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First documentation
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+119
@@ -1,10 +1,129 @@
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.. _api_PF:
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.. math::
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\renewcommand{\div}{\nabla\cdot\,}
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\newcommand{\grad}{\vec \nabla}
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\newcommand{\curl}{{\vec \nabla}\times\,}
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\newcommand {\J}{{\vec J}}
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\renewcommand{\H}{{\vec H}}
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\newcommand {\E}{{\vec E}}
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\newcommand{\dcurl}{{\mathbf C}}
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\newcommand{\dgrad}{{\mathbf G}}
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\newcommand{\Acf}{{\mathbf A_c^f}}
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\newcommand{\Ace}{{\mathbf A_c^e}}
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\renewcommand{\S}{{\mathbf \Sigma}}
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\newcommand{\St}{{\mathbf \Sigma_\tau}}
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\newcommand{\T}{{\mathbf T}}
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\newcommand{\Tt}{{\mathbf T_\tau}}
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\newcommand{\diag}[1]{\,{\sf diag}\left( #1 \right)}
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\newcommand{\M}{{\mathbf M}}
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\newcommand{\MfMui}{{\M^f_{\mu^{-1}}}}
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\newcommand{\MeSig}{{\M^e_\sigma}}
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\newcommand{\MeSigInf}{{\M^e_{\sigma_\infty}}}
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\newcommand{\MeSigO}{{\M^e_{\sigma_0}}}
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\newcommand{\Me}{{\M^e}}
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\newcommand{\Mes}[1]{{\M^e_{#1}}}
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\newcommand{\Mee}{{\M^e_e}}
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\newcommand{\Mej}{{\M^e_j}}
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\newcommand{\BigO}[1]{\mathcal{O}\bigl(#1\bigr)}
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\newcommand{\bE}{\mathbf{E}}
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\newcommand{\bH}{\mathbf{H}}
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\newcommand{\B}{\vec{B}}
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\newcommand{\D}{\vec{D}}
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\renewcommand{\H}{\vec{H}}
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\newcommand{\s}{\vec{s}}
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\newcommand{\bfJ}{\bf{J}}
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\newcommand{\vecm}{\vec m}
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\renewcommand{\Re}{\mathsf{Re}}
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\renewcommand{\Im}{\mathsf{Im}}
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\renewcommand {\j} { {\vec j} }
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\newcommand {\h} { {\vec h} }
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\renewcommand {\b} { {\vec b} }
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\newcommand {\e} { {\vec e} }
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\newcommand {\c} { {\vec c} }
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\renewcommand {\d} { {\vec d} }
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\renewcommand {\u} { {\vec u} }
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\newcommand{\I}{\vec{I}}
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Magnetics
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*********
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The geomagnetic field can be ranked as the longest studied of all the geophysical properties of the earth. In addition, magnetic survey, has been used broadly in diverse realm e.g., minining, oil and gas industry and envrionmental engineering. Although, this geophysical application is quite common in geoscience; however, we do not have modular, well-documented and well-tested open-source codes, which perform forward and inverse problems of magnetic survey. Therefore, here we are going to build up magnetic forward and inverse modeling code based on two common methodologies for forward problem - differential equation and integral equation approaches. \
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First, we start with some backgrounds of magnetics, e.g., Maxwell's equations. Based on that secondly, we use differential equation approach to solve forward problem with seocondary field formulation. In order to discretzie our system here, we use finite volume approach with weak formulation. Third, we solve inverse problem through Gauss-Newton method.
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Backgrounds
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===========
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Maxwell's equations for static case with out current source can be written as
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.. math::
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\nabla U = \frac{1}{\mu}\vec{B} \\
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\nabla \cdot \vec{B} = 0
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where \\(\\vec{B}\\) is magnetic flux (\\(\T\\)) and \\(\U\\) is magnetic potential and \\(\\mu\\) is permeability. Since we do not have any source term in above equations, boundary condition is going to be the driving force of our system as given below
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.. math ::
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(\vec{B}\cdot{\vec{n}})_{\partial\Omega} = B_{BC}
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where \\(\\vec{n}\\) means the unit normal vector on the boundary surface (\\(\\partial \\Omega\\)). By using seocondary field formulation we can rewrite above equations as
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.. math ::
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\frac{1}{\mu}\vec{B}_s = (\frac{1}{\mu}_0-\frac{1}{\mu})\vec{B}_0+\nabla\phi_s
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\nabla \cdot \vec{B}_s = 0
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(\vec{B}_s\cdot{\vec{n}})_{\partial\Omega} = B_{sBC}
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where \\(\\vec{B}_s\\) is the secondary magnetic flux and \\(\\vec{B}_0\\) is the backgroud or primary magnetic flux. In practice, we consider our earth field, which we can get from International Geomagnetic Reference Field (IGRF) by specifying the time and location, as \\(\\vec{B}_0\\). And based on this background fields, we compute secondary fields (\\(\\vec{B}_s\\)). Now we introduce the susceptibility as
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.. math ::
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\chi = \frac{\mu}{\mu_0} - 1 \\
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\mu = \mu_0(1+\chi)
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Since most materials in the earth have lower permeability than \\(\\mu_0\\), usually \\(\\chi\\) is greater than 0.
