def MagneticsDiffSecondaryInv(mesh, model, data, **kwargs): """ Inversion module for MagneticsDiffSecondary """ from SimPEG import Optimization, Regularization, Parameters, ObjFunction, Inversion prob = MagneticsDiffSecondary(mesh, model) miter = kwargs.get('maxIter', 10) if prob.ispaired: prob.unpair() if data.ispaired: data.unpair() prob.pair(data) # Create an optimization program opt = Optimization.InexactGaussNewton(maxIter=miter) opt.bfgsH0 = Solver(sp.identity(model.nP), flag='D') # Create a regularization program reg = Regularization.Tikhonov(model) # Create an objective function beta = Parameters.BetaSchedule(beta0=1e0) obj = ObjFunction.BaseObjFunction(data, reg, beta=beta) # Create an inversion object inv = Inversion.BaseInversion(obj, opt) return inv, reg
def setUp(self): cs = 25. hx = [(cs, 0, -1.3), (cs, 21), (cs, 0, 1.3)] hz = [(cs, 0, -1.3), (cs, 20)] mesh = Mesh.TensorMesh([hx, hz], x0="CN") blkind0 = Utils.ModelBuilder.getIndicesSphere(np.r_[-100., -200.], 75., mesh.gridCC) blkind1 = Utils.ModelBuilder.getIndicesSphere(np.r_[100., -200.], 75., mesh.gridCC) sigma = np.ones(mesh.nC) * 1e-2 eta = np.zeros(mesh.nC) tau = np.ones_like(sigma) * 1. eta[blkind0] = 0.1 eta[blkind1] = 0.1 tau[blkind0] = 0.1 tau[blkind1] = 0.1 x = mesh.vectorCCx[(mesh.vectorCCx > -155.) & (mesh.vectorCCx < 155.)] Aloc = np.r_[-200., 0.] Bloc = np.r_[200., 0.] M = Utils.ndgrid(x - 25., np.r_[0.]) N = Utils.ndgrid(x + 25., np.r_[0.]) times = np.arange(10) * 1e-3 + 1e-3 rx = SIP.Rx.Dipole(M, N, times) src = SIP.Src.Dipole([rx], Aloc, Bloc) survey = SIP.Survey([src]) wires = Maps.Wires(('eta', mesh.nC), ('taui', mesh.nC)) problem = SIP.Problem2D_CC(mesh, rho=1. / sigma, etaMap=wires.eta, tauiMap=wires.taui, verbose=False) problem.Solver = Solver problem.pair(survey) mSynth = np.r_[eta, 1. / tau] problem.model = mSynth survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov(mesh) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
def setUp(self, parallel=False): frequency = np.array([900, 7200, 56000], dtype=float) hz = np.r_[1.] n_sounding = 10 dx = 20. hx = np.ones(n_sounding) * dx e = np.ones(n_sounding) mSynth = np.r_[e * np.log(1. / 100.), e * 20] x = np.arange(n_sounding) y = np.zeros_like(x) z = np.ones_like(x) * 30. rx_locations = np.c_[x, y, z] src_locations = np.c_[x, y, z] topo = np.c_[x, y, z - 30.].astype(float) wires = Maps.Wires(('sigma', n_sounding), ('h', n_sounding)) expmap = Maps.ExpMap(nP=n_sounding) sigmaMap = expmap * wires.sigma survey = GlobalEM1DSurveyFD(rx_locations=rx_locations, src_locations=src_locations, frequency=frequency, offset=np.ones_like(frequency) * 8., src_type="VMD", rx_type="ppm", field_type='secondary', topo=topo, half_switch=True) problem = GlobalEM1DProblemFD([], sigmaMap=sigmaMap, hMap=wires.h, hz=hz, parallel=parallel, n_cpu=2) problem.pair(survey) survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization mesh = Mesh.TensorMesh([int(n_sounding * 2)]) dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov(mesh) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=0.) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth * 1.2 self.survey = survey self.dmis = dmis
def setUp(self, parallel=True): frequency = np.array([900, 7200, 56000], dtype=float) hz = get_vertical_discretization_frequency( frequency, sigma_background=1./10. ) n_sounding = 10 dx = 20. hx = np.ones(n_sounding) * dx mesh = Mesh.TensorMesh([hx, hz], x0='00') inds = mesh.gridCC[:, 1] < 25 inds_1 = mesh.gridCC[:, 1] < 50 sigma = np.ones(mesh.nC) * 1./100. sigma[inds_1] = 1./10. sigma[inds] = 1./50. sigma_em1d = sigma.reshape(mesh.vnC, order='F').flatten() mSynth = np.log(sigma_em1d) x = mesh.vectorCCx y = np.zeros_like(x) z = np.ones_like(x) * 30. rx_locations = np.c_[x, y, z] src_locations = np.c_[x, y, z] topo = np.c_[x, y, z-30.].astype(float) mapping = Maps.ExpMap(mesh) survey = GlobalEM1DSurveyFD( rx_locations=rx_locations, src_locations=src_locations, frequency=frequency, offset=np.ones_like(frequency) * 8., src_type="VMD", rx_type="Hz", field_type='secondary', topo=topo ) problem = GlobalEM1DProblemFD( [], sigmaMap=mapping, hz=hz, parallel=parallel, n_cpu=5 ) problem.pair(survey) survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov(mesh) opt = Optimization.InexactGaussNewton( maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6 ) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=0.) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
def run(N=100, plotIt=True): np.random.seed(1) mesh = Mesh.TensorMesh([N]) nk = 20 jk = np.linspace(1., 60., nk) p = -0.25 q = 0.25 def g(k): return (np.exp(p * jk[k] * mesh.vectorCCx) * np.cos(np.pi * q * jk[k] * mesh.vectorCCx)) G = np.empty((nk, mesh.nC)) for i in range(nk): G[i, :] = g(i) mtrue = np.zeros(mesh.nC) mtrue[mesh.vectorCCx > 0.3] = 1. mtrue[mesh.vectorCCx > 0.45] = -0.5 mtrue[mesh.vectorCCx > 0.6] = 0 prob = Problem.LinearProblem(mesh, G=G) survey = Survey.LinearSurvey() survey.pair(prob) survey.makeSyntheticData(mtrue, std=0.01) M = prob.mesh reg = Regularization.Tikhonov(mesh, alpha_s=1., alpha_x=1.) dmis = DataMisfit.l2_DataMisfit(survey) opt = Optimization.InexactGaussNewton(maxIter=60) invProb = InvProblem.BaseInvProblem(dmis, reg, opt) directives = [ Directives.BetaEstimate_ByEig(beta0_ratio=1e-2), Directives.TargetMisfit() ] inv = Inversion.BaseInversion(invProb, directiveList=directives) m0 = np.zeros_like(survey.mtrue) mrec = inv.run(m0) if plotIt: fig, axes = plt.subplots(1, 2, figsize=(12 * 1.2, 4 * 1.2)) for i in range(prob.G.shape[0]): axes[0].plot(prob.G[i, :]) axes[0].set_title('Columns of matrix G') axes[1].plot(M.vectorCCx, survey.mtrue, 'b-') axes[1].plot(M.vectorCCx, mrec, 'r-') axes[1].legend(('True Model', 'Recovered Model')) axes[1].set_ylim([-2, 2]) return prob, survey, mesh, mrec
def setUp(self): cs = 25. hx = [(cs,0, -1.3),(cs,21),(cs,0, 1.3)] hy = [(cs,0, -1.3),(cs,21),(cs,0, 1.3)] hz = [(cs,0, -1.3),(cs,20),(cs,0, 1.3)] mesh = Mesh.TensorMesh([hx, hy, hz],x0="CCC") blkind0 = Utils.ModelBuilder.getIndicesSphere(np.r_[-100., -100., -200.], 75., mesh.gridCC) blkind1 = Utils.ModelBuilder.getIndicesSphere(np.r_[100., 100., -200.], 75., mesh.gridCC) sigma = np.ones(mesh.nC)*1e-2 airind = mesh.gridCC[:,2]>0. sigma[airind] = 1e-8 eta = np.zeros(mesh.nC) tau = np.ones_like(sigma)*1. eta[blkind0] = 0.1 eta[blkind1] = 0.1 tau[blkind0] = 0.1 tau[blkind1] = 0.01 actmapeta = Maps.InjectActiveCells(mesh, ~airind, 0.) actmaptau = Maps.InjectActiveCells(mesh, ~airind, 1.) x = mesh.vectorCCx[(mesh.vectorCCx>-155.)&(mesh.vectorCCx<155.)] y = mesh.vectorCCx[(mesh.vectorCCy>-155.)&(mesh.vectorCCy<155.)] Aloc = np.r_[-200., 0., 0.] Bloc = np.r_[200., 0., 0.] M = Utils.ndgrid(x-25.,y, np.r_[0.]) N = Utils.ndgrid(x+25.,y, np.r_[0.]) times = np.arange(10)*1e-3 + 1e-3 rx = SIP.Rx.Dipole(M, N, times) src = SIP.Src.Dipole([rx], Aloc, Bloc) survey = SIP.Survey([src]) colemap = [("eta", Maps.IdentityMap(mesh)*actmapeta), ("taui", Maps.IdentityMap(mesh)*actmaptau)] problem = SIP.Problem3D_N(mesh, sigma=sigma, mapping=colemap) problem.Solver = Solver problem.pair(survey) mSynth = np.r_[eta[~airind], 1./tau[~airind]] survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) regmap = Maps.IdentityMap(nP=int(mSynth[~airind].size*2)) reg = SIP.MultiRegularization(mesh, mapping=regmap, nModels=2, indActive=~airind) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
def test_inv(self): reg = Regularization.Tikhonov(self.mesh) opt = Optimization.InexactGaussNewton(maxIter=10) invProb = InvProblem.BaseInvProblem(self.dmiscobmo, reg, opt) directives = [ Directives.BetaEstimate_ByEig(beta0_ratio=1e-2), ] inv = Inversion.BaseInversion(invProb, directiveList=directives) m0 = self.model.mean() * np.ones_like(self.model) mrec = inv.run(m0)
