def setUp(self): np.random.seed(0) # Define the inducing field parameter H0 = (50000, 90, 0) # Create a mesh dx = 5. hxind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)] hyind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)] hzind = [(dx, 5, -1.3), (dx, 6)] mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC') # Get index of the center midx = int(mesh.nCx / 2) midy = int(mesh.nCy / 2) # Lets create a simple Gaussian topo and set the active cells [xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy) zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.vectorNz[-1] # Go from topo to actv cells topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)] actv = Utils.surface2ind_topo(mesh, topo, 'N') actv = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype=int) - 1 # Create active map to go from reduce space to full actvMap = Maps.InjectActiveCells(mesh, actv, -100) nC = len(actv) # Create and array of observation points xr = np.linspace(-20., 20., 20) yr = np.linspace(-20., 20., 20) X, Y = np.meshgrid(xr, yr) # Move the observation points 5m above the topo Z = -np.exp((X**2 + Y**2) / 75**2) + mesh.vectorNz[-1] + 5. # Create a MAGsurvey rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)] rxLoc = PF.BaseMag.RxObs(rxLoc) srcField = PF.BaseMag.SrcField([rxLoc], param=H0) survey = PF.BaseMag.LinearSurvey(srcField) # We can now create a susceptibility model and generate data # Here a simple block in half-space model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz)) model[(midx - 2):(midx + 2), (midy - 2):(midy + 2), -6:-2] = 0.02 model = Utils.mkvc(model) self.model = model[actv] # Create active map to go from reduce set to full actvMap = Maps.InjectActiveCells(mesh, actv, -100) # Creat reduced identity map idenMap = Maps.IdentityMap(nP=nC) # Create the forward model operator prob = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap, actInd=actv) # Pair the survey and problem survey.pair(prob) # Compute linear forward operator and compute some data d = prob.fields(self.model) # Add noise and uncertainties (1nT) data = d + np.random.randn(len(d)) wd = np.ones(len(data)) * 1. survey.dobs = data survey.std = wd # Create sensitivity weights from our linear forward operator wr = np.sum(prob.G**2., axis=0)**0.5 wr = (wr / np.max(wr)) # Create a regularization reg = Regularization.Sparse(mesh, indActive=actv, mapping=idenMap) reg.cell_weights = wr reg.norms = [0, 1, 1, 1] reg.eps_p, reg.eps_q = 1e-3, 1e-3 # Data misfit function dmis = DataMisfit.l2_DataMisfit(survey) dmis.W = 1 / wd # Add directives to the inversion opt = Optimization.ProjectedGNCG(maxIter=100, lower=0., upper=1., maxIterLS=20, maxIterCG=10, tolCG=1e-3) invProb = InvProblem.BaseInvProblem(dmis, reg, opt) betaest = Directives.BetaEstimate_ByEig() # Here is where the norms are applied IRLS = Directives.Update_IRLS(f_min_change=1e-3, minGNiter=3) update_Jacobi = Directives.UpdatePreconditioner() self.inv = Inversion.BaseInversion( invProb, directiveList=[IRLS, betaest, update_Jacobi])
# ## Create a survey and forward data #rx = DC.Rx.Dipole(rxlocM, rxlocN) #src = DC.Src.Dipole([rx], srclocA, srclocB) #survey = DC.Survey([src]) actv = sigma != 1e-8 nC = int(actv.sum()) midLocs = survey.srcList[0].rxList[0].locs[0]+ survey.srcList[0].rxList[0].locs[1] midLocs /= 2 idenMap = Maps.IdentityMap(nP=nC) expmap = Maps.ExpMap(mesh) logmap = Maps.LogMap(mesh) actmap = Maps.InjectActiveCells(mesh, actv, (1e-8)) mapping = actmap m0 = np.ones_like(sigma)*mref_val mref = np.ones_like(sigma)*mref_val problem = DC.Problem3D_N(mesh, sigmaMap=mapping, storeJ=True) problem.Solver = PardisoSolver problem.pair(survey) mtrue = sigma # Create data dobs = survey.makeSyntheticData(mtrue, std=0.02)
def run(plotIt=True): """ 1D FDEM and TDEM inversions =========================== This example is used in the paper Heagy et al 2016 (in prep) """ # 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.]]) bzi = FDEM.Rx.Point_bSecondary(rxlocs, 'z', 'real') bzr = 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) 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) 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) ax0.semilogx(np.exp(moptFD), mesh.vectorCCz[active], 'bo', ms=6) ax0.semilogx(np.exp(moptTD), mesh.vectorCCz[active], 'r*', ms=10) 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(['True', 'FDEM', 'TDEM'], 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) ax1.plot(freqs, -surveyFD.dobs[1::2], 'k--', lw=2) dpredFD = surveyFD.dpred(moptTD) ax1.loglog(freqs, -dpredFD[::2], 'bo', ms=6) ax1.loglog(freqs, -dpredFD[1::2], 'b+', markeredgewidth=2., ms=10) ax2.loglog(times, surveyTD.dobs, 'k-', lw=2) ax2.loglog(times, surveyTD.dpred(moptTD), 'r*', ms=10) ax2.set_xlim(times.min(), times.max()) # 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(("Obs", "Pred"), fontsize=fs) ax1.legend(("Obs (real)", "Obs (imag)", "Pred (real)", "Pred (imag)"), fontsize=fs) ax1.set_xlim(freqs.max(), freqs.min()) 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)