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.. note ::
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Actually, this is an asumption, which means we are not sure exactly this is true, although we are sure, it is very rare that we can encounter those materials. Anyway, practical range of the susceptibility is \\(0 < \\chi < 1 \\).
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Since we compute secondary field based on the earth field, which can be different from different locations in the world, we can expect different anomalous responses in different locations in the earth. For instance, assume we have two susceptible spheres, which are exactly same. However, anomalous responses in Canada and South Korea is going to be different.
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.. plot ::
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:include-source:
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from simpegPF.MagAnalytics import MagSphereAnalFunA
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from SimPEG import *
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hxind = ((0,25,1.3),(81, 5),(0,25,1.3))
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hyind = ((0,25,1.3),(81, 5),(0,25,1.3))
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hzind = ((0,25,1.3),(80, 5),(0,25,1.3))
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hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
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M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])
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bx,by,bz = MagSphereAnalFunA(M3.gridCC[:,0],M3.gridCC[:,1],M3.gridCC[:,2],100.,0.,0.,0.,0.01,np.array([1.,1.,0.]),'secondary')
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fig, ax = subplots(1,1, figsize = (5, 5))
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M3.plotSlice(np.c_[bx, by, bz], vType='CCv', view='vec', ind=21, ax = ax, grid=False, gridOpts={'color':'b','lw':0.5, 'alpha':0.8});
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Forward problem
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===============
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Inverse problem
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===============
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.. automodule:: simpegPF.PF
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:show-inheritance:
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+2
-2
@@ -11,8 +11,8 @@ simpegPF uses SimPEG as the framework for the forward and inverse
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gravity and magnetics geophysical problems.
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PF
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==
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Potential fields
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================
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.. toctree::
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:maxdepth: 2
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@@ -91,7 +91,7 @@ if __name__ == '__main__':
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import matplotlib.pyplot as plt
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hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))
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hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))
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hzind = ((5,25,1.3),(40, 12.5),(1,25,1.3))
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hzind = ((5,25,1.3),(40, 12.5),(5,25,1.3))
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hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)
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mesh = Mesh.TensorMesh([hx, hy, hz], [-hx.sum()/2,-hy.sum()/2,-hz.sum()/2])
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@@ -121,9 +121,9 @@ if __name__ == '__main__':
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dpred = data.dpred(chi, u=B)
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plt.pcolor(X, Y, dpred.reshape(X.shape, order='F'))
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# plt.pcolor(X, Y, dpred.reshape(X.shape, order='F'))
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plt.show()
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# plt.show()
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@@ -1,131 +0,0 @@
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from SimPEG.Utils.matutils import kron3, speye, sdiag, spzeros
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import numpy as np
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import scipy.sparse as sp
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def ddxFaceDivBC(n, bc):
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ij = (np.array([0, n-1]),np.array([0, 1]))
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vals = np.zeros(2)
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# Set the first side
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if(bc[0] == 'dirichlet'):
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vals[0] = 0
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elif(bc[0] == 'neumann'):
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vals[0] = -1
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# Set the second side
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if(bc[1] == 'dirichlet'):
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vals[1] = 0
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elif(bc[1] == 'neumann'):
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vals[1] = 1
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D = sp.csr_matrix((vals, ij), shape=(n,2))
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return D
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def faceDivBC(mesh, BC, ind):
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"""
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The facd divergence boundary condtion matrix
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"""
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# The number of cell centers in each direction
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n = mesh.vnC
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# Compute faceDivergence operator on faces
