.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/examples/01-maps/plot_sumMap.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_01-maps_plot_sumMap.py: Maps: ComboMaps =============== Invert synthetic magnetic data with variable background values and a single block anomaly buried at depth. We will use the Sum Map to invert for both the background values and an heterogeneous susceptibiilty model. .. code-block:: python :linenos: .. GENERATED FROM PYTHON SOURCE LINES 15-207 .. rst-class:: sphx-glr-horizontal * .. image-sg:: /content/examples/01-maps/images/sphx_glr_plot_sumMap_001.png :alt: plot sumMap :srcset: /content/examples/01-maps/images/sphx_glr_plot_sumMap_001.png :class: sphx-glr-multi-img * .. image-sg:: /content/examples/01-maps/images/sphx_glr_plot_sumMap_002.png :alt: plot sumMap :srcset: /content/examples/01-maps/images/sphx_glr_plot_sumMap_002.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none Running inversion with SimPEG v0.22.2 simpeg.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv. ***Done using the default solver Pardiso and no solver_opts.*** model has any nan: 0 =============================== Projected GNCG =============================== # beta phi_d phi_m f |proj(x-g)-x| LS Comment ----------------------------------------------------------------------------- x0 has any nan: 0 0 5.39e+05 9.12e+06 4.27e-04 9.12e+06 6.29e+01 0 1 2.70e+05 1.27e+05 8.03e-02 1.49e+05 3.50e+01 0 2 1.35e+05 4.31e+04 2.43e-01 7.58e+04 4.95e+01 0 3 6.74e+04 1.84e+04 3.71e-01 4.34e+04 5.56e+01 0 Skip BFGS 4 3.37e+04 5.87e+03 4.81e-01 2.21e+04 4.86e+01 0 Skip BFGS 5 1.69e+04 4.44e+03 5.14e-01 1.31e+04 3.56e+01 1 Skip BFGS 6 8.43e+03 9.06e+02 6.01e-01 5.97e+03 4.79e+01 0 7 4.21e+03 9.00e+02 6.02e-01 3.44e+03 5.34e+01 4 Skip BFGS 8 2.11e+03 4.64e+02 6.45e-01 1.82e+03 4.58e+01 0 9 1.05e+03 4.64e+02 6.45e-01 1.14e+03 3.66e+01 6 Skip BFGS 10 5.27e+02 4.15e+02 6.64e-01 7.65e+02 4.73e+01 0 11 2.63e+02 4.14e+02 6.66e-01 5.89e+02 6.15e+01 2 Skip BFGS 12 1.32e+02 4.11e+02 6.68e-01 4.99e+02 4.19e+01 3 13 6.58e+01 4.11e+02 6.68e-01 4.55e+02 4.20e+01 13 Skip BFGS 14 3.29e+01 4.11e+02 6.68e-01 4.33e+02 5.78e+01 3 15 1.65e+01 4.07e+02 6.74e-01 4.18e+02 3.78e+01 2 16 8.23e+00 4.07e+02 6.74e-01 4.12e+02 3.78e+01 13 Skip BFGS 17 4.12e+00 4.07e+02 6.75e-01 4.09e+02 5.30e+01 4 18 2.06e+00 4.00e+02 7.28e-01 4.02e+02 3.90e+01 0 Reached starting chifact with l2-norm regularization: Start IRLS steps... irls_threshold 0.010162946390113451 irls_threshold 0.012178787591916965 19 1.03e+00 3.84e+02 1.02e+00 3.85e+02 3.87e+01 0 20 1.03e+00 3.84e+02 1.09e+00 3.85e+02 6.08e+01 2 Skip BFGS 21 1.03e+00 3.83e+02 1.15e+00 3.84e+02 5.08e+01 1 22 1.03e+00 3.83e+02 1.19e+00 3.84e+02 4.93e+01 6 Skip BFGS 23 1.03e+00 3.82e+02 1.22e+00 3.84e+02 3.62e+01 2 Skip BFGS 24 1.03e+00 3.82e+02 1.22e+00 3.83e+02 3.67e+01 3 Skip BFGS Minimum decrease in regularization.End of IRLS ------------------------- STOP! ------------------------- 1 : |fc-fOld| = 0.0000e+00 <= tolF*(1+|f0|) = 9.1165e+05 1 : |xc-x_last| = 6.0182e-04 <= tolX*(1+|x0|) = 1.0075e-01 0 : |proj(x-g)-x| = 3.6723e+01 <= tolG = 1.0000e-03 0 : |proj(x-g)-x| = 3.6723e+01 <= 1e3*eps = 1.0000e-03 0 : maxIter = 100 <= iter = 25 ------------------------- DONE! ------------------------- | .. code-block:: Python from discretize import TensorMesh from discretize.utils import active_from_xyz from simpeg import ( utils, maps, regularization, data_misfit, optimization, inverse_problem, directives, inversion, ) from simpeg.potential_fields import magnetics import numpy as np import matplotlib.pyplot as plt def run(plotIt=True): h0_amplitude, h0_inclination, h0_declination = (50000.0, 90.0, 0.0) # Create a mesh dx = 5.0 hxind = [(dx, 5, -1.3), (dx, 10), (dx, 5, 1.3)] hyind = [(dx, 5, -1.3), (dx, 10), (dx, 5, 1.3)] hzind = [(dx, 5, -1.3), (dx, 10)] mesh = TensorMesh([hxind, hyind, hzind], "CCC") # Lets create a simple Gaussian topo and set the active cells [xx, yy] = np.meshgrid(mesh.nodes_x, mesh.nodes_y) zz = -np.exp((xx**2 + yy**2) / 75**2) + mesh.nodes_z[-1] # We would usually load a topofile topo = np.c_[utils.mkvc(xx), utils.mkvc(yy), utils.mkvc(zz)] # Go from topo to array of indices of active cells actv = active_from_xyz(mesh, topo, "N") nC = int(actv.sum()) # Create and array of observation