def test_nC_residual(self): # x-direction cs, ncx, ncz, npad = 1.0, 10.0, 10.0, 20 hx = [(cs, ncx), (cs, npad, 1.3)] # z direction npad = 12 temp = np.logspace(np.log10(1.0), np.log10(12.0), 19) temp_pad = temp[-1] * 1.3**np.arange(npad) hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad] mesh = discretize.CylMesh([hx, 1, hz], "00C") active = mesh.vectorCCz < 0.0 active = mesh.vectorCCz < 0.0 actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = regularization.Simple(regMesh) self.assertTrue(reg._nC_residual == regMesh.nC) self.assertTrue( all([fct._nC_residual == regMesh.nC for fct in reg.objfcts]))
def test_tripleMultiply(self): M = discretize.TensorMesh([2, 4], "0C") expMap = maps.ExpMap(M) vertMap = maps.SurjectVertical1D(M) actMap = maps.InjectActiveCells(M, M.vectorCCy <= 0, 10, nC=M.nCy) m = np.r_[1.0, 2.0] t_true = np.exp(np.r_[1, 1, 2, 2, 10, 10, 10, 10.0]) self.assertLess( np.linalg.norm((expMap * vertMap * actMap * m) - t_true, np.inf), TOL) self.assertLess( np.linalg.norm(((expMap * vertMap * actMap) * m) - t_true, np.inf), TOL) self.assertLess( np.linalg.norm((expMap * vertMap * (actMap * m)) - t_true, np.inf), TOL) self.assertLess( np.linalg.norm((expMap * (vertMap * actMap) * m) - t_true, np.inf), TOL) self.assertLess( np.linalg.norm(((expMap * vertMap) * actMap * m) - t_true, np.inf), TOL) self.assertRaises(ValueError, lambda: expMap * actMap * vertMap) self.assertRaises(ValueError, lambda: actMap * vertMap * expMap)
def run(plotIt=True): M = discretize.TensorMesh([7, 5]) v1dMap = maps.SurjectVertical1D(M) expMap = maps.ExpMap(M) myMap = expMap * v1dMap m = np.r_[0.2, 1, 0.1, 2, 2.9] # only 5 model parameters! sig = myMap * m if not plotIt: return figs, axs = plt.subplots(1, 2) axs[0].plot(m, M.vectorCCy, "b-o") axs[0].set_title("Model") axs[0].set_ylabel("Depth, y") axs[0].set_xlabel("Value, $m_i$") axs[0].set_xlim(0, 3) axs[0].set_ylim(0, 1) clbar = plt.colorbar( M.plotImage(sig, ax=axs[1], grid=True, gridOpts=dict(color="grey"))[0] ) axs[1].set_title("Physical Property") axs[1].set_ylabel("Depth, y") clbar.set_label("$\sigma = \exp(\mathbf{P}m)$") plt.tight_layout()
def setThreeLayerParam(self, h1=12, h2=12, sig0=1e-8, sig1=1e-1, sig2=1e-2, sig3=1e-2, chi=0.0): self.h1 = h1 # 1st layer thickness self.h2 = h2 # 2nd layer thickness self.z0 = 0.0 self.z1 = self.z0 - h1 self.z2 = self.z0 - h1 - h2 self.sig0 = sig0 # 0th layer \sigma (assumed to be air) self.sig1 = sig1 # 1st layer \sigma self.sig2 = sig2 # 2nd layer \sigma self.sig3 = sig3 # 3rd layer \sigma active = self.mesh.vectorCCz < self.z0 ind1 = (self.mesh.vectorCCz < self.z0) & (self.mesh.vectorCCz >= self.z1) ind2 = (self.mesh.vectorCCz < self.z1) & (self.mesh.vectorCCz >= self.z2) self.mapping = maps.SurjectVertical1D( self.mesh) * maps.InjectActiveCells( self.mesh, active, sig0, nC=self.mesh.nCz) model = np.ones(self.mesh.nCz) * sig3 model[ind1] = sig1 model[ind2] = sig2 self.m = model[active] self.mu = np.ones(self.mesh.nC) * mu_0 self.mu[self.mesh.gridCC[:, 2] < 0.0] = (1.0 + chi) * mu_0 return self.m
def test_mapMultiplication(self): M = discretize.TensorMesh([2, 3]) expMap = maps.ExpMap(M) vertMap = maps.SurjectVertical1D(M) combo = expMap * vertMap m = np.arange(3.0) t_true = np.exp(np.r_[0, 0, 1, 1, 2, 2.0]) self.assertLess(np.linalg.norm((combo * m) - t_true, np.inf), TOL) self.assertLess( np.linalg.norm((expMap * vertMap * m) - t_true, np.inf), TOL) self.assertLess( np.linalg.norm(expMap * (vertMap * m) - t_true, np.inf), TOL) self.assertLess( np.linalg.norm((expMap * vertMap) * m - t_true, np.inf), TOL) # Try making a model mod = models.Model(m, mapping=combo) # print mod.transform # import matplotlib.pyplot as plt # plt.colorbar(M.plotImage(mod.transform)[0]) # plt.show() self.assertLess(np.linalg.norm(mod.transform - t_true, np.inf), TOL) self.assertRaises(Exception, models.Model, np.r_[1.0], mapping=combo) self.assertRaises(ValueError, lambda: combo * (vertMap * expMap)) self.assertRaises(ValueError, lambda: (combo * vertMap) * expMap) self.assertRaises(ValueError, lambda: vertMap * expMap) self.assertRaises(ValueError, lambda: expMap * np.ones(100)) self.assertRaises(ValueError, lambda: expMap * np.ones((100, 1))) self.assertRaises(ValueError, lambda: expMap * np.ones((100, 5))) self.assertRaises(ValueError, lambda: combo * np.ones(100)) self.assertRaises(ValueError, lambda: combo * np.ones((100, 1))) self.assertRaises(ValueError, lambda: combo * np.ones((100, 5)))