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if(mesh.dim == 1):
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D = ddxFaceDivBC(n[0], BC[0])
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elif(mesh.dim == 2):
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D1 = sp.kron(speye(n[1]), ddxFaceDivBC(n[0], BC[0]))
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D2 = sp.kron(ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
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D = sp.hstack((D1, D2), format="csr")
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elif(mesh.dim == 3):
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D1 = kron3(speye(n[2]), speye(n[1]), ddxFaceDivBC(n[0], BC[0]))
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D2 = kron3(speye(n[2]), ddxFaceDivBC(n[1], BC[1]), speye(n[0]))
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D3 = kron3(ddxFaceDivBC(n[2], BC[2]), speye(n[1]), speye(n[0]))
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D = sp.hstack((D1, D2, D3), format="csr")
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# Compute areas of cell faces & volumes
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S = mesh.area[ind]
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V = mesh.vol
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mesh._faceDiv = sdiag(1/V)*D*sdiag(S)
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return mesh._faceDiv
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def faceBCind(mesh):
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"""
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Find indices of boundary faces in each direction
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"""
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if(mesh.dim==1):
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indxd = (mesh.gridFx==min(mesh.gridFx))
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indxu = (mesh.gridFx==max(mesh.gridFx))
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return indxd, indxu
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elif(mesh.dim==2):
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indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
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indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
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indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
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indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
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return indxd, indxu, indyd, indyu
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elif(mesh.dim==3):
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indxd = (mesh.gridFx[:,0]==min(mesh.gridFx[:,0]))
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indxu = (mesh.gridFx[:,0]==max(mesh.gridFx[:,0]))
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indyd = (mesh.gridFy[:,1]==min(mesh.gridFy[:,1]))
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indyu = (mesh.gridFy[:,1]==max(mesh.gridFy[:,1]))
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indzd = (mesh.gridFz[:,2]==min(mesh.gridFz[:,2]))
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indzu = (mesh.gridFz[:,2]==max(mesh.gridFz[:,2]))
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return indxd, indxu, indyd, indyu, indzd, indzu
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def faceDivProj(mesh, flag):
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""""
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Construct divergence operator (face-stg to cell-centres).
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"""
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# The number of cell centers in each direction
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n = mesh.vnC
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# Compute faceDivergence operator on faces
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if (flag=='in'):
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if(mesh.dim == 1):
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Pin = ddxPin(n[0])
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elif(mesh.dim == 2):
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P1 = sp.kron(speye(n[1]), ddxPin(n[0]))
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P2 = sp.kron(ddxPin(n[1]), speye(n[0]))
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Pin = sp.block_diag((P1, P2), format="csr")
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elif(mesh.dim == 3):
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P1 = kron3(speye(n[2]), speye(n[1]), ddxPin(n[0]))
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P2 = kron3(speye(n[2]), ddxPin(n[1]), speye(n[0]))
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P3 = kron3(ddxPin(n[2]), speye(n[1]), speye(n[0]))
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Pin = sp.block_diag((P1, P2, P3), format="csr")
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# Compute areas of cell faces & volumes
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return Pin
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elif(flag=='out'):
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if(mesh.dim == 1):
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Pout = ddxPout(n[0])
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elif(mesh.dim == 2):
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P1 = sp.kron(speye(n[1]), ddxPout(n[0]))
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P2 = sp.kron(ddxPout(n[1]), speye(n[0]))
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Pout = sp.block_diag((P1, P2), format="csr")
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elif(mesh.dim == 3):
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P1 = kron3(speye(n[2]), speye(n[1]), ddxPout(n[0]))
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P2 = kron3(speye(n[2]), ddxPout(n[1]), speye(n[0]))
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P3 = kron3(ddxPout(n[2]), speye(n[1]), speye(n[0]))
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Pout = sp.block_diag((P1, P2, P3), format="csr")
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# Compute areas of cell faces & volumes