def setUp(self): mesh = Mesh.TensorMesh([20, 20, 20], "CCN") sigma = np.ones(mesh.nC) * 1. / 100. actind = mesh.gridCC[:, 2] < -0.2 # actMap = Maps.InjectActiveCells(mesh, actind, 0.) xyzM = Utils.ndgrid( np.ones_like(mesh.vectorCCx[:-1]) * -0.4, np.ones_like(mesh.vectorCCy) * -0.4, np.r_[-0.3]) xyzN = Utils.ndgrid(mesh.vectorCCx[1:], mesh.vectorCCy, np.r_[-0.3]) problem = SP.Problem_CC(mesh, sigma=sigma, qMap=Maps.IdentityMap(mesh), Solver=PardisoSolver) rx = SP.Rx.Dipole(xyzN, xyzM) src = SP.Src.StreamingCurrents([rx], L=np.ones(mesh.nC), mesh=mesh, modelType="CurrentSource") survey = SP.Survey([src]) survey.pair(problem) q = np.zeros(mesh.nC) inda = Utils.closestPoints(mesh, np.r_[-0.5, 0., -0.8]) indb = Utils.closestPoints(mesh, np.r_[0.5, 0., -0.8]) q[inda] = 1. q[indb] = -1. mSynth = q.copy() survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Simple(mesh) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e-2) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
def setUp(self): cs = 12.5 hx = [(cs, 7, -1.3), (cs, 61), (cs, 7, 1.3)] hy = [(cs, 7, -1.3), (cs, 20)] mesh = Mesh.TensorMesh([hx, hy], x0="CN") # x = np.linspace(-200, 200., 20) x = np.linspace(-200, 200., 2) M = Utils.ndgrid(x - 12.5, np.r_[0.]) N = Utils.ndgrid(x + 12.5, np.r_[0.]) A0loc = np.r_[-150, 0.] A1loc = np.r_[-130, 0.] B0loc = np.r_[-130, 0.] B1loc = np.r_[-110, 0.] rx = DC.Rx.Dipole_ky(M, N) src0 = DC.Src.Dipole([rx], A0loc, B0loc) src1 = DC.Src.Dipole([rx], A1loc, B1loc) survey = IP.Survey([src0, src1]) sigma = np.ones(mesh.nC) * 1. problem = IP.Problem2D_CC(mesh, sigma=sigma, etaMap=Maps.IdentityMap(mesh), verbose=False) problem.pair(survey) mSynth = np.ones(mesh.nC) * 0.1 survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov(mesh) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
def test_inv_mref_setting(self): reg1 = Regularization.Tikhonov(self.mesh) reg2 = Regularization.Tikhonov(self.mesh) reg = reg1 + reg2 opt = Optimization.InexactGaussNewton(maxIter=10) invProb = InvProblem.BaseInvProblem(self.dmiscobmo, reg, opt) directives = [ Directives.BetaEstimate_ByEig(beta0_ratio=1e-2), ] inv = Inversion.BaseInversion(invProb, directiveList=directives) m0 = self.model.mean() * np.ones_like(self.model) mrec = inv.run(m0) self.assertTrue(np.all(reg1.mref == m0)) self.assertTrue(np.all(reg2.mref == m0))
def setUp(self): aSpacing = 2.5 nElecs = 10 surveySize = nElecs * aSpacing - aSpacing cs = surveySize / nElecs / 4 mesh = Mesh.TensorMesh( [ [(cs, 10, -1.3), (cs, surveySize / cs), (cs, 10, 1.3)], [(cs, 3, -1.3), (cs, 3, 1.3)], # [(cs, 5, -1.3), (cs, 10)] ], 'CN') srcList = DC.Utils.WennerSrcList(nElecs, aSpacing, in2D=True) survey = DC.Survey(srcList) problem = DC.Problem3D_N(mesh, rhoMap=Maps.IdentityMap(mesh), storeJ=True) problem.pair(survey) mSynth = np.ones(mesh.nC) survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov(mesh) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
def setUp(self): cs = 12.5 hx = [(cs, 7, -1.3), (cs, 61), (cs, 7, 1.3)] hy = [(cs, 7, -1.3), (cs, 20)] mesh = Mesh.TensorMesh([hx, hy], x0="CN") x = np.linspace(-135, 250., 20) M = Utils.ndgrid(x - 12.5, np.r_[0.]) N = Utils.ndgrid(x + 12.5, np.r_[0.]) A0loc = np.r_[-150, 0.] A1loc = np.r_[-130, 0.] rxloc = [np.c_[M, np.zeros(20)], np.c_[N, np.zeros(20)]] rx = DC.Rx.Dipole_ky(M, N) src0 = DC.Src.Pole([rx], A0loc) src1 = DC.Src.Pole([rx], A1loc) survey = DC.Survey_ky([src0, src1]) problem = DC.Problem2D_N(mesh, mapping=[('rho', Maps.IdentityMap(mesh))]) problem.pair(survey) mSynth = np.ones(mesh.nC) * 1. survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov(mesh) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e0) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
def solve(self): # initial values/model m0 = numpy.median(-4) * numpy.ones(self.mapping.nP) # Data Misfit dataMisfit = DataMisfit.l2_DataMisfit(self.survey) # Regularization regT = Regularization.Simple(self.mesh, indActive=self.activeCellIndices, alpha_s=1e-6, alpha_x=1., alpha_y=1., alpha_z=1.) # Optimization Scheme opt = Optimization.InexactGaussNewton(maxIter=10) # Form the problem opt.remember('xc') invProb = InvProblem.BaseInvProblem(dataMisfit, regT, opt) # Directives for Inversions beta = Directives.BetaEstimate_ByEig(beta0_ratio=0.5e+1) Target = Directives.TargetMisfit() betaSched = Directives.BetaSchedule(coolingFactor=5., coolingRate=2) inversion = Inversion.BaseInversion(invProb, directiveList=[beta, Target, betaSched]) # Run Inversion self.invModelOnActiveCells = inversion.run(m0) self.invModelOnAllCells = self.givenModelCond * numpy.ones_like(self.givenModelCond) self.invModelOnAllCells[self.activeCellIndices] = self.invModelOnActiveCells self.invModelOnCoreCells = self.invModelOnAllCells[self.coreMeshCellIndices] pass
def MagneticsDiffSecondaryInv(mesh, model, data, **kwargs): """ Inversion module for MagneticsDiffSecondary """ from SimPEG import Optimization, Regularization, Parameters, ObjFunction, Inversion prob = Simulation3DDifferential(mesh, survey=data, mu=model) miter = kwargs.get("maxIter", 10) # Create an optimization program opt = Optimization.InexactGaussNewton(maxIter=miter) opt.bfgsH0 = Solver(sp.identity(model.nP), flag="D") # Create a regularization program reg = Regularization.Tikhonov(model) # Create an objective function beta = Parameters.BetaSchedule(beta0=1e0) obj = ObjFunction.BaseObjFunction(prob, reg, beta=beta) # Create an inversion object inv = Inversion.BaseInversion(obj, opt) return inv, reg
def setUp(self): time = np.logspace(-3, 0, 21) n_loc = 5 wires = Maps.Wires(('eta', n_loc), ('tau', n_loc), ('c', n_loc)) taumap = Maps.ExpMap(nP=n_loc) * wires.tau etamap = Maps.ExpMap(nP=n_loc) * wires.eta cmap = Maps.ExpMap(nP=n_loc) * wires.c survey = SEMultiSurvey(time=time, locs=np.zeros((n_loc, 3)), n_pulse=0) mesh = Mesh.TensorMesh([np.ones(int(n_loc * 3))]) prob = SEMultiInvProblem(mesh, etaMap=etamap, tauMap=taumap, cMap=cmap) prob.pair(survey) eta0, tau0, c0 = 0.1, 10., 0.5 m0 = np.log(np.r_[eta0 * np.ones(n_loc), tau0 * np.ones(n_loc), c0 * np.ones(n_loc)]) survey.makeSyntheticData(m0) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) reg = regularization.Tikhonov(mesh) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=0.) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = prob self.survey = survey self.m0 = m0 self.dmis = dmis self.mesh = mesh
def run(plotIt=True, saveFig=False, cleanup=True): """ Run 1D inversions for a single sounding of the RESOLVE and SkyTEM bookpurnong data :param bool plotIt: show the plots? :param bool saveFig: save the figure :param bool cleanup: remove the downloaded results """ downloads, directory = download_and_unzip_data() resolve = h5py.File( os.path.sep.join([directory, "booky_resolve.hdf5"]), "r" ) skytem = h5py.File( os.path.sep.join([directory, "booky_skytem.hdf5"]), "r" ) river_path = resolve["river_path"].value # Choose a sounding location to invert xloc, yloc = 462100.0, 6196500.0 rxind_skytem = np.argmin( abs(skytem["xy"][:, 0]-xloc)+abs(skytem["xy"][:, 1]-yloc) ) rxind_resolve = np.argmin( abs(resolve["xy"][:, 0]-xloc)+abs(resolve["xy"][:, 1]-yloc) ) # Plot both resolve and skytem data on 2D plane fig = plt.figure(figsize=(13, 6)) title = ["RESOLVE In-phase 400 Hz", "SkyTEM High moment 156 $\mu$s"] ax1 = plt.subplot(121) ax2 = plt.subplot(122) axs = [ax1, ax2] out_re = Utils.plot2Ddata( resolve["xy"], resolve["data"][:, 0], ncontour=100, contourOpts={"cmap": "viridis"}, ax=ax1 ) vmin, vmax = out_re[0].get_clim() cb_re = plt.colorbar( out_re[0], ticks=np.linspace(vmin, vmax, 