) else: mesh.writeModelUBC( 'ActiveSurface.act', activeCells ) if "adjust_clearance" in list(input_dict.keys()): print("Forming cKDTree for clearance calculations") tree = cKDTree(mesh.gridCC[activeCells, :]) # Get the layer of cells directly below topo nC = int(activeCells.sum()) # Number of active cells # Create active map to go from reduce set to full activeCellsMap = Maps.InjectActiveCells(mesh, activeCells, no_data_value) # Create identity map if input_dict["inversion_type"] in ['mvi', 'mvis']: global_weights = np.zeros(3*nC) else: idenMap = Maps.IdentityMap(nP=nC) global_weights = np.zeros(nC) def createLocalProb(meshLocal, local_survey, global_weights, ind): """ CreateLocalProb(rxLoc, global_weights, lims, ind) Generate a problem, calculate/store sensitivities for given data points
def test_mappingDepreciation(self): with self.assertRaises(Exception): self.prob.mapping with self.assertRaises(Exception): self.prob.mapping = Maps.IdentityMap(self.mesh)
locA = np.r_[-14. + 2 * (i - 11) + 1., z] locB = np.r_[14. - 1., z] #M = np.c_[np.arange(locA[0]+1.,12.,2),np.ones(nSrc-i)*z] #N = np.c_[np.arange(locA[0]+3.,14.,2),np.ones(nSrc-i)*z] M = np.c_[np.arange(-12., 10 + 1, 2), np.ones(12) * z] N = np.c_[np.arange(-10., 12 + 1, 2), np.ones(12) * z] rx = DC.Rx.Dipole(M, N) src = DC.Src.Dipole([rx], locA, locB) srclist.append(src) #print "line2",locA,locB,"\n",[M,N],"\n" #rx = DC.Rx.Dipole(-M,-N) #src= DC.Src.Dipole([rx],-locA,-locB) #srclist.append(src) mapping = Maps.ExpMap(mesh) survey = DC.Survey(srclist) problem = DC.Problem3D_CC(mesh, sigmaMap=mapping) problem.pair(survey) problem.Solver = PardisoSolver dmis = DataMisfit.l2_DataMisfit(survey) survey.dpred(mtrue) survey.makeSyntheticData(mtrue, std=0.05, force=True) survey.eps = 1e-5 * np.linalg.norm(survey.dobs) print '# of data: ', survey.dobs.shape import spgl1 #Parameter for SPGL1 iterations nits = 10
mstart = np.r_[mUnit,m0] else: mref = np.r_[mUnit*0, m0*0] mstart = np.r_[mUnit*0, m0] #actv = mrho!=-100 # Build list of indecies for the geounits index = [] for unit in geoUnits: # if unit!=0: index += [mgeo==unit] nC = len(index) # Create active map to go from reduce set to full actvMap = Maps.InjectActiveCells(mesh, actv, -100) # Creat reduced identity map homogMap = Maps.HomogeneousMap(index) homogMap.P # Create a wire map for a second model space wires = Maps.Wires(('h**o', nC), ('hetero', len(actv))) # Create Sum map sumMap = Maps.SumMap([homogMap*wires.h**o, wires.hetero]) #%% Plot obs data static = np.r_[np.ones(nC, dtype='bool'), np.zeros(len(actv), dtype='bool')] dynamic = np.r_[np.zeros(nC, dtype='bool'), np.ones(len(actv), dtype='bool')]
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, mapping=Maps.IdentityMap(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, mapping=Maps.IdentityMap(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, cleanAfterRun=True): # Start by downloading files from the remote repository # directory where the downloaded files are url = "https://storage.googleapis.com/simpeg/Chile_GRAV_4_Miller/Chile_GRAV_4_Miller.tar.gz" downloads = download(url, overwrite=True) basePath = downloads.split(".")[0] # unzip the tarfile tar = tarfile.open(downloads, "r") tar.extractall() tar.close() input_file = basePath + os.path.sep + 'LdM_input_file.inp' # %% User input # Plotting parameters, max and min densities in g/cc vmin = -0.6 vmax = 0.6 # weight exponent for default weighting wgtexp = 3. # %% # Read in the input file which included all parameters at once # (mesh, topo, model, survey, inv param, etc.) driver = PF.GravityDriver.GravityDriver_Inv(input_file) # %% # Now we need to create the survey and model information. # Access the mesh and survey information mesh = driver.mesh survey = driver.survey # define gravity survey locations rxLoc = survey.srcField.rxList[0].locs # define gravity data and errors d = survey.dobs wd = survey.std # Get the active cells active = driver.activeCells nC = len(active) # Number of active cells # Create active map to go from reduce set to full activeMap = Maps.InjectActiveCells(mesh, active, -100) # Create static map static = driver.staticCells dynamic = driver.dynamicCells staticCells = Maps.InjectActiveCells( None, dynamic, driver.m0[static], nC=nC ) mstart = driver.m0[dynamic] # Get index of the center midx = int(mesh.nCx/2) # %% # Now that we have a model and a survey we can build the linear system ... # Create the forward model operator prob = PF.Gravity.GravityIntegral(mesh, rhoMap=staticCells, actInd=active) prob.solverOpts['accuracyTol'] = 1e-4 # Pair the survey and problem survey.pair(prob) # Apply depth weighting wr = PF.Magnetics.get_dist_wgt(mesh, rxLoc, active, wgtexp, np.min(mesh.hx)/4.) wr = wr**2. # %% Create inversion objects reg = Regularization.Sparse(mesh, indActive=active, mapping=staticCells, gradientType='total') reg.mref = driver.mref[dynamic] reg.cell_weights = wr * mesh.vol[active] reg.norms = np.c_[0., 1., 1., 1.] # reg.norms = driver.lpnorms # Specify how the optimization will proceed opt = Optimization.ProjectedGNCG(maxIter=20, lower=driver.bounds[0], upper=driver.bounds[1], maxIterLS=10, maxIterCG=20, tolCG=1e-3) # Define