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return Pout
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def ddxPin(n):
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p0 =spzeros(n-1, 1)
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P = sdiag(np.ones(n-1))
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P = sp.hstack((p0, P, p0))
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return P
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def ddxPout(n):
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ij = (np.array([0, 1]),np.array([0, n]))
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vals = np.ones(2)
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P = sp.csr_matrix((vals, ij), shape=(2,n+1))
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return P
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@@ -19,14 +19,5 @@ class MagProblemTests(unittest.TestCase):
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self.assertTrue(passed)
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def test_DirchletBC(self):
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q = lambda x: np.sin(x)
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M = self.M
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order = 2
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self.assertTrue(order > 1)
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if __name__ == '__main__':
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unittest.main()
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@@ -1,3 +1,3 @@
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import MagAnalytics
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import MagData
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import BaseMag
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import Magnetics
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@@ -12,7 +12,7 @@
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"collapsed": false,
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"input": [
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"from SimPEG import *\n",
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"from MagAnalytics import spheremodel, MagSphereAnalFun, CongruousMagBC\n",
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"from simpegPF.MagAnalytics import spheremodel, MagSphereAnalFun, CongruousMagBC\n",
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"%pylab inline"
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],
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"language": "python",
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@@ -22,21 +22,11 @@
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"Warning: Python backend is being used for solver. Run setup.py from the command line.\n",
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"Warning: mumps solver not available.\n",
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"Warning: upgrade your scipy to 0.13.0"
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]
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},
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{
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"output_type": "stream",
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"stream": "stdout",
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"text": [
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"\n",
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"Populating the interactive namespace from numpy and matplotlib\n"
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]
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}
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],
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"prompt_number": 1
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"prompt_number": 9
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},
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{
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"cell_type": "markdown",
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@@ -60,14 +50,14 @@
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"input": [
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"hxind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
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"hyind = ((5,25,1.3),(41, 12.5),(5,25,1.3))\n",
|
||||
"hzind = ((5,25,1.3),(40, 12.5),(1,25,1.3))\n",
|
||||
"hzind = ((5,25,1.3),(40, 12.5),(5,25,1.3))\n",
|
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"hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
|
||||
"M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])"
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||||
],
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||||
"language": "python",
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"metadata": {},
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||||
"outputs": [],
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"prompt_number": 2
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"prompt_number": 10
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||||
},
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||||
{
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||||
"cell_type": "markdown",
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@@ -90,7 +80,7 @@
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 3
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"prompt_number": 11
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},
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{
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"cell_type": "code",
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@@ -103,7 +93,7 @@
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"language": "python",
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"metadata": {},
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||||
"outputs": [],
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"prompt_number": 4
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"prompt_number": 12
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},
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{
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"cell_type": "markdown",
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@@ -125,7 +115,7 @@
