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https://github.com/wassname/simpeg.git
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- name cleanup in Jvec and Jtvec (use u instead of f to be consistent with the rest of SimPEG)
- example 1D inversion for FDEM
This commit is contained in:
Lindsey Heagy
+15
-15
@@ -53,13 +53,13 @@ class BaseFDEMProblem(BaseEMProblem):
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return F
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def Jvec(self, m, v, f=None):
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def Jvec(self, m, v, u=None):
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"""
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Sensitivity times a vector
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"""
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if f is None:
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f = self.fields(m)
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if u is None:
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u = self.fields(m)
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self.curModel = m
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@@ -71,33 +71,33 @@ class BaseFDEMProblem(BaseEMProblem):
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for src in self.survey.getSrcByFreq(freq):
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ftype = self._fieldType + 'Solution'
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u_src = f[src, ftype]
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u_src = u[src, ftype]
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dA_dm = self.getADeriv_m(freq, u_src, v)
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dRHS_dm = self.getRHSDeriv_m(freq, src, v)
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du_dm = Ainv * ( - dA_dm + dRHS_dm )
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for rx in src.rxList:
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df_duFun = getattr(f, '_%sDeriv_u'%rx.projField, None)
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df_duFun = getattr(u, '_%sDeriv_u'%rx.projField, None)
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df_dudu_dm = df_duFun(src, du_dm, adjoint=False)
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df_dmFun = getattr(f, '_%sDeriv_m'%rx.projField, None)
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df_dmFun = getattr(u, '_%sDeriv_m'%rx.projField, None)
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df_dm = df_dmFun(src, v, adjoint=False)
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Df_Dm = np.array(df_dudu_dm + df_dm,dtype=complex)
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P = lambda v: rx.projectFieldsDeriv(src, self.mesh, f, v) # wrt u, also have wrt m
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P = lambda v: rx.projectFieldsDeriv(src, self.mesh, u, v) # wrt u, also have wrt m
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Jv[src, rx] = P(Df_Dm)
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return Utils.mkvc(Jv)
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def Jtvec(self, m, v, f=None):
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def Jtvec(self, m, v, u=None):
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"""
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Sensitivity transpose times a vector
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"""
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if f is None:
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f = self.fields(m)
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if u is None:
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u = self.fields(m)
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self.curModel = m
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@@ -113,12 +113,12 @@ class BaseFDEMProblem(BaseEMProblem):
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for src in self.survey.getSrcByFreq(freq):
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ftype = self._fieldType + 'Solution'
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u_src = f[src, ftype]
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u_src = u[src, ftype]
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for rx in src.rxList:
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PTv = rx.projectFieldsDeriv(src, self.mesh, f, v[src, rx], adjoint=True) # wrt u, need possibility wrt m
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PTv = rx.projectFieldsDeriv(src, self.mesh, u, v[src, rx], adjoint=True) # wrt u, need possibility wrt m
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df_duTFun = getattr(f, '_%sDeriv_u'%rx.projField, None)
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df_duTFun = getattr(u, '_%sDeriv_u'%rx.projField, None)
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df_duT = df_duTFun(src, PTv, adjoint=True)
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ATinvdf_duT = ATinv * df_duT
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@@ -127,7 +127,7 @@ class BaseFDEMProblem(BaseEMProblem):
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dRHS_dmT = self.getRHSDeriv_m(freq,src, ATinvdf_duT, adjoint=True)
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du_dmT = -dA_dmT + dRHS_dmT
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df_dmFun = getattr(f, '_%sDeriv_m'%rx.projField, None)
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df_dmFun = getattr(u, '_%sDeriv_m'%rx.projField, None)
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dfT_dm = df_dmFun(src, PTv, adjoint=True)
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du_dmT += dfT_dm
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@@ -140,7 +140,7 @@ class BaseFDEMProblem(BaseEMProblem):
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else:
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raise Exception('Must be real or imag')
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return Jtv
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return Utils.mkvc(Jtv)
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def getSourceTerm(self, freq):
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"""
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@@ -0,0 +1,116 @@
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from SimPEG import *
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import SimPEG.EM as EM
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from scipy.constants import mu_0
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def run(plotIt=True):
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"""
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EM: FDEM: 1D: Inversion
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=======================
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Here we will create and run a FDEM 1D inversion.