3), ax=ax1, fraction=0.046, pad=0.04 ) temp_skytem = skytem["data"][:, 5].copy() temp_skytem[skytem["data"][:, 5] > 7e-10] = 7e-10 out_sky = Utils.plot2Ddata( skytem["xy"][:, :2], temp_skytem, ncontour=100, contourOpts={"cmap": "viridis", "vmax": 7e-10}, ax=ax2 ) vmin, vmax = out_sky[0].get_clim() cb_sky = plt.colorbar( out_sky[0], ticks=np.linspace(vmin, vmax*0.99, 3), ax=ax2, format="%.1e", fraction=0.046, pad=0.04 ) cb_re.set_label("Bz (ppm)") cb_sky.set_label("dB$_z$ / dt (V/A-m$^4$)") for i, ax in enumerate(axs): xticks = [460000, 463000] yticks = [6195000, 6198000, 6201000] ax.set_xticks(xticks) ax.set_yticks(yticks) ax.plot(xloc, yloc, 'wo') ax.plot(river_path[:, 0], river_path[:, 1], 'k', lw=0.5) ax.set_aspect("equal") if i == 1: ax.plot( skytem["xy"][:, 0], skytem["xy"][:, 1], 'k.', alpha=0.02, ms=1 ) ax.set_yticklabels([str(" ") for f in yticks]) else: ax.plot( resolve["xy"][:, 0], resolve["xy"][:, 1], 'k.', alpha=0.02, ms=1 ) ax.set_yticklabels([str(f) for f in yticks]) ax.set_ylabel("Northing (m)") ax.set_xlabel("Easting (m)") ax.set_title(title[i]) ax.axis('equal') # plt.tight_layout() if saveFig is True: fig.savefig("resolve_skytem_data.png", dpi=600) # ------------------ Mesh ------------------ # # Step1: Set 2D cylindrical mesh cs, ncx, ncz, npad = 1., 10., 10., 20 hx = [(cs, ncx), (cs, npad, 1.3)] npad = 12 temp = np.logspace(np.log10(1.), np.log10(12.), 19) temp_pad = temp[-1] * 1.3 ** np.arange(npad) hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad] mesh = Mesh.CylMesh([hx, 1, hz], '00C') active = mesh.vectorCCz < 0. # Step2: Set a SurjectVertical1D mapping # Note: this sets our inversion model as 1D log conductivity # below subsurface active = mesh.vectorCCz < 0. actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap sig_half = 1e-1 sig_air = 1e-8 sigma = np.ones(mesh.nCz)*sig_air sigma[active] = sig_half # Initial and reference model m0 = np.log(sigma[active]) # ------------------ RESOLVE Forward Simulation ------------------ # # Step3: Invert Resolve data # Bird height from the surface b_height_resolve = resolve["src_elevation"].value src_height_resolve = b_height_resolve[rxind_resolve] # Set Rx (In-phase and Quadrature) rxOffset = 7.86 bzr = EM.FDEM.Rx.Point_bSecondary( np.array([[rxOffset, 0., src_height_resolve]]), orientation='z', component='real' ) bzi = EM.FDEM.Rx.Point_b( np.array([[rxOffset, 0., src_height_resolve]]), orientation='z', component='imag' ) # Set Source (In-phase and Quadrature) frequency_cp = resolve["frequency_cp"].value freqs = frequency_cp.copy() srcLoc = np.array([0., 0., src_height_resolve]) srcList = [EM.FDEM.Src.MagDipole([bzr, bzi], freq, srcLoc, orientation='Z') for freq in freqs] # Set FDEM survey (In-phase and Quadrature) survey = EM.FDEM.Survey(srcList) prb = EM.FDEM.Problem3D_b(mesh, sigmaMap=mapping, Solver=Solver) prb.pair(survey) # ------------------ RESOLVE Inversion ------------------ # # Primary field bp = - mu_0/(4*np.pi*rxOffset**3) # Observed data cpi_inds = [0, 2, 6, 8, 10] cpq_inds = [1, 3, 7, 9, 11] dobs_re = np.c_[ resolve["data"][rxind_resolve, :][cpi_inds], resolve["data"][rxind_resolve, :][cpq_inds] ].flatten() * bp * 1e-6 # Uncertainty std = np.repeat(np.r_[np.ones(3)*0.1, np.ones(2)*0.15], 2) floor = 20 * abs(bp) * 1e-6 uncert = abs(dobs_re) * std + floor # Data Misfit survey.dobs = dobs_re dmisfit = DataMisfit.l2_DataMisfit(survey) dmisfit.W = 1./uncert # Regularization regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Simple(regMesh) # Optimization opt = Optimization.InexactGaussNewton(maxIter=5) # statement of the inverse problem invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # Inversion directives and parameters target = Directives.TargetMisfit() # stop when we hit target misfit invProb.beta = 2. # betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0) inv = Inversion.BaseInversion(invProb, directiveList=[target]) reg.alpha_s = 1e-3 reg.alpha_x = 1. reg.mref = m0.copy() opt.LSshorten = 0.5 opt.remember('xc') # run the inversion mopt_re = inv.run(m0) dpred_re = invProb.dpred # ------------------ SkyTEM Forward Simulation ------------------ # # Step4: Invert SkyTEM data # Bird height from the surface b_height_skytem = skytem["src_elevation"].value src_height = b_height_skytem[rxind_skytem] srcLoc = np.array([[0., 0., src_height]]) # Radius of the source loop area = skytem["area"].value radius = np.sqrt(area/np.pi) rxLoc = np.array([[radius, 0., src_height]]) # Parameters for current waveform t0 = skytem["t0"].value times = skytem["times"].value waveform_skytem = skytem["waveform"].value offTime = t0 times_off = times - t0 # Note: we are Using theoretical VTEM waveform, # but effectively fits SkyTEM waveform peakTime = 1.0000000e-02 a = 3. dbdt_z = EM.TDEM.Rx.Point_dbdt( locs=rxLoc, times=times_off[:-3]+offTime, orientation='z' ) # vertical db_dt rxList = [dbdt_z] # list of receivers srcList = [ EM.TDEM.Src.CircularLoop( rxList, loc=srcLoc, radius=radius, orientation='z', waveform=EM.TDEM.Src.VTEMWaveform( offTime=offTime, peakTime=peakTime, a=3. ) ) ] # solve the problem at these times timeSteps = [ (peakTime/5, 5), ((offTime-peakTime)/5, 5), (1e-5, 5), (5e-5, 5), (1e-4, 10), (5e-4, 15) ] prob = EM.TDEM.Problem3D_e( mesh, timeSteps=timeSteps, sigmaMap=mapping, Solver=Solver ) survey = EM.TDEM.Survey(srcList) prob.pair(survey) src = srcList[0] rx = src.rxList[0] wave = [] for time in prob.times: wave.append(src.waveform.eval(time)) wave = np.hstack(wave) out = survey.dpred(m0) # plot the waveform fig = plt.figure(figsize=(5, 3)) times_off = times-t0 plt.plot(waveform_skytem[:, 0], waveform_skytem[:, 1], 'k.') plt.plot(prob.times, wave, 'k-', lw=2) plt.legend(("SkyTEM waveform", "Waveform (fit)"), fontsize=10) for t in rx.times: plt.plot(np.ones(2)*t, np.r_[-0.03, 0.03], 'k-') plt.ylim(-0.1, 1.1) plt.grid(True) plt.xlabel("Time (s)") plt.ylabel("Normalized current") if saveFig: fig.savefig("skytem_waveform", dpi=200) # Observed data dobs_sky = skytem["data"][rxind_skytem, :-3] * area # ------------------ SkyTEM Inversion ------------------ # # Uncertainty std = 0.12 floor = 7.5e-12 uncert = abs(dobs_sky) * std + floor # Data Misfit survey.dobs = -dobs_sky dmisfit = DataMisfit.l2_DataMisfit(survey) uncert = 0.12*abs(dobs_sky) + 7.5e-12 dmisfit.W = Utils.sdiag(1./uncert) # Regularization regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Simple(regMesh) # Optimization opt = Optimization.InexactGaussNewton(maxIter=5) # statement of the inverse problem invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # Directives and Inversion Parameters target = Directives.TargetMisfit() # betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0) invProb.beta = 20. inv = Inversion.BaseInversion(invProb, directiveList=[target]) reg.alpha_s = 1e-1 reg.alpha_x = 1. opt.LSshorten = 0.5 opt.remember('xc') reg.mref = mopt_re # Use RESOLVE model as a reference model # run the inversion mopt_sky = inv.run(m0) dpred_sky = invProb.dpred # Plot the figure from the paper plt.figure(figsize=(12, 8)) fs = 13 # fontsize matplotlib.rcParams['font.size'] = fs ax0 = plt.subplot2grid((2, 2), (0, 0), rowspan=2) ax1 = plt.subplot2grid((2, 2), (0, 1)) ax2 = plt.subplot2grid((2, 2), (1, 1)) # Recovered Models sigma_re = np.repeat(np.exp(mopt_re), 2, axis=0) sigma_sky = np.repeat(np.exp(mopt_sky), 2, axis=0) z = np.repeat(mesh.vectorCCz[active][1:], 2, axis=0) z = np.r_[mesh.vectorCCz[active][0], z, mesh.vectorCCz[active][-1]] ax0.semilogx(sigma_re, z, 'k', lw=2, label="RESOLVE") ax0.semilogx(sigma_sky, z, 'b', lw=2, label="SkyTEM") ax0.set_ylim(-50, 0) # ax0.set_xlim(5e-4, 1e2) ax0.grid(True) ax0.set_ylabel("Depth (m)") ax0.set_xlabel("Conducivity (S/m)") ax0.legend(loc=3) ax0.set_title("(a) Recovered Models") # RESOLVE Data ax1.loglog( frequency_cp, dobs_re.reshape((5, 2))[:, 0]/bp*1e6, 'k-', label="Obs (real)" ) ax1.loglog( frequency_cp, dobs_re.reshape((5, 2))[:, 1]/bp*1e6, 'k--', label="Obs (imag)" ) ax1.loglog( frequency_cp, dpred_re.reshape((5, 2))[:, 0]/bp*1e6, 'k+', ms=10, markeredgewidth=2., label="Pred (real)" ) ax1.loglog( frequency_cp, dpred_re.reshape((5, 2))[:, 1]/bp*1e6, 'ko', ms=6, markeredgecolor='k', markeredgewidth=0.5, label="Pred (imag)" ) ax1.set_title("(b) RESOLVE") ax1.set_xlabel("Frequency (Hz)") ax1.set_ylabel("Bz (ppm)") ax1.grid(True) ax1.legend(loc=3, fontsize=11) # SkyTEM data ax2.loglog(times_off[3:]*1e6, dobs_sky/area, 'b-', label="Obs") ax2.loglog( times_off[3:]*1e6, -dpred_sky/area, 'bo', ms=4, markeredgecolor='k', markeredgewidth=0.5, label="Pred" ) ax2.set_xlim(times_off.min()*1e6*1.2, times_off.max()*1e6*1.1) ax2.set_xlabel("Time ($\mu s$)") ax2.set_ylabel("dBz / dt (V/A-m$^4$)") ax2.set_title("(c) SkyTEM High-moment") ax2.grid(True) ax2.legend(loc=3) a3 = plt.axes([0.86, .33, .1, .09], facecolor=[0.8, 0.8, 0.8, 0.6]) a3.plot(prob.times*1e6, wave, 'k-') a3.plot( rx.times*1e6, np.zeros_like(rx.times), 'k|', markeredgewidth=1, markersize=12 ) a3.set_xlim([prob.times.min()*1e6*0.75, prob.times.max()*1e6*1.1]) a3.set_title('(d) Waveform', fontsize=11) a3.set_xticks([prob.times.min()*1e6, t0*1e6, prob.times.max()*1e6]) a3.set_yticks([]) # a3.set_xticklabels(['0', '2e4']) a3.set_xticklabels(['-1e4', '0', '1e4']) plt.tight_layout() if saveFig: plt.savefig("booky1D_time_freq.png", dpi=600) if plotIt: plt.show() if cleanup: print( os.path.split(directory)[:-1]) os.remove( os.path.sep.join( directory.split()[:-1] + ["._bookpurnong_inversion"] ) ) os.remove(downloads) shutil.rmtree(directory)
def run(plotIt=True): """ 1D FDEM Mu Inversion ==================== 1D inversion of Magnetic Susceptibility from FDEM data assuming a fixed electrical conductivity """ # Set up cylindrically symmeric mesh cs, ncx, ncz, npad = 10., 15, 25, 13 # padded cyl mesh hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') # Geologic Parameters model layerz = np.r_[-100., -50.] layer = (mesh.vectorCCz >= layerz[0]) & (mesh.vectorCCz <= layerz[1]) active = mesh.vectorCCz < 0. # Electrical Conductivity sig_half = 1e-2 # Half-space conductivity sig_air = 1e-8 # Air conductivity sig_layer = 1e-2 # Layer conductivity sigma = np.ones(mesh.nCz) * sig_air sigma[active] = sig_half sigma[layer] = sig_layer # mur - relative magnetic permeability mur_half = 1. mur_air = 1. mur_layer = 2. mur = np.ones(mesh.nCz) * mur_air mur[active] = mur_half mur[layer] = mur_layer mtrue = mur[active] # Maps actMap = Maps.InjectActiveCells(mesh, active, mur_air, nC=mesh.nCz) surj1Dmap = Maps.SurjectVertical1D(mesh) murMap = Maps.MuRelative(mesh) # Mapping muMap = murMap * surj1Dmap * actMap # ----- FDEM problem & survey ----- rxlocs = Utils.ndgrid([np.r_[10.], np.r_[0], np.r_[30.]]) bzr = FDEM.Rx.Point_bSecondary(rxlocs, 'z', 'real') # bzi = FDEM.Rx.Point_bSecondary(rxlocs, 'z', 'imag') freqs = np.linspace(2000, 10000, 10) #np.logspace(3, 4, 10) srcLoc = np.array([0., 0., 30.]) print('min skin depth = ', 500. / np.sqrt(freqs.max() * sig_half), 'max skin depth = ', 500. / np.sqrt(freqs.min() * sig_half)) print('max x ', mesh.vectorCCx.max(), 'min z ', mesh.vectorCCz.min(), 'max z ', mesh.vectorCCz.max()) srcList = [ FDEM.Src.MagDipole([bzr], freq, srcLoc, orientation='Z') for freq in freqs ] surveyFD = FDEM.Survey(srcList) prbFD = FDEM.Problem3D_b(mesh, sigma=surj1Dmap * sigma, muMap=muMap, Solver=Solver) prbFD.pair(surveyFD) std = 0.03 surveyFD.makeSyntheticData(mtrue, std) surveyFD.eps = np.linalg.norm(surveyFD.dtrue) * 1e-6 # FDEM inversion np.random.seed(13472) dmisfit = DataMisfit.l2_DataMisfit(surveyFD) regMesh = Mesh.TensorMesh([mesh.hz[muMap.maps[-1].indActive]]) reg = Regularization.Simple(regMesh) opt = Optimization.InexactGaussNewton(maxIterCG=10) invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # Inversion Directives betaest = Directives.BetaEstimate_ByEig(beta0_ratio=2.) beta = Directives.BetaSchedule(coolingFactor=4, coolingRate=3) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=2.) target = Directives.TargetMisfit() directiveList = [beta, betaest, target] inv = Inversion.BaseInversion(invProb, directiveList=directiveList) m0 = mur_half * np.ones(mtrue.size) reg.alpha_s = 2e-2 reg.alpha_x = 1. prbFD.counter = opt.counter = Utils.Counter() opt.remember('xc') moptFD = inv.run(m0) dpredFD = surveyFD.dpred(moptFD) if plotIt: fig, ax = plt.subplots(1, 3, figsize=(10, 6)) fs = 13 # fontsize matplotlib.rcParams['font.size'] = fs # Plot the conductivity model ax[0].semilogx(sigma[active], mesh.vectorCCz[active], 'k-', lw=2) ax[0].set_ylim(-500, 0) ax[0].set_xlim(5e-3, 1e-1) ax[0].set_xlabel('Conductivity (S/m)', fontsize=fs) ax[0].set_ylabel('Depth (m)', fontsize=fs) ax[0].grid(which='both', color='k', alpha=0.5, linestyle='-', linewidth=0.2) ax[0].legend(['Conductivity Model'], fontsize=fs, loc=4) # Plot the permeability model ax[1].plot(mur[active], mesh.vectorCCz[active], 'k-', lw=2) ax[1].plot(moptFD, mesh.vectorCCz[active], 'b-', lw=2) ax[1].set_ylim(-500, 0) ax[1].set_xlim(0.5, 2.1) ax[1].set_xlabel('Relative Permeability', fontsize=fs) ax[1].set_ylabel('Depth (m)', fontsize=fs) ax[1].grid(which='both', color='k', alpha=0.5, linestyle='-', linewidth=0.2) ax[1].legend(['True', 'Predicted'], fontsize=fs, loc=4) # plot the data misfits - negative b/c we choose positive to be in the # direction of primary ax[2].plot(freqs, -surveyFD.dobs, 'k-', lw=2) # ax[2].plot(freqs, -surveyFD.dobs[1::2], 'k--', lw=2) ax[2].loglog(freqs, -dpredFD, 'bo', ms=6) # ax[2].loglog(freqs, -dpredFD[1::2], 'b+', markeredgewidth=2., ms=10) # Labels, gridlines, etc ax[2].grid(which='both', alpha=0.5, linestyle='-', linewidth=0.2) ax[2].grid(which='both', alpha=0.5, linestyle='-', linewidth=0.2) ax[2].set_xlabel('Frequency (Hz)', fontsize=fs) ax[2].set_ylabel('Vertical magnetic field (-T)', fontsize=fs) # ax[2].legend(("Obs", "Pred"), fontsize=fs) ax[2].legend(("z-Obs (real)", "z-Pred (real)"), fontsize=fs) ax[2].set_xlim(freqs.max(), freqs.min()) ax[0].set_title("(a) Conductivity Model", fontsize=fs) ax[1].set_title("(b) $\mu_r$ Model", fontsize=fs) ax[2].set_title("(c) FDEM observed vs. predicted", fontsize=fs) # ax[2].set_title("(c) TDEM observed vs. predicted", fontsize=fs) plt.tight_layout(pad=1.5)
def run(plotIt=True): cs, ncx, ncz, npad = 5., 25, 15, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') layerz = -100. active = mesh.vectorCCz < 0. layer = (mesh.vectorCCz < 0.) & (mesh.vectorCCz >= layerz) actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap sig_half = 2e-2 sig_air = 1e-8 sig_layer = 1e-2 sigma = np.ones(mesh.nCz) * sig_air sigma[active] = sig_half sigma[layer] = sig_layer mtrue = np.log(sigma[active]) if plotIt: fig, ax = plt.subplots(1, 1, figsize=(3, 6)) plt.semilogx(sigma[active], mesh.vectorCCz[active]) ax.set_ylim(-500, 0) ax.set_xlim(1e-3, 1e-1) ax.set_xlabel('Conductivity (S/m)', fontsize=14) ax.set_ylabel('Depth (m)', fontsize=14) ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5) rxOffset = 10. bzi = EM.FDEM.Rx.Point_b(np.array([[rxOffset, 0., 1e-3]]), orientation='z', component='imag') freqs = np.logspace(1, 3, 10) srcLoc = np.array([0., 0., 10.]) srcList = [ EM.FDEM.Src.MagDipole([bzi], freq, srcLoc, orientation='Z') for freq in freqs ] survey = EM.FDEM.Survey(srcList) prb = EM.FDEM.Problem3D_b(mesh, sigmaMap=mapping, Solver=Solver) prb.pair(survey) std = 0.05 survey.makeSyntheticData(mtrue, std) survey.std = std survey.eps = np.linalg.norm(survey.dtrue) * 1e-5 if plotIt: fig, ax = plt.subplots(1, 1, figsize=(6, 6)) ax.semilogx(freqs, survey.dtrue[:freqs.size], 'b.