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 5
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"prompt_number": 13
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},
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{
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"cell_type": "code",
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@@ -136,7 +126,7 @@
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"language": "python",
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"metadata": {},
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"outputs": [],
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"prompt_number": 6
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"prompt_number": 14
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},
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||||
{
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"cell_type": "code",
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@@ -152,20 +142,20 @@
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"output_type": "stream",
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"stream": "stderr",
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"text": [
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"C:\\Users\\SEOGI\\AppData\\Local\\Enthought\\Canopy\\App\\appdata\\canopy-1.0.1.1189.win-x86_64\\lib\\site-packages\\matplotlib\\lines.py:483: RuntimeWarning: invalid value encountered in greater_equal\n",
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"/usr/lib/pymodules/python2.7/matplotlib/lines.py:483: RuntimeWarning: invalid value encountered in greater_equal\n",
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" return np.alltrue(x[1:]-x[0:-1]>=0)\n"
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]
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},
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{
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"metadata": {},
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"output_type": "display_data",
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||||
"png": 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||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa21a860>"
|
||||
"<matplotlib.figure.Figure at 0x40c9c90>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 7
|
||||
"prompt_number": 15
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -179,21 +169,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 8,
|
||||
"prompt_number": 16,
|
||||
"text": [
|
||||
"<matplotlib.collections.QuadMesh at 0xa646390>"
|
||||
"<matplotlib.collections.QuadMesh at 0x44e4a90>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa18f8d0>"
|
||||
"<matplotlib.figure.Figure at 0x44c6910>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 8
|
||||
"prompt_number": 16
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -243,7 +233,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 9
|
||||
"prompt_number": 17
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -258,11 +248,11 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"(366231, 366231) (366231, 119646)\n"
|
||||
"(397851, 397851) (397851, 130050)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 10
|
||||
"prompt_number": 18
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -281,7 +271,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 11
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -296,7 +286,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 12
|
||||
"prompt_number": 20
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -322,7 +312,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 13
|
||||
"prompt_number": 21
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -342,11 +332,12 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Wall time: 1.33 s\n"
|
||||
"CPU times: user 974 ms, sys: 0 ns, total: 974 ms\n",
|
||||
"Wall time: 974 ms\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 14
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -363,11 +354,11 @@
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"0\n",
|
||||
"119646\n"
|
||||
"130050\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 15
|
||||
"prompt_number": 23
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -386,11 +377,11 @@
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"0\n",
|
||||
"8.8645586939e-07\n"
|
||||
"9.90412957826e-07\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 16
|
||||
"prompt_number": 24
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -412,13 +403,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x9e95b70>"
|
||||
"<matplotlib.figure.Figure at 0x44d7850>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 19
|
||||
"prompt_number": 25
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -462,7 +453,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 20
|
||||
"prompt_number": 26
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -476,7 +467,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 21
|
||||
"prompt_number": 27
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -497,7 +488,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 22
|
||||
"prompt_number": 28
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -517,21 +508,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 23,
|
||||
"prompt_number": 29,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0x9f5e4a8>]"
|
||||
"[<matplotlib.lines.Line2D at 0x44c5210>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa5c0908>"
|
||||
"<matplotlib.figure.Figure at 0x5010ad0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 23
|
||||
"prompt_number": 29
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -551,21 +542,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 24,
|
||||
"prompt_number": 30,
|
||||
"text": [
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x0000000012B67688>"
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x9e54ef0>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa5c0dd8>"
|
||||
"<matplotlib.figure.Figure at 0x4c6d1d0>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 24
|
||||
"prompt_number": 30
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -594,13 +585,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x12b87908>"
|
||||
"<matplotlib.figure.Figure at 0xa095650>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 25
|
||||
"prompt_number": 31
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -610,9 +601,9 @@