misfit function (obs-calc) dmis = DataMisfit.l2_DataMisfit(survey) dmis.W = 1./wd # create the default L2 inverse problem from the above objects invProb = InvProblem.BaseInvProblem(dmis, reg, opt) # Specify how the initial beta is found betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e-2) # IRLS sets up the Lp inversion problem # Set the eps parameter parameter in Line 11 of the # input file based on the distribution of model (DEFAULT = 95th %ile) IRLS = Directives.Update_IRLS(f_min_change=1e-4, maxIRLSiter=40, beta_tol=5e-1) # Preconditioning refreshing for each IRLS iteration update_Jacobi = Directives.UpdatePreconditioner() # Create combined the L2 and Lp problem inv = Inversion.BaseInversion(invProb, directiveList=[IRLS, update_Jacobi, betaest]) # %% # Run L2 and Lp inversion mrec = inv.run(mstart) if cleanAfterRun: os.remove(downloads) shutil.rmtree(basePath) # %% if plotIt: # Plot observed data Utils.PlotUtils.plot2Ddata(rxLoc, d) # %% # Write output model and data files and print misft stats. # reconstructing l2 model mesh with air cells and active dynamic cells L2out = activeMap * invProb.l2model # reconstructing lp model mesh with air cells and active dynamic cells Lpout = activeMap*mrec # %% # Plot out sections and histograms of the smooth l2 model. # The ind= parameter is the slice of the model from top down. yslice = midx + 1 L2out[L2out == -100] = np.nan # set "air" to nan plt.figure(figsize=(10, 7)) plt.suptitle('Smooth Inversion: Depth weight = ' + str(wgtexp)) ax = plt.subplot(221) dat1 = mesh.plotSlice(L2out, ax=ax, normal='Z', ind=-16, clim=(vmin, vmax), pcolorOpts={'cmap': 'bwr'}) plt.plot(np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]), np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]), c='gray', linestyle='--') plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color='k', s=1) plt.title('Z: ' + str(mesh.vectorCCz[-16]) + ' m') plt.xlabel('Easting (m)') plt.ylabel('Northing (m)') plt.gca().set_aspect('equal', adjustable='box') cb = plt.colorbar(dat1[0], orientation="vertical", ticks=np.linspace(vmin, vmax, 4)) cb.set_label('Density (g/cc$^3$)') ax = plt.subplot(222) dat = mesh.plotSlice(L2out, ax=ax, normal='Z', ind=-27, clim=(vmin, vmax), pcolorOpts={'cmap': 'bwr'}) plt.plot(np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]), np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]), c='gray', linestyle='--') plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color='k', s=1) plt.title('Z: ' + str(mesh.vectorCCz[-27]) + ' m') plt.xlabel('Easting (m)') plt.ylabel('Northing (m)') plt.gca().set_aspect('equal', adjustable='box') cb = plt.colorbar(dat1[0], orientation="vertical", ticks=np.linspace(vmin, vmax, 4)) cb.set_label('Density (g/cc$^3$)') ax = plt.subplot(212) mesh.plotSlice(L2out, ax=ax, normal='Y', ind=yslice, clim=(vmin, vmax), pcolorOpts={'cmap': 'bwr'}) plt.title('Cross Section') plt.xlabel('Easting(m)') plt.ylabel('Elevation') plt.gca().set_aspect('equal', adjustable='box') cb = plt.colorbar(dat1[0], orientation="vertical", ticks=np.linspace(vmin, vmax, 4), cmap='bwr') cb.set_label('Density (g/cc$^3$)') # %% # Make plots of Lp model yslice = midx + 1 Lpout[Lpout == -100] = np.nan # set "air" to nan plt.figure(figsize=(10, 7)) plt.suptitle('Compact Inversion: Depth weight = ' + str(wgtexp) + ': $\epsilon_p$ = ' + str(round(reg.eps_p, 1)) + ': $\epsilon_q$ = ' + str(round(reg.eps_q, 2))) ax = plt.subplot(221) dat = mesh.plotSlice(Lpout, ax=ax, normal='Z', ind=-16, clim=(vmin, vmax), pcolorOpts={'cmap': 'bwr'}) plt.plot(np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]), np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]), c='gray', linestyle='--') plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color='k', s=1) plt.title('Z: ' + str(mesh.vectorCCz[-16]) + ' m') plt.xlabel('Easting (m)') plt.ylabel('Northing (m)') plt.gca().set_aspect('equal', adjustable='box') cb = plt.colorbar(dat[0], orientation="vertical", ticks=np.linspace(vmin, vmax, 4)) cb.set_label('Density (g/cc$^3$)') ax = plt.subplot(222) dat = mesh.plotSlice(Lpout, ax=ax, normal='Z', ind=-27, clim=(vmin, vmax), pcolorOpts={'cmap': 'bwr'}) plt.plot(np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]), np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]), c='gray', linestyle='--') plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color='k', s=1) plt.title('Z: ' + str(mesh.vectorCCz[-27]) + ' m') plt.xlabel('Easting (m)') plt.ylabel('Northing (m)') plt.gca().set_aspect('equal', adjustable='box') cb = plt.colorbar(dat[0], orientation="vertical", ticks=np.linspace(vmin, vmax, 4)) cb.set_label('Density (g/cc$^3$)') ax = plt.subplot(212) dat = mesh.plotSlice(Lpout, ax=ax, normal='Y', ind=yslice, clim=(vmin, vmax), pcolorOpts={'cmap': 'bwr'}) plt.title('Cross Section') plt.xlabel('Easting (m)') plt.ylabel('Elevation (m)') plt.gca().set_aspect('equal', adjustable='box') cb = plt.colorbar(dat[0], orientation="vertical", ticks=np.linspace(vmin, vmax, 4)) cb.set_label('Density (g/cc$^3$)')