-') ax.semilogx(freqs, survey.dobs[:freqs.size], 'r.-') ax.legend(('Noisefree', '$d^{obs}$'), fontsize=16) ax.set_xlabel('Time (s)', fontsize=14) ax.set_ylabel('$B_z$ (T)', fontsize=16) ax.set_xlabel('Time (s)', fontsize=14) ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5) dmisfit = DataMisfit.l2_DataMisfit(survey) regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Tikhonov(regMesh) opt = Optimization.InexactGaussNewton(maxIter=6) invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # Create an inversion object beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0) inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest]) m0 = np.log(np.ones(mtrue.size) * sig_half) reg.alpha_s = 1e-3 reg.alpha_x = 1. prb.counter = opt.counter = Utils.Counter() opt.LSshorten = 0.5 opt.remember('xc') mopt = inv.run(m0) if plotIt: fig, ax = plt.subplots(1, 1, figsize=(3, 6)) plt.semilogx(sigma[active], mesh.vectorCCz[active]) plt.semilogx(np.exp(mopt), mesh.vectorCCz[active]) ax.set_ylim(-500, 0) ax.set_xlim(1e-3, 1e-1) ax.set_xlabel('Conductivity (S/m)', fontsize=14) ax.set_ylabel('Depth (m)', fontsize=14) ax.grid(color='k', alpha=0.5, linestyle='dashed', linewidth=0.5) plt.legend(['$\sigma_{true}$', '$\sigma_{pred}$'], loc='best')
def setUp(self): cs = 25. hx = [(cs, 0, -1.3), (cs, 21), (cs, 0, 1.3)] hy = [(cs, 0, -1.3), (cs, 21), (cs, 0, 1.3)] hz = [(cs, 0, -1.3), (cs, 20), (cs, 0, 1.3)] mesh = Mesh.TensorMesh([hx, hy, hz], x0="CCC") blkind0 = Utils.ModelBuilder.getIndicesSphere( np.r_[-100., -100., -200.], 75., mesh.gridCC ) blkind1 = Utils.ModelBuilder.getIndicesSphere( np.r_[100., 100., -200.], 75., mesh.gridCC ) sigma = np.ones(mesh.nC)*1e-2 airind = mesh.gridCC[:, 2] > 0. sigma[airind] = 1e-8 eta = np.zeros(mesh.nC) tau = np.ones_like(sigma) * 1. c = np.ones_like(sigma) * 0.5 eta[blkind0] = 0.1 eta[blkind1] = 0.1 tau[blkind0] = 0.1 tau[blkind1] = 0.01 actmapeta = Maps.InjectActiveCells(mesh, ~airind, 0.) actmaptau = Maps.InjectActiveCells(mesh, ~airind, 1.) actmapc = Maps.InjectActiveCells(mesh, ~airind, 1.) x = mesh.vectorCCx[(mesh.vectorCCx > -155.) & (mesh.vectorCCx < 155.)] y = mesh.vectorCCy[(mesh.vectorCCy > -155.) & (mesh.vectorCCy < 155.)] Aloc = np.r_[-200., 0., 0.] Bloc = np.r_[200., 0., 0.] M = Utils.ndgrid(x-25., y, np.r_[0.]) N = Utils.ndgrid(x+25., y, np.r_[0.]) times = np.arange(10)*1e-3 + 1e-3 rx = SIP.Rx.Dipole(M, N, times) src = SIP.Src.Dipole([rx], Aloc, Bloc) survey = SIP.Survey([src]) wires = Maps.Wires(('eta', actmapeta.nP), ('taui', actmaptau.nP), ('c', actmapc.nP)) problem = SIP.Problem3D_N( mesh, sigma=sigma, etaMap=actmapeta*wires.eta, tauiMap=actmaptau*wires.taui, cMap=actmapc*wires.c, actinds=~airind, storeJ = True, verbose=False ) problem.Solver = Solver problem.pair(survey) mSynth = np.r_[eta[~airind], 1./tau[~airind], c[~airind]] survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) dmis = DataMisfit.l2_DataMisfit(survey) reg_eta = Regularization.Simple(mesh, mapping=wires.eta, indActive=~airind) reg_taui = Regularization.Simple(mesh, mapping=wires.taui, indActive=~airind) reg_c = Regularization.Simple(mesh, mapping=wires.c, indActive=~airind) reg = reg_eta + reg_taui + reg_c opt = Optimization.InexactGaussNewton( maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6 ) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e4) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
def run(plotIt=True, survey_type="dipole-dipole", rho_background=1e3, rho_block=1e2, block_x0=100, block_dx=10, block_y0=-10, block_dy=5): np.random.seed(1) # Initiate I/O class for DC IO = DC.IO() # Obtain ABMN locations xmin, xmax = 0., 200. ymin, ymax = 0., 0. zmin, zmax = 0, 0 endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]]) # Generate DC survey object survey = DC.Utils.gen_DCIPsurvey(endl, survey_type=survey_type, dim=2, a=10, b=10, n=10) survey.getABMN_locations() survey = IO.from_ambn_locations_to_survey(survey.a_locations, survey.b_locations, survey.m_locations, survey.n_locations, survey_type, data_dc_type='volt') # Obtain 2D TensorMesh mesh, actind = IO.set_mesh() # Flat topography actind = Utils.surface2ind_topo(mesh, np.c_[mesh.vectorCCx, mesh.vectorCCx * 0.]) survey.drapeTopo(mesh, actind, option="top") # Use Exponential Map: m = log(rho) actmap = Maps.InjectActiveCells(mesh, indActive=actind, valInactive=np.log(1e8)) parametric_block = Maps.ParametricBlock(mesh, slopeFact=1e2) mapping = Maps.ExpMap(mesh) * parametric_block # Set true model # val_background,val_block, block_x0, block_dx, block_y0, block_dy mtrue = np.r_[np.log(1e3), np.log(10), 100, 10, -20, 10] # Set initial model m0 = np.r_[np.log(rho_background), np.log(rho_block), block_x0, block_dx, block_y0, block_dy] rho = mapping * mtrue rho0 = mapping * m0 # Show the true conductivity model fig = plt.figure(figsize=(12, 3)) ax = plt.subplot(111) temp = rho.copy() temp[~actind] = np.nan out = mesh.plotImage(temp, grid=False, ax=ax, gridOpts={'alpha': 0.2}, clim=(10, 1000), pcolorOpts={ "cmap": "viridis", "norm": colors.LogNorm() }) ax.plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1], 'k.') ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max()) ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min()) cb = plt.colorbar(out[0]) cb.set_label("Resistivity (ohm-m)") ax.set_aspect('equal') ax.set_title("True resistivity model") plt.show() # Show the true conductivity model fig = plt.figure(figsize=(12, 3)) ax = plt.subplot(111) temp = rho0.copy() temp[~actind] = np.nan out = mesh.plotImage(temp, grid=False, ax=ax, gridOpts={'alpha': 0.2}, clim=(10, 1000), pcolorOpts={ "cmap": "viridis", "norm": colors.LogNorm() }) ax.plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1], 'k.') ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max()) ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min()) cb = plt.colorbar(out[0]) cb.set_label("Resistivity (ohm-m)") ax.set_aspect('equal') ax.set_title("Initial resistivity model") plt.show() # Generate 2.5D DC problem # "N" means potential is defined at nodes prb = DC.Problem2D_N(mesh, rhoMap=mapping, storeJ=True, Solver=Solver) # Pair problem with survey try: prb.pair(survey) except: survey.unpair() prb.pair(survey) # Make synthetic DC data with 5% Gaussian noise dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True) # Show apparent resisitivty pseudo-section IO.plotPseudoSection(data=survey.dobs / IO.G, data_type='apparent_resistivity') # Show apparent resisitivty histogram fig = plt.figure() out = hist(survey.dobs / IO.G, bins=20) plt.show() # Set uncertainty # floor eps = 10**(-3.2) # percentage std = 0.05 dmisfit = DataMisfit.l2_DataMisfit(survey) uncert = abs(survey.dobs) * std + eps dmisfit.W = 1. / uncert # Map for a regularization mesh_1d = Mesh.TensorMesh([parametric_block.nP]) # Related to inversion reg = Regularization.Simple(mesh_1d, alpha_x=0.) opt = Optimization.InexactGaussNewton(maxIter=10) invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0) target = Directives.TargetMisfit() updateSensW = Directives.UpdateSensitivityWeights() update_Jacobi = Directives.UpdatePreconditioner() invProb.beta = 0. inv = Inversion.BaseInversion(invProb, directiveList=[target]) prb.counter = opt.counter = Utils.Counter() opt.LSshorten = 0.5 opt.remember('xc') # Run inversion mopt = inv.run(m0) # Convert obtained inversion model to resistivity # rho = M(m), where M(.) is a mapping rho_est = mapping * mopt rho_true = rho.copy() # show recovered conductivity vmin, vmax = rho.min(), rho.max() fig, ax = plt.subplots(2, 1, figsize=(20, 6)) out1 = mesh.plotImage(rho_true, clim=(10, 1000), pcolorOpts={ "cmap": "viridis", "norm": colors.LogNorm() }, ax=ax[0]) out2 = mesh.plotImage(rho_est, clim=(10, 1000), pcolorOpts={ "cmap": "viridis", "norm": colors.LogNorm() }, ax=ax[1]) out = [out1, out2] for i in range(2): ax[i].plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1], 'kv') ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max()) ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min()) cb = plt.colorbar(out[i][0], ax=ax[i]) cb.set_label("Resistivity ($\Omega$m)") ax[i].set_xlabel("Northing (m)") ax[i].set_ylabel("Elevation (m)") ax[i].set_aspect('equal') ax[0].set_title("True resistivity model") ax[1].set_title("Recovered resistivity model") plt.tight_layout() plt.show()
