.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/user-guide/tutorials/06-ip/plot_inv_3_dcip3d.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_user-guide_tutorials_06-ip_plot_inv_3_dcip3d.py: 3D Least-Squares Inversion of DC and IP Data ============================================ Here we invert 5 lines of DC and IP data to recover both an electrical conductivity and a chargeability model. We formulate the corresponding inverse problems as least-squares optimization problems. For this tutorial, we focus on the following: - Generating a mesh based on survey geometry - Including surface topography - Defining the inverse problem (data misfit, regularization, directives) - Applying sensitivity weighting - Plotting the recovered model and data misfit The DC data are measured voltages normalized by the source current in V/A and the IP data are defined as apparent chargeabilities and V/V. .. GENERATED FROM PYTHON SOURCE LINES 24-27 Import Modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 27-70 .. code-block:: Python import os import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt import tarfile from discretize import TreeMesh from discretize.utils import refine_tree_xyz, active_from_xyz from simpeg.utils import model_builder from simpeg.utils.io_utils.io_utils_electromagnetics import read_dcip_xyz from simpeg import ( maps, data_misfit, regularization, optimization, inverse_problem, inversion, directives, utils, ) from simpeg.electromagnetics.static import resistivity as dc from simpeg.electromagnetics.static import induced_polarization as ip from simpeg.electromagnetics.static.utils.static_utils import ( apparent_resistivity_from_voltage, ) # To plot DC/IP data in 3D, the user must have the plotly package try: import plotly from simpeg.electromagnetics.static.utils.static_utils import plot_3d_pseudosection has_plotly = True except ImportError: has_plotly = False pass mpl.rcParams.update({"font.size": 16}) # sphinx_gallery_thumbnail_number = 7 .. GENERATED FROM PYTHON SOURCE LINES 71-82 Define File Names ----------------- Here we provide the file paths to assets we need to run the inversion. The path to the true model conductivity and chargeability models are also provided for comparison with the inversion results. These files are stored as a tar-file on our google cloud bucket: "https://storage.googleapis.com/simpeg/doc-assets/dcip3d.tar.gz" .. GENERATED FROM PYTHON SOURCE LINES 82-102 .. code-block:: Python # storage bucket where we have the data data_source = "https://storage.googleapis.com/simpeg/doc-assets/dcip3d.tar.gz" # download the data downloaded_data = utils.download(data_source, overwrite=True) # unzip the tarfile tar = tarfile.open(downloaded_data, "r") tar.extractall() tar.close() # path to the directory containing our data dir_path = downloaded_data.split(".")[0] + os.path.sep # files to work with topo_filename = dir_path + "topo_xyz.txt" dc_data_filename = dir_path + "dc_data.xyz" ip_data_filename = dir_path + "ip_data.xyz" .. rst-class:: sphx-glr-script-out .. code-block:: none Downloading https://storage.googleapis.com/simpeg/doc-assets/dcip3d.tar.gz saved to: /home/vsts/work/1/s/tutorials/06-ip/dcip3d.tar.gz Download completed! .. GENERATED FROM PYTHON SOURCE LINES 103-109 Load Data and Topography ------------------------ Here we load the observed data and topography. .. GENERATED FROM PYTHON SOURCE LINES 109-128 .. code-block:: Python topo_xyz = np.loadtxt(str(topo_filename)) dc_data = read_dcip_xyz( dc_data_filename, "volt", data_header="V/A", uncertainties_header="UNCERT", is_surface_data=False, ) ip_data = read_dcip_xyz( ip_data_filename, "apparent_chargeability", data_header="APP_CHG", uncertainties_header="UNCERT", is_surface_data=False, ) .. GENERATED FROM PYTHON SOURCE LINES 129-136 Plot Observed DC Data in Pseudosection -------------------------------------- Here we plot the observed DC data in 3D pseudosection. To use this utility, you must have Python's *plotly* package. Here, we represent the DC data as apparent conductivities. .. GENERATED FROM PYTHON SOURCE LINES 136-166 .. code-block:: Python # Convert predicted data to apparent conductivities apparent_conductivity = 1 / apparent_resistivity_from_voltage( dc_data.survey, dc_data.dobs, ) if has_plotly: # Plot DC Data fig = plot_3d_pseudosection( dc_data.survey, apparent_conductivity, scale="log", units="S/m" ) fig.update_layout( title_text="Apparent Conductivity", title_x=0.5, title_font_size=24, width=650, height=500, scene_camera=dict( center=dict(x=0, y=0, z=-0.4), eye=dict(x=1.5, y=-1.5, z=1.8) ), ) plotly.io.show(fig) else: print("INSTALL 