geoUnits = np.unique(mgeo).tolist() # Build a dictionary for the units mstart = np.asarray([np.median(m0[mgeo == unit]) for unit in geoUnits]) #actv = mrho!=-100 # Build list of indecies for the geounits index = [] for unit in geoUnits: # if unit!=0: index += [mgeo == unit] nC = len(index) # Create active map to go from reduce set to full actvMap = Maps.InjectActiveCells(mesh, actv, -100) # Creat reduced identity map homogMap = Maps.HomogeneousMap(index) #ndata = survey.srcField.rxList[0].locs.shape[0] # #actv = driver.activeCells #nC = len(actv) # Create static map #static = driver.staticCells #dynamic = driver.dynamicCells # #staticCells = Maps.InjectActiveCells(None, dynamic, driver.m0[static], nC=nC)
class MyPropMap(Maps.PropMap): sigma = Maps.Property("Electrical Conductivity", defaultInvProp=True) mu = Maps.Property("Mu", defaultVal=mu_0)
# Get cells inside the sphere sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., rad) # Adjust susceptibility for volume difference Vratio = (4. / 3. * np.pi * rad**3.) / (np.sum(sph_ind) * cs**3.) model = np.ones(mesh.nC) * 1e-8 model[sph_ind] = 0.01 rxLoc = np.asarray([np.r_[0, 0, 4.]]) bzi = FDEM.Rx.Point_bSecondary(rxLoc, 'z', 'real') bzr = FDEM.Rx.Point_bSecondary(rxLoc, 'z', 'imag') freqs = [400] #np.logspace(2, 3, 5) srcLoc = np.r_[0, 0, 4.] srcList = [ FDEM.Src.MagDipole([bzr, bzi], freq, srcLoc, orientation='Z') for freq in freqs ] mapping = Maps.IdentityMap(mesh) surveyFD = FDEM.Survey(srcList) prbFD = FDEM.Problem3D_b(mesh, sigmaMap=mapping, Solver=PardisoSolver) prbFD.pair(surveyFD) std = 0.03 surveyFD.makeSyntheticData(model, std) #Mesh.TensorMesh.writeUBC(mesh,'MeshGrav.msh') #Mesh.TensorMesh.writeModelUBC(mesh,'MeshGrav.den',model) #PF.Gravity.writeUBCobs("Obs.grv",survey,d)
survey = driver.survey # %% STEP 1: EQUIVALENT SOURCE LAYER # The first step inverts for an equiavlent source layer in order to convert the # observed TMI data to magnetic field Amplitude. # Get the active cells for equivalent source is the top only active = driver.activeCells surf = PF.MagneticsDriver.actIndFull2layer(mesh, active) # Get the layer of cells directyl below topo #surf = Utils.actIndFull2layer(mesh, active) nC = len(surf) # Number of active cells # Create active map to go from reduce set to full surfMap = Maps.InjectActiveCells(mesh, surf, -100) # Create identity map idenMap = Maps.IdentityMap(nP=nC) # Create static map prob = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap, actInd=surf, equiSourceLayer=True) prob.solverOpts['accuracyTol'] = 1e-4 # Pair the survey and problem survey.pair(prob) # Create a regularization function, in this case l2l2
def run(plotIt=True): """ EM: FDEM: 1D: Inversion ======================= Here we will create and run a FDEM 1D inversion. """ 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 halfSpaceProblemAnaDiff(meshType, srctype="MagDipole", sig_half=1e-2, rxOffset=50., bounds=None, plotIt=False): if bounds is None: bounds = [1e-5, 1e-3] if meshType == 'CYL': cs, ncx, ncz, npad = 5., 30, 10, 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') elif meshType == 'TENSOR': cs, nc, npad = 20., 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 = Mesh.TensorMesh([hx, hy, hz], 'CCC') active = mesh.vectorCCz < 0. actMap = Maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz) mapping = Maps.ExpMap(mesh) * Maps.SurjectVertical1D(mesh) * actMap rx = EM.TDEM.Rx(np.array([[rxOffset, 0., 0.]]), np.logspace(-5, -4, 21), 'bz') if srctype == "MagDipole": src = EM.TDEM.Src.MagDipole([rx], waveform=EM.TDEM.Src.StepOffWaveform(), loc=np.array([0., 0., 0.])) elif srctype == "CircularLoop": src = EM.TDEM.Src.CircularLoop([rx], waveform=EM.TDEM.Src.StepOffWaveform(), loc=np.array([0., 0., 0.]), radius=0.1) survey = EM.TDEM.Survey([src]) prb = EM.TDEM.Problem3D_b(mesh, sigmaMap=mapping) prb.Solver = Solver prb.timeSteps = [(1e-06, 40), (5e-06, 40), (1e-05, 40), (5e-05, 40), (0.0001, 40), (0.0005, 40)] sigma = np.ones(mesh.nCz) * 1e-8 sigma[active] = sig_half sigma = np.log(sigma[active]) prb.pair(survey) if srctype == "MagDipole": bz_ana = mu_0 * EM.Analytics.hzAnalyticDipoleT(rx.locs[0][0] + 1e-3, rx.times, sig_half) elif srctype == "CircularLoop": bz_ana = mu_0 * EM.Analytics.hzAnalyticDipoleT(13, rx.times, sig_half) bz_calc = survey.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
# mesh csx, ncx, npadx = 25., 16, 10 csz, ncz, npadz = 25., 8, 10 pf = 1.5 # primary mesh hx = [(csx, ncx), (csx, npadx, pf)] hz = [(csz, npadz, -pf), (csz, ncz), (csz, npadz, pf)] meshp = Mesh.CylMesh([hx, 1., hz], x0='0CC') # secondary mesh h = [(csz, npadz - 4, -pf), (csz, ncz), (csz, npadz - 4, pf)] meshs = Mesh.TensorMesh(3 * [h], x0='CCC') # mappings primaryMapping = (Maps.ExpMap(meshp) * Maps.SurjectFull(meshp) * Maps.Projection(nP=8, index=[0])) mapping = ( Maps.ExpMap(meshs) * Maps.ParametrizedBlockInLayer(meshs) * Maps.Projection(nP=8, index=np.hstack([np.r_[0], np.arange(0, 8)]))) primaryMap2Meshs = (Maps.ExpMap(meshs) * Maps.SurjectFull(meshs) * Maps.Projection(nP=8, index=[0])) class PrimSecFDEMTest(object): # --------------------- Run some tests! --------------------- # def