def getCoreModel(self, Type): if Type == "Layer": active = self.mesh2D.vectorCCy < self.z0 ind1 = (self.mesh2D.vectorCCy < self.z0) & (self.mesh2D.vectorCCy >= self.z1) ind2 = (self.mesh2D.vectorCCy < self.z1) & (self.mesh2D.vectorCCy >= self.z2) mapping2D = maps.SurjectVertical1D( self.mesh2D) * maps.InjectActiveCells( self.mesh2D, active, self.sig0, nC=self.mesh2D.nCy) model2D = np.ones(self.mesh2D.nCy) * self.sig3 model2D[ind1] = self.sig1 model2D[ind2] = self.sig2 model2D = model2D[active] elif Type == "Sphere": active = self.mesh2D.gridCC[:, 1] < self.z0 ind1 = (self.mesh2D.gridCC[:, 1] < self.z1) & (self.mesh2D.gridCC[:, 1] >= self.z1 - self.h) ind2 = (np.sqrt((self.mesh2D.gridCC[:, 0])**2 + (self.mesh2D.gridCC[:, 1] - self.z2)**2) <= self.R) mapping2D = maps.InjectActiveCells(self.mesh2D, active, self.sig0, nC=self.mesh2D.nC) model2D = np.ones(self.mesh2D.nC) * self.sigb model2D[ind1] = self.sig1 model2D[ind2] = self.sig2 model2D = model2D[active] return model2D, mapping2D
def setUp_TDEM(prbtype="MagneticFluxDensity", rxcomp="bz", waveform="stepoff"): cs = 5.0 ncx = 8 ncy = 8 ncz = 8 npad = 4 # hx = [(cs, ncx), (cs, npad, 1.3)] # hz = [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)] mesh = discretize.TensorMesh( [ [(cs, npad, -1.3), (cs, ncx), (cs, npad, 1.3)], [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)], [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)], ], "CCC", ) active = mesh.vectorCCz < 0.0 activeMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * activeMap prb = getattr(tdem, "Simulation3D{}".format(prbtype))(mesh, sigmaMap=mapping) rxtimes = np.logspace(-4, -3, 20) if waveform.upper() == "RAW": out = utils.VTEMFun(prb.times, 0.00595, 0.006, 100) wavefun = interp1d(prb.times, out) t0 = 0.006 waveform = tdem.Src.RawWaveform(offTime=t0, waveFct=wavefun) prb.timeSteps = [(1e-3, 5), (1e-4, 5), (5e-5, 10), (5e-5, 10), (1e-4, 10)] rxtimes = t0 + rxtimes else: waveform = tdem.Src.StepOffWaveform() prb.timeSteps = [(1e-05, 10), (5e-05, 10), (2.5e-4, 10)] rxOffset = 10.0 rx = getattr(tdem.Rx, "Point{}".format(rxcomp[:-1]))(np.r_[rxOffset, 0.0, -1e-2], rxtimes, rxcomp[-1]) src = tdem.Src.MagDipole([rx], loc=np.array([0.0, 0.0, 0.0]), waveform=waveform) survey = tdem.Survey([src]) prb.Solver = Solver m = np.log(1e-1) * np.ones(prb.sigmaMap.nP) + 1e-2 * np.random.rand( prb.sigmaMap.nP) prb.pair(survey) mesh = mesh return prb, m, mesh
def setUp_TDEM(prbtype="ElectricField", rxcomp="ElectricFieldx"): cs = 5.0 ncx = 8 ncy = 8 ncz = 8 npad = 0 # hx = [(cs, ncx), (cs, npad, 1.3)] # hz = [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)] mesh = discretize.TensorMesh( [ [(cs, npad, -1.3), (cs, ncx), (cs, npad, 1.3)], [(cs, npad, -1.3), (cs, ncy), (cs, npad, 1.3)], [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)], ], "CCC", ) # active = mesh.vectorCCz < 0.0 activeMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * activeMap rxOffset = 0.0 rxlocs = np.array([[20, 20.0, 0.0]]) rxtimes = np.logspace(-4, -3, 20) rx = getattr(tdem.Rx, "Point{}".format(rxcomp[:-1]))(locations=rxlocs, times=rxtimes, orientation=rxcomp[-1]) Aloc = np.r_[-10.0, 0.0, 0.0] Bloc = np.r_[10.0, 0.0, 0.0] srcloc = np.vstack((Aloc, Bloc)) src = tdem.Src.LineCurrent([rx], location=srcloc, waveform=tdem.Src.StepOffWaveform()) survey = tdem.Survey([src]) prb = getattr(tdem, "Simulation3D{}".format(prbtype))(mesh, sigmaMap=mapping) prb.time_steps = [(1e-05, 10), (5e-05, 10), (2.5e-4, 10)] prb.solver = Solver m = np.log(1e-1) * np.ones(prb.sigmaMap.nP) + 1e-3 * np.random.randn( prb.sigmaMap.nP) prb.pair(survey) mesh = mesh return prb, m, mesh
