (len(xn)-1) * (len(yn)-1) * (len(zn)-1)
ndata = rxLoc.shape[0]
# Convert declination from north to cartesian
Md = (450.-float(M[1]))%360.
# Create magnetization matrix
mx = np.cos(np.deg2rad(M[0])) * np.cos(np.deg2rad(Md))
my = np.cos(np.deg2rad(M[0])) * np.sin(np.deg2rad(Md))
mz = np.sin(np.deg2rad(M[0]))
Mx = Utils.sdiag(np.ones([mcell])*mx*B[2])
My = Utils.sdiag(np.ones([mcell])*my*B[2])
Mz = Utils.sdiag(np.ones([mcell])*mz*B[2])
#matplotlib.pyplot.spy(scipy.sparse.csr_matrix(Mx))
#plt.show()
Mxyz = sp.vstack((Mx,My,Mz));
#%% Create TMI projector
# Convert Bdecination from north to cartesian
D = (450.-float(B[1]))%360.
Ptmi = mkvc(np.r_[np.cos(np.deg2rad(B[0]))*np.cos(np.deg2rad(D)),np.cos(np.deg2rad(B[0]))*np.sin(np.deg2rad(D)),np.sin(np.deg2rad(B[0]))],2).T;
if flag=='tmi':
d = np.zeros(ndata)
elif flag=='xyz':
d = np.zeros(int(3*ndata))
# Loop through all observations and create forward operator (ndata-by-mcell)
print "Begin forward modeling " +str(int(ndata)) + " data points..."
# Add counter to dsiplay progress. Good for large problems
progress = -1;
for ii in range(ndata):
tx, ty, tz = get_T_mat(xn,yn,zn,rxLoc[ii,:])
Gxyz = np.vstack((tx,ty,tz))*Mxyz
if flag=='xyz':
d[ii:ndata:] = mkvc(Gxyz.dot(model))
elif flag=='tmi':
d[ii] = Ptmi.dot(Gxyz.dot(model))
#%%
# Forward operator
d_iter = np.floor(float(ii)/float(ndata)*10.);
if d_iter > progress:
arg = "Done " + str(d_iter*10) + " %"
print arg
progress = d_iter;
print "Done 100% ...forward modeling completed!!\n"
return d
simpegPF/Dev/Archives/get_MAG_F.py
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@@ -0,0 +1,132 @@
def fwr_MAG_F(mesh,B,M,rxLoc,flag):
"""
Forward model magnetic data using integral equation
INPUT:
mesh = Mesh in SimPEG format
B = Inducing field parameter [Binc, Bdecl, B0]
M = Magnetization information
[OPTIONS]
1- [Minc, Mdecl] : Assumes uniform magnetization orientation
2- [mx1,mx2,..., my1,...,mz1] : cell-based defined magnetization direction
3- diag(M): Block diagonal matrix with [Mx, My, Mz] along the diagonal
rxLox = Observation location informat [obsx, obsy, obsz]
flag = 'tmi' | 'xyz' | 'full'
[OPTIONS]
1- tmi : Magnetization direction used and data are projected onto the
inducing field direction F.shape([ndata, nc])
2- xyz : Magnetization direction used and data are given in 3-components
F.shape([3*ndata, nc])
3- full: Full tensor matrix stored with shape([3*ndata, 3*nc])
OUTPUT:
F = Linear forward modeling operation
Created on Dec, 20th 2015
@author: dominiquef
"""
#%%
from SimPEG import np, Utils, sp, mkvc
from get_T_mat import get_T_mat
xn = mesh.vectorNx;
yn = mesh.vectorNy;
zn = mesh.vectorNz;
mcell = (len(xn)-1) * (len(yn)-1) * (len(zn)-1)
ndata = rxLoc.shape[0]
#%% Create TMI projector
# Convert Bdecination from north to cartesian
D = (450.-float(B[1]))%360.
Ptmi = mkvc(np.r_[np.cos(np.deg2rad(B[0]))*np.cos(np.deg2rad(D)),
np.cos(np.deg2rad(B[0]))*np.sin(np.deg2rad(D)),
np.sin(np.deg2rad(B[0]))],2).T;
# Pre-allocate space
if flag=='tmi' | flag == 'xyz':
# If assumes uniform magnetization direction
if len(M) == 2:
# Convert declination from north to cartesian
Md = (450.-float(M[1]))%360.
# Create magnetization matrix
mx = np.cos(np.deg2rad(M[0])) * np.cos(np.deg2rad(Md))
my = np.cos(np.deg2rad(M[0])) * np.sin(np.deg2rad(Md))
mz = np.sin(np.deg2rad(M[0]))
Mx = Utils.sdiag(np.ones([mcell])*mx*B[2])
My = Utils.sdiag(np.ones([mcell])*my*B[2])
Mz = Utils.sdiag(np.ones([mcell])*mz*B[2])
Mxyz = sp.vstack((Mx,My,Mz));
# Otherwise if given a vector 3*ncells
elif len(M) == mesh.nC * 3:
Mxyz = sp.spdiags(M,0,mesh.nC * 3,mesh.nC * 3)
if flag == 'tmi':
F = np.zeros((ndata, mesh.nC))
elif flag == 'xyz':
F = np.zeros((int(3*ndata), mesh.nC))
elif flag == 'full':
F = np.zeros((int(3*ndata), int(3*mesh.nC)))
else:
print """Flag must be either 'tmi' | 'xyz' | 'full', please revised"""
return
# Loop through all observations and create forward operator (ndata-by-mcell)
print "Begin calculation of forward operator: " + flag
# Add counter to dsiplay progress. Good for large problems
progress = -1;
for ii in range(ndata):
tx, ty, tz = get_T_mat(xn,yn,zn,rxLoc[ii,:])
if flag=='tmi':
F[ii,:] = Ptmi.dot(np.vstack((tx,ty,tz)))*Mxyz
elif flag == 'xyz':
F[ii,:] = tx*Mxyz
F[ii+ndata,:] = ty*Mxyz
F[ii+2*ndata,:] = tz*Mxyz
elif flag == 'full':
F[ii,:] = tx
F[ii+ndata,:] = ty
F[ii+2*ndata,:] = tz
# Display progress
counter = np.floor(float(ii)/float(ndata)*10.);
if counter > progress:
arg = "Done " + str(counter*10) + " %"
print arg
progress = counter;
print "Done 100% ...forward modeling completed!!\n"
return F
simpegPF/Dev/Archives/get_T_mat.py
+133
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@@ -0,0 +1,133 @@
'''
Created on Sep 27, 2015
@author: dominiquef
'''
def get_T_mat(xn,yn,zn,rxLoc):
"""
Load in the nodes of a tensor mesh and computes the magnetic tensor
for a given observation location [obsx, obsy, obsz]
OUTPUT:
Tx = [Txx Txy Txz]
Ty = [Tyx Tyy Tyz]
Tz = [Tzx Tzy Tzz]
where each elements have dimension 1-by-mcell.
Only the upper half 5 elements have to be computed since symetric.
Currently done as for-loops but will eventually be changed to vector
indexing, once the topography has been figured out.
"""
from SimPEG import np, mkvc
ncx = len(xn)-1
ncy = len(yn)-1
ncz = len(zn)-1
mcell = ncx*ncy*ncz
# Pre-allocate space for 1D array
Tx = np.zeros((1,3*mcell))
Ty = np.zeros((1,3*mcell))
Tz = np.zeros((1,3*mcell))
yn2,xn2,zn2 = np.meshgrid(yn[1:], xn[1:], zn[1:])
yn1,xn1,zn1 = np.meshgrid(yn[0:ncy], xn[0:ncx], zn[0:ncz])
yn2 = mkvc(yn2)
yn1 = mkvc(yn1)
zn2 = mkvc(zn2)
zn1 = mkvc(zn1)
xn2 = mkvc(xn2)
xn1 = mkvc(xn1)
#%%
#==============================================================================
dz2 = rxLoc[2] - zn1;
dz1 = rxLoc[2] - zn2;
dy2 = yn2 - rxLoc[1];
dy1 = yn1 - rxLoc[1];
dx2 = xn2 - rxLoc[0];
dx1 = xn1 - rxLoc[0];
R1 = ( dy2**2 + dx2**2 );
R2 = ( dy2**2 + dx1**2 );
R3 = ( dy1**2 + dx2**2 );
R4 = ( dy1**2 + dx1**2 );
arg1 = np.sqrt( dz2**2 + R2 );
arg2 = np.sqrt( dz2**2 + R1 );
arg3 = np.sqrt( dz1**2 + R1 );
arg4 = np.sqrt( dz1**2 + R2 );
arg5 = np.sqrt( dz2**2 + R3 );
arg6 = np.sqrt( dz2**2 + R4 );
arg7 = np.sqrt( dz1**2 + R4 );
arg8 = np.sqrt( dz1**2 + R3 );
Tx[0,0:mcell] = np.arctan2( dy1 * dz2 , ( dx2 * arg5 ) ) +\
- np.arctan2( dy2 * dz2 , ( dx2 * arg2 ) ) +\
np.arctan2( dy2 * dz1 , ( dx2 * arg3 ) ) +\
- np.arctan2( dy1 * dz1 , ( dx2 * arg8 ) ) +\
np.arctan2( dy2 * dz2 , ( dx1 * arg1 ) ) +\
- np.arctan2( dy1 * dz2 , ( dx1 * arg6 ) ) +\
np.arctan2( dy1 * dz1 , ( dx1 * arg7 ) ) +\
- np.arctan2( dy2 * dz1 , ( dx1 * arg4 ) );
Ty[0,0:mcell] = np.log( ( dz2 + arg2 ) / (dz1 + arg3 ) ) +\
-np.log( ( dz2 + arg1 ) / (dz1 + arg4 ) ) +\
np.log( ( dz2 + arg6 ) / (dz1 + arg7 ) ) +\
-np.log( ( dz2 + arg5 ) / (dz1 + arg8 ) );
Ty[0,mcell:2*mcell] = np.arctan2( dx1 * dz2 , ( dy2 * arg1 ) ) +\
- np.arctan2( dx2 * dz2 , ( dy2 * arg2 ) ) +\
np.arctan2( dx2 * dz1 , ( dy2 * arg3 ) ) +\
- np.arctan2( dx1 * dz1 , ( dy2 * arg4 ) ) +\
np.arctan2( dx2 * dz2 , ( dy1 * arg5 ) ) +\
- np.arctan2( dx1 * dz2 , ( dy1 * arg6 ) ) +\
np.arctan2( dx1 * dz1 , ( dy1 * arg7 ) ) +\
- np.arctan2( dx2 * dz1 , ( dy1 * arg8 ) );
R1 = (dy2**2 + dz1**2);
R2 = (dy2**2 + dz2**2);
R3 = (dy1**2 + dz1**2);
R4 = (dy1**2 + dz2**2);
Ty[0,2*mcell:] = np.log( ( dx1 + np.sqrt( dx1**2 + R1 ) ) / (dx2 + np.sqrt( dx2**2 + R1 ) ) ) +\
-np.log( ( dx1 + np.sqrt( dx1**2 + R2 ) ) / (dx2 + np.sqrt( dx2**2 + R2 ) ) ) +\
np.log( ( dx1 + np.sqrt( dx1**2 + R4 ) ) / (dx2 + np.sqrt( dx2**2 + R4 ) ) ) +\
-np.log( ( dx1 + np.sqrt( dx1**2 + R3 ) ) / (dx2 + np.sqrt( dx2**2 + R3 ) ) );
R1 = (dx2**2 + dz1**2);
R2 = (dx2**2 + dz2**2);
R3 = (dx1**2 + dz1**2);
R4 = (dx1**2 + dz2**2);
Tx[0,2*mcell:] = np.log( ( dy1 + np.sqrt( dy1**2 + R1 ) ) / (dy2 + np.sqrt( dy2**2 + R1 ) ) ) +\
-np.log( ( dy1 + np.sqrt( dy1**2 + R2 ) ) / (dy2 + np.sqrt( dy2**2 + R2 ) ) ) +\
np.log( ( dy1 + np.sqrt( dy1**2 + R4 ) ) / (dy2 + np.sqrt( dy2**2 + R4 ) ) ) +\
-np.log( ( dy1 + np.sqrt( dy1**2 + R3 ) ) / (dy2 + np.sqrt( dy2**2 + R3 ) ) );
Tz[0,2*mcell:] = -( Ty[0,mcell:2*mcell] + Tx[0,0:mcell] );
Tz[0,mcell:2*mcell] = Ty[0,2*mcell:];
Tx[0,mcell:2*mcell] = Ty[0,0:mcell];
Tz[0,0:mcell] = Tx[0,2*mcell:];
Tx = Tx/(4*np.pi);
Ty = Ty/(4*np.pi);
Tz = Tz/(4*np.pi);
return Tx,Ty,Tz
simpegPF/Dev/Archives/get_UBC_mesh.py
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@@ -0,0 +1,117 @@
'''
Created on Jul 17, 2013
@author: dominiquef
'''
def get_UBC_mesh(meshfile):
""" Read UBC mesh file and extract parameters
Works for the condenced version (20 * 3) --> [20 20 20] """