points xr = np.linspace(-20.0, 20.0, 20) yr = np.linspace(-20.0, 20.0, 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.nodes_z[-1] + 5.0 # Create a MAGsurvey rxLoc = np.c_[utils.mkvc(X.T), utils.mkvc(Y.T), utils.mkvc(Z.T)] rxLoc = magnetics.Point(rxLoc) srcField = magnetics.UniformBackgroundField( receiver_list=[rxLoc], amplitude=h0_amplitude, inclination=h0_inclination, declination=h0_declination, ) survey = magnetics.Survey(srcField) # We can now create a susceptibility model and generate data model = np.zeros(mesh.nC) # Change values in half the domain model[mesh.gridCC[:, 0] < 0] = 0.01 # Add a block in half-space model = utils.model_builder.add_block( mesh.gridCC, model, np.r_[-10, -10, 20], np.r_[10, 10, 40], 0.05 ) model = utils.mkvc(model) model = model[actv] # Create active map to go from reduce set to full actvMap = maps.InjectActiveCells(mesh, actv, np.nan) # Create reduced identity map idenMap = maps.IdentityMap(nP=nC) # Create the forward model operator prob = magnetics.Simulation3DIntegral( mesh, survey=survey, chiMap=idenMap, ind_active=actv, store_sensitivities="forward_only", ) # Compute linear forward operator and compute some data data = prob.make_synthetic_data( model, relative_error=0.0, noise_floor=1, add_noise=True ) # Create a homogenous maps for the two domains domains = [mesh.gridCC[actv, 0] < 0, mesh.gridCC[actv, 0] >= 0] homogMap = maps.SurjectUnits(domains) # Create a wire map for a second model space, voxel based wires = maps.Wires(("homo", len(domains)), ("hetero", nC)) # Create Sum map sumMap = maps.SumMap([homogMap * wires.homo, wires.hetero]) # Create the forward model operator prob = magnetics.Simulation3DIntegral( mesh, survey=survey, chiMap=sumMap, ind_active=actv, store_sensitivities="ram" ) # Make sensitivity weighting # Take the cell number out of the scaling. # Want to keep high sens for large volumes wr = ( prob.getJtJdiag(np.ones(sumMap.shape[1])) / np.r_[homogMap.P.T * mesh.cell_volumes[actv], mesh.cell_volumes[actv]] ** 2.0 ) # Scale the model spaces independently wr[wires.homo.index] /= np.max((wires.homo * wr)) * utils.mkvc( homogMap.P.sum(axis=0).flatten() ) wr[wires.hetero.index] /= np.max(wires.hetero * wr) wr = wr**0.5 ## Create a regularization # For the homogeneous model regMesh = TensorMesh([len(domains)]) reg_m1 = regularization.Sparse(regMesh, mapping=wires.homo) reg_m1.set_weights(weights=wires.homo * wr) reg_m1.norms = [0, 2] reg_m1.reference_model = np.zeros(sumMap.shape[1]) # Regularization for the voxel model reg_m2 = regularization.Sparse( mesh, active_cells=actv, mapping=wires.hetero, gradient_type="components" ) reg_m2.set_weights(weights=wires.hetero * wr) reg_m2.norms = [0, 0, 0, 0] reg_m2.reference_model = np.zeros(sumMap.shape[1]) reg = reg_m1 + reg_m2 # Data misfit function dmis = data_misfit.L2DataMisfit(simulation=prob, data=data) # Add directives to the inversion opt = optimization.ProjectedGNCG( maxIter=100, lower=0.0, upper=1.0, maxIterLS=20, maxIterCG=10, tolCG=1e-3, tolG=1e-3, eps=1e-6, ) invProb = inverse_problem.BaseInvProblem(dmis, reg, opt) betaest = directives.BetaEstimate_ByEig(beta0_ratio=1e-2) # Here is where the norms are applied # Use pick a threshold parameter empirically based on the distribution of # model parameters IRLS = directives.Update_IRLS(f_min_change=1e-3, minGNiter=1) update_Jacobi = directives.UpdatePreconditioner() inv = inversion.BaseInversion(invProb, directiveList=[IRLS, betaest, update_Jacobi]) # Run the inversion m0 = np.ones(sumMap.shape[1]) * 1e-4 # Starting model prob.model = m0 mrecSum = inv.run(m0) if plotIt: mesh.plot_3d_slicer( actvMap * model, aspect="equal", zslice=30, pcolor_opts={"cmap": "inferno_r"}, transparent="slider", ) mesh.plot_3d_slicer( actvMap * sumMap * mrecSum, aspect="equal", zslice=30, pcolor_opts={"cmap": "inferno_r"}, transparent="slider", ) if __name__ == "__main__": run() plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 21.987 seconds) **Estimated memory usage:** 202 MB .. _sphx_glr_download_content_examples_01-maps_plot_sumMap.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_sumMap.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_sumMap.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_sumMap.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_