def test_activeCells(self): M = discretize.TensorMesh([2, 4], "0C") for actMap in [ maps.InjectActiveCells(M, M.vectorCCy <= 0, 10, nC=M.nCy), ]: vertMap = maps.SurjectVertical1D(M) combo = vertMap * actMap m = np.r_[1.0, 2.0] mod = models.Model(m, combo) self.assertLess( np.linalg.norm(mod.transform - np.r_[1, 1, 2, 2, 10, 10, 10, 10.0]), TOL ) self.assertLess((mod.transformDeriv - combo.deriv(m)).toarray().sum(), TOL)
def run(plotIt=True): cs, ncx, ncz, npad = 5.0, 25, 24, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = discretize.CylMesh([hx, 1, hz], "00C") active = mesh.vectorCCz < 0.0 layer = (mesh.vectorCCz < -50.0) & (mesh.vectorCCz >= -150.0) actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap sig_half = 1e-3 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]) x = np.r_[30, 50, 70, 90] rxloc = np.c_[x, x * 0.0, np.zeros_like(x)] prb = TDEM.Simulation3DMagneticFluxDensity(mesh, sigmaMap=mapping, solver=Solver) prb.time_steps = [ (1e-3, 5), (1e-4, 5), (5e-5, 10), (5e-5, 5), (1e-4, 10), (5e-4, 10), ] # Use VTEM waveform out = EMutils.VTEMFun(prb.times, 0.00595, 0.006, 100) # Forming function handle for waveform using 1D linear interpolation wavefun = interp1d(prb.times, out) t0 = 0.006 waveform = TDEM.Src.RawWaveform(offTime=t0, waveFct=wavefun) rx = TDEM.Rx.PointMagneticFluxTimeDerivative( rxloc, np.logspace(-4, -2.5, 11) + t0, "z") src = TDEM.Src.CircularLoop([rx], waveform=waveform, loc=np.array([0.0, 0.0, 0.0]), radius=10.0) survey = TDEM.Survey([src]) prb.survey = survey # create observed data data = prb.make_synthetic_data(mtrue, relative_error=0.02, noise_floor=1e-11) dmisfit = data_misfit.L2DataMisfit(simulation=prb, data=data) regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = regularization.Simple(regMesh) opt = optimization.InexactGaussNewton(maxIter=5, LSshorten=0.5) invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt) target = directives.TargetMisfit() # Create an inversion object beta = directives.BetaSchedule(coolingFactor=1.0, coolingRate=2.0) betaest = directives.BetaEstimate_ByEig(beta0_ratio=1e0) invProb.beta = 1e2 inv = inversion.BaseInversion(invProb, directiveList=[beta, target]) m0 = np.log(np.ones(mtrue.size) * sig_half) prb.counter = opt.counter = utils.Counter() opt.remember("xc") mopt = inv.run(m0) if plotIt: fig, ax = plt.subplots(1, 2, figsize=(10, 6)) Dobs = data.dobs.reshape((len(rx.times), len(x))) Dpred = invProb.dpred.reshape((len(rx.times), len(x))) for i in range(len(x)): ax[0].loglog(rx.times - t0, -Dobs[:, i].flatten(), "k") ax[0].loglog(rx.times - t0, -Dpred[:, i].flatten(), "k.") if i == 0: ax[0].legend(("$d^{obs}$", "$d^{pred}$"), fontsize=16) ax[0].set_xlabel("Time (s)", fontsize=14) ax[0].set_ylabel("$db_z / dt$ (nT/s)", fontsize=16) ax[0].set_xlabel("Time (s)", fontsize=14) ax[0].grid(color="k", alpha=0.5, linestyle="dashed", linewidth=0.5) plt.semilogx(sigma[active], mesh.vectorCCz[active]) plt.semilogx(np.exp(mopt), mesh.vectorCCz[active]) ax[1].set_ylim(-600, 0) ax[1].set_xlim(1e-4, 1e-1) ax[1].set_xlabel("Conductivity (S/m)", fontsize=14) ax[1].set_ylabel("Depth (m)", fontsize=14) ax[1].grid(color="k", alpha=0.5, linestyle="dashed", linewidth=0.5) plt.legend(["$\sigma_{true}$", "$\sigma_{pred}$"])
def run(plotIt=True): cs, ncx, ncz, npad = 5.0, 25, 15, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = discretize.CylMesh([hx, 1, hz], "00C") active = mesh.vectorCCz < 0.0 layer = (mesh.vectorCCz < 0.0) & (mesh.vectorCCz >= -100.0) actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap sig_half = 2e-3 sig_air = 1e-8 sig_layer = 1e-3 sigma = np.ones(mesh.nCz) * sig_air sigma[active] = sig_half sigma[layer] = sig_layer mtrue = np.log(sigma[active]) rxOffset = 1e-3 rx = time_domain.Rx.PointMagneticFluxTimeDerivative( np.array([[rxOffset, 0.0, 30]]), np.logspace(-5, -3, 31), "z" ) src = time_domain.Src.MagDipole([rx], location=np.array([0.0, 0.0, 80])) survey = time_domain.Survey([src]) time_steps = [(1e-06, 20), (1e-05, 20), (0.0001, 20)] simulation = time_domain.Simulation3DElectricField( mesh, sigmaMap=mapping, survey=survey, time_steps=time_steps ) # d_true = simulation.dpred(mtrue) # create observed data rel_err = 0.05 data = simulation.make_synthetic_data(mtrue, relative_error=rel_err) dmisfit = data_misfit.L2DataMisfit(simulation=simulation, data=data) regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = regularization.Tikhonov(regMesh, alpha_s=1e-2, alpha_x=1.0) opt = optimization.InexactGaussNewton(maxIter=5, LSshorten=0.5) invProb = inverse_problem.