fid = open(meshfile,'r')
from numpy import zeros
# Go through the log file and extract data and the last achieved misfit
for ii in range (1, 6):
line = fid.readline()
line = line.split(' ')
# First line: number of cells in i, j, k
if ii == 1:
numcell=[]
for jj in range(len(line)):
t = int(line[jj])
numcell.append(t)
nX = numcell[0]
nY = numcell[1]
nZ = numcell[2]
# Second line: origin coordinate (X,Y,Z)
elif ii==2:
origin = []
for jj in range(len(line)):
t = float(line[jj])
origin.append(t)
# Other lines for the xn, yn, zn (nodes location)
elif ii==3:
xn=zeros((nX+1,1), dtype=float)
xn[0] = origin[0]
count_entry = 0;
count = 0;
while (count<nX):
if line[count_entry].find('*') != -1:
ndx = line[count_entry].split('*')
for kk in range(int(ndx[0])):
xn[count+1] = xn[count] + (ndx[1])
count = count+1
count_entry=count_entry+1
else:
t = float(line[count_entry])
xn[count+1]= xn[count] +t
count = count+1;
count_entry=count_entry+1
elif ii==4:
yn=zeros((nY+1,1), dtype=float)
yn[0] = origin[0]
count_entry = 0;
count = 0;
while (count<nY):
if line[count_entry].find('*') != -1:
ndx = line[count_entry].split('*')
for kk in range(int(ndx[0])):
yn[count+1] = yn[count] + (ndx[1])
count = count+1
count_entry=count_entry+1
else:
t = float(line[count_entry])
yn[count+1]= yn[count] +t
count = count+1;
count_entry=count_entry+1
elif ii==5:
zn=zeros((nZ+1,1), dtype=float)
zn[0] = origin[0]
count_entry = 0;
count = 0;
while (count<nZ):
if line[count_entry].find('*') != -1:
ndx = line[count_entry].split('*')
for kk in range(int(ndx[0])):
zn[count+1] = zn[count] + (ndx[1])
count = count+1
count_entry=count_entry+1
else:
t = float(line[count_entry])
zn[count+1]= zn[count] +t
count = count+1;
count_entry=count_entry+1
fid.close();
return xn,yn,zn
simpegPF/Dev/Archives/read_MAG_obs.py
+58
View File
@@ -0,0 +1,58 @@
'''
Created on Jul 17, 2013
@author: dominiquef
'''
def read_MAG_obs(obs_file):
"""Read input files for the lp_norm script"""
from numpy import zeros
fid = open(obs_file,'r')
# First line has the declination, inclination and amplitude of B0
line = fid.readline()
line = line.split()
Incl = float(line[0])
Decl = float(line[1])
B0 = float(line[2])
# Second line has the magnetization orientation and a flag
line = fid.readline()
line = line.split()
Minc = float(line[0])
Mdec = float(line[1])
FLAG = float(line[2])
# Third line has the number of rows
line = fid.readline()
line = line.split()
ndat = int(line[0])
# Pre-allocate space for obsx, obsy, obsz, data, uncert
obsx = zeros((ndat,1), dtype=float)
obsy = zeros((ndat,1), dtype=float)
obsz = zeros((ndat,1), dtype=float)
data = zeros((ndat,1), dtype=float)
unct = zeros((ndat,1), dtype=float)
for ii in range(ndat):
line = fid.readline()
line = line.split()
obsx[ii] = line[0]
obsy[ii] = line[1]
obsz[ii] = line[2]
if len(line)>3:
data[ii] = line[3]
if len(line)>4:
unct[ii] = line[4]
return Decl, Incl, B0, Mdec, Minc, obsx, obsy, obsz, data, unct
simpegPF/Dev/Archives/read_MAGfwr_inp.py
+52
View File
@@ -0,0 +1,52 @@
def read_MAGfwr_inp(input_file):
"""Read input files for forward modeling MAG data with integral form
INPUT:
input_file: File name containing the forward parameter
OUTPUT:
mshfile
obsfile
modfile
magfile
topofile
# All files should be in the working directory, otherwise the path must
# be specified.
Created on Jul 17, 2013
@author: dominiquef
"""
fid = open(input_file,'r')
line = fid.readline()
l_input = line.split('!')
mshfile = l_input[0].rstrip()
line = fid.readline()
l_input = line.split('!')
obsfile = l_input[0].rstrip()
line = fid.readline()
l_input = line.split('!')
modfile = l_input[0].rstrip()
line = fid.readline()
l_input = line.split('!')
if l_input=='null':
magfile = []
else:
magfile = l_input[0].rstrip()
line = fid.readline()
l_input = line.split('!')
if l_input=='null':
topofile = []
else:
topofile = l_input[0].rstrip()
return mshfile, obsfile, modfile, magfile, topofile
simpegPF/Dev/FWR_data.dat
+628
View File
@@ -0,0 +1,628 @@
45.00 315.00 50000.00
-45.00 135.00 1.00
625
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simpegPF/Dev/FWR_test.dat
+103
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@@ -0,0 +1,103 @@
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simpegPF/Dev/Intgrl_MAG_Fwr_Driver.py
+63
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import os
home_dir = 'C:\Users\dominiquef.MIRAGEOSCIENCE\ownCloud\Research\Modelling\Synthetic\Block_Gaussian_topo'
inpfile = 'PYMAG3C_fwr.inp'
dsep = '\\'
os.chdir(home_dir)
#%%
from SimPEG import np, sp, Utils, mkvc, Maps
import simpegPF as PF
import pylab as plt
## New scripts to be added to basecode
#from fwr_MAG_data import fwr_MAG_data
#from read_MAGfwr_inp import read_MAGfwr_inp
#%%
# Read input file
[mshfile, obsfile, modfile, magfile, topofile] = PF.BaseMag.read_MAGfwr_inp(inpfile)
# Load mesh file
mesh = Utils.meshutils.readUBCTensorMesh(mshfile)
# Load model file
model = Utils.meshutils.readUBCTensorModel(modfile,mesh)
# Load in topofile or create flat surface
if topofile == 'null':
actv = np.ones(mesh.nC)
else:
topo = np.genfromtxt(topofile,skip_header=1)
actv = PF.Magnetics.getActiveTopo(mesh,topo,'N')
Utils.writeUBCTensorModel('nullcell.dat',mesh,actv)
# Load in observation file
[B,M,dobs] = PF.BaseMag.readUBCmagObs(obsfile)
rxLoc = dobs[:,0:3]
#rxLoc[:,2] += 5 # Temporary change for test
ndata = rxLoc.shape[0]
# Load GOCAD surf
tsfile = 'SphereA.ts'
[vrtx, trgl] = PF.BaseMag.read_GOCAD_ts(tsfile)
#%% Run forward modeling
# Compute forward model using integral equation
d = PF.Magnetics.Intgrl_Fwr_Data(mesh,B,M,rxLoc,model,actv,'tmi')
# Form data object with coordinates and write to file
wd = np.zeros((ndata,1))
# Save forward data to file
PF.Magnetics.writeUBCobs(home_dir + dsep + 'FWR_data.dat',B,M,rxLoc,d,wd)
simpegPF/Dev/Intgrl_MAG_Fwr_DualSphereTopo_Test.py
+187
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import os
home_dir = 'C:\\LC\\Private\\dominiquef\\Projects\\4414_Minsim\\Modeling\\MAG'
os.chdir(home_dir)
#%%
from SimPEG import *
import matplotlib.pyplot as plt
import simpegPF as PF
import scipy.interpolate as interpolation
import time
#from fwr_MAG_data import fwr_MAG_data
plt.close('all')
topofile = 'Gaussian.topo'
zoffset = 2
#%% Create survey
# Load in topofile or create flat surface
if not topofile:
actv = np.ones(mesh.nC)
else:
topo = np.genfromtxt(topofile,skip_header=1)
B = np.array(([90.,0.,50000.]))
M = np.array(([90.,0.,315.]))
# Sphere radius
R = 25.
# # Or create juste a plane grid
xr = np.linspace(-99., 99., 40)
yr = np.linspace(-49., 49., 20)
X, Y = np.meshgrid(xr, yr)
sclx = 100.
dx = np.asarray([15., 10., 5., 2.5])
d_iter = len(dx)
l1_r = np.zeros(d_iter)
l2_r = np.zeros(d_iter)
linf_r = np.zeros(d_iter)
timer = np.zeros(d_iter)
mcell = np.zeros(d_iter)
#%% Loop through decreasing meshes and measure the residual
# Create mesh using simpeg and write out in GIF format
for ii in range(d_iter):
nc = int(sclx/dx[ii])
hxind = [(dx[ii], 2*nc)]
hyind = [(dx[ii], nc)]
hzind = [(dx[ii], nc)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')
mcell[ii] = mesh.nC
actv = PF.Magnetics.getActiveTopo(mesh,topo,'N')
# Drape observations on topo + offset
if not topofile:
Z = np.ones((xr.size, yr.size)) * 2.5
else:
F = interpolation.NearestNDInterpolator(topo[:,0:2],topo[:,2])
Z = F(X,Y) + zoffset
rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)]
ndata = rxLoc.shape[0]
xn = mesh.vectorNx
yn = mesh.vectorNy
zn = mesh.vectorNz
print 'Mesh size: ' + str(mcell[ii])
#%% Create model
chibkg = 0.
chiblk = 0.01
model = np.ones(mcell[ii])*chibkg
# Do a three sphere problem for more frequencies
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., -sclx/3, R)
model[sph_ind] = 0.5*chiblk
sph_ind = PF.MagAnalytics.spheremodel(mesh, -sclx/2., 0., -sclx/3., R/3.)
model[sph_ind] = 4.*chiblk
sph_ind = PF.MagAnalytics.spheremodel(mesh, sclx/2., 0., -sclx/2.5, R/2.5)
model[sph_ind] = 2.5*chiblk
Utils.writeUBCTensorMesh('Mesh.msh',mesh)
Utils.writeUBCTensorModel('Model.sus',mesh,model)
#actv = np.ones(mesh.nC)
#%% Forward mode ldata
start_time = time.time()
d = PF.Magnetics.Intgrl_Fwr_Data(mesh,B,M,rxLoc,model,actv,'tmi')
timer[ii] = (time.time() - start_time)
#fwr_tmi = d[0:ndata]
#fwr_y = d[ndata:2*ndata]
#fwr_z = d[2*ndata:]
#%% Get the analystical answer and compute the residual
#bxa,bya,bza = PF.MagAnalytics.MagSphereAnaFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R,0.,0.,0.,chiblk, np.array(([0.,0.,B[2]])),'secondary')
Bd = (450.-float(B[1]))%360.