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"""
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cs, ncx, ncz, npad = 5., 25, 15, 15
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hx = [(cs,ncx), (cs,npad,1.3)]
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hz = [(cs,npad,-1.3), (cs,ncz), (cs,npad,1.3)]
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mesh = Mesh.CylMesh([hx,1,hz], '00C')
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layerz = -100.
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active = mesh.vectorCCz<0.
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layer = (mesh.vectorCCz<0.) & (mesh.vectorCCz>=layerz)
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actMap = Maps.ActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
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mapping = Maps.ExpMap(mesh) * Maps.Vertical1DMap(mesh) * actMap
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sig_half = 2e-2
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sig_air = 1e-8
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sig_layer = 1e-2
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sigma = np.ones(mesh.nCz)*sig_air
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sigma[active] = sig_half
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sigma[layer] = sig_layer
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mtrue = np.log(sigma[active])
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if plotIt:
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import matplotlib.pyplot as plt
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fig, ax = plt.subplots(1,1, figsize = (3, 6))
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plt.semilogx(sigma[active], mesh.vectorCCz[active])
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ax.set_ylim(-500, 0)
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ax.set_xlim(1e-3, 1e-1)
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ax.set_xlabel('Conductivity (S/m)', fontsize = 14)
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ax.set_ylabel('Depth (m)', fontsize = 14)
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ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
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rxOffset=10.
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bzi = EM.FDEM.Rx(np.array([[rxOffset, 0., 1e-3]]), 'bzi')
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freqs = np.logspace(1,3,10)
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srcLoc = np.array([0., 0., 10.])
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srcList = []
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[srcList.append(EM.FDEM.Src.MagDipole([bzi],freq, srcLoc,orientation='Z')) for freq in freqs]
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survey = EM.FDEM.Survey(srcList)
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prb = EM.FDEM.Problem_b(mesh, mapping=mapping)
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try:
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from pymatsolver import MumpsSolver
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prb.Solver = MumpsSolver
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except ImportError, e:
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prb.Solver = SolverLU
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prb.pair(survey)
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std = 0.05
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survey.makeSyntheticData(mtrue, std)
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survey.std = std
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survey.eps = np.linalg.norm(survey.dtrue)*1e-5
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if plotIt:
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import matplotlib.pyplot as plt
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fig, ax = plt.subplots(1,1, figsize = (6, 6))
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ax.semilogx(freqs,survey.dtrue[:freqs.size], 'b.-')
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ax.semilogx(freqs,survey.dobs[:freqs.size], 'r.-')
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ax.legend(('Noisefree', '$d^{obs}$'), fontsize = 16)
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ax.set_xlabel('Time (s)', fontsize = 14)
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ax.set_ylabel('$B_z$ (T)', fontsize = 16)
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ax.set_xlabel('Time (s)', fontsize = 14)
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ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
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dmisfit = DataMisfit.l2_DataMisfit(survey)
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regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]])
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reg = Regularization.Tikhonov(regMesh)
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opt = Optimization.InexactGaussNewton(maxIter = 6)
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invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt)
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# Create an inversion object
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beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2)
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betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0)
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inv = Inversion.BaseInversion(invProb, directiveList=[beta,betaest])
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m0 = np.log(np.ones(mtrue.size)*sig_half)
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reg.alpha_s = 1e-3
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reg.alpha_x = 1.
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prb.counter = opt.counter = Utils.Counter()
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opt.LSshorten = 0.5
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opt.remember('xc')
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mopt = inv.run(m0)
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if plotIt:
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import matplotlib.pyplot as plt
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fig, ax = plt.subplots(1,1, figsize = (3, 6))
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plt.semilogx(sigma[active], mesh.vectorCCz[active])
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plt.semilogx(np.exp(mopt), mesh.vectorCCz[active])
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ax.set_ylim(-500, 0)
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ax.set_xlim(1e-3, 1e-1)
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ax.set_xlabel('Conductivity (S/m)', fontsize = 14)
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ax.set_ylabel('Depth (m)', fontsize = 14)
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ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5)
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plt.legend(['$\sigma_{true}$', '$\sigma_{pred}$'],loc='best')
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plt.show()
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if __name__ == '__main__':
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run()
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