def setUp(self, parallel=True): time = np.logspace(-6, -3, 21) hz = get_vertical_discretization_time(time, facter_tmax=0.5, factor_tmin=10.) time_input_currents = wave.current_times[-7:] input_currents = wave.currents[-7:] n_sounding = 10 dx = 20. hx = np.ones(n_sounding) * dx mesh = Mesh.TensorMesh([hx, hz], x0='00') inds = mesh.gridCC[:, 1] < 25 inds_1 = mesh.gridCC[:, 1] < 50 sigma = np.ones(mesh.nC) * 1. / 100. sigma[inds_1] = 1. / 10. sigma[inds] = 1. / 50. sigma_em1d = sigma.reshape(mesh.vnC, order='F').flatten() mSynth = np.log(sigma_em1d) x = mesh.vectorCCx y = np.zeros_like(x) z = np.ones_like(x) * 30. rx_locations = np.c_[x, y, z] src_locations = np.c_[x, y, z] topo = np.c_[x, y, z - 30.].astype(float) n_sounding = rx_locations.shape[0] rx_type_global = np.array(["dBzdt"], dtype=str).repeat(n_sounding, axis=0) field_type_global = np.array(['secondary'], dtype=str).repeat(n_sounding, axis=0) wave_type_global = np.array(['general'], dtype=str).repeat(n_sounding, axis=0) time_global = [time for i in range(n_sounding)] src_type_global = np.array(["CircularLoop"], dtype=str).repeat(n_sounding, axis=0) a_global = np.array([13.], dtype=float).repeat(n_sounding, axis=0) input_currents_global = [input_currents for i in range(n_sounding)] time_input_currents_global = [ time_input_currents for i in range(n_sounding) ] mapping = Maps.ExpMap(mesh) survey = GlobalEM1DSurveyTD( rx_locations=rx_locations, src_locations=src_locations, topo=topo, time=time_global, src_type=src_type_global, rx_type=rx_type_global, field_type=field_type_global, wave_type=wave_type_global, a=a_global, input_currents=input_currents_global, time_input_currents=time_input_currents_global) problem = GlobalEM1DProblemTD(mesh, sigmaMap=mapping, hz=hz, parallel=parallel, n_cpu=5) problem.pair(survey) survey.makeSyntheticData(mSynth) # Now set up the problem to do some minimization dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov(mesh) opt = Optimization.InexactGaussNewton(maxIterLS=20, maxIter=10, tolF=1e-6, tolX=1e-6, tolG=1e-6, maxIterCG=6) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=0.) inv = Inversion.BaseInversion(invProb) self.inv = inv self.reg = reg self.p = problem self.mesh = mesh self.m0 = mSynth self.survey = survey self.dmis = dmis
problem.unpair() problem.pair(survey_r) d = survey_r.dpred(mtrue) survey_r.dobs = d survey_r.std = np.ones_like(d) * 0.05 print '# of data: ', survey_r.dobs.shape regmesh = mesh dmis = DataMisfit.l2_DataMisfit(survey_r) reg = Regularization.Tikhonov( regmesh) #,mapping = mapping)#,indActive=actind) reg.mref = miter opt = Optimization.InexactGaussNewton(maxIter=InnerIt, tolX=1e-6) opt.remember('xc') invProb = InvProblem.BaseInvProblem(dmis, reg, opt) #beta = Directives.BetaEstimate_ByEig(beta0= 10.,beta0_ratio=1e0) reg.alpha_s = 1e-6 invProb.beta = beta #betaSched = Directives.BetaSchedule(coolingFactor=5, coolingRate=2) #sav0 = Directives.SaveEveryIteration() #sav1 = Directives.SaveModelEveryIteration() sav2 = Directives.SaveOutputDictEveryIteration() inv = Inversion.BaseInversion( invProb, directiveList=[sav2]) #[beta,betaSched])#sav0,sav1, msimple = inv.run(miter) beta = invProb.beta if np.mod(it + 1, coolingRate) == 0:
def run(plotIt=True, survey_type="dipole-dipole", p=0., qx=2., qz=2.): np.random.seed(1) # Initiate I/O class for DC IO = DC.IO() # Obtain ABMN locations xmin, xmax = 0., 200. ymin, ymax = 0., 0. zmin, zmax = 0, 0 endl = np.array([[xmin, ymin, zmin], [xmax, ymax, zmax]]) # Generate DC survey object survey = DC.Utils.gen_DCIPsurvey(endl, survey_type=survey_type, dim=2, a=10, b=10, n=10) survey.getABMN_locations() survey = IO.from_ambn_locations_to_survey(survey.a_locations, survey.b_locations, survey.m_locations, survey.n_locations, survey_type, data_dc_type='volt') # Obtain 2D TensorMesh mesh, actind = IO.set_mesh() topo, mesh1D = DC.Utils.genTopography(mesh, -10, 0, its=100) actind = Utils.surface2ind_topo(mesh, np.c_[mesh1D.vectorCCx, topo]) survey.drapeTopo(mesh, actind, option="top") # Build a conductivity model blk_inds_c = Utils.ModelBuilder.getIndicesSphere(np.r_[60., -25.], 12.5, mesh.gridCC) blk_inds_r = Utils.ModelBuilder.getIndicesSphere(np.r_[140., -25.], 12.5, mesh.gridCC) layer_inds = mesh.gridCC[:, 1] > -5. sigma = np.ones(mesh.nC) * 1. / 100. sigma[blk_inds_c] = 1. / 10. sigma[blk_inds_r] = 1. / 1000. sigma[~actind] = 1. / 1e8 rho = 1. / sigma # Show the true conductivity model if plotIt: fig = plt.figure(figsize=(12, 3)) ax = plt.subplot(111) temp = rho.copy() temp[~actind] = np.nan out = mesh.plotImage(temp, grid=True, ax=ax, gridOpts={'alpha': 0.2}, clim=(10, 1000), pcolorOpts={ "cmap": "viridis", "norm": colors.LogNorm() }) ax.plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1], 'k.') ax.set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max()) ax.set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min()) cb = plt.colorbar(out[0]) cb.set_label("Resistivity (ohm-m)") ax.set_aspect('equal') plt.show() # Use Exponential Map: m = log(rho) actmap = Maps.InjectActiveCells(mesh, indActive=actind, valInactive=np.log(1e8)) mapping = Maps.ExpMap(mesh) * actmap # Generate mtrue mtrue = np.log(rho[actind]) # Generate 2.5D DC problem # "N" means potential is defined at nodes prb = DC.Problem2D_N(mesh, rhoMap=mapping, storeJ=True, Solver=Solver, verbose=True) # Pair problem with survey try: prb.pair(survey) except: survey.unpair() prb.pair(survey) # Make synthetic DC data with 5% Gaussian noise dtrue = survey.makeSyntheticData(mtrue, std=0.05, force=True) IO.data_dc = dtrue # Show apparent resisitivty pseudo-section if plotIt: IO.plotPseudoSection(data=survey.dobs / IO.G, data_type='apparent_resistivity') # Show apparent resisitivty histogram if plotIt: fig = plt.figure() out = hist(survey.dobs / IO.G, bins=20) plt.xlabel("Apparent Resisitivty ($\Omega$m)") plt.show() # Set initial model based upon histogram m0 = np.ones(actmap.nP) * np.log(100.) # Set uncertainty # floor eps = 10**(-3.2) # percentage std = 0.05 dmisfit = DataMisfit.l2_DataMisfit(survey) uncert = abs(survey.dobs) * std + eps dmisfit.W = 1. / uncert # Map for a regularization regmap = Maps.IdentityMap(nP=int(actind.sum())) # Related to inversion reg = Regularization.Sparse(mesh, indActive=actind, mapping=regmap, gradientType='components') # gradientType = 'components' reg.norms = np.c_[p, qx, qz, 0.] IRLS = Directives.Update_IRLS(maxIRLSiter=20, minGNiter=1, betaSearch=False, fix_Jmatrix=True) opt = Optimization.InexactGaussNewton(maxIter=40) invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=2) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e0) target = Directives.TargetMisfit() update_Jacobi = Directives.UpdatePreconditioner() inv = Inversion.BaseInversion(invProb, directiveList=[betaest, IRLS]) prb.counter = opt.counter = Utils.Counter() opt.LSshorten = 0.5 opt.remember('xc') # Run inversion mopt = inv.run(m0) rho_est = mapping * mopt rho_est_l2 = mapping * invProb.l2model rho_est[~actind] = np.nan rho_est_l2[~actind] = np.nan rho_true = rho.copy() rho_true[~actind] = np.nan # show recovered conductivity if plotIt: vmin, vmax = rho.min(), rho.max() fig, ax = plt.subplots(3, 1, figsize=(20, 9)) out1 = mesh.plotImage(rho_true, clim=(10, 1000), pcolorOpts={ "cmap": "viridis", "norm": colors.LogNorm() }, ax=ax[0]) out2 = mesh.plotImage(rho_est_l2, clim=(10, 1000), pcolorOpts={ "cmap": "viridis", "norm": colors.LogNorm() }, ax=ax[1]) out3 = mesh.plotImage(rho_est, clim=(10, 1000), pcolorOpts={ "cmap": "viridis", "norm": colors.LogNorm() }, ax=ax[2]) out = [out1, out2, out3] titles = ["True", "L2", ("L%d, Lx%d, Lz%d") % (p, qx, qz)] for i in range(3): ax[i].plot(survey.electrode_locations[:, 0], survey.electrode_locations[:, 1], 'kv') ax[i].set_xlim(IO.grids[:, 0].min(), IO.grids[:, 0].max()) ax[i].set_ylim(-IO.grids[:, 1].max(), IO.grids[:, 1].min()) cb = plt.colorbar(out[i][0], ax=ax[i]) cb.set_label("Resistivity ($\Omega$m)") ax[i].set_xlabel("Northing (m)") ax[i].set_ylabel("Elevation (m)") ax[i].set_aspect('equal') ax[i].set_title(titles[i]) plt.tight_layout() plt.show()
def run(plotIt=True, saveFig=False): # Set up cylindrically symmeric mesh cs, ncx, ncz, npad = 10., 15, 25, 13 # padded cyl mesh hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = Mesh.CylMesh([hx, 1, hz], '00C') # Conductivity model layerz = np.r_[-200., -100.] layer = (mesh.vectorCCz >= layerz[0]) & (mesh.vectorCCz <= layerz[1]) active = mesh.vectorCCz < 0. sig_half = 1e-2 # Half-space conductivity sig_air = 1e-8 # Air conductivity sig_layer = 5e-2 # Layer conductivity sigma = np.ones(mesh.nCz) * sig_air sigma[active] = sig_half sigma[layer] = sig_layer # Mapping actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap mtrue = np.log(sigma[active]) # ----- FDEM problem & survey ----- # rxlocs = Utils.ndgrid([np.r_[50.], np.r_[0], np.r_[0.]]) bzr = FDEM.Rx.Point_bSecondary(rxlocs, 'z', 'real') bzi = FDEM.Rx.Point_bSecondary(rxlocs, 'z', 'imag') freqs = np.logspace(2, 3, 5) srcLoc = np.array([0., 0., 0.]) print('min skin depth = ', 500. / np.sqrt(freqs.max() * sig_half), 'max skin depth = ', 500. / np.sqrt(freqs.min() * sig_half)) print('max x ', mesh.vectorCCx.max(), 'min z ', mesh.vectorCCz.min(), 'max z ', mesh.vectorCCz.max()) srcList = [ FDEM.Src.MagDipole([bzr, bzi], freq, srcLoc, orientation='Z') for freq in freqs ] surveyFD = FDEM.Survey(srcList) prbFD = FDEM.Problem3D_b(mesh, sigmaMap=mapping, Solver=Solver) prbFD.pair(surveyFD) std = 0.03 surveyFD.makeSyntheticData(mtrue, std) surveyFD.eps = np.linalg.norm(surveyFD.dtrue) * 1e-5 # FDEM inversion np.random.seed(1) dmisfit = DataMisfit.l2_DataMisfit(surveyFD) regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Simple(regMesh) opt = Optimization.InexactGaussNewton(maxIterCG=10) invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # Inversion Directives beta = Directives.BetaSchedule(coolingFactor=4, coolingRate=3) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=2.) target = Directives.TargetMisfit() directiveList = [beta, betaest, target] inv = Inversion.BaseInversion(invProb, directiveList=directiveList) m0 = np.log(np.ones(mtrue.size) * sig_half) reg.alpha_s = 5e-1 reg.alpha_x = 1. prbFD.counter = opt.counter = Utils.Counter() opt.remember('xc') moptFD = inv.run(m0) # TDEM problem times = np.logspace(-4, np.log10(2e-3), 10) print('min diffusion distance ', 1.28 * np.sqrt(times.min() / (sig_half * mu_0)), 'max diffusion distance ', 1.28 * np.sqrt(times.max() / (sig_half * mu_0))) rx = TDEM.Rx.Point_b(rxlocs, times, 'z') src = TDEM.Src.MagDipole( [rx], waveform=TDEM.Src.StepOffWaveform(), loc=srcLoc # same src location as FDEM problem ) surveyTD = TDEM.Survey([src]) prbTD = TDEM.Problem3D_b(mesh, sigmaMap=mapping, Solver=Solver) prbTD.timeSteps = [(5e-5, 10), (1e-4, 10), (5e-4, 10)] prbTD.pair(surveyTD) std = 0.03 surveyTD.makeSyntheticData(mtrue, std) surveyTD.std = std surveyTD.eps = np.linalg.norm(surveyTD.dtrue) * 1e-5 # TDEM inversion dmisfit = DataMisfit.l2_DataMisfit(surveyTD) regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Simple(regMesh) opt = Optimization.InexactGaussNewton(maxIterCG=10) invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # directives beta = Directives.BetaSchedule(coolingFactor=4, coolingRate=3) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=2.) target = Directives.TargetMisfit() directiveList = [beta, betaest, target] inv = Inversion.BaseInversion(invProb, directiveList=directiveList) m0 = np.log(np.ones(mtrue.size) * sig_half) reg.alpha_s = 5e-1 reg.alpha_x = 1. prbTD.counter = opt.counter = Utils.Counter() opt.remember('xc') moptTD = inv.run(m0) # Plot the results if plotIt: plt.figure(figsize=(10, 8)) ax0 = plt.subplot2grid((2, 2), (0, 0), rowspan=2) ax1 = plt.subplot2grid((2, 2), (0, 1)) ax2 = plt.subplot2grid((2, 2), (1, 1)) fs = 13 # fontsize matplotlib.rcParams['font.size'] = fs # Plot the model ax0.semilogx(sigma[active], mesh.vectorCCz[active], 'k-', lw=2, label="True") ax0.semilogx(np.exp(moptFD), mesh.vectorCCz[active], 'bo', ms=6, markeredgecolor='k', markeredgewidth=0.5, label="FDEM") ax0.semilogx(np.exp(moptTD), mesh.vectorCCz[active], 'r*', ms=10, markeredgecolor='k', markeredgewidth=0.5, label="TDEM") ax0.set_ylim(-700, 0) ax0.set_xlim(5e-3, 1e-1) ax0.set_xlabel('Conductivity (S/m)', fontsize=fs) ax0.set_ylabel('Depth (m)', fontsize=fs) ax0.grid(which='both', color='k', alpha=0.5, linestyle='-', linewidth=0.2) ax0.legend(fontsize=fs, loc=4) # plot the data misfits - negative b/c we choose positive to be in the # direction of primary ax1.plot(freqs, -surveyFD.dobs[::2], 'k-', lw=2, label="Obs (real)") ax1.plot(freqs, -surveyFD.dobs[1::2], 'k--', lw=2, label="Obs (imag)") dpredFD = surveyFD.dpred(moptTD) ax1.loglog(freqs, -dpredFD[::2], 'bo', ms=6, markeredgecolor='k', markeredgewidth=0.5, label="Pred (real)") ax1.loglog(freqs, -dpredFD[1::2], 'b+', ms=10, markeredgewidth=2., label="Pred (imag)") ax2.loglog(times, surveyTD.dobs, 'k-', lw=2, label='Obs') ax2.loglog(times, surveyTD.dpred(moptTD), 'r*', ms=10, markeredgecolor='k', markeredgewidth=0.5, label='Pred') ax2.set_xlim(times.min() - 1e-5, times.max() + 1e-4) # Labels, gridlines, etc ax2.grid(which='both', alpha=0.5, linestyle='-', linewidth=0.2) ax1.grid(which='both', alpha=0.5, linestyle='-', linewidth=0.2) ax1.set_xlabel('Frequency (Hz)', fontsize=fs) ax1.set_ylabel('Vertical magnetic field (-T)', fontsize=fs) ax2.set_xlabel('Time (s)', fontsize=fs) ax2.set_ylabel('Vertical magnetic field (T)', fontsize=fs) ax2.legend(fontsize=fs, loc=3) ax1.legend(fontsize=fs, loc=3) ax1.set_xlim(freqs.max() + 1e2, freqs.min() - 1e1) ax0.set_title("(a) Recovered Models", fontsize=fs) ax1.set_title("(b) FDEM observed vs. predicted", fontsize=fs) ax2.set_title("(c) TDEM observed vs. predicted", fontsize=fs) plt.tight_layout(pad=1.5) if saveFig is True: plt.savefig('example1.png', dpi=600)
#################### # Initial Model m0 = np.median(ln_sigback) * np.ones(mapping.nP) # Data Misfit dmis = DataMisfit.l2_DataMisfit(survey) # Regularization regT = Regularization.Simple(mesh, indActive=actind, alpha_s=1e-6, alpha_x=1., alpha_y=1., alpha_z=1.) # Optimization Scheme opt = Optimization.InexactGaussNewton(maxIter=10) # Form the problem opt.remember('xc') invProb = InvProblem.BaseInvProblem(dmis, regT, opt) # Directives for Inversions beta = Directives.BetaEstimate_ByEig(beta0_ratio=1e+1) Target = Directives.TargetMisfit() betaSched = Directives.BetaSchedule(coolingFactor=5., coolingRate=2) inv = Inversion.BaseInversion(invProb, directiveList=[beta, Target, betaSched]) # Run Inversion minv = inv.run(m0) # Final Plot