Bi = B[0]; # Convert dip to horizontal to cartesian
Bx = np.cos(np.deg2rad(Bi)) * np.cos(np.deg2rad(Bd)) * B[2]
By = np.cos(np.deg2rad(Bi)) * np.sin(np.deg2rad(Bd)) * B[2]
Bz = np.sin(np.deg2rad(Bi)) * B[2]
Bo = np.c_[Bx, By, Bz]
Ptmi = mkvc(np.r_[np.cos(np.deg2rad(Bi))*np.cos(np.deg2rad(Bd)),np.cos(np.deg2rad(Bi))*np.sin(np.deg2rad(Bd)),np.sin(np.deg2rad(Bi))],2).T;
bxa,bya,bza = PF.MagAnalytics.MagSphereFreeSpace(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R,0., 0., -sclx/3, 0.5*chiblk, Bo)
bxb,byb,bzb = PF.MagAnalytics.MagSphereFreeSpace(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R/3., -sclx/2., 0., -sclx/3.,4.*chiblk, Bo)
bxc,byc,bzc = PF.MagAnalytics.MagSphereFreeSpace(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R/2.5, sclx/2., 0., -sclx/2.5,2.5*chiblk, Bo)
bx = bxa + bxb + bxc
by = bya + byb + byc
bz = bza + bzb + bzc
b_tmi = mkvc(Ptmi.dot(np.c_[bx,by,bz].T))
r_tmi = d - b_tmi
#r_By = fwr_y - bya
#r_Bz = fwr_z - bza
l2_r[ii] = np.sum( r_tmi**2 ) **0.5
l1_r[ii] = np.sum( np.abs( r_tmi ) )
linf_r[ii] = np.max( np.abs( r_tmi ) )
#%% Write predicted to file
PF.Magnetics.writeUBCobs('Obsloc.loc',B,M,rxLoc,d,np.ones(len(d)))
#%% Plot results
print 'Residual between analytical sphere and integral forward'
print "dx \t nc \t l1 \t l2 \t linf \t Runtime"
for ii in range(d_iter):
print str(dx[ii]) + "\t" + str(mcell[ii]) + "\t" + str(l1_r[ii]) + "\t" + str(l2_r[ii]) + "\t" + str(linf_r[ii]) + "\t" + str(timer[ii])
#%% Plot fields
plt.figure(1)
ax = plt.subplot()
plt.imshow(np.reshape(b_tmi,X.shape), interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.02)
plt.contour(X,Y, np.reshape(b_tmi,X.shape),10)
plt.scatter(X,Y, c=np.reshape(b_tmi,X.shape), s=20)
ax.set_title('Analytical')
#%% Plot the forward solution from integral
plt.figure(2)
ax = plt.subplot()
plt.imshow(np.reshape(d,X.shape), interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max() ], origin = 'lower')
plt.colorbar(fraction=0.02)
plt.contour(X,Y, np.reshape(d,X.shape),10)
plt.scatter(X,Y, c=np.reshape(d,X.shape), s=20)
ax.set_title('Numerical')
#%% Plot residual data
plt.figure(3)
ax = plt.subplot()
plt.imshow(np.reshape(r_tmi,X.shape), interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.02)
plt.contour(X,Y, np.reshape(r_tmi,X.shape),10)
plt.scatter(X,Y, c=np.reshape(r_tmi,X.shape), s=20)
ax.set_title('Sphere Ana Bx')
simpegPF/Dev/Intgrl_MAG_Fwr_SphereTest.py
+173
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import os
# home_dir = 'C:\Users\dominiquef.MIRAGEOSCIENCE\Documents\GIT\SimPEG\simpegpf\simpegPF\Dev'
# os.chdir(home_dir)
#%%
from SimPEG import *
import matplotlib.pyplot as plt
import simpegPF as PF
#from fwr_MAG_data import fwr_MAG_data
plt.close('all')
#%% Create survey
B = np.array(([-45.,315.,50000.]))
M = np.array(([-45.,315.]))
# Sphere radius
R = 0.25
# # Or create juste a plane grid
xr = np.linspace(-2., 2., 5)
yr = np.linspace(-2., 2., 5)
X, Y = np.meshgrid(xr, yr)
Z = np.ones((xr.size, yr.size)) * 2.5
rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]
ndata = rxLoc.shape[0]
d_iter = 4
lrl = np.zeros(d_iter)
#%% Loop through decreasing meshes and measure the residual
# Create mesh using simpeg and write out in GIF format
for ii in range(d_iter):
nc = 3**(ii+1)
hxind = [(1./nc, nc)]
hyind = [(1./nc, nc)]
hzind = [(1./nc, nc)]
mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')
xn = mesh.vectorNx
yn = mesh.vectorNy
zn = mesh.vectorNz
mcell = mesh.nC
print 'Mesh size: ' + str(mcell)
sph_ind = PF.MagAnalytics.spheremodel(mesh, 0, 0, 0, R)
chibkg = 0.
chiblk = 0.01
model = np.ones(mcell)*chibkg
model[sph_ind] = chiblk
actv = np.ones(mcell)
#%% Forward mode ldata
d = PF.Magnetics.Intgrl_Fwr_Data(mesh,B,M,rxLoc,model,actv,'xyz')
fwr_x = d[0:ndata]
fwr_y = d[ndata:2*ndata]
fwr_z = d[2*ndata:]
#%% Get the analystical answer and compute the residual
bxa,bya,bza = PF.MagAnalytics.MagSphereAnaFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R,0.,0.,0.,chiblk, np.array(([0.,0.,B[2]])),'secondary')
Bd = (450.-float(B[1]))%360.
Bi = B[0]; # Convert dip to horizontal to cartesian
Bx = np.cos(np.deg2rad(Bi)) * np.cos(np.deg2rad(Bd)) * B[2]
By = np.cos(np.deg2rad(Bi)) * np.sin(np.deg2rad(Bd)) * B[2]
Bz = np.sin(np.deg2rad(Bi)) * B[2]
Bo = np.c_[Bx, By, Bz]
bxa,bya,bza = PF.MagAnalytics.MagSphereFreeSpace(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R,0.,0.,0.,chiblk, Bo)
#bxa,bya,bza = PF.MagAnalytics.MagSphereAnaFunA(rxLoc[:,0],rxLoc[:,1],rxLoc[:,2],R,0.,0.,0.,chiblk, np.array(([0.,0.,B[2]])),'secondary')
r_Bx = fwr_x - bxa
r_By = fwr_y - bya
r_Bz = fwr_z - bza
lrl[ii] = sum( r_Bx**2 + r_By**2 + r_Bz**2 ) **0.5
#%% Plot results
print 'Residual between analytical sphere and integral forward'
for ii in range(d_iter):
nc = 3**(ii+1)
print "||r||= " + str(lrl[ii]) + "\t dx= " + str(1./nc)
#%% Plot fields
plt.figure(1)
ax = plt.subplot(221)
plt.imshow(np.reshape(bxa,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(bxa,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(bxa,X.shape).T, s=20)
ax.set_title('Sphere Ana Bx')
ax = plt.subplot(222)
plt.imshow(np.reshape(bya,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(bya,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(bya,X.shape).T, s=20)
ax.set_title('Sphere Ana By')
ax = plt.subplot(212)
plt.imshow(np.reshape(bza,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(bza,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(bza,X.shape).T, s=20)
ax.set_title('Sphere Ana Bz')
#%% Plot the forward solution from integral
plt.figure(2)
ax = plt.subplot(221)
plt.imshow(np.reshape(fwr_x,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max() ], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(fwr_x,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(fwr_x,X.shape).T, s=20)
ax.set_title('Sphere Ana Bx')
ax = plt.subplot(222)
plt.imshow(np.reshape(fwr_y,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(fwr_y,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(fwr_y,X.shape).T, s=20)
ax.set_title('Sphere Ana By')
ax = plt.subplot(212)
plt.imshow(np.reshape(fwr_z,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(fwr_z,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(fwr_z,X.shape).T, s=20)
ax.set_title('Sphere Ana Bz')
#%% Plot foward data
plt.figure(3)
ax = plt.subplot(221)
plt.imshow(np.reshape(r_Bx,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(r_Bx,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(r_Bx,X.shape).T, s=20)
ax.set_title('Sphere Ana Bx')
ax = plt.subplot(222)
plt.imshow(np.reshape(r_By,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(r_By,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(r_By,X.shape).T, s=20)
ax.set_title('Sphere Ana By')
ax = plt.subplot(212)
plt.imshow(np.reshape(r_Bz,X.shape).T, interpolation="bicubic", extent=[xr.min(), xr.max(), yr.min(), yr.max()], origin = 'lower')
plt.colorbar(fraction=0.04)
plt.contour(X,Y, np.reshape(r_Bz,X.shape).T,10)
plt.scatter(X,Y, c=np.reshape(r_Bz,X.shape).T, s=20)
ax.set_title('Sphere Ana Bz')
plt.show()
simpegPF/Dev/Intgrl_MAG_Inv_Driver.py
+242
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#%%
from SimPEG import *
import simpegPF as PF
import pylab as plt
import os
#home_dir = 'C:\Users\dominiquef.MIRAGEOSCIENCE\Documents\GIT\SimPEG\simpegpf\simpegPF\Dev'
#home_dir = 'C:\\Users\\dominiquef.MIRAGEOSCIENCE\\ownCloud\\Research\\Modelling\\Synthetic\\Block_Gaussian_topo'
home_dir = '.\\'
inpfile = 'PYMAG3D_inv.inp'
dsep = '\\'
os.chdir(home_dir)
## New scripts to be added to basecode
#from fwr_MAG_data import fwr_MAG_data
#from read_MAGfwr_inp import read_MAGfwr_inp
#%%
# Read input file
[mshfile, obsfile, topofile, mstart, mref, magfile, wgtfile, chi, alphas, bounds, lpnorms] = PF.BaseMag.read_MAGinv_inp(home_dir + dsep + inpfile)
# Load mesh file
mesh = Mesh.TensorMesh.readUBC(mshfile)
#mesh = Utils.meshutils.readUBCTensorMesh(mshfile)
# Load in observation file
[B,M,dobs] = PF.BaseMag.readUBCmagObs(obsfile)
rxLoc = dobs[:,0:3]
d = dobs[:,3]
wd = dobs[:,4]
ndata = rxLoc.shape[0]
beta_in = 1e+2
# Load in topofile or create flat surface
if topofile == 'null':
# All active
actv = np.ones(mesh.nC)
else:
topo = np.genfromtxt(topofile,skip_header=1)
# Find the active cells
actv = PF.Magnetics.getActiveTopo(mesh,topo,'N')
nC = int(sum(actv))
# Load starting model file
if isinstance(mstart, float):
mstart = np.ones(nC) * mstart
else:
mstart = Utils.meshutils.readUBCTensorModel(mstart,mesh)
mstart = mstart[actv==1]
# Load reference file
if isinstance(mref, float):
mref = np.ones(nC) * mref
else:
mref = Utils.meshutils.readUBCTensorModel(mref,mesh)
mref = mref[actv==1]
# Get magnetization vector for MOF
if magfile=='DEFAULT':
M_xyz = PF.Magnetics.dipazm_2_xyz(np.ones(nC) * M[0], np.ones(nC) * M[1])
else:
M_xyz = np.genfromtxt(magfile,delimiter=' \n',dtype=np.str,comments='!')
