.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/examples/06-tdem/plot_inv_tdem_1D_raw_waveform.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_content_examples_06-tdem_plot_inv_tdem_1D_raw_waveform.py: EM: TDEM: 1D: Inversion with VTEM waveform ========================================== Here we will create and run a TDEM 1D inversion, with VTEM waveform of which initial condition is zero, but have some on- and off-time. .. GENERATED FROM PYTHON SOURCE LINES 9-123 .. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_inv_tdem_1D_raw_waveform_001.png :alt: plot inv tdem 1D raw waveform :srcset: /content/examples/06-tdem/images/sphx_glr_plot_inv_tdem_1D_raw_waveform_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none SimPEG.InvProblem will set Regularization.reference_model to m0. SimPEG.InvProblem will set Regularization.reference_model to m0. SimPEG.InvProblem will set Regularization.reference_model to m0. SimPEG.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv. ***Done using same Solver, and solver_opts as the Simulation3DMagneticFluxDensity problem*** model has any nan: 0 ============================ Inexact Gauss Newton ============================ # beta phi_d phi_m f |proj(x-g)-x| LS Comment ----------------------------------------------------------------------------- x0 has any nan: 0 0 1.00e+02 1.92e+04 0.00e+00 1.92e+04 1.75e+03 0 1 1.00e+02 1.56e+04 1.21e+01 1.68e+04 1.19e+03 0 2 1.00e+02 1.18e+04 3.22e+01 1.50e+04 1.33e+03 0 Skip BFGS 3 1.00e+02 9.15e+03 4.76e+01 1.39e+04 9.41e+02 0 4 1.00e+02 8.42e+03 5.26e+01 1.37e+04 3.82e+02 0 Skip BFGS 5 1.00e+02 8.30e+03 5.35e+01 1.37e+04 1.38e+02 0 Skip BFGS ------------------------- STOP! ------------------------- 1 : |fc-fOld| = 3.2096e+01 <= tolF*(1+|f0|) = 1.9220e+03 1 : |xc-x_last| = 1.5739e-01 <= tolX*(1+|x0|) = 3.6894e+00 0 : |proj(x-g)-x| = 1.3810e+02 <= tolG = 1.0000e-01 0 : |proj(x-g)-x| = 1.3810e+02 <= 1e3*eps = 1.0000e-02 1 : maxIter = 5 <= iter = 5 ------------------------- DONE! ------------------------- | .. code-block:: default import numpy as np import discretize from SimPEG import ( maps, data_misfit, regularization, optimization, inverse_problem, inversion, directives, utils, ) from SimPEG.electromagnetics import time_domain as TDEM, utils as EMutils import matplotlib.pyplot as plt from scipy.interpolate import interp1d try: from pymatsolver import Pardiso as Solver except ImportError: from SimPEG import SolverLU as Solver 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.CylindricalMesh([hx, 1, hz], "00C") active = mesh.cell_centers_z < 0.0 layer = (mesh.cell_centers_z < -50.0) & (mesh.cell_centers_z >= -150.0) actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.shape_cells[2]) mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap sig_half = 1e-3 sig_air = 1e-8 sig_layer = 1e-2 sigma = np.ones(mesh.shape_cells[2]) * 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(off_time=t0, waveform_function=wavefun) rx = TDEM.Rx.PointMagneticFluxTimeDerivative( rxloc, np.logspace(-4, -2.5, 11) + t0, "z" ) src = TDEM.Src.CircularLoop( [rx], waveform=waveform, location=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.h[2][mapping.maps[-1].indActive]]) reg = regularization.WeightedLeastSquares(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) 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.cell_centers_z[active]) plt.semilogx(np.exp(mopt), mesh.cell_centers_z[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([r"$\sigma_{true}$", r"$\sigma_{pred}$"]) if __name__ == "__main__": run() plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 33.871 seconds) **Estimated memory usage:** 8 MB .. _sphx_glr_download_content_examples_06-tdem_plot_inv_tdem_1D_raw_waveform.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_inv_tdem_1D_raw_waveform.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_inv_tdem_1D_raw_waveform.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_