def run_inversion_cg( self, maxIter=60, m0=0.0, mref=0.0, percentage=5, floor=0.1, chifact=1, beta0_ratio=1.0, coolingFactor=1, coolingRate=1, alpha_s=1.0, alpha_x=1.0, use_target=False, ): survey, prob = self.get_problem_survey() survey.eps = percentage survey.std = floor survey.dobs = self.data.copy() self.uncertainty = percentage * abs(survey.dobs) * 0.01 + floor m0 = np.ones(self.M) * m0 mref = np.ones(self.M) * mref reg = Regularization.Tikhonov( self.mesh, alpha_s=alpha_s, alpha_x=alpha_x, mref=mref ) dmis = DataMisfit.l2_DataMisfit(survey) dmis.W = 1.0 / self.uncertainty opt = Optimization.InexactGaussNewton(maxIter=maxIter, maxIterCG=20) opt.remember("xc") opt.tolG = 1e-10 opt.eps = 1e-10 invProb = InvProblem.BaseInvProblem(dmis, reg, opt) save = Directives.SaveOutputEveryIteration() beta_schedule = Directives.BetaSchedule( coolingFactor=coolingFactor, coolingRate=coolingRate ) target = Directives.TargetMisfit(chifact=chifact) if use_target: directives = [ Directives.BetaEstimate_ByEig(beta0_ratio=beta0_ratio), beta_schedule, target, save, ] else: directives = [ Directives.BetaEstimate_ByEig(beta0_ratio=beta0_ratio), beta_schedule, save, ] inv = Inversion.BaseInversion(invProb, directiveList=directives) mopt = inv.run(m0) model = opt.recall("xc") model.append(mopt) pred = [] for m in model: pred.append(survey.dpred(m)) return model, pred, save
problem = DC.Problem3D_CC(mesh, sigmaMap=mapping) problem.pair(survey) problem.Solver = PardisoSolver survey.dpred(mtrue) survey.makeSyntheticData(mtrue, std=0.05, force=True) print '# of data: ', survey.dobs.shape #Simple Inversion regmesh = mesh m0 = (-5.) * np.ones(mapping.nP) dmis = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov(regmesh) #,mapping = mapping)#,indActive=actind) reg.mref = m0 opt = Optimization.InexactGaussNewton(maxIter=20, tolX=1e-6) opt.remember('xc') invProb = InvProblem.BaseInvProblem(dmis, reg, opt) beta = Directives.BetaEstimate_ByEig(beta0=10., beta0_ratio=1e0) reg.alpha_s = 1e-2 #beta = 0. #invProb.beta = beta betaSched = Directives.BetaSchedule(coolingFactor=5, coolingRate=2) #sav0 = Directives.SaveEveryIteration() #sav1 = Directives.SaveModelEveryIteration() sav2 = Directives.SaveOutputDictEveryIteration() inv = Inversion.BaseInversion(invProb, directiveList=[sav2, beta, betaSched]) #sav0,sav1, mtest = np.load('../Update_W_each_3it_5s_rademacher/finalresult.npy') print "check misfit with W: ", dmis.eval(mtest) / survey.nD
def run(plotIt=False): O = np.r_[-1.2, -1.] D = np.r_[10., 10.] x = np.r_[0., 1.] y = np.r_[0., 1.] print('length:', StraightRay.lengthInCell(O, D, x, y, plotIt=plotIt)) O = np.r_[0, -1.] D = np.r_[1., 1.] * 1.5 print('length:', StraightRay.lengthInCell(O, D, x * 2, y * 2, plotIt=plotIt)) nC = 20 M = Mesh.TensorMesh([nC, nC]) y = np.linspace(0., 1., nC / 2) rlocs = np.c_[y * 0 + M.vectorCCx[-1], y] rx = StraightRay.Rx(rlocs, None) srcList = [ StraightRay.Src(loc=np.r_[M.vectorCCx[0], yi], rxList=[rx]) for yi in y ] survey = StraightRay.Survey(srcList) problem = StraightRay.Problem(M, slownessMap=Maps.IdentityMap(M)) problem.pair(survey) s = Utils.mkvc(Utils.ModelBuilder.randomModel(M.vnC)) + 1. survey.dobs = survey.dpred(s) survey.std = 0.01 # Create an optimization program reg = Regularization.Tikhonov(M) dmis = DataMisfit.l2_DataMisfit(survey) opt = Optimization.InexactGaussNewton(maxIter=40) opt.remember('xc') invProb = InvProblem.BaseInvProblem(dmis, reg, opt) beta = Directives.BetaSchedule() betaest = Directives.BetaEstimate_ByEig() inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest]) # Start the inversion with a model of zeros, and run the inversion m0 = np.ones(M.nC) * 1.5 mopt = inv.run(m0) if plotIt is True: fig, ax = plt.subplots(1, 2, figsize=(8, 4)) ax[1].plot(survey.dobs) ax[1].plot(survey.dpred(m0), 's') ax[1].plot(survey.dpred(mopt), 'o') ax[1].legend(['dobs', 'starting dpred', 'dpred']) M.plotImage(s, ax=ax[0]) survey.plot(ax=ax[0]) ax[0].set_title('survey') plt.tight_layout() if plotIt is True: fig, ax = plt.subplots(1, 3, figsize=(12, 4)) plt.colorbar(M.plotImage(m0, ax=ax[0])[0], ax=ax[0]) plt.colorbar(M.plotImage(mopt, ax=ax[1])[0], ax=ax[1]) plt.colorbar(M.plotImage(s, ax=ax[2])[0], ax=ax[2]) ax[0].set_title('Starting Model') ax[1].set_title('Recovered Model') ax[2].set_title('True Model') plt.tight_layout()
def resolve_1Dinversions(mesh, dobs, src_height, freqs, m0, mref, mapping, std=0.08, floor=1e-14, rxOffset=7.86): """ Perform a single 1D inversion for a RESOLVE sounding for Horizontal Coplanar Coil data (both real and imaginary). :param discretize.CylMesh mesh: mesh used for the forward simulation :param numpy.array dobs: observed data :param float src_height: height of the source above the ground :param numpy.array freqs: frequencies :param numpy.array m0: starting model :param numpy.array mref: reference model :param Maps.IdentityMap mapping: mapping that maps the model to electrical conductivity :param float std: percent error used to construct the data misfit term :param float floor: noise floor used to construct the data misfit term :param float rxOffset: offset between source and receiver. """ # ------------------- Forward Simulation ------------------- # # set up the receivers bzr = EM.FDEM.Rx.Point_bSecondary(np.array([[rxOffset, 0., src_height]]), orientation='z', component='real') bzi = EM.FDEM.Rx.Point_b(np.array([[rxOffset, 0., src_height]]), orientation='z', component='imag') # source location srcLoc = np.array([0., 0., src_height]) srcList = [ EM.FDEM.Src.MagDipole([bzr, bzi], freq, srcLoc, orientation='Z') for freq in freqs ] # construct a forward simulation survey = EM.FDEM.Survey(srcList) prb = EM.FDEM.Problem3D_b(mesh, sigmaMap=mapping, Solver=PardisoSolver) prb.pair(survey) # ------------------- Inversion ------------------- # # data misfit term survey.dobs = dobs dmisfit = DataMisfit.l2_DataMisfit(survey) uncert = abs(dobs) * std + floor dmisfit.W = 1. / uncert # regularization regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Simple(regMesh) reg.mref = mref # optimization opt = Optimization.InexactGaussNewton(maxIter=10) # statement of the inverse problem invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # Inversion directives and parameters target = Directives.TargetMisfit() inv = Inversion.BaseInversion(invProb, directiveList=[target]) invProb.beta = 2. # Fix beta in the nonlinear iterations reg.alpha_s = 1e-3 reg.alpha_x = 1. prb.counter = opt.counter = Utils.Counter() opt.LSshorten = 0.5 opt.remember('xc') # run the inversion mopt = inv.run(m0) return mopt, invProb.dpred, survey.dobs
m0 = mref.copy() #sigma0 = np.ones(mesh_2d.nC) * 1e-3 #sigma0[blk1] = 1. #m0 = np.log(sigma0[actind]) from SimPEG import (EM, Mesh, Maps, DataMisfit, Regularization, Optimization, InvProblem, Inversion, Directives, Utils) survey.dobs = dobs_dbdtz survey.std = 0.05 survey.eps = 1e-14 dmisfit = DataMisfit.l2_DataMisfit(survey) reg = Regularization.Tikhonov( mesh_2d, alpha_s=1./mesh_2d.hx.min()**2, alpha_x=1., alpha_y=1., indActive=actind ) opt = Optimization.InexactGaussNewton(maxIter=20, LSshorten=0.5) opt.remember('xc') invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) # Create an inversion object beta = Directives.BetaSchedule(coolingFactor=5, coolingRate=3) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1.) target=Directives.TargetMisfit() save_model = Directives.SaveModelEveryIteration() save = Directives.SaveOutputEveryIteration() inv = Inversion.BaseInversion(invProb, directiveList=[beta, betaest, target, save_model, save]) prb.counter = opt.counter = Utils.Counter() reg.mref = mref mopt = inv.run(m0) np.save('mopt', mopt)