# Get index of the center
midx = int(mesh.nCx/2)
midy = int(mesh.nCy/2)
# Create forward operator
F = PF.Magnetics.Intrgl_Fwr_Op(mesh,B,M_xyz,rxLoc,actv,'tmi')
# Get distance weighting function
wr = PF.Magnetics.get_dist_wgt(mesh,rxLoc,actv,3.,np.min(mesh.hx)/4)
wrMap = PF.BaseMag.WeightMap(mesh, wr)
wr_out = np.zeros(mesh.nC)
wr_out[actv==1] = wr
Mesh.TensorMesh.writeModelUBC(mesh,home_dir+dsep+'wr.dat',wr_out)
#Utils.meshutils.writeUBCTensorModel(home_dir+dsep+'wr.dat',mesh,wr_out)
# Write out the predicted
pred = F.dot(mstart)
PF.Magnetics.writeUBCobs(home_dir + dsep + 'Pred.dat',B,M,rxLoc,pred,wd)
#%%
plt.figure()
ax = plt.subplot()
mesh.plotSlice(wr_out, ax = ax, normal = 'Y', ind=midx )
plt.title('Distance weighting')
plt.xlabel('x');plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
#%% Plot obs data
PF.Magnetics.plot_obs_2D(rxLoc,d,wd,'Observed Data')
#%% Run inversion
prob = PF.Magnetics.MagneticIntegral(mesh, F)
prob.solverOpts['accuracyTol'] = 1e-4
survey = Survey.LinearSurvey()
survey.pair(prob)
#survey.makeSyntheticData(data, std=0.01)
survey.dobs=d
#survey.mtrue = model
reg = Regularization.Simple(mesh, mapping=wrMap)
reg.mref = mref
#reg.alpha_s = 1.
# Create pre-conditioner
diagA = np.sum(F**2.,axis=0) + beta_in*(reg.W.T*reg.W).diagonal()*(wr**2.0)
PC = Utils.sdiag(diagA**-1.)
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = wd
opt = Optimization.ProjectedGNCG(maxIter=10,lower=0.,upper=1.)
opt.approxHinv = PC
# opt = Optimization.InexactGaussNewton(maxIter=6)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = beta_in)
beta = Directives.BetaSchedule(coolingFactor=2, coolingRate=1)
#betaest = Directives.BetaEstimate_ByEig()
target = Directives.TargetMisfit()
inv = Inversion.BaseInversion(invProb, directiveList=[beta,target])
m0 = mstart
# Run inversion
mrec = inv.run(m0)
m_out = np.ones(mesh.nC)
m_out[actv==1] = mrec
# Write result
Mesh.TensorMesh.writeModelUBC(mesh,'SimPEG_inv_l2l2.sus',m_out)
#Utils.meshutils.writeUBCTensorModel(home_dir+dsep+'wr.dat',mesh,wr_out)
# Plot predicted
pred = F.dot(mrec)
#PF.Magnetics.plot_obs_2D(rxLoc,pred,wd,'Predicted Data')
#PF.Magnetics.plot_obs_2D(rxLoc,(d-pred),wd,'Residual Data')
print "Final misfit:" + str(np.sum( ((d-pred)/wd)**2. ) )
#%% Plot out a section of the model
yslice = midx-7
plt.figure()
ax = plt.subplot(221)
mesh.plotSlice(m_out, ax = ax, normal = 'Z', ind=-5, clim = (-mrec.min(), mrec.max()))
plt.plot(np.array([mesh.vectorCCx[0],mesh.vectorCCx[-1]]), np.array([mesh.vectorCCy[yslice],mesh.vectorCCy[yslice]]),c='w',linestyle = '--')
plt.title('Z Section')
plt.xlabel('x');plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
ax = plt.subplot(222)
mesh.plotSlice(m_out, ax = ax, normal = 'Z', ind=-1, clim = (-mrec.min(), mrec.max()))
plt.plot(np.array([mesh.vectorCCx[0],mesh.vectorCCx[-1]]), np.array([mesh.vectorCCy[yslice],mesh.vectorCCy[yslice]]),c='w',linestyle = '--')
plt.title('Top')
plt.xlabel('x');plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
ax = plt.subplot(212)
mesh.plotSlice(m_out, ax = ax, normal = 'Y', ind=yslice, clim = (-mrec.min(), mrec.max()))
plt.title('Cross Section')
plt.xlabel('x');plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
#%% Run one more round for sparsity
phim = invProb.phi_m_last
reg = Regularization.SparseRegularization(mesh, mapping=wrMap, eps=1e-4)
reg.m = mrec
reg.mref = mref
diagA = np.sum(F**2.,axis=0) + beta_in*(reg.W.T*reg.W).diagonal()*(wr**2.0)
PC = Utils.sdiag(diagA**-1.)
#reg.alpha_s = 1.
dmis = DataMisfit.l2_DataMisfit(survey)
dmis.Wd = wd
opt = Optimization.ProjectedGNCG(maxIter=8 ,maxIterLS=10, maxIterCG = 20,tolCG = 1e-4,lower=0.,upper=1.)
opt.approxHinv = PC
#opt.phim_last = reg.eval(mrec)
# opt = Optimization.InexactGaussNewton(maxIter=6)
invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta = invProb.beta)
beta = Directives.BetaSchedule(coolingFactor=1, coolingRate=1)
#betaest = Directives.BetaEstimate_ByEig()
target = Directives.TargetMisfit()
IRLS =Directives.update_IRLS( eps_min=1e-3, phi_m_last = phim )
inv = Inversion.BaseInversion(invProb, directiveList=[beta,IRLS])
m0 = mrec
# Run inversion
mrec = inv.run(m0)
m_out[actv==1] = mrec
Mesh.TensorMesh.writeModelUBC(mesh,'SimPEG_inv_l0l2.sus',m_out)
#%% Plot out a section of the model
yslice = midx-7
plt.figure()
ax = plt.subplot(221)
mesh.plotSlice(m_out, ax = ax, normal = 'Z', ind=-5, clim = (-mrec.min(), mrec.max()))
plt.plot(np.array([mesh.vectorCCx[0],mesh.vectorCCx[-1]]), np.array([mesh.vectorCCy[yslice],mesh.vectorCCy[yslice]]),c='w',linestyle = '--')
plt.title('Z Section')
plt.xlabel('x');plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
ax = plt.subplot(222)
mesh.plotSlice(m_out, ax = ax, normal = 'Z', ind=-1, clim = (-mrec.min(), mrec.max()))
plt.plot(np.array([mesh.vectorCCx[0],mesh.vectorCCx[-1]]), np.array([mesh.vectorCCy[yslice],mesh.vectorCCy[yslice]]),c='w',linestyle = '--')
plt.title('Top')
plt.xlabel('x');plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
ax = plt.subplot(212)
mesh.plotSlice(m_out, ax = ax, normal = 'Y', ind=yslice, clim = (-mrec.min(), mrec.max()))
plt.title('Cross Section')
plt.xlabel('x');plt.ylabel('z')
plt.gca().set_aspect('equal', adjustable='box')
simpegPF/Dev/MAG3Cfwr.inp
+5
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Mesh.msh ! Mesh file
Obs_loc.dat ! Obsfile
Model.dat ! Susceptibility model
null ! M_azm_dip.dat ! Magnetization model | null
null ! Topography file | null
simpegPF/Dev/MAG3Csen.inp
+5
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Mesh.msh ! Mesh file
Obs_loc.dat ! Obsfile
null ! Topofile | null
DISTANCE ! weighting flag DISTANCE | DEPTH
G ! Define output TxTyTz | G
simpegPF/Dev/MAG3Csen.log
+35
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MAG3Csen
Generates sparse matrices for magnetostatic forward modeling: Tx, Ty, Tz
Topographic model: nullcell.dat
DISTANCE | DEPTH weighting: wr.dat
Written by: Dominique Fournier
Last update: July 14th, 2014
INPUT FILES:
Mesh: Mesh.msh
Obsfile: Obs_loc.dat
Topography:
Weighting: DISTANCE
Computed 0 pct of data in 0.04128 sec
Computed 5 pct of data in 0.04634 sec
Computed 10 pct of data in 0.05386 sec
Computed 15 pct of data in 0.06035 sec
Computed 20 pct of data in 0.06507 sec
Computed 25 pct of data in 0.07160 sec
Computed 30 pct of data in 0.08211 sec
Computed 35 pct of data in 0.08901 sec
Computed 40 pct of data in 0.09365 sec
Computed 45 pct of data in 0.10179 sec
Computed 50 pct of data in 0.10963 sec
Computed 55 pct of data in 0.11704 sec
Computed 60 pct of data in 0.12449 sec
Computed 65 pct of data in 0.13205 sec
Computed 70 pct of data in 0.13838 sec
Computed 75 pct of data in 0.14311 sec
Computed 80 pct of data in 0.14761 sec
Computed 85 pct of data in 0.15447 sec
Computed 90 pct of data in 0.15941 sec
Computed 95 pct of data in 0.16424 sec
Computed 100 pct of data in 0.17136 sec
Sensitivity calculation completed in: 0.002860 min
simpegPF/Dev/MAG3D_inv.inp
+11
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Mesh.msh ! Mesh file
FWR_data.dat ! Obsfile
null ! Topofile
Model.dat ! Starting model
VALUE 0.0 ! Reference model
DEFAULT !..\AzmDip.dat ! Magnetization vector model
DEFAULT ! Cell based weight file
1 ! target chi factor | DEFAULT=1
1 1 1 1 ! alpha s, x ,y ,z
VALUE 0 1 ! Lower and Upper Bounds for p-component
VALUE 0 2 2 2 1 ! lp-norm for amplitude inversion FILE pqxqyqzr.dat ! Norms VALUE p, qx, qy, qz, r | FILE m-by-5 matrix
simpegPF/Dev/MagForward_Intergral.ipynb
+536
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Efficiency Warning: Interpolation will be slow, use setup.py!\n",
"\n",
" python setup.py build_ext --inplace\n",
" \n"
]
},
{
"ename": "SyntaxError",
"evalue": "'return' outside function (get_T_mat.py, line 131)",
"output_type": "error",
"traceback": [
"\u001b[1;36m File \u001b[1;32m\"get_T_mat.py\"\u001b[1;36m, line \u001b[1;32m131\u001b[0m\n\u001b[1;33m return Tx,Ty,Tz\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m 'return' outside function\n"
]
}
],
"source": [
"from SimPEG import *\n",
"import matplotlib.pyplot as plt\n",
"import simpegPF as PF\n",
"import matplotlib\n",
"#from get_UBC_mesh import get_UBC_mesh\n",
"from read_MAG_obs import read_MAG_obs\n",
"from get_T_mat import get_T_mat"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Writing magnetostatic problem with integral formulation\n",
"\n",
"## - Create tensor matrix TxTyTz"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step:1 Generating mesh and operators"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"#mesh = Utils.meshutils.readUBCTensorMesh(\"Tile1.msh\")\n",
"cs = 25.\n",
"hxind = [(cs,5,-1.3), (cs/2.0, 21),(cs,5,1.3)]\n",
"hyind = [(cs,5,-1.3), (cs/2.0, 21),(cs,5,1.3)]\n",
"hzind = [(cs,5,-1.3),(cs/2.0, 20)]\n",
"\n",
"mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')\n",
"\n",
"xn = mesh.vectorNx\n",
"yn = mesh.vectorNy\n",
"zn = mesh.vectorNz\n",
"\n",
"\n",
"mcell = (xn.size-1) * (yn.size-1) * (zn.size-1)\n",
"\n",
"N = mesh.gridN\n",
"\n",
"Utils.meshutils.writeUBCTensorMesh('Mesh.msh',mesh)\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"sph_ind = PF.MagAnalytics.spheremodel(mesh, 0, 0, 175, 50)\n",
"\n",
"Utils.meshutils.writeUBCTensorModel('Mesh.dat',mesh,sph_ind)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[[0 0 0]\n",
" [1 1 1]]\n"
]
}
],
"source": [
"# Load in obsfile\n",
"#Decl, Incl, B0, Mdec, Minc, obsx, obsy, obsz, data, unct = read_MAG_obs('Obs_RAW_REM_GRID_TMI.obs')\n",
"\n",
"Incl = 90.\n",
"Decl = 00.\n",
"B0 = 50000\n",
" \n",
"# Or create juste a plane grid\n",
"xr = np.linspace(-125, 125, 25)\n",
"yr = np.linspace(-125, 125, 25)\n",
"X, Y = np.meshgrid(xr, yr)\n",
"Z = np.ones((xr.size, yr.size))*280\n",
"rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]\n",
" \n",
"aa = np.array([[0,0,0],[0,0,0]])\n",
"\n",
"aa[1,0:3] = 1\n",
"print aa\n",
"ndata = rxLoc.shape[0]\n",
"\n",
"# Write obsfile in UBC format\n",
"with file('Obs_loc.dat','w') as fid:\n",
" fid.write('%6.2f %6.2f %6.2f\\n' %(Incl, Decl, B0) )\n",
" fid.write('%6.2f %6.2f %6.2f\\n' %(Incl, Decl, 1) ) \n",
" np.savetxt(fid, rxLoc, fmt='%-7.2f',delimiter=' ',newline='\\n')\n"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Create magnetization matrix\n",
"mx = np.cos(np.deg2rad(Incl)) * np.cos(np.deg2rad(Decl))\n",
"my = np.cos(np.deg2rad(Incl)) * np.sin(np.deg2rad(Decl))\n",
"mz = np.sin(np.deg2rad(Incl))"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"Mx = Utils.sdiag(np.ones([mcell])*mx*B0)\n",