DataTest(self): print('\nTesting Data')
orientation="z", radius=100, waveform=quarter_sine) src_list_magnetostatic = [src_magnetostatic] src_list_ramp_on = [src_ramp_on] ############################################################################### # Create the simulations # ---------------------- # # To simulate magnetic flux data, we use the b-formulation of Maxwell's # equations prob_magnetostatic = TDEM.Problem3D_b(mesh=mesh, sigmaMap=Maps.IdentityMap(mesh), timeSteps=ramp, Solver=Pardiso) prob_ramp_on = TDEM.Problem3D_b(mesh=mesh, sigmaMap=Maps.IdentityMap(mesh), timeSteps=ramp, Solver=Pardiso) survey_magnetostatic = TDEM.Survey(srcList=src_list_magnetostatic) survey_ramp_on = TDEM.Survey(src_list_ramp_on) prob_magnetostatic.pair(survey_magnetostatic) prob_ramp_on.pair(survey_ramp_on) ############################################################################### # Run the long on-time simulation
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 ) # 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) 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()
import matplotlib.pyplot as plt from pymatsolver import PardisoSolver from SimPEG import Maps cs, ncx, ncy, ncz, = 50., 20, 1, 20 npad_x, npad_y, npad_z = 10, 10, 10 pad_rate = 1.3 hx = [(cs,npad_x,-pad_rate), (cs,ncx), (cs,npad_x,pad_rate)] hy = [(cs,npad_y,-pad_rate), (cs,ncy), (cs,npad_y,pad_rate)] hz = [(cs,npad_z,-pad_rate), (cs,ncz), (cs,npad_z,pad_rate)] mesh_3d = Mesh.TensorMesh([hx,hy,hz], 'CCC') mesh_2d = Mesh.TensorMesh([hx,hz], 'CC') inds = mesh_2d.vectorCCy<0. mesh_2d_inv = Mesh.TensorMesh([hx,mesh_2d.hy[inds]], 'CN') actind = mesh_2d.gridCC[:,1]<0. map_2Dto3D = Maps.Surject2Dto3D(mesh_3d) parametric_block = Maps.ParametricBlock(mesh_2d_inv) #, slopeFact=1 expmap = Maps.ExpMap(mesh_2d) actmap = Maps.InjectActiveCells(mesh_2d, indActive=actind, valInactive=np.log(1e-8)) mapping = map_2Dto3D* expmap * actmap * parametric_block x = mesh_3d.vectorCCx[np.logical_and(mesh_3d.vectorCCx>-450, mesh_3d.vectorCCx<450)] time = np.logspace(np.log10(5e-5), np.log10(2.5e-3), 21) srcList = [] ind_start=0 for xloc in x: location = np.array([[xloc, 0., 30.]]) rx_z = EM.TDEM.Rx.Point_dbdt(location, time[ind_start:], 'z') rx_x = EM.TDEM.Rx.Point_dbdt(location, time[ind_start:], 'x') src = EM.TDEM.Src.CircularLoop([rx_z], orientation='z', loc=location) srcList.append(src)
def run_inversion( m0, survey, actind, mesh, std, eps, maxIter=15, beta0_ratio=1e0, coolingFactor=5, coolingRate=2, upper=np.inf, lower=-np.inf, use_sensitivity_weight=False, alpha_s=1e-4, alpha_x=1., alpha_y=1., alpha_z=1., ): """ Run IP inversion """ 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 if use_sensitivity_weight: reg = Regularization.Sparse( mesh, indActive=actind, mapping=regmap ) reg.alpha_s = alpha_s reg.alpha_x = alpha_x reg.alpha_y = alpha_y reg.alpha_z = alpha_z else: reg = Regularization.Sparse( mesh, indActive=actind, mapping=regmap, cell_weights=mesh.vol[actind] ) reg.alpha_s = alpha_s reg.alpha_x = alpha_x reg.alpha_y = alpha_y reg.alpha_z = alpha_z opt = Optimization.ProjectedGNCG(maxIter=maxIter, upper=upper, lower=lower) invProb = InvProblem.BaseInvProblem(dmisfit, reg, opt) beta = Directives.BetaSchedule( coolingFactor=coolingFactor, coolingRate=coolingRate ) betaest = Directives.BetaEstimate_ByEig(beta0_ratio=beta0_ratio) target = Directives.TargetMisfit() # Need to have basice saving function if use_sensitivity_weight: updateSensW = Directives.UpdateSensitivityWeights() update_Jacobi = Directives.UpdatePreconditioner() directiveList = [ beta, betaest, target, update_Jacobi ] else: directiveList = [ beta, betaest, target ] inv = Inversion.BaseInversion( invProb, directiveList=directiveList ) opt.LSshorten = 0.5 opt.remember('xc') # Run inversion mopt = inv.run(m0) return mopt, invProb.dpred
locx = [int(mesh.nCx / 2)] #[int(mesh.nCx/2)-3, int(mesh.nCx/2)+3] midy = int(mesh.nCy / 2) midz = -5 # Lets create a simple flat topo and set the active cells [xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy) zz = np.ones_like(xx) * mesh.vectorNz[-1] topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)] # Go from topo to actv cells actv = Utils.surface2ind_topo(mesh, topo, 'N') actv = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype=int) - 1 # Create active map to go from reduce space to full actvMap = Maps.InjectActiveCells(mesh, actv, -100) nC = int(len(actv)) # Create and array of observation points xr = np.linspace(-25., 25., 20) yr = np.linspace(-25., 25., 20) X, Y = np.meshgrid(xr, yr) # Move the observation points 5m above the topo Z = np.ones_like(X) * mesh.vectorNz[-1] + dx # Create a MAGsurvey rxLoc = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)] rxLoc = PF.BaseMag.RxObs(rxLoc) srcField = PF.BaseMag.SrcField([rxLoc], param=(B[0], B[1], B[2])) survey = PF.BaseMag.LinearSurvey(srcField)