|
||||
"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((Bxtter[:,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.')"
|
||||
"axes[0].plot(Y[:,id], abs((Bxr[:,id]-Bxra[:,id])/(Bxra[:,id]+epsx)), 'r.')\n",
|
||||
"axes[1].plot(Y[:,id], abs((Byr[:,id]-Byra[:,id])/(Byra[:,id]+epsy)), 'r.')\n",
|
||||
"axes[2].plot(Y[:,id], abs((Bzr[:,id]-Bzra[:,id])/(Bzra[:,id]+epsz)), 'r.')"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
@@ -620,21 +611,21 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 34,
|
||||
"prompt_number": 32,
|
||||
"text": [
|
||||
"[<matplotlib.lines.Line2D at 0x1971ad68>]"
|
||||
"[<matplotlib.lines.Line2D at 0x9989610>]"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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|
||||
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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x198a90b8>"
|
||||
"<matplotlib.figure.Figure at 0x9142a10>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 34
|
||||
"prompt_number": 32
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
@@ -647,6 +638,15 @@
|
||||
"### - Secondary field shows better accuracy than total field approach as expected\n",
|
||||
"### - Anyway every piece works well for forward modeling!!"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 32
|
||||
}
|
||||
],
|
||||
"metadata": {}
|
||||
|
||||
@@ -21,47 +21,37 @@
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"Warning: Python backend is being used for solver. Run setup.py from the command line.\n",
|
||||
"Warning: mumps solver not available.\n",
|
||||
"Warning: upgrade your scipy to 0.13.0"
|
||||
]
|
||||
},
|
||||
{
|
||||
"output_type": "stream",
|
||||
"stream": "stdout",
|
||||
"text": [
|
||||
"\n",
|
||||
"Populating the interactive namespace from numpy and matplotlib\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 1
|
||||
"prompt_number": 4
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"hxind = ((10,25,1.3),(41, 12.5),(10,25,1.3))\n",
|
||||
"hyind = ((10,25,1.3),(41, 12.5),(10,25,1.3))\n",
|
||||
"hzind = ((10,25,1.3),(40, 12.5),(10,25,1.3))\n",
|
||||
"hxind = ((0,25,1.3),(81, 5),(0,25,1.3))\n",
|
||||
"hyind = ((0,25,1.3),(81, 5),(0,25,1.3))\n",
|
||||
"hzind = ((0,25,1.3),(80, 5),(0,25,1.3))\n",
|
||||
"hx, hy, hz = Utils.meshTensors(hxind, hyind, hzind)\n",
|
||||
"M3 = Mesh.TensorMesh([hx, hy, hz], [-sum(hx)/2,-sum(hy)/2,-sum(hz)/2])"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 2
|
||||
"prompt_number": 18
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"from MagAnalytics import MagSphereAnalFunA, MagSphereAnalFun"
|
||||
"from simpegPF.MagAnalytics import MagSphereAnalFunA, MagSphereAnalFun"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 3
|
||||
"prompt_number": 19
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -77,7 +67,7 @@
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"prompt_number": 10
|
||||
"prompt_number": 20
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
@@ -91,31 +81,31 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 11,
|
||||
"prompt_number": 21,
|
||||
"text": [
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x000000000AAF71C8>"
|
||||
"<matplotlib.colorbar.Colorbar instance at 0x5c49878>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xabe94e0>"
|
||||
"<matplotlib.figure.Figure at 0x302fc90>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 11
|
||||
"prompt_number": 21
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, axes = subplots(1,3, figsize = (15, 5))\n",
|
||||
"bx,by,bz = MagSphereAnalFunA(M3.gridCC[:,0],M3.gridCC[:,1],M3.gridCC[:,2],100.,0.,0.,0.,0.01,np.array([0.,0.,1.]),'secondary') \n",
|
||||
"M3.plotSlice(bx, vType='CC', ind=5, ax = axes[0], grid=True, gridOpts={'color':'b','lw':0.3, 'alpha':0.5}); axes[0].set_title('$b_x$', fontsize = 16); #axes[0].set_xlim(0,500); axes[0].set_ylim(0,500)\n",
|
||||
"M3.plotSlice(by, vType='CC', ind=5, ax = axes[1]); axes[1].set_title('$b_y$', fontsize = 16);# axes[1].set_xlim(0,500); axes[1].set_ylim(0,500)\n",
|
||||
"M3.plotSlice(bz, vType='CC', ind=5, ax = axes[2]); axes[2].set_title('$b_z$', fontsize = 16);# axes[2].set_xlim(0,500); axes[2].set_ylim(0,500)"
|
||||
"bx,by,bz = MagSphereAnalFunA(M3.gridCC[:,0],M3.gridCC[:,1],M3.gridCC[:,2],100.,0.,0.,0.,0.01,np.array([1.,1.,0.]),'secondary') \n",
|
||||
"M3.plotSlice(bx, vType='CC', ind=5, ax = axes[0], grid=True, gridOpts={'color':'b','lw':0.3, 'alpha':0.5}); axes[0].set_title('$B_x$', fontsize = 16); #axes[0].set_xlim(0,500); axes[0].set_ylim(0,500)\n",
|
||||
"M3.plotSlice(by, vType='CC', ind=5, ax = axes[1]); axes[1].set_title('$B_y$', fontsize = 16);# axes[1].set_xlim(0,500); axes[1].set_ylim(0,500)\n",
|
||||
"M3.plotSlice(bz, vType='CC', ind=5, ax = axes[2]); axes[2].set_title('$B_z$', fontsize = 16);# axes[2].set_xlim(0,500); axes[2].set_ylim(0,500)"
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
@@ -123,28 +113,28 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "pyout",
|
||||
"prompt_number": 12,
|
||||
"prompt_number": 22,
|
||||
"text": [
|
||||
"<matplotlib.text.Text at 0x120c3f60>"
|
||||
"<matplotlib.text.Text at 0x741e150>"
|
||||
]
|
||||
},
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0x1073cb70>"
|
||||
"<matplotlib.figure.Figure at 0x3d45d50>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 12
|
||||
"prompt_number": 22
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"collapsed": false,
|
||||
"input": [
|
||||
"fig, ax = subplots(1,1, figsize = (5, 5))\n",
|
||||
"M3.plotSlice(np.c_[bx, by, bz], vType='CCv', view='vec', ind=1, ax = ax, grid=False, gridOpts={'color':'b','lw':0.5, 'alpha':0.8}); "
|
||||
"M3.plotSlice(np.c_[bx, by, bz], vType='CCv', view='vec', ind=21, ax = ax, grid=False, gridOpts={'color':'b','lw':0.5, 'alpha':0.8}); "
|
||||
],
|
||||
"language": "python",
|
||||
"metadata": {},
|
||||
@@ -152,13 +142,13 @@
|
||||
{
|
||||
"metadata": {},
|
||||
"output_type": "display_data",
|
||||
"png": 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truncated
|
||||
"png": 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truncated
|
||||
"text": [
|
||||
"<matplotlib.figure.Figure at 0xa397518>"
|
||||
"<matplotlib.figure.Figure at 0x38b9490>"
|
||||
]
|
||||
}
|
||||
],
|
||||
"prompt_number": 9
|
||||
"prompt_number": 23
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
|
||||
Reference in new issue
Block a user