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) simulation.counter = opt.counter = utils.Counter() opt.remember("xc") mopt = inv.run(m0) if plotIt: fig, ax = plt.subplots(1, 2, figsize=(10, 6)) ax[0].loglog(rx.times, -invProb.dpred, "b.-") ax[0].loglog(rx.times, -data.dobs, "r.-") ax[0].legend(("Noisefree", "$d^{obs}$"), fontsize=16) ax[0].set_xlabel("Time (s)", fontsize=14) ax[0].set_ylabel("$B_z$ (T)", fontsize=16) ax[0].set_xlabel("Time (s)", fontsize=14) ax[0].grid(color="k", alpha=0.5, linestyle="dashed", linewidth=0.5) plt.semilogx(sigma[active], mesh.vectorCCz[active]) plt.semilogx(np.exp(mopt), mesh.vectorCCz[active]) ax[1].set_ylim(-600, 0) ax[1].set_xlim(1e-4, 1e-2) ax[1].set_xlabel("Conductivity (S/m)", fontsize=14) ax[1].set_ylabel("Depth (m)", fontsize=14) ax[1].grid(color="k", alpha=0.5, linestyle="dashed", linewidth=0.5) plt.legend(["$\sigma_{true}$", "$\sigma_{pred}$"])
def run(runIt=False, plotIt=True, saveIt=False, saveFig=False, cleanup=True): """ Run the bookpurnong 1D stitched RESOLVE inversions. :param bool runIt: re-run the inversions? Default downloads and plots saved results :param bool plotIt: show the plots? :param bool saveIt: save the re-inverted results? :param bool saveFig: save the figure :param bool cleanup: remove the downloaded results """ # download the data downloads, directory = download_and_unzip_data() # Load resolve data resolve = h5py.File(os.path.sep.join([directory, "booky_resolve.hdf5"]), "r") river_path = resolve["river_path"][()] # River path nSounding = resolve["data"].shape[0] # the # of soundings # Bird height from surface b_height_resolve = resolve["src_elevation"][()] # fetch the frequencies we are considering cpi_inds = [0, 2, 6, 8, 10] # Indices for HCP in-phase cpq_inds = [1, 3, 7, 9, 11] # Indices for HCP quadrature frequency_cp = resolve["frequency_cp"][()] # build a mesh cs, ncx, ncz, npad = 1.0, 10.0, 10.0, 20 hx = [(cs, ncx), (cs, npad, 1.3)] npad = 12 temp = np.logspace(np.log10(1.0), np.log10(12.0), 19) temp_pad = temp[-1] * 1.3**np.arange(npad) hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad] mesh = discretize.CylMesh([hx, 1, hz], "00C") active = mesh.vectorCCz < 0.0 # survey parameters rxOffset = 7.86 # tx-rx separation bp = -mu_0 / (4 * np.pi * rxOffset**3) # primary magnetic field # re-run the inversion if runIt: # set up the mappings - we are inverting for 1D log conductivity # below the earth's surface. actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap # build starting and reference model sig_half = 1e-1 sig_air = 1e-8 sigma = np.ones(mesh.nCz) * sig_air sigma[active] = sig_half m0 = np.log(1e-1) * np.ones(active.sum()) # starting model mref = np.log(1e-1) * np.ones(active.sum()) # reference model # initalize empty lists for storing inversion results mopt_re = [] # recovered model dpred_re = [] # predicted data dobs_re = [] # observed data # downsample the data for the inversion nskip = 40 # set up a noise model # 10% for the 3 lowest frequencies, 15% for the two highest relative = np.repeat(np.r_[np.ones(3) * 0.1, np.ones(2) * 0.15], 2) floor = abs(20 * bp * 1e-6) # floor of 20ppm # loop over the soundings and invert each for rxind in range(nSounding): # convert data from ppm to magnetic field (A/m^2) dobs = (np.c_[resolve["data"][rxind, :][cpi_inds].astype(float), resolve["data"][ rxind, :][cpq_inds].astype(float), ].flatten() * bp * 1e-6) # perform the inversion src_height = b_height_resolve[rxind].astype(float) mopt, dpred, dobs = resolve_1Dinversions( mesh, dobs, src_height, frequency_cp, m0, mref, mapping, relative=relative, floor=floor, ) # add results to our list mopt_re.append(mopt) dpred_re.append(dpred) dobs_re.append(dobs) # save results mopt_re = np.vstack(mopt_re) dpred_re = np.vstack(dpred_re) dobs_re = np.vstack(dobs_re) if saveIt: np.save("mopt_re_final", mopt_re) np.save("dobs_re_final", dobs_re) np.save("dpred_re_final", dpred_re) mopt_re = resolve["mopt"][()] dobs_re = resolve["dobs"][()] dpred_re = resolve["dpred"][()] sigma = np.exp(mopt_re) indz = -7 # depth index # so that we can visually compare with literature (eg Viezzoli, 2010) cmap = "jet" # dummy figure for colobar fig = plt.figure() out = plt.scatter(np.ones(3), np.ones(3), c=np.linspace(-2, 1, 3), cmap=cmap) plt.close(fig) # plot from the paper fs = 13 # fontsize # matplotlib.rcParams['font.size'] = fs plt.figure(figsize=(13, 7)) ax0 = plt.subplot2grid((2, 3), (0, 0), rowspan=2, colspan=2) ax1 = plt.subplot2grid((2, 3), (0, 2)) ax2 = plt.subplot2grid((2, 3), (1, 2)) # titles of plots title = [ ("(a) Recovered model, %.1f m depth") % (-mesh.vectorCCz[active][indz]), "(b) Obs (Real 400 Hz)", "(c) Pred (Real 400 Hz)", ] temp = sigma[:, indz] tree = cKDTree(list(zip(resolve["xy"][:, 0], resolve["xy"][:, 1]))) d, d_inds = tree.query(list(zip(resolve["xy"][:, 0], resolve["xy"][:, 1])), k=20) w = 1.0 / (d + 100.0)**2.0 w = utils.sdiag(1.0 / np.sum(w, axis=1)) * (w) xy = resolve["xy"] temp = (temp.flatten()[d_inds] * w).sum(axis=1) utils.plot2Ddata( xy, temp, ncontour=100, scale="log", dataloc=False, contourOpts={ "cmap": cmap, "vmin": 1e-2, "vmax": 1e1 }, ax=ax0, ) ax0.plot(resolve["xy"][:, 0], resolve["xy"][:, 1], "k.", alpha=0.02, ms=1) cb = plt.colorbar(out, ax=ax0, ticks=np.linspace(-2, 1, 4), format="$10^{%.1f}$") cb.set_ticklabels(["0.01", "0.1", "1", "10"]) cb.set_label("Conductivity (S/m)") ax0.plot(river_path[:, 0], river_path[:, 1], "k-", lw=0.5) # plot observed and predicted data freq_ind = 0 axs = [ax1, ax2] temp_dobs = dobs_re[:, freq_ind].copy() ax1.plot(river_path[:, 0], river_path[:, 1], "k-", lw=0.5) inf = temp_dobs / abs(bp) * 1e6 print(inf.min(), inf.max()) out = utils.plot2Ddata( resolve["xy"][()], temp_dobs / abs(bp) * 1e6, ncontour=100, scale="log", dataloc=False, ax=ax1, contourOpts={"cmap": "viridis"}, ) vmin, vmax = out[0].get_clim() print(vmin, vmax) cb = plt.colorbar( out[0], ticks=np.logspace(np.log10(vmin), np.log10(vmax), 3), ax=ax1, format="%.1e", fraction=0.046, pad=0.04, ) cb.set_label("Bz (ppm)") temp_dpred = dpred_re[:, freq_ind].copy() # temp_dpred[mask_:_data] = np.nan ax2.plot(river_path[:, 0], river_path[:, 1], "k-", lw=0.5) utils.plot2Ddata( resolve["xy"][()], temp_dpred / abs(bp) * 1e6, ncontour=100, scale="log", dataloc=False, contourOpts={ "vmin": vmin, "vmax": vmax, "cmap": "viridis" }, ax=ax2, ) cb = plt.colorbar( out[0], ticks=np.logspace(np.log10(vmin), np.log10(vmax), 3), ax=ax2, format="%.1e", fraction=0.046, pad=0.04, ) cb.set_label("Bz (ppm)") for i, ax in enumerate([ax0, ax1, ax2]): xticks = [460000, 463000] yticks = [6195000, 6198000, 6201000] xloc, yloc = 462100.0, 6196500.0 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") 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]) plt.tight_layout() if plotIt: plt.show() if saveFig is True: fig.savefig("obspred_resolve.png", dpi=200) resolve.close() if cleanup: os.remove(downloads) shutil.rmtree(directory)
def run(plotIt=True, saveFig=False): # Set up cylindrically symmeric mesh cs, ncx, ncz, npad = 10.0, 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 = discretize.CylMesh([hx, 1, hz], "00C") # Conductivity model layerz = np.r_[-200.0, -100.0] layer = (mesh.vectorCCz >= layerz[0]) & (mesh.vectorCCz <= layerz[1]) active = mesh.vectorCCz < 0.0 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_[50.0], np.r_[0], np.r_[0.0]]) bzr = FDEM.Rx.PointMagneticFluxDensitySecondary(rxlocs, "z", "real") bzi = FDEM.Rx.PointMagneticFluxDensitySecondary(rxlocs, "z", "imag") freqs = np.logspace(2, 3, 5) srcLoc = np.array([0.0, 