"My = Utils.sdiag(np.ones([mcell])*my*B0)\n",
"Mz = Utils.sdiag(np.ones([mcell])*mz*B0)\n",
"\n",
"#matplotlib.pyplot.spy(scipy.sparse.csr_matrix(Mx))\n",
"#plt.show()\n",
"M = sp.vstack((Mx,My,Mz));\n"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "NameError",
"evalue": "name 'empty' is not defined",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mNameError\u001b[0m Traceback (most recent call last)",
"\u001b[1;32m<ipython-input-44-eff1564841a7>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m 1\u001b[0m \u001b[1;31m# Call the function to build tensor matrix\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 2\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 3\u001b[1;33m \u001b[0mTx\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mempty\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mndata\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mmcell\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 4\u001b[0m \u001b[0mTy\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mempty\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mndata\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mmcell\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 5\u001b[0m \u001b[0mTz\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mempty\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mndata\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0mmcell\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mdtype\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
"\u001b[1;31mNameError\u001b[0m: name 'empty' is not defined"
]
}
],
"source": [
"# Call the function to build tensor matrix\n",
"\n",
"Tx = empty([ndata,3*mcell], dtype=float)\n",
"Ty = empty([ndata,3*mcell], dtype=float)\n",
"Tz = empty([ndata,3*mcell], dtype=float)\n",
" \n",
"Tx, Ty, Tz = get_T_mat(xn,yn,zn,rxLoc)\n",
"\n",
"print Tx[0,0],Ty[0,0],Tz[0,0]\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For sparse matrix\n",
"b = A*x\n",
"\n",
"For dense matrix \n",
"b = A.dot(x)"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x = np.ones(10)\n",
"y = np.ones(10)*3"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"30.0"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x.dot(y)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"Gx = Tx*M"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"cs = 25.\n",
"hxind = [(cs,5,-1.3), (cs/2.0, 41),(cs,5,1.3)]\n",
"hyind = [(cs,5,-1.3), (cs/2.0, 41),(cs,5,1.3)]\n",
"hzind = [(cs,5,-1.3), (cs/2.0, 40),(cs,5,1.3)]\n",
"M3 = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step4: Compute analytic function (sphere in whole space)\n",
"Outside of the sphere $(r>R)$\n",
"\n",
"$$\\mathbf{H}_1 = H_0 \\hat{x} + H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}[(2x^2-y^2-z^2)\\hat{x}+(3xy)\\hat{y}+(3xz)\\hat{z}]$$\n",
"\n",
"$$H_{x1} = H_0 + H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(2x^2-y^2-z^2)$$\n",
"\n",
"$$H_{y1} = H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(3xy)$$\n",
"\n",
"$$H_{z1} = H_0\\frac{R}{r^5}\\frac{\\mu_2-\\mu_1}{\\mu_2+2\\mu_1}(3xz)$$\n",
"\n",
"Inside of the sphere $(r\\le R)$\n",
"\n",
"$$\\mathbf{H}_2 = H_0\\frac{3\\mu_1}{\\mu_2+2\\mu_1}\\hat{x}$$\n",
"\n",
"$$H_{x2} = H_0\\frac{3\\mu_1}{\\mu_2+2\\mu_1}$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Step5: Projection to receiver plane"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"rxLoc = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)]\n",
"Qfx = M3.getInterpolationMat(rxLoc,'Fx')\n",
"Qfy = M3.getInterpolationMat(rxLoc,'Fy')\n",
"Qfz = M3.getInterpolationMat(rxLoc,'Fz')"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"100.0 kang\n"
]
}
],
"source": [
"Bxr = np.reshape(Qfx*B, (size(xr), size(yr)), order='F')\n",
"Byr = np.reshape(Qfy*B, (size(xr), size(yr)), order='F')\n",
"Bzr = np.reshape(Qfz*B, (size(xr), size(yr)), order='F')\n",
"H0 = Box/mu0\n",
"flag = 'secondary'\n",
"if flag=='secondary':\n",
" Bxr = Bxr-Box\n",
"\n",
"# Bxra, Byra, Bzra = MagSphereAnalFun(X, Y, Z, 100, 0., 0., 0., mu0, mu0*(1+chiblk), H0, flag)\n",
"Bxra, Byra, Bzra = MagSphereAnalFunA(X, Y, Z, 100., 0., 0., 0., chiblk, np.array([1., 0., 0.]), flag)\n",
"\n",
"Bxra = np.reshape(Bxra, (size(xr), size(yr)), order='F')\n",
"Byra = np.reshape(Byra, (size(xr), size(yr)), order='F')\n",
"Bzra = np.reshape(Bzra, (size(xr), size(yr)), order='F')"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0xa11f550>]"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x1826c630>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"figsize(10, 4)\n",
"plot(Utils.mkvc(Bxra))\n",
"plot(Utils.mkvc(Bxr), 'k:')\n",
"plot(Utils.mkvc(Byra))\n",
"plot(Utils.mkvc(Byr), 'k:')\n",
"plot(Utils.mkvc(Bzra))\n",
"plot(Utils.mkvc(Bzr), 'k:')"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.colorbar.Colorbar instance at 0x000000001244C608>"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x12fb62e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = subplots(3,2, figsize = (10,15))\n",
"dat1 = ax[0,0].imshow(Bxr); fig.colorbar(dat1, ax=ax[0,0])\n",
"dat2 = ax[0,1].imshow(Bxra); fig.colorbar(dat2, ax=ax[0,1])\n",
"dat3 = ax[1,0].imshow(Byr); fig.colorbar(dat3, ax=ax[1,0])\n",
"dat4 = ax[1,1].imshow(Byra); fig.colorbar(dat4, ax=ax[1,1])\n",
"dat5 = ax[2,0].imshow(Bzr); fig.colorbar(dat5, ax=ax[2,0])\n",
"dat6 = ax[2,1].imshow(Bzra); fig.colorbar(dat6, ax=ax[2,1])"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-285. -285. -285. -285. -285. -285. -285. -285. -285. -285. -285. -285.\n",
" -285. -285. -285. -285. -285. -285. -285. -285. -285. -285. -285. -285.\n",
" -285. -285. -285. -285. -285. -285. -285. -285. -285. -285. -285. -285.\n",
" -285. -285. -285. -285. -285.]\n"
]
},
{
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0xaa70e80>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"id = 21\n",
"fig, axes = subplots(1,3, figsize=(14,5))\n",
"epsx = np.linalg.norm(Utils.mkvc(Bxr))*1e-6\n",
"epsy = np.linalg.norm(Utils.mkvc(Byr))*1e-6\n",
"epsz = np.linalg.norm(Utils.mkvc(Bzr))*1e-6\n",
"axes[0].plot(Y[:,id], Bxra[:,id], 'b', Y[:,id], Bxr[:,id], 'r.')\n",
"axes[1].plot(Y[:,id], Byra[:,id], 'b', Y[:,id], Byr[:,id], 'r.')\n",
"axes[2].plot(Y[:,id], Bzra[:,id], 'b', Y[:,id], Bzr[:,id], 'r.')\n",
"print X[:,1]"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x139014e0>]"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x12897198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, axes = subplots(1,3, figsize=(14,5))\n",
"epsx = np.linalg.norm(Utils.mkvc(Bxr))*1e-6\n",
"epsy = np.linalg.norm(Utils.mkvc(Byr))*1e-6\n",
"epsz = np.linalg.norm(Utils.mkvc(Bzr))*1e-6\n",
"axes[0].plot(Y[:,1], abs((Bxr[:,1]-Bxra[:,1])/(Bxra[:,1]+epsx)), 'r.')\n",
"axes[1].plot(Y[:,1], abs((Byr[:,1]-Byra[:,1])/(Byra[:,1]+epsy)), 'r.')\n",
"axes[2].plot(Y[:,1], abs((Bzr[:,1]-Bzra[:,1])/(Bzra[:,1]+epsz)), 'r.')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Thoughts\n",
"\n",
"- It works well with non-uniform mesh!!\n",
"- Actual accuray is ~10% relative error in secondary fields. As we pad more we can get better accuracy, since we did not consider secondary field at the boudnary ($\\partial\\Omega$). \n",
"- Here, we can try primary secondary field approach to get better accuracy. \n",
"- In addition, we can use the congruous sphere method to handle this secondary fields at boundaries"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
simpegPF/Dev/Mesh.msh
+5
View File
@@ -0,0 +1,5 @@
20 20 20
-0.50 -0.50 0.50
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
simpegPF/Dev/Mesh_40m.msh
+5
View File
@@ -0,0 +1,5 @@
38 31 12
421780.00 544950.00 1600.00
151.00 108.00 77.00 55.00 30*40.00 55.00 77.00 108.00 151.00
151.00 108.00 77.00 55.00 23*40.00 55.00 77.00 108.00 151.00
12*40.00
simpegPF/Dev/Model.dat
+8000
View File
File diff suppressed because it is too large. Load diff
simpegPF/Dev/Obs_IND_GRID_TMI.obs
+345
View File
@@ -0,0 +1,345 @@
90.00 0.00 50000.00
90.00 0.00 1.00
342
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4.22510000e+05 5.45450000e+05 1.62000000e+03 -3.74409264e+00 1.00000000e+00
4.22630000e+05 5.45450000e+05 1.62000000e+03 -6.97509886e+00 1.00000000e+00
4.22750000e+05 5.45450000e+05 1.62000000e+03 -4.20768955e+00 1.00000000e+00
4.22870000e+05 5.45450000e+05 1.62000000e+03 -5.10228750e+00 1.00000000e+00
4.22990000e+05 5.45450000e+05 1.62000000e+03 -6.05608453e+00 1.00000000e+00
4.23110000e+05 5.45450000e+05 1.62000000e+03 -1.66763425e+00 1.00000000e+00
4.23230000e+05 5.45450000e+05 1.62000000e+03 2.89389762e+00 1.00000000e+00
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4.23110000e+05 5.45650000e+05 1.62000000e+03 3.43616857e+01 1.00000000e+00
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simpegPF/Dev/PYMAG3D_inv.inp
+11
View File
@@ -0,0 +1,11 @@
Mesh_40m.msh ! Mesh file
Obs_IND_GRID_TMI.obs ! Obsfile
null ! Topofile | null
VALUE 1e-4 ! Starting model
VALUE 0 ! Reference model
DEFAULT !..\AzmDip.dat ! Magnetization vector model
DEFAULT ! Cell based weight file
1 ! target chi factor | DEFAULT=1
1 1 1 1 ! alpha s, x ,y ,z
VALUE 0 1 ! Lower and Upper Bounds for p-component
VALUE 0 2 2 2 1 ! lp-norm for amplitude inversion FILE pqxqyqzr.dat ! Norms VALUE p, qx, qy, qz, r | FILE m-by-5 matrix
simpegPF/Dev/Pred.dat
+345
View File
@@ -0,0 +1,345 @@
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simpegPF/Dev/SimPEG_inv.sus
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simpegPF/Dev/SimPEG_inv_l0l2.sus
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simpegPF/Dev/SimPEG_inv_l2l2.sus
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simpegPF/Dev/Tile1.msh
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66 52 24
421780 544950 1600
151.00 108.00 77.00 55.00 40.00 28.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 28.00 40.00 55.00 77.00 108.00 151.00
151.00 108.00 77.00 55.00 40.00 28.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 28.00 40.00 55.00 77.00 108.00 151.00
20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 20.00 28.00 39.00 55.00 75.00 105.00 130.00
simpegPF/Dev/magfor3d.log
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Parallelized with OpenMP. # of threads: 4
MAG3D - Version 5.0 : MAGFOR3D
Developed by University of British Columbia
Geophysical Inversion Facility (UBC-GIF)
(C) Copyright 1992 - 2013, UBC-GIF,
Department of Earth and Ocean Sciences, UBC
http://gif.eos.ubc.ca/
This program is licensed to:
For internal use within UBC-GIF.