hxind = [(cs,10,1.3),(cs, 21),(cs,10,1.3)] hyind = [(cs,10,1.3),(cs, 21),(cs,10,1.3)] hzind = [(cs,10,1.3),(cs, 21),(cs,10,1.3)] mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC') # Get cells inside the sphere sph_ind = PF.MagAnalytics.spheremodel(mesh, 0., 0., 0., rad) # Adjust susceptibility for volume difference Vratio = (4./3.*np.pi*rad**3.) / (np.sum(sph_ind)*cs**3.) model = np.zeros(mesh.nC) model[sph_ind] = chi*Vratio m = model[sph_ind] # Creat reduced identity map for Linear Pproblem idenMap = Maps.IdentityMap(nP=int(sum(sph_ind))) # Create plane of observations xr = np.linspace(-10, 10, 21) yr = np.linspace(-10, 10, 21) X, Y = np.meshgrid(xr, yr) # Move obs plane 2 radius away from sphere Z = np.ones((xr.size, yr.size))*2.*rad locXyz = np.c_[Utils.mkvc(X), Utils.mkvc(Y), Utils.mkvc(Z)] rxLoc = PF.BaseMag.RxObs(locXyz) srcField = PF.BaseMag.SrcField([rxLoc], param=H0) survey = PF.BaseMag.LinearSurvey(srcField) prob_xyz = PF.Magnetics.MagneticIntegral(mesh, chiMap=idenMap, actInd=sph_ind,
def createLocalProb(meshLocal, local_survey, global_weights, ind): """ CreateLocalProb(rxLoc, global_weights, lims, ind) Generate a problem, calculate/store sensitivities for given data points """ # Need to find a way to compute sensitivities only for intersecting cells activeCells_t = np.ones(meshLocal.nC, dtype='bool') # meshUtils.modelutils.activeTopoLayer(meshLocal, topo) # Create reduced identity map if input_dict["inversion_type"] in ['mvi', 'mvis']: nBlock = 3 else: nBlock = 1 tileMap = Maps.Tile((mesh, activeCells), (meshLocal, activeCells_t), nBlock=nBlock) activeCells_t = tileMap.activeLocal if "adjust_clearance" in list(input_dict.keys()): print("Setting Z values of data to respect clearance height") _, c_ind = tree.query(local_survey.rxLoc) dz = input_dict["adjust_clearance"] z = mesh.gridCC[activeCells, 2][c_ind] + mesh.h_gridded[activeCells, 2][c_ind]/2 + dz local_survey.srcField.rxList[0].locs[:, 2] = z if input_dict["inversion_type"] == 'grav': prob = PF.Gravity.GravityIntegral( meshLocal, rhoMap=tileMap, actInd=activeCells_t, parallelized=parallelized, Jpath=outDir + "Tile" + str(ind) + ".zarr", maxRAM=max_ram, n_cpu=n_cpu, max_chunk_size=max_chunk_size ) elif input_dict["inversion_type"] == 'mag': prob = PF.Magnetics.MagneticIntegral( meshLocal, chiMap=tileMap, actInd=activeCells_t, parallelized=parallelized, Jpath=outDir + "Tile" + str(ind) + ".zarr", maxRAM=max_ram, n_cpu=n_cpu, max_chunk_size=max_chunk_size ) elif input_dict["inversion_type"] in ['mvi', 'mvis']: prob = PF.Magnetics.MagneticIntegral( meshLocal, chiMap=tileMap, actInd=activeCells_t, parallelized=parallelized, Jpath=outDir + "Tile" + str(ind) + ".zarr", maxRAM=max_ram, modelType='vector', n_cpu=n_cpu, max_chunk_size=max_chunk_size ) local_survey.pair(prob) # Data misfit function local_misfit = DataMisfit.l2_DataMisfit(local_survey) local_misfit.W = 1./local_survey.std wr = prob.getJtJdiag(np.ones(tileMap.shape[1]), W=local_misfit.W) activeCellsTemp = Maps.InjectActiveCells(mesh, activeCells, 1e-8) global_weights += wr del meshLocal if output_tile_files: if input_dict["inversion_type"] == 'grav': Utils.io_utils.writeUBCgravityObservations(outDir + 'Survey_Tile' + str(ind) +'.dat', local_survey, local_survey.dobs) elif input_dict["inversion_type"] == 'mag': Utils.io_utils.writeUBCmagneticsObservations(outDir + 'Survey_Tile' + str(ind) +'.dat', local_survey, local_survey.dobs) Mesh.TreeMesh.writeUBC( mesh, outDir + 'Octree_Tile' + str(ind) + '.msh', models={outDir + 'JtJ_Tile' + str(ind) + ' .act': activeCellsTemp*wr[:nC]} ) return local_misfit, global_weights
# Compute active cells activeCells = Utils.surface2ind_topo(mesh, topo) # activeCells = Utils.modelutils.activeTopoLayer(mesh, topo) Mesh.TreeMesh.writeUBC( mesh, workDir + dsep + outDir + 'OctreeMeshGlobal.msh', models={workDir + dsep + outDir + 'ActiveSurface.act': activeCells}) # Get the layer of cells directly below topo #activeCells = Utils.actIndFull2layer(mesh, active) nC = int(activeCells.sum()) # Number of active cells print(nC) # Create active map to go from reduce set to full activeCellsMap = Maps.InjectActiveCells(mesh, activeCells, ndv) # Create identity map idenMap = Maps.IdentityMap(nP=nC) wrGlobal = np.zeros(nC) if tileProblem: # Loop over different tile size and break problem until # memory footprint false below maxRAM usedRAM = np.inf count = 1 while usedRAM > maxRAM: print("Tiling:" + str(count)) tiles, binCount = Utils.modelutils.tileSurveyPoints(rxLoc, count)
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"].value # River path nSounding = resolve["data"].shape[0] # the # of soundings # Bird height from surface b_height_resolve = resolve["src_elevation"].value # 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"].value # build a 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. # 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 std = 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, std=std, 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"].value dobs_re = resolve["dobs"].value dpred_re = resolve["dpred"].value 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. / (d + 100.)**2. w = Utils.sdiag(1. / 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": -2, "vmax": 1. }, 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) out = Utils.plot2Ddata(resolve["xy"].value, temp_dobs / abs(bp) * 1e6, ncontour=100, scale="log", dataloc=False, ax=ax1, contourOpts={"cmap": "viridis"}) vmin, vmax = out[0].get_clim() cb = plt.colorbar(out[0], ticks=np.linspace(vmin, 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"].value, 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.linspace(vmin, 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) if cleanup: os.remove(downloads) shutil.rmtree(directory)