0.0, 0.0]) print( "min skin depth = ", 500.0 / np.sqrt(freqs.max() * sig_half), "max skin depth = ", 500.0 / np.sqrt(freqs.min() * sig_half), ) print( "max x ", mesh.vectorCCx.max(), "min z ", mesh.vectorCCz.min(), "max z ", mesh.vectorCCz.max(), ) source_list = [ FDEM.Src.MagDipole([bzr, bzi], freq, srcLoc, orientation="Z") for freq in freqs ] surveyFD = FDEM.Survey(source_list) prbFD = FDEM.Simulation3DMagneticFluxDensity( mesh, survey=surveyFD, sigmaMap=mapping, solver=Solver ) rel_err = 0.03 dataFD = prbFD.make_synthetic_data(mtrue, relative_error=rel_err, add_noise=True) dataFD.noise_floor = np.linalg.norm(dataFD.dclean) * 1e-5 # FDEM inversion np.random.seed(1) dmisfit = data_misfit.L2DataMisfit(simulation=prbFD, data=dataFD) regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = regularization.Simple(regMesh) opt = optimization.InexactGaussNewton(maxIterCG=10) invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt) # Inversion Directives beta = directives.BetaSchedule(coolingFactor=4, coolingRate=3) betaest = directives.BetaEstimate_ByEig(beta0_ratio=1.0, seed=518936) 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 = 1.0 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.PointMagneticFluxDensity(rxlocs, times, "z") src = TDEM.Src.MagDipole( [rx], waveform=TDEM.Src.StepOffWaveform(), location=srcLoc, # same src location as FDEM problem ) surveyTD = TDEM.Survey([src]) prbTD = TDEM.Simulation3DMagneticFluxDensity( mesh, survey=surveyTD, sigmaMap=mapping, solver=Solver ) prbTD.time_steps = [(5e-5, 10), (1e-4, 10), (5e-4, 10)] rel_err = 0.03 dataTD = prbTD.make_synthetic_data(mtrue, relative_error=rel_err, add_noise=True) dataTD.noise_floor = np.linalg.norm(dataTD.dclean) * 1e-5 # TDEM inversion dmisfit = data_misfit.L2DataMisfit(simulation=prbTD, data=dataTD) regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = regularization.Simple(regMesh) opt = optimization.InexactGaussNewton(maxIterCG=10) invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt) # directives beta = directives.BetaSchedule(coolingFactor=4, coolingRate=3) betaest = directives.BetaEstimate_ByEig(beta0_ratio=1.0, seed=518936) 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 = 1.0 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 # z_true = np.repeat(mesh.vectorCCz[active][1:], 2, axis=0) # z_true = np.r_[mesh.vectorCCz[active][0], z_true, mesh.vectorCCz[active][-1]] activeN = mesh.vectorNz <= 0.0 + cs / 2.0 z_true = np.repeat(mesh.vectorNz[activeN][1:-1], 2, axis=0) z_true = np.r_[mesh.vectorNz[activeN][0], z_true, mesh.vectorNz[activeN][-1]] sigma_true = np.repeat(sigma[active], 2, axis=0) ax0.semilogx(sigma_true, z_true, "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, -dataFD.dobs[::2], "k-", lw=2, label="Obs (real)") ax1.plot(freqs, -dataFD.dobs[1::2], "k--", lw=2, label="Obs (imag)") dpredFD = prbFD.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=2.0, label="Pred (imag)" ) ax2.loglog(times, dataTD.dobs, "k-", lw=2, label="Obs") ax2.loglog( times, prbTD.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)
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 = 1.0, 10.0, 10.0, 20 hx = [(cs, ncx), (cs, npad, 1.3)] npad = 12 temp = np.logspace(np.log10(1.0), np.log10(12.0), 19) temp_pad = temp[-1] * 1.3**np.arange(npad) hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad] mesh = discretize.CylMesh([hx, 1, hz], "00C") active = mesh.vectorCCz < 0.0 # Step2: Set a SurjectVertical1D mapping # Note: this sets our inversion model as 1D log conductivity # below subsurface active = mesh.vectorCCz < 0.0 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 = FDEM.Rx.PointMagneticFluxDensitySecondary( np.array([[rxOffset, 0.0, src_height_resolve]]), orientation="z", component="real", ) bzi = FDEM.Rx.PointMagneticFluxDensity( np.array([[rxOffset, 0.0, 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, 0.0, src_height_resolve]) srcList = [ FDEM.Src.MagDipole([bzr, bzi], freq, srcLoc, orientation="Z") for freq in freqs ] # Set FDEM