MAGFOR3D started on: 12/21/2015 08:35:38
magfor3d Mesh.msh Obs_loc.dat Model.dat
# of surface data: 625
# of borehole data: 0
model was read from file: Model.dat
TOTAL cpu time: 0:00:00.16
MAGFOR3D ended on: 12/21/2015 08:35:39
simpegPF/Dev/magfor3d.mag
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45.00 315.00 50000.00 !! incl, decl, geomag
-45.00 135.00 1 !! aincl, adecl, idir
625 !! # of data
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simpegPF/notebooks/model.png → simpegPF/Dev/model.png
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simpegPF/Dev/nullcell.dat
+27
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@@ -0,0 +1,27 @@
1.0000000e+00
1.0000000e+00
1.0000000e+00
1.0000000e+00
1.0000000e+00
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1.0000000e+00
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1.0000000e+00
1.0000000e+00
1.0000000e+00
1.0000000e+00
1.0000000e+00
1.0000000e+00
simpegPF/notebooks/obspred.png → simpegPF/Dev/obspred.png
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File renamed without changes.
simpegPF/Dev/test.out
+3
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@@ -0,0 +1,3 @@
0.000000000000000000e+00 1.000000000000000000e+00 2.000000000000000000e+00 3.000000000000000000e+00 4.000000000000000000e+00
0.000000000000000000e+00 1.000000000000000000e+00 2.000000000000000000e+00 3.000000000000000000e+00 4.000000000000000000e+00
0.000000000000000000e+00 1.000000000000000000e+00 2.000000000000000000e+00 3.000000000000000000e+00 4.000000000000000000e+00
simpegPF/Dev/wr.dat
+14136
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File diff suppressed because it is too large. Load diff
simpegPF/MagAnalytics.py
+56 -7
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@@ -15,11 +15,11 @@ def spheremodel(mesh, x0, y0, z0, r):
def MagSphereAnaFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
def MagSphereAnaFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag='total'):
"""
test
Analytic function for Magnetics problem. The set up here is
magnetic sphere in whole-space.
magnetic sphere in whole-space assuming that the inducing field is oriented in the x-direction.
* (x0,y0,z0)
* (x0, y0, z0 ): is the center location of sphere
@@ -31,6 +31,8 @@ def MagSphereAnaFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
"""
print H0
if (~np.size(x)==np.size(y)==np.size(z)):
print "Specify same size of x, y, z"
return
@@ -47,7 +49,7 @@ def MagSphereAnaFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
# Inside of the sphere
rf2 = 3*mu1/(mu2+2*mu1)
if (flag == 'total'):
if flag is 'total' and any(ind):
Bx[ind] = mu2*H0*(rf2)
elif (flag == 'secondary'):
Bx[ind] = mu2*H0*(rf2)-mu1*H0
@@ -57,12 +59,12 @@ def MagSphereAnaFun(x, y, z, R, x0, y0, z0, mu1, mu2, H0, flag):
# Outside of the sphere
rf1 = (mu2-mu1)/(mu2+2*mu1)
if (flag == 'total'):
Bx[~ind] = mu1*(H0+H0/r[~ind]**5*(R**3)*rf1*(2*x[~ind]**2-y[~ind]**2-z[~ind]**2))
Bx[~ind] = mu1*(H0+H0/r[~ind]**5*(R**3)*rf1*(2*(x[~ind]-x0)**2-(y[~ind]-y0)**2-(z[~ind]-z0)**2))
elif (flag == 'secondary'):
Bx[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(2*x[~ind]**2-y[~ind]**2-z[~ind]**2))
Bx[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(2*(x[~ind]-x0)**2-(y[~ind]-y0)**2-(z[~ind]-z0)**2))
By[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*x[~ind]*y[~ind]))
Bz[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*x[~ind]*z[~ind]))
By[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*(x[~ind]-x0)*(y[~ind]-y0)))
Bz[~ind] = mu1*(H0/r[~ind]**5*(R**3)*rf1*(3*(x[~ind]-x0)*(z[~ind]-z0)))
return np.reshape(Bx, x.shape, order='F'), np.reshape(By, x.shape, order='F'), np.reshape(Bz, x.shape, order='F')
@@ -190,6 +192,53 @@ def IDTtoxyz(Inc, Dec, Btot):
return np.r_[Bx, By, Bz]
def MagSphereFreeSpace(x, y, z, R, xc, yc, zc, chi, Bo):
"""
Computing boundary condition using Congrous sphere method.
This is designed for secondary field formulation.
>> Input
mesh: Mesh class
Bo: np.array([Box, Boy, Boz]): Primary magnetic flux
Chi: susceptibility at cell volume
.. math::
\\vec{B}(r) = \\frac{\mu_0}{4\pi}\\frac{m}{\| \\vec{r}-\\vec{r}_0\|^3}[3\hat{m}\cdot\hat{r}-\hat{m}]
"""
if (~np.size(x)==np.size(y)==np.size(z)):
print "Specify same size of x, y, z"
return
x = Utils.mkvc(x)
y = Utils.mkvc(y)
z = Utils.mkvc(z)
nobs = len(x)
Bot = np.sqrt(sum(Bo**2))
mx = np.ones([nobs]) * Bo[0,0] * R**3 / 3. * chi
my = np.ones([nobs]) * Bo[0,1] * R**3 / 3. * chi
mz = np.ones([nobs]) * Bo[0,2] * R**3 / 3. * chi
M = np.c_[mx, my, mz]
rx = (x - xc)
ry = (y - yc)
rz = (zc - z)
rvec = np.c_[rx, ry, rz]
r = np.sqrt((rx)**2+(ry)**2+(rz)**2 )
B = -Utils.sdiag(1./r**3)*M + Utils.sdiag((3 * np.sum(M*rvec,axis=1))/r**5)*rvec
Bx = B[:,0]
By = B[:,1]
Bz = B[:,2]
return Bx, By, Bz
if __name__ == '__main__':
hxind = [(0,25,1.3),(21, 12.5),(0,25,1.3)]
simpegPF/MagSurveyIE.py
+18
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@@ -0,0 +1,18 @@
from BaseMag import BaseMagSurvey
class MagSurveyIE(BaseMagSurvey):
"""Base Magnetics Survey"""
rxLoc = None #: receiver locations
rxType = None #: receiver type
def __init__(self, **kwargs):
Survey.BaseSurvey.__init__(self, **kwargs)
def setBackgroundField(self, Inc, Dec, Btot):
Bx = Btot*np.cos(Inc/180.*np.pi)*np.sin(Dec/180.*np.pi)
By = Btot*np.cos(Inc/180.*np.pi)*np.cos(Dec/180.*np.pi)
Bz = -Btot*np.sin(Inc/180.*np.pi)
self.B0 = np.r_[Bx,By,Bz]
simpegPF/Magnetics.py
+639 -3
View File
@@ -3,6 +3,25 @@ import BaseMag
from scipy.constants import mu_0
from MagAnalytics import spheremodel, CongruousMagBC
class MagneticIntegral(Problem.BaseProblem):
surveyPair = Survey.LinearSurvey
def __init__(self, mesh, G, mapping=None, **kwargs):
Problem.BaseProblem.__init__(self, mesh, mapping=mapping, **kwargs)
self.G = G
def fields(self, m):
return self.G.dot(self.mapping*(m))
def Jvec(self, m, v, u=None):
dmudm = self.mapping.deriv(m)
return self.G.dot(dmudm*v)
def Jtvec(self, m, v, u=None):
dmudm = self.mapping.deriv(m)
return dmudm.T * (self.G.T.dot(v))
class MagneticsDiffSecondary(Problem.BaseProblem):
@@ -55,7 +74,7 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
.. math ::
\mathbf{rhs} = \Div(\MfMui)^{-1}\mathbf{M}^f_{\mu_0^{-1}}\mathbf{B}_0 - \Div\mathbf{B}_0+\diag(v)\mathbf{D} \mathbf{P}_{out}^T \mathbf{B}_{sBC}
"""
B0 = self.getB0()
Dface = self.mesh.faceDiv
@@ -64,13 +83,13 @@ class MagneticsDiffSecondary(Problem.BaseProblem):
mu = self.mapping*m
chi = mu/mu_0-1
#temporary fix
Bbc, Bbc_const = CongruousMagBC(self.mesh, self.survey.B0, chi)
self.Bbc = Bbc
self.Bbc_const = Bbc_const
# return self._Div*self.MfMuI*self.MfMu0*B0 - self._Div*B0 + Mc*Dface*self._Pout.T*Bbc
return self._Div*self.MfMuI*self.MfMu0*B0 - self._Div*B0
return self._Div*self.MfMuI*self.MfMu0*B0 - self._Div*B0
def getA(self, m):
"""
@@ -405,11 +424,628 @@ if __name__ == '__main__':
# plt.show()
def Intgrl_Fwr_Data(mesh,B,M,rxLoc,model,actv,flag):
"""
Forward model magnetic data using integral equation
INPUT:
mesh = SimPEG.TensorMesh
B = Inducing field parameter [Binc, Bdecl, B0]
M = Magnetization matrix [Minc, Mdecl] -90:90, 0:360
rxLox = Observation location informat [obsx, obsy, obsz]
model = Model associated with mesh
actv = Active cells from topo (from getActiveTopo)
flag = Data type "tmi" | "xyz"
OUTPUT:
dobs =Observation array in format [obsx, obsy, obsz, data]
Created on Oct 7, 2015
@author: dominiquef
"""
if actv.dtype=='bool':
inds = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype = int) - 1
else:
inds = actv
nC = len(inds)
P = sp.csr_matrix((np.ones(nC),(inds, range(nC))), shape=(mesh.nC, nC))
xn = mesh.vectorNx;
yn = mesh.vectorNy;
zn = mesh.vectorNz;
yn2,xn2,zn2 = np.meshgrid(yn[1:], xn[1:], zn[1:])
yn1,xn1,zn1 = np.meshgrid(yn[0:-1], xn[0:-1], zn[0:-1])
Yn = P.T*np.c_[mkvc(yn1), mkvc(yn2)]
Xn = P.T*np.c_[mkvc(xn1), mkvc(xn2)]
Zn = P.T*np.c_[mkvc(zn1), mkvc(zn2)]
nC = len(inds)
ndata = rxLoc.shape[0]
# Convert declination from north to cartesian
Md = (450.-float(M[1]))%360.