'PLOTLY' TO VISUALIZE 3D PSEUDOSECTIONS") .. raw:: html :file: images/sphx_glr_plot_inv_3_dcip3d_001.html .. GENERATED FROM PYTHON SOURCE LINES 167-174 Plot Observed IP Data in Pseudosection -------------------------------------- Here we plot the observed IP data in 3D pseudosection. To use this utility, you must have Python's *plotly* package. Here, we represent the IP data as apparent chargeabilities. .. GENERATED FROM PYTHON SOURCE LINES 174-203 .. code-block:: Python if has_plotly: # Plot IP Data fig = plot_3d_pseudosection( ip_data.survey, ip_data.dobs, scale="linear", units="V/V", vlim=[0, np.max(ip_data.dobs)], marker_opts={"colorscale": "plasma"}, ) fig.update_layout( title_text="Apparent Chargeability", title_x=0.5, title_font_size=24, width=650, height=500, scene_camera=dict( center=dict(x=0, y=0, z=-0.4), eye=dict(x=1.5, y=-1.5, z=1.8) ), ) plotly.io.show(fig) else: print("INSTALL 'PLOTLY' TO VISUALIZE 3D PSEUDOSECTIONS") .. raw:: html :file: images/sphx_glr_plot_inv_3_dcip3d_002.html .. GENERATED FROM PYTHON SOURCE LINES 204-213 Assign Uncertainties -------------------- Inversion with SimPEG requires that we define the uncertainties on our data. This represents our estimate of the standard deviation of the noise in our data. For DC data, the uncertainties are 10% of the absolute value. For IP data, the uncertainties are 5e-3 V/V. .. GENERATED FROM PYTHON SOURCE LINES 213-218 .. code-block:: Python dc_data.standard_deviation = 0.1 * np.abs(dc_data.dobs) ip_data.standard_deviation = 5e-3 * np.ones_like(ip_data.dobs) .. GENERATED FROM PYTHON SOURCE LINES 219-225 Create Tree Mesh ---------------- Here, we create the Tree mesh that will be used to invert both DC resistivity and IP data. .. GENERATED FROM PYTHON SOURCE LINES 225-262 .. code-block:: Python dh = 25.0 # base cell width dom_width_x = 6000.0 # domain width x dom_width_y = 6000.0 # domain width y dom_width_z = 4000.0 # domain width z nbcx = 2 ** int(np.round(np.log(dom_width_x / dh) / np.log(2.0))) # num. base cells x nbcy = 2 ** int(np.round(np.log(dom_width_y / dh) / np.log(2.0))) # num. base cells y nbcz = 2 ** int(np.round(np.log(dom_width_z / dh) / np.log(2.0))) # num. base cells z # Define the base mesh hx = [(dh, nbcx)] hy = [(dh, nbcy)] hz = [(dh, nbcz)] mesh = TreeMesh([hx, hy, hz], x0="CCN") # Mesh refinement based on topography k = np.sqrt(np.sum(topo_xyz[:, 0:2] ** 2, axis=1)) < 1200 mesh = refine_tree_xyz( mesh, topo_xyz[k, :], octree_levels=[0, 6, 8], method="surface", finalize=False ) # Mesh refinement near sources and receivers. electrode_locations = np.r_[ dc_data.survey.locations_a, dc_data.survey.locations_b, dc_data.survey.locations_m, dc_data.survey.locations_n, ] unique_locations = np.unique(electrode_locations, axis=0) mesh = refine_tree_xyz( mesh, unique_locations, octree_levels=[4, 6, 4], method="radial", finalize=False ) # Finalize the mesh mesh.finalize() .. rst-class:: sphx-glr-script-out .. code-block:: none /home/vsts/work/1/s/tutorials/06-ip/plot_inv_3_dcip3d.py:239: FutureWarning: In discretize v1.0 the TreeMesh will change the default value of diagonal_balance to True, which will likely slightly change meshes you have previously created. If you need to keep the current behavior, explicitly set diagonal_balance=False. /home/vsts/work/1/s/tutorials/06-ip/plot_inv_3_dcip3d.py:243: DeprecationWarning: The surface option is deprecated as of `0.9.0` please update your code to use the `TreeMesh.refine_surface` functionality. It will be removed in a future version of discretize. /home/vsts/work/1/s/tutorials/06-ip/plot_inv_3_dcip3d.py:255: DeprecationWarning: The radial option is deprecated as of `0.9.0` please update your code to use the `TreeMesh.refine_points` functionality. It will be removed in a future version of discretize. .. GENERATED FROM PYTHON SOURCE LINES 263-271 Project Electrodes to Discretized Topography -------------------------------------------- It is important that electrodes are not modeled as being in the air. Even if the electrodes are properly located along surface topography, they may lie above the discretized topography. This step is carried out to ensure all electrodes lie on the discretized surface. .. GENERATED FROM PYTHON SOURCE LINES 271-287 .. code-block:: Python # Find cells that lie below surface topography ind_active = active_from_xyz(mesh, topo_xyz) # Extract survey from data object dc_survey = dc_data.survey ip_survey = ip_data.survey # Shift electrodes to the surface of discretized topography dc_survey.drape_electrodes_on_topography(mesh, ind_active, option="top") ip_survey.drape_electrodes_on_topography(mesh, ind_active, option="top") # Reset