survey (In-phase and Quadrature) survey = FDEM.Survey(srcList) prb = FDEM.Simulation3DMagneticFluxDensity(mesh, sigmaMap=mapping, Solver=Solver) prb.survey = 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 relative = np.repeat(np.r_[np.ones(3) * 0.1, np.ones(2) * 0.15], 2) floor = 20 * abs(bp) * 1e-6 std = abs(dobs_re) * relative + floor # Data Misfit data_resolve = data.Data(dobs=dobs_re, survey=survey, standard_deviation=std) dmisfit = data_misfit.L2DataMisfit(simulation=prb, data=data_resolve) # Regularization regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = regularization.Simple(regMesh, mapping=maps.IdentityMap(regMesh)) # Optimization opt = optimization.InexactGaussNewton(maxIter=5) # statement of the inverse problem invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt) # Inversion directives and parameters target = directives.TargetMisfit() # stop when we hit target misfit invProb.beta = 2.0 inv = inversion.BaseInversion(invProb, directiveList=[target]) reg.alpha_s = 1e-3 reg.alpha_x = 1.0 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, 0.0, src_height]) # Radius of the source loop area = skytem["area"].value radius = np.sqrt(area / np.pi) rxLoc = np.array([[radius, 0.0, 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 = 3.0 dbdt_z = TDEM.Rx.PointMagneticFluxTimeDerivative( locations=rxLoc, times=times_off[:-3] + offTime, orientation="z") # vertical db_dt rxList = [dbdt_z] # list of receivers srcList = [ TDEM.Src.CircularLoop( rxList, loc=srcLoc, radius=radius, orientation="z", waveform=TDEM.Src.VTEMWaveform(offTime=offTime, peakTime=peakTime, a=3.0), ) ] # 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 = TDEM.Simulation3DElectricField(mesh, time_steps=timeSteps, sigmaMap=mapping, Solver=Solver) survey = TDEM.Survey(srcList) prob.survey = survey src = srcList[0] rx = src.receiver_list[0] wave = [] for time in prob.times: wave.append(src.waveform.eval(time)) wave = np.hstack(wave) out = prob.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 relative = 0.12 floor = 7.5e-12 std = abs(dobs_sky) * relative + floor # Data Misfit data_sky = data.Data(dobs=-dobs_sky, survey=survey, standard_deviation=std) dmisfit = data_misfit.L2DataMisfit(simulation=prob, data=data_sky) # Regularization regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = regularization.Simple(regMesh, mapping=maps.IdentityMap(regMesh)) # Optimization opt = optimization.InexactGaussNewton(maxIter=5) # statement of the inverse problem invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt) # Directives and Inversion Parameters target = directives.TargetMisfit() invProb.beta = 20.0 inv = inversion.BaseInversion(invProb, directiveList=[target]) reg.alpha_s = 1e-1 reg.alpha_x = 1.0 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=2.0, 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, 0.33, 0.1, 0.09], 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() resolve.close() skytem.close() 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 halfSpaceProblemAnaDiff( meshType, srctype="MagDipole", sig_half=1e-2, rxOffset=50.0, bounds=None, plotIt=False, rxType="MagneticFluxDensityz", ): if bounds is None: bounds = [1e-5, 1e-3] if meshType == "CYL": cs, ncx, ncz, npad = 15.0, 30, 10, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = discretize.CylMesh([hx, 1, hz], "00C") elif meshType == "TENSOR": cs, nc, npad = 20.0, 13, 5 hx = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] hy = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] mesh = discretize.TensorMesh([hx, hy, hz], "CCC") active = mesh.vectorCCz < 0.0 actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap prb = tdem.Simulation3DMagneticFluxDensity(mesh, sigmaMap=mapping) prb.Solver = Solver prb.timeSteps = [(1e-3, 5), (1e-4, 5), (5e-5, 10), (5e-5, 10), (1e-4, 10)] out = utils.VTEMFun(prb.times, 0.00595, 0.006, 100) wavefun = interp1d(prb.times, out) t0 = 0.006 waveform = tdem.Src.RawWaveform(offTime=t0, waveFct=wavefun) rx = getattr(tdem.Rx, "Point{}".format(rxType[:-1]))(np.array([[rxOffset, 0.0, 0.0]]), np.logspace(-4, -3, 31) + t0, rxType[-1]) if srctype == "MagDipole": src = tdem.Src.MagDipole([rx], waveform=waveform, loc=np.array([0, 0.0, 0.0])) elif srctype == "CircularLoop": src = tdem.Src.CircularLoop([rx], waveform=waveform, loc=np.array([0.0, 0.0, 0.0]), radius=13.0) survey = tdem.Survey([src]) prb.pair(survey) sigma = np.ones(mesh.nCz) * 1e-8 sigma[active] = sig_half sigma = np.log(sigma[active]) if srctype == "MagDipole": bz_ana = mu_0 * analytics.hzAnalyticDipoleT(rx.locations[0][0] + 1e-3, rx.times - t0, sig_half) elif srctype == "CircularLoop": bz_ana = mu_0 * analytics.hzAnalyticCentLoopT(13, rx.times - t0, sig_half) bz_calc = prb.dpred(sigma) ind = np.logical_and(rx.times - t0 > bounds[0], rx.times - t0 < bounds[1]) log10diff = np.linalg.norm( np.log10(np.abs(bz_calc[ind])) - np.log10(np.abs(bz_ana[ind]))) / np.linalg.norm( np.log10(np.abs(bz_ana[ind]))) print(" |bz_ana| = {ana} |bz_num| = {num} |bz_ana-bz_num| = {diff}".format( ana=np.linalg.norm(bz_ana), num=np.linalg.norm(bz_calc), diff=np.linalg.norm(bz_ana - bz_calc), )) print("Difference: {}".format(log10diff)) if plotIt is True: plt.loglog( rx.times[bz_calc > 0] - t0, bz_calc[bz_calc > 0], "r", rx.times[bz_calc < 0] - t0, -bz_calc[bz_calc < 0], "r--", ) plt.loglog(rx.times - t0, abs(bz_ana), "b*") plt.title("sig_half = {:e}".format(sig_half)) plt.show() return log10diff
def halfSpaceProblemAnaDiff( meshType, srctype="MagDipole", sig_half=1e-2, rxOffset=50.0, bounds=None, plotIt=False, rxType="MagneticFluxDensityz", ): if bounds is None: bounds = [1e-5, 1e-3] if meshType == "CYL": cs, ncx, ncz, npad = 5.0, 30, 10, 15 hx = [(cs, ncx), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, ncz), (cs, npad, 1.3)] mesh = discretize.CylMesh([hx, 1, hz], "00C") elif meshType == "TENSOR": cs, nc, npad = 20.0, 13, 5 hx = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] hy = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] hz = [(cs, npad, -1.3), (cs, nc), (cs, npad, 1.3)] mesh = discretize.TensorMesh([hx, hy, hz], "CCC") active = mesh.vectorCCz < 0.0 actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap rx = getattr(tdem.Rx, "Point{}".format(rxType[:-1]))(np.array([[rxOffset, 0.0, 0.0]]), np.logspace(-5, -4, 21), rxType[-1]) if srctype == "MagDipole": src = tdem.Src.MagDipole( [rx], waveform=tdem.Src.StepOffWaveform(), location=np.array([0.0, 0.0, 0.0]), ) elif srctype == "CircularLoop": src = tdem.Src.CircularLoop( [rx], waveform=tdem.Src.StepOffWaveform(), location=np.array([0.0, 0.0, 0.0]), radius=0.1, ) survey = tdem.Survey([src]) time_steps = [ (1e-06, 40), (5e-06, 40), (1e-05, 40), (5e-05, 40), (0.0001, 40), (0.0005, 40), ] prb = tdem.Simulation3DMagneticFluxDensity(mesh, survey=survey, time_steps=time_steps, sigmaMap=mapping) prb.solver = Solver sigma = np.ones(mesh.nCz) * 1e-8 sigma[active] = sig_half sigma = np.log(sigma[active]) if srctype == "MagDipole": bz_ana = mu_0 * analytics.hzAnalyticDipoleT(rx.locations[0][0] + 1e-3, rx.times, sig_half) elif srctype == "CircularLoop": bz_ana = mu_0 * analytics.hzAnalyticDipoleT(13, rx.times, sig_half) bz_calc = prb.dpred(sigma) ind = np.logical_and(rx.times > bounds[0], rx.times < bounds[1]) log10diff = np.linalg.norm( np.log10(np.abs(bz_calc[ind])) - np.log10(np.abs(bz_ana[ind]))) / np.linalg.norm( np.log10(np.abs(bz_ana[ind]))) print(" |bz_ana| = {ana} |bz_num| = {num} |bz_ana-bz_num| = {diff}".format( ana=np.linalg.norm(bz_ana), num=np.linalg.norm(bz_calc), diff=np.linalg.norm(bz_ana - bz_calc), )) print("Difference: {}".format(log10diff)) if plotIt is True: plt.loglog( rx.times[bz_calc > 0], bz_calc[bz_calc > 0], "r", rx.times[bz_calc < 0], -bz_calc[bz_calc < 0], "r--", ) plt.loglog(rx.times, abs(bz_ana), "b*") plt.title("sig_half = {0:e}".format(sig_half)) plt.show() return log10diff
def get_mapping(mesh): active = mesh.vectorCCz < 0.0 activeMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) return maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * activeMap