# Create magnetization matrix
mx = np.cos(np.deg2rad(M[0])) * np.cos(np.deg2rad(Md))
my = np.cos(np.deg2rad(M[0])) * np.sin(np.deg2rad(Md))
mz = np.sin(np.deg2rad(M[0]))
Mx = Utils.sdiag(np.ones([nC])*mx*B[2])
My = Utils.sdiag(np.ones([nC])*my*B[2])
Mz = Utils.sdiag(np.ones([nC])*mz*B[2])
#matplotlib.pyplot.spy(scipy.sparse.csr_matrix(Mx))
#plt.show()
Mxyz = sp.vstack((Mx,My,Mz));
#%% Create TMI projector
# Convert Bdecination from north to cartesian
D = (450.-float(B[1]))%360.
if flag=='tmi':
Ptmi = mkvc(np.r_[np.cos(np.deg2rad(B[0]))*np.cos(np.deg2rad(D)),np.cos(np.deg2rad(B[0]))*np.sin(np.deg2rad(D)),np.sin(np.deg2rad(B[0]))],2).T;
d = np.zeros(ndata)
elif flag=='xyz':
d = np.zeros(int(3*ndata))
# Loop through all observations and create forward operator (ndata-by-nC)
print "Begin forward modeling " +str(int(ndata)) + " data points..."
# Add counter to dsiplay progress.
count = -1
for ii in range(ndata):
tx, ty, tz = get_T_mat(Xn,Yn,Zn,rxLoc[ii,:])
Gxyz = np.vstack((tx,ty,tz))*Mxyz
# Remove non-active cells
if flag=='xyz':
d[ii::ndata] = mkvc(Gxyz.dot(P.T*model))
elif flag=='tmi':
d[ii] = Ptmi.dot(Gxyz.dot(P.T*model))
# Display progress
count = progress(ii,count,ndata)
print "Done 100% ...forward modeling completed!!\n"
return d
def Intrgl_Fwr_Op(mesh,B,M,rxLoc,actv,flag):
"""
Magnetic forward operator in integral form
INPUT:
mesh = Mesh in SimPEG format
B = Inducing field parameter [Binc, Bdecl, B0]
M = Magnetization information
[OPTIONS]
1- [Minc, Mdecl] : Assumes uniform magnetization orientation
2- [mx1,mx2,..., my1,...,mz1] : cell-based defined magnetization direction
3- diag(M): Block diagonal matrix with [Mx, My, Mz] along the diagonal
rxLox = Observation location informat [obsx, obsy, obsz]
flag = 'tmi' | 'xyz' | 'full'
[OPTIONS]
1- tmi : Magnetization direction used and data are projected onto the
inducing field direction F.shape([ndata, nc])
2- xyz : Magnetization direction used and data are given in 3-components
F.shape([3*ndata, nc])
3- full: Full tensor matrix stored with shape([3*ndata, 3*nc])
OUTPUT:
F = Linear forward modeling operation
Created on Dec, 20th 2015
@author: dominiquef
"""
# Find non-zero cells
#inds = np.nonzero(actv)[0]
if actv.dtype=='bool':
inds = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype = int) - 1
else:
inds = actv
nC = len(inds)
# Create active cell projector
P = sp.csr_matrix((np.ones(nC),(inds, range(nC))),
shape=(mesh.nC, nC))
# Create vectors of nodal location (lower and upper coners for each cell)
xn = mesh.vectorNx;
yn = mesh.vectorNy;
zn = mesh.vectorNz;
yn2,xn2,zn2 = np.meshgrid(yn[1:], xn[1:], zn[1:])
yn1,xn1,zn1 = np.meshgrid(yn[0:-1], xn[0:-1], zn[0:-1])
Yn = P.T*np.c_[mkvc(yn1), mkvc(yn2)]
Xn = P.T*np.c_[mkvc(xn1), mkvc(xn2)]
Zn = P.T*np.c_[mkvc(zn1), mkvc(zn2)]
ndata = rxLoc.shape[0]
# Convert Bdecination from north to cartesian
D = (450.-float(B[1]))%360.
# Pre-allocate space and create magnetization matrix if required
if (flag=='tmi') | (flag == 'xyz'):
# If assumes uniform magnetization direction
if M.shape != (nC,3):
print 'Magnetization vector must be Nc x 3'
return
Mx = Utils.sdiag(M[:,0]*B[2])
My = Utils.sdiag(M[:,1]*B[2])
Mz = Utils.sdiag(M[:,2]*B[2])
Mxyz = sp.vstack((Mx,My,Mz))
if flag == 'tmi':
F = np.zeros((ndata, nC))
# Projection matrix
Ptmi = mkvc(np.r_[np.cos(np.deg2rad(B[0]))*np.cos(np.deg2rad(D)),
np.cos(np.deg2rad(B[0]))*np.sin(np.deg2rad(D)),
np.sin(np.deg2rad(B[0]))],2).T;
elif flag == 'xyz':
F = np.zeros((int(3*ndata), nC))
elif flag == 'full':
F = np.zeros((int(3*ndata), int(3*nC)))
else:
print """Flag must be either 'tmi' | 'xyz' | 'full', please revised"""
return
# Loop through all observations and create forward operator (ndata-by-nC)
print "Begin calculation of forward operator: " + flag
# Add counter to dsiplay progress. Good for large problems
count = -1;
for ii in range(ndata):
tx, ty, tz = get_T_mat(Xn,Yn,Zn,rxLoc[ii,:])
if flag=='tmi':
F[ii,:] = Ptmi.dot(np.vstack((tx,ty,tz)))*Mxyz
elif flag == 'xyz':
F[ii,:] = tx*Mxyz
F[ii+ndata,:] = ty*Mxyz
F[ii+2*ndata,:] = tz*Mxyz
elif flag == 'full':
F[ii,:] = tx
F[ii+ndata,:] = ty
F[ii+2*ndata,:] = tz
# Display progress
count = progress(ii,count,ndata)
print "Done 100% ...forward operator completed!!\n"
return F
def get_T_mat(Xn,Yn,Zn,rxLoc):
"""
Load in the active nodes of a tensor mesh and computes the magnetic tensor
for a given observation location rxLoc[obsx, obsy, obsz]
INPUT:
Xn, Yn, Zn: Node location matrix for the lower and upper most corners of
all cells in the mesh shape[nC,2]
M
OUTPUT:
Tx = [Txx Txy Txz]
Ty = [Tyx Tyy Tyz]
Tz = [Tzx Tzy Tzz]
where each elements have dimension 1-by-nC.
Only the upper half 5 elements have to be computed since symetric.
Currently done as for-loops but will eventually be changed to vector
indexing, once the topography has been figured out.
Created on Oct, 20th 2015
@author: dominiquef
"""
eps = 1e-10 # add a small value to the locations to avoid /0
nC = Xn.shape[0]
# Pre-allocate space for 1D array
Tx = np.zeros((1,3*nC))
Ty = np.zeros((1,3*nC))
Tz = np.zeros((1,3*nC))
dz2 = rxLoc[2] - Zn[:,0] + eps
dz1 = rxLoc[2] - Zn[:,1] + eps
dy2 = Yn[:,1] - rxLoc[1] + eps
dy1 = Yn[:,0] - rxLoc[1] + eps
dx2 = Xn[:,1] - rxLoc[0] + eps
dx1 = Xn[:,0] - rxLoc[0] + eps
R1 = ( dy2**2 + dx2**2 )
R2 = ( dy2**2 + dx1**2 )
R3 = ( dy1**2 + dx2**2 )
R4 = ( dy1**2 + dx1**2 )
arg1 = np.sqrt( dz2**2 + R2 )
arg2 = np.sqrt( dz2**2 + R1 )
arg3 = np.sqrt( dz1**2 + R1 )
arg4 = np.sqrt( dz1**2 + R2 )
arg5 = np.sqrt( dz2**2 + R3 )
arg6 = np.sqrt( dz2**2 + R4 )
arg7 = np.sqrt( dz1**2 + R4 )
arg8 = np.sqrt( dz1**2 + R3 )
Tx[0,0:nC] = np.arctan2( dy1 * dz2 , ( dx2 * arg5 ) ) +\
- np.arctan2( dy2 * dz2 , ( dx2 * arg2 ) ) +\
np.arctan2( dy2 * dz1 , ( dx2 * arg3 ) ) +\
- np.arctan2( dy1 * dz1 , ( dx2 * arg8 ) ) +\
np.arctan2( dy2 * dz2 , ( dx1 * arg1 ) ) +\
- np.arctan2( dy1 * dz2 , ( dx1 * arg6 ) ) +\
np.arctan2( dy1 * dz1 , ( dx1 * arg7 ) ) +\
- np.arctan2( dy2 * dz1 , ( dx1 * arg4 ) );
Ty[0,0:nC] = np.log( ( dz2 + arg2 ) / (dz1 + arg3 ) ) +\
-np.log( ( dz2 + arg1 ) / (dz1 + arg4 ) ) +\
np.log( ( dz2 + arg6 ) / (dz1 + arg7 ) ) +\
-np.log( ( dz2 + arg5 ) / (dz1 + arg8 ) );
Ty[0,nC:2*nC] = np.arctan2( dx1 * dz2 , ( dy2 * arg1 ) ) +\
- np.arctan2( dx2 * dz2 , ( dy2 * arg2 ) ) +\
np.arctan2( dx2 * dz1 , ( dy2 * arg3 ) ) +\
- np.arctan2( dx1 * dz1 , ( dy2 * arg4 ) ) +\
np.arctan2( dx2 * dz2 , ( dy1 * arg5 ) ) +\
- np.arctan2( dx1 * dz2 , ( dy1 * arg6 ) ) +\
np.arctan2( dx1 * dz1 , ( dy1 * arg7 ) ) +\
- np.arctan2( dx2 * dz1 , ( dy1 * arg8 ) );
R1 = (dy2**2 + dz1**2);
R2 = (dy2**2 + dz2**2);
R3 = (dy1**2 + dz1**2);
R4 = (dy1**2 + dz2**2);
Ty[0,2*nC:] = np.log( ( dx1 + np.sqrt( dx1**2 + R1 ) ) / (dx2 + np.sqrt( dx2**2 + R1 ) ) ) +\
-np.log( ( dx1 + np.sqrt( dx1**2 + R2 ) ) / (dx2 + np.sqrt( dx2**2 + R2 ) ) ) +\
np.log( ( dx1 + np.sqrt( dx1**2 + R4 ) ) / (dx2 + np.sqrt( dx2**2 + R4 ) ) ) +\
-np.log( ( dx1 + np.sqrt( dx1**2 + R3 ) ) / (dx2 + np.sqrt( dx2**2 + R3 ) ) );
R1 = (dx2**2 + dz1**2);
R2 = (dx2**2 + dz2**2);
R3 = (dx1**2 + dz1**2);
R4 = (dx1**2 + dz2**2);
Tx[0,2*nC:] = np.log( ( dy1 + np.sqrt( dy1**2 + R1 ) ) / (dy2 + np.sqrt( dy2**2 + R1 ) ) ) +\
-np.log( ( dy1 + np.sqrt( dy1**2 + R2 ) ) / (dy2 + np.sqrt( dy2**2 + R2 ) ) ) +\
np.log( ( dy1 + np.sqrt( dy1**2 + R4 ) ) / (dy2 + np.sqrt( dy2**2 + R4 ) ) ) +\
-np.log( ( dy1 + np.sqrt( dy1**2 + R3 ) ) / (dy2 + np.sqrt( dy2**2 + R3 ) ) );
Tz[0,2*nC:] = -( Ty[0,nC:2*nC] + Tx[0,0:nC] );
Tz[0,nC:2*nC] = Ty[0,2*nC:];
Tx[0,nC:2*nC] = Ty[0,0:nC];
Tz[0,0:nC] = Tx[0,2*nC:];
Tx = Tx/(4*np.pi);
Ty = Ty/(4*np.pi);
Tz = Tz/(4*np.pi);
return Tx,Ty,Tz
def progress(iter,prog,final):
"""
progress(iter,prog,final)
Function measuring the progress of a process and print to screen the %.
Useful to estimate the remaining runtime of a large problem.