def createLocalProb(rxLoc, wrGlobal, lims, ind): # createLocalProb(rxLoc, wrGlobal, lims, ind) # Generate a problem, calculate/store sensitivities for # given data points # Grab the data for current tile ind_t = np.all([ rxLoc[:, 0] >= lims[0], rxLoc[:, 0] <= lims[1], rxLoc[:, 1] >= lims[2], rxLoc[:, 1] <= lims[3], surveyMask ], axis=0) # Remember selected data in case of tile overlap surveyMask[ind_t] = False # Create new survey if driver["dataFile"][0] == 'GRAV': rxLoc_t = PF.BaseGrav.RxObs(rxLoc[ind_t, :]) srcField = PF.BaseGrav.SrcField([rxLoc_t]) survey_t = PF.BaseGrav.LinearSurvey(srcField) survey_t.dobs = survey.dobs[ind_t] survey_t.std = survey.std[ind_t] survey_t.ind = ind_t Utils.io_utils.writeUBCgravityObservations( workDir + dsep + outDir + "Tile" + str(ind) + '.dat', survey_t, survey_t.dobs) elif driver["dataFile"][0] == 'MAG': rxLoc_t = PF.BaseMag.RxObs(rxLoc[ind_t, :]) srcField = PF.BaseMag.SrcField([rxLoc_t], param=survey.srcField.param) survey_t = PF.BaseMag.LinearSurvey(srcField) survey_t.dobs = survey.dobs[ind_t] survey_t.std = survey.std[ind_t] survey_t.ind = ind_t Utils.io_utils.writeUBCmagneticsObservations( workDir + dsep + outDir + "Tile" + str(ind) + '.dat', survey_t, survey_t.dobs) meshLocal = Utils.modelutils.meshBuilder(newTopo, h, padDist, meshType='TREE', meshGlobal=meshInput, verticalAlignment='center') if topo is not None: meshLocal = Utils.modelutils.refineTree(meshLocal, topo, dtype='surface', octreeLevels=octreeTopo, finalize=False) # Refine the mesh around loc meshLocal = Utils.modelutils.refineTree( meshLocal, newTopo[ind_t, :], dtype='surface', octreeLevels=octreeObs, octreeLevels_XY=octreeLevels_XY, finalize=True) # Need to find a way to compute sensitivities only for intersecting cells activeCells_t = np.ones( meshLocal.nC, dtype='bool' ) # meshUtils.modelutils.activeTopoLayer(meshLocal, topo) # Create reduced identity map tileMap = Maps.Tile((mesh, activeCells), (meshLocal, activeCells_t)) activeCells_t = tileMap.activeLocal print(activeCells_t.sum(), meshLocal.nC) if driver["dataFile"][0] == 'GRAV': prob = PF.Gravity.GravityIntegral(meshLocal, rhoMap=tileMap, actInd=activeCells_t, parallelized=parallelized, Jpath=workDir + dsep + outDir + "Tile" + str(ind) + ".zarr", maxRAM=maxRAM / n_cpu, n_cpu=n_cpu, n_chunks=n_chunks) elif driver["dataFile"][0] == 'MAG': prob = PF.Magnetics.MagneticIntegral( meshLocal, chiMap=tileMap, actInd=activeCells_t, parallelized=parallelized, Jpath=workDir + dsep + outDir + "Tile" + str(ind) + ".zarr", maxRAM=maxRAM / n_cpu, n_cpu=n_cpu, n_chunks=n_chunks) survey_t.pair(prob) # Write out local active and obs for validation Mesh.TreeMesh.writeUBC( meshLocal, workDir + dsep + outDir + dsep + 'Octree_Tile' + str(ind) + '.msh', models={ workDir + dsep + outDir + dsep + 'ActiveGlobal_Tile' + str(ind) + ' .act': activeCells_t }) if driver["dataFile"][0] == 'GRAV': Utils.io_utils.writeUBCgravityObservations( workDir + dsep + outDir + dsep + 'Tile' + str(ind) + '.dat', survey_t, survey_t.dobs) elif driver["dataFile"][0] == 'MAG': Utils.io_utils.writeUBCmagneticsObservations( workDir + dsep + outDir + dsep + 'Tile' + str(ind) + '.dat', survey_t, survey_t.dobs) # Data misfit function dmis = DataMisfit.l2_DataMisfit(survey_t) dmis.W = 1. / survey_t.std wr = prob.getJtJdiag(np.ones(tileMap.P.shape[1]), W=dmis.W) wrGlobal += wr del meshLocal # Create combo misfit function return dmis
def run(plotIt=True): """ EM: TDEM: 1D: Inversion ======================= Here we will create and run a TDEM 1D inversion. """ 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') active = mesh.vectorCCz < 0. layer = (mesh.vectorCCz < 0.) & (mesh.vectorCCz >= -100.) 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 = EM.TDEM.Rx.Point_b(np.array([[rxOffset, 0., 30]]), np.logspace(-5, -3, 31), 'z') src = EM.TDEM.Src.MagDipole([rx], loc=np.array([0., 0., 80])) survey = EM.TDEM.Survey([src]) prb = EM.TDEM.Problem3D_b(mesh, sigmaMap=mapping) prb.Solver = SolverLU prb.timeSteps = [(1e-06, 20), (1e-05, 20), (0.0001, 20)] prb.pair(survey) # create observed data std = 0.05 survey.dobs = survey.makeSyntheticData(mtrue, std) survey.std = std survey.eps = 1e-5 * np.linalg.norm(survey.dobs) dmisfit = DataMisfit.l2_DataMisfit(survey) regMesh = Mesh.TensorMesh([mesh.hz[mapping.maps[-1].indActive]]) reg = Regularization.Tikhonov(regMesh, alpha_s=1e-2, alpha_x=1.) opt = Optimization.InexactGaussNewton(maxIter=5, LSshorten=0.5) 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) prb.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, survey.dtrue, 'b.-') ax[0].loglog(rx.times, survey.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(plotIt=True): # Set up cylindrically symmetric mesh cs, ncx, ncz, npad = 10., 15, 25, 13 # padded cylindrical 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 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(("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) plt.tight_layout(pad=1.5)