Created on Dec, 20th 2015
@author: dominiquef
"""
arg = np.floor(float(iter)/float(final)*10.);
if arg > prog:
strg = "Done " + str(arg*10) + " %"
print strg
prog = arg;
return prog
def dipazm_2_xyz(dip,azm_N):
"""
dipazm_2_xyz(dip,azm_N)
Function converting degree angles for dip and azimuth from north to a
3-components in cartesian coordinates.
INPUT
dip : Value or vector of dip from horizontal in DEGREE
azm_N : Value or vector of azimuth from north in DEGREE
OUTPUT
M : [n-by-3] Array of xyz components of a unit vector in cartesian
Created on Dec, 20th 2015
@author: dominiquef
"""
nC = len(azm_N)
M = np.zeros((nC,3))
# Modify azimuth from North to Cartesian-X
azm_X = (450.- azm_N) % 360.
D = np.deg2rad(dip)
I = np.deg2rad(azm_X)
M[:,0] = np.cos(D) * np.cos(I) ;
M[:,1] = np.cos(D) * np.sin(I) ;
M[:,2] = np.sin(D) ;
return M
def get_dist_wgt(mesh,rxLoc,actv,R,R0):
"""
get_dist_wgt(xn,yn,zn,rxLoc,R,R0)
Function creating a distance weighting function required for the magnetic
inverse problem.
INPUT
xn, yn, zn : Node location
rxLoc : Observation locations [obsx, obsy, obsz]
actv : Active cell vector [0:air , 1: ground]
R : Decay factor (mag=3, grav =2)
R0 : Small factor added (default=dx/4)
OUTPUT
wr : [nC] Vector of distance weighting
Created on Dec, 20th 2015
@author: dominiquef
"""
# Find non-zero cells
if actv.dtype=='bool':
inds = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype=int) - 1
else:
inds = actv
nC = len(inds)
# Create active cell projector
P = sp.csr_matrix((np.ones(nC),(inds, range(nC))),
shape=(mesh.nC, nC))
# Geometrical constant
p = 1/np.sqrt(3);
# Create cell center location
Ym,Xm,Zm = np.meshgrid(mesh.vectorCCy, mesh.vectorCCx, mesh.vectorCCz)
hY,hX,hZ = np.meshgrid(mesh.hy, mesh.hx, mesh.hz)
# Rmove air cells
Xm = P.T*mkvc(Xm)
Ym = P.T*mkvc(Ym)
Zm = P.T*mkvc(Zm)
hX = P.T*mkvc(hX)
hY = P.T*mkvc(hY)
hZ = P.T*mkvc(hZ)
V = P.T * mkvc(mesh.vol)
wr = np.zeros(nC)
ndata = rxLoc.shape[0]
count = -1
print "Begin calculation of distance weighting for R= " + str(R)
for dd in range(ndata):
nx1 = (Xm - hX * p - rxLoc[dd,0])**2
nx2 = (Xm + hX * p - rxLoc[dd,0])**2
ny1 = (Ym - hY * p - rxLoc[dd,1])**2
ny2 = (Ym + hY * p - rxLoc[dd,1])**2
nz1 = (Zm - hZ * p - rxLoc[dd,2])**2
nz2 = (Zm + hZ * p - rxLoc[dd,2])**2
R1 = np.sqrt(nx1 + ny1 + nz1)
R2 = np.sqrt(nx1 + ny1 + nz2)
R3 = np.sqrt(nx2 + ny1 + nz1)
R4 = np.sqrt(nx2 + ny1 + nz2)
R5 = np.sqrt(nx1 + ny2 + nz1)
R6 = np.sqrt(nx1 + ny2 + nz2)
R7 = np.sqrt(nx2 + ny2 + nz1)
R8 = np.sqrt(nx2 + ny2 + nz2)
temp = (R1 + R0)**-R + (R2 + R0)**-R + (R3 + R0)**-R + (R4 + R0)**-R + (R5 + R0)**-R + (R6 + R0)**-R + (R7 + R0)**-R + (R8 + R0)**-R
wr = wr + (V*temp/8.)**2
count = progress(dd,count,ndata)
wr = np.sqrt(wr)/V
wr = mkvc(wr)
wr = np.sqrt(wr/(np.max(wr)))
print "Done 100% ...distance weighting completed!!\n"
return wr
def writeUBCobs(filename,B,M,rxLoc,d,wd):
"""
writeUBCobs(filename,B,M,rxLoc,d,wd)
Function writing an observation file in UBC-MAG3D format.
INPUT
filename : Name of out file including directory
B : Inducing field parameters [Inc, Decl, Intensity]
M : Magnetization orientation [Inc, Decl, dtype]
rxLoc : Observation locations [obsx, obsy, obsz]
d : Data vector
wd : Uncertainty vector
OUTPUT
Obsfile
Created on Dec, 27th 2015
@author: dominiquef
"""
data = np.c_[rxLoc , d , wd]
with file(filename,'w') as fid:
fid.write('%6.2f %6.2f %6.2f\n' %(B[0], B[1], B[2]) )
fid.write('%6.2f %6.2f %6.2f\n' %(M[0], M[1], 1) )
fid.write('%i\n' %len(d) )
np.savetxt(fid, data, fmt='%e',delimiter=' ',newline='\n')
print "Observation file saved to: " + filename
def getActiveTopo(mesh,topo,flag):
"""
getActiveTopo(mesh,topo)
Function creates an active cell model from topography
INPUT
mesh : Mesh in SimPEG format
topo : Scatter points defining topography [x,y,z]
OUTPUT
actv : Active cell model
Created on Dec, 27th 2015
@founrdo
"""
import scipy.interpolate as interpolation
if (flag=='N'):
Zn = np.zeros((mesh.nNx,mesh.nNy))
# wght = np.zeros((mesh.nNx,mesh.nNy))
cx = mesh.vectorNx
cy = mesh.vectorNy
F = interpolation.NearestNDInterpolator(topo[:,0:2],topo[:,2])
[Y,X] = np.meshgrid(cy,cx)
Zn = F(X,Y)
actv = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
if (flag=='N'):
Nz = mesh.vectorNz[1:]
for jj in range(mesh.nCy):
for ii in range(mesh.nCx):
temp = [kk for kk in range(len(Nz)) if np.all(Zn[ii:(ii+2),jj:(jj+2)] > Nz[kk]) ]
actv[ii,jj,temp] = 1
actv = mkvc(actv==1)
inds = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype = int) - 1
return inds
def plot_obs_2D(rxLoc,d,wd,varstr):
""" Function plot_obs(rxLoc,d,wd)
Generate a 2d interpolated plot from scatter points of data
INPUT
rxLoc : Observation locations [x,y,z]
d : Data vector
wd : Uncertainty vector
OUTPUT
figure()
Created on Dec, 27th 2015
@author: dominiquef
"""
from scipy.interpolate import griddata
import pylab as plt
# Create grid of points
x = np.linspace(rxLoc[:,0].min(), rxLoc[:,0].max(), 100)
y = np.linspace(rxLoc[:,1].min(), rxLoc[:,1].max(), 100)
X, Y = np.meshgrid(x,y)
# Interpolate
d_grid = griddata(rxLoc[:,0:2],d,(X,Y), method ='linear')
# Plot result
plt.figure()
plt.subplot()
plt.imshow(d_grid, extent=[x.min(), x.max(), y.min(), y.max()],origin = 'lower')
plt.colorbar(fraction=0.02)
plt.contour(X,Y, d_grid,10)
plt.scatter(rxLoc[:,0],rxLoc[:,1], c=d, s=20)
plt.title(varstr)
plt.gca().set_aspect('equal', adjustable='box')
simpegPF/notebooks/BioSavartInv.ipynb
+1130
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simpegPF/notebooks/MagInversion.ipynb
+2117 -99
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simpegPF/notebooks/SimPEG Tutorial - MAG Linear Problem.ipynb
+3515
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simpegPF/notebooks/Untitled.ipynb
+36
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@@ -0,0 +1,36 @@
{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"obs = BaseMag.UBCmagObs('Obs_loc.dat')"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
simpegPF/notebooks/tutorials/Tutorial_1_Mag forward modeling.ipynb
+31 -31
View File
@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 3,
"execution_count": 1,
"metadata": {
"collapsed": false
},
@@ -32,7 +32,7 @@
},
{
"cell_type": "code",
"execution_count": 16,
"execution_count": 2,
"metadata": {
"collapsed": false
},
@@ -72,7 +72,7 @@
},
{
"cell_type": "code",
"execution_count": 17,
"execution_count": 3,
"metadata": {
"collapsed": false
},
@@ -80,18 +80,18 @@
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x3a99ad0>"
"<matplotlib.text.Text at 0x13415908>"
]
},
"execution_count": 17,
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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truncated
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x3b6b310>"
"<matplotlib.figure.Figure at 0x13302320>"
]
},
"metadata": {},
@@ -129,7 +129,7 @@
},
{
"cell_type": "code",
"execution_count": 19,
"execution_count": 4,
"metadata": {
"collapsed": false
},
@@ -144,7 +144,7 @@
},
{
"cell_type": "code",
"execution_count": 20,
"execution_count": 5,
"metadata": {
"collapsed": false
},
@@ -157,16 +157,16 @@
},
{
"cell_type": "code",
"execution_count": 21,
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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truncated
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x42450d0>"
"<matplotlib.figure.Figure at 0x13547e48>"
]
},
"metadata": {},
@@ -211,7 +211,7 @@
},
{
"cell_type": "code",
"execution_count": 22,
"execution_count": 7,
"metadata": {
"collapsed": false
},
@@ -225,7 +225,7 @@
},
{
"cell_type": "code",
"execution_count": 24,
"execution_count": 8,
"metadata": {
"collapsed": false
},
@@ -233,18 +233,18 @@
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x56e54d0>]"
"[<matplotlib.lines.Line2D at 0x17706b70>]"
]
},
"execution_count": 24,
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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truncated
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAWAAAAFeCAYAAAC7EcWRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x482ae10>"
"<matplotlib.figure.Figure at 0x138492e8>"
]
},
"metadata": {},
@@ -274,13 +274,13 @@
},
{
"cell_type": "code",
"execution_count": 25,
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"Bxra, Byra, Bzra = MagSphereAnalFunA(X, Y, Z, 80., 0., 0., -100, chiblk, np.array([0., 0., 1.]), flag)\n",
"Bxra, Byra, Bzra = MagSphereAnaFunA(X, Y, Z, 80., 0., 0., -100, chiblk, np.array([0., 0., 1.]), flag)\n",
"Bxra = np.reshape(Bxra, (size(xr), size(yr)), order='F')\n",
"Byra = np.reshape(Byra, (size(xr), size(yr)), order='F')\n",
"Bzra = np.reshape(Bzra, (size(xr), size(yr)), order='F')"
@@ -288,16 +288,16 @@
},
{
"cell_type": "code",
"execution_count": 26,
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x56f2150>"
"<matplotlib.figure.Figure at 0x132b8d30>"
]
},
"metadata": {},
@@ -336,7 +336,7 @@
},
{
"cell_type": "code",
"execution_count": 27,
"execution_count": 11,
"metadata": {
"collapsed": false
},
@@ -360,7 +360,7 @@
},
{
"cell_type": "code",
"execution_count": 28,
"execution_count": 12,
"metadata": {
"collapsed": false
},
@@ -379,7 +379,7 @@
},
{
"cell_type": "code",
"execution_count": 29,
"execution_count": 13,
"metadata": {
"collapsed": false
},
@@ -397,7 +397,7 @@
},
{
"cell_type": "code",
"execution_count": 30,
"execution_count": 15,
"metadata": {
"collapsed": false
},
@@ -405,18 +405,18 @@
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x4858f10>"
"<matplotlib.text.Text at 0x13826278>"
]
},
"execution_count": 30,
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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truncated
"text/plain": [
"<matplotlib.figure.Figure at 0x6054210>"
"<matplotlib.figure.Figure at 0x1a54e9e8>"
]
},
"metadata": {},