def setUp(self): ndv = -100 # Create a self.mesh dx = 5. hxind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)] hyind = [(dx, 5, -1.3), (dx, 5), (dx, 5, 1.3)] hzind = [(dx, 5, -1.3), (dx, 6)] self.mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCC') # Get index of the center midx = int(self.mesh.nCx / 2) midy = int(self.mesh.nCy / 2) # Lets create a simple Gaussian topo and set the active cells [xx, yy] = np.meshgrid(self.mesh.vectorNx, self.mesh.vectorNy) zz = -np.exp((xx**2 + yy**2) / 75**2) + self.mesh.vectorNz[-1] # Go from topo to actv cells topo = np.c_[Utils.mkvc(xx), Utils.mkvc(yy), Utils.mkvc(zz)] actv = Utils.surface2ind_topo(self.mesh, topo, 'N') actv = np.asarray([inds for inds, elem in enumerate(actv, 1) if elem], dtype=int) - 1 # Create active map to go from reduce space to full self.actvMap = Maps.InjectActiveCells(self.mesh, actv, -100) nC = len(actv) # Create and array of observation points xr = np.linspace(-20., 20., 20) yr = np.linspace(-20., 20., 20) X, Y = np.meshgrid(xr, yr) # Move the observation points 5m above the topo Z = -np.exp((X**2 + Y**2) / 75**2) + self.mesh.vectorNz[-1] + 5. # Create a MAGsurvey locXYZ = np.c_[Utils.mkvc(X.T), Utils.mkvc(Y.T), Utils.mkvc(Z.T)] rxLoc = PF.BaseGrav.RxObs(locXYZ) srcField = PF.BaseGrav.SrcField([rxLoc]) survey = PF.BaseGrav.LinearSurvey(srcField) # We can now create a density model and generate data # Here a simple block in half-space model = np.zeros((self.mesh.nCx, self.mesh.nCy, self.mesh.nCz)) model[(midx - 2):(midx + 2), (midy - 2):(midy + 2), -6:-2] = 0.5 model = Utils.mkvc(model) self.model = model[actv] # Create active map to go from reduce set to full actvMap = Maps.InjectActiveCells(self.mesh, actv, ndv) # Create reduced identity map idenMap = Maps.IdentityMap(nP=nC) # Create the forward model operator prob = PF.Gravity.GravityIntegral(self.mesh, rhoMap=idenMap, actInd=actv) # Pair the survey and problem survey.pair(prob) # Compute linear forward operator and compute some data d = prob.fields(self.model) # Add noise and uncertainties (1nT) data = d + np.random.randn(len(d)) * 0.001 wd = np.ones(len(data)) * .001 survey.dobs = data survey.std = wd # PF.Gravity.plot_obs_2D(survey.srcField.rxList[0].locs, d=data) # Create sensitivity weights from our linear forward operator wr = PF.Magnetics.get_dist_wgt(self.mesh, locXYZ, actv, 2., 2.) wr = wr**2. # Create a regularization reg = Regularization.Sparse(self.mesh, indActive=actv, mapping=idenMap) reg.cell_weights = wr reg.norms = np.c_[0, 0, 0, 0] reg.gradientType = 'component' # reg.eps_p, reg.eps_q = 5e-2, 1e-2 # Data misfit function dmis = DataMisfit.l2_DataMisfit(survey) dmis.W = 1 / wd # Add directives to the inversion opt = Optimization.ProjectedGNCG(maxIter=100, lower=-1., upper=1., maxIterLS=20, maxIterCG=10, tolCG=1e-3) invProb = InvProblem.BaseInvProblem(dmis, reg, opt, beta=1e+8) # Here is where the norms are applied IRLS = Directives.Update_IRLS(f_min_change=1e-4, minGNiter=1) update_Jacobi = Directives.UpdatePreconditioner(mapping=idenMap) self.inv = Inversion.BaseInversion(invProb, directiveList=[IRLS, update_Jacobi])
def run(N=100, plotIt=True): np.random.seed(1) std_noise = 1e-2 mesh = Mesh.TensorMesh([N]) m0 = np.ones(mesh.nC) * 1e-4 mref = np.zeros(mesh.nC) 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.dobs = prob.fields(mtrue) + std_noise * np.random.randn(nk) wd = np.ones(nk) * std_noise # Distance weighting wr = np.sum(prob.getJ(m0)**2., axis=0)**0.5 wr = wr / np.max(wr) dmis = DataMisfit.l2_DataMisfit(survey) dmis.W = 1. / wd betaest = Directives.BetaEstimate_ByEig(beta0_ratio=1e-2) # Creat reduced identity map idenMap = Maps.IdentityMap(nP=mesh.nC) reg = Regularization.Sparse(mesh, mapping=idenMap) reg.mref = mref reg.cell_weights = wr reg.norms = [0., 0., 2., 2.] reg.mref = np.zeros(mesh.nC) opt = Optimization.ProjectedGNCG(maxIter=100, lower=-2., upper=2., maxIterLS=20, maxIterCG=10, tolCG=1e-3) invProb = InvProblem.BaseInvProblem(dmis, reg, opt) update_Jacobi = Directives.UpdatePreconditioner() # Set the IRLS directive, penalize the lowest 25 percentile of model values # Start with an l2-l2, then switch to lp-norms IRLS = Directives.Update_IRLS(prctile=25, maxIRLSiter=15, minGNiter=3) inv = Inversion.BaseInversion(invProb, directiveList=[IRLS, betaest, update_Jacobi]) # Run inversion mrec = inv.run(m0) print("Final misfit:" + str(invProb.dmisfit(mrec))) 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(mesh.vectorCCx, mtrue, 'b-') axes[1].plot(mesh.vectorCCx, invProb.l2model, 'r-') # axes[1].legend(('True Model', 'Recovered Model')) axes[1].set_ylim(-1.0, 1.25) axes[1].plot(mesh.vectorCCx, mrec, 'k-', lw=2) axes[1].legend(('True Model', 'Smooth l2-l2', 'Sparse lp: {0}, lqx: {1}'.format(*reg.norms)), fontsize=12) return prob, survey, mesh, mrec