survey in data object dc_data.survey = dc_survey ip_data.survey = ip_survey .. rst-class:: sphx-glr-script-out .. code-block:: none /home/vsts/work/1/s/tutorials/06-ip/plot_inv_3_dcip3d.py:280: FutureWarning: Argument ``option`` is deprecated in favor of ``topo_cell_cutoff`` and will be removed in SimPEG v0.27.0. /home/vsts/work/1/s/tutorials/06-ip/plot_inv_3_dcip3d.py:281: FutureWarning: Argument ``option`` is deprecated in favor of ``topo_cell_cutoff`` and will be removed in SimPEG v0.27.0. .. GENERATED FROM PYTHON SOURCE LINES 288-297 Starting/Reference Model and Mapping on OcTree Mesh --------------------------------------------------- Here, we create starting and/or reference models for the DC inversion as well as the mapping from the model space to the active cells. Starting and reference models can be a constant background value or contain a-priori structures. Here, the starting model is the natural log of 0.01 S/m. .. GENERATED FROM PYTHON SOURCE LINES 297-312 .. code-block:: Python # Define conductivity model in S/m (or resistivity model in Ohm m) air_conductivity = np.log(1e-8) background_conductivity = np.log(1e-2) # Define the mapping from active cells to the entire domain active_map = maps.InjectActiveCells(mesh, ind_active, np.exp(air_conductivity)) nC = int(ind_active.sum()) # Define the mapping from the model to the conductivity of the entire domain conductivity_map = active_map * maps.ExpMap() # Define starting model starting_conductivity_model = background_conductivity * np.ones(nC) .. GENERATED FROM PYTHON SOURCE LINES 313-319 Define the Physics of the DC Simulation --------------------------------------- Here, we define the physics of the DC resistivity simulation. .. GENERATED FROM PYTHON SOURCE LINES 319-324 .. code-block:: Python dc_simulation = dc.Simulation3DNodal( mesh, survey=dc_survey, sigmaMap=conductivity_map, storeJ=True ) .. GENERATED FROM PYTHON SOURCE LINES 325-335 Define DC Inverse Problem ------------------------- The inverse problem is defined by 3 things: 1) Data Misfit: a measure of how well our recovered model explains the field data 2) Regularization: constraints placed on the recovered model and a priori information 3) Optimization: the numerical approach used to solve the inverse problem .. GENERATED FROM PYTHON SOURCE LINES 335-364 .. code-block:: Python # Define the data misfit. Here the data misfit is the L2 norm of the weighted # residual between the observed data and the data predicted for a given model. # Within the data misfit, the residual between predicted and observed data are # normalized by the data's standard deviation. dc_data_misfit = data_misfit.L2DataMisfit(data=dc_data, simulation=dc_simulation) # Define the regularization (model objective function) dc_regularization = regularization.WeightedLeastSquares( mesh, active_cells=ind_active, reference_model=starting_conductivity_model, ) dc_regularization.reference_model_in_smooth = ( True # Include reference model in smoothness ) # Define how the optimization problem is solved. dc_optimization = optimization.InexactGaussNewton( maxIter=15, cg_maxiter=30, cg_rtol=1e-2 ) # Here we define the inverse problem that is to be solved dc_inverse_problem = inverse_problem.BaseInvProblem( dc_data_misfit, dc_regularization, dc_optimization ) .. GENERATED FROM PYTHON SOURCE LINES 365-373 Define DC Inversion Directives ------------------------------ Here we define any directives that are carried out during the inversion. This includes the cooling schedule for the trade-off parameter (beta), stopping criteria for the inversion and saving inversion results at each iteration. .. GENERATED FROM PYTHON SOURCE LINES 373-404 .. code-block:: Python # Apply and update sensitivity weighting as the model updates update_sensitivity_weighting = directives.UpdateSensitivityWeights() # Defining a starting value for the trade-off parameter (beta) between the data # misfit and the regularization. starting_beta = directives.BetaEstimate_ByEig(beta0_ratio=1e1) # Set the rate of reduction in trade-off parameter (beta) each time the # the inverse problem is solved. And set the number of Gauss-Newton iterations # for each trade-off paramter value. beta_schedule = directives.BetaSchedule(coolingFactor=2.5, coolingRate=2) # Options for outputting recovered models and predicted data for each beta. save_iteration = directives.SaveOutputEveryIteration(save_txt=False) # Setting a stopping criteria for the inversion. target_misfit = directives.TargetMisfit(chifact=1) # Apply and update preconditioner as the model updates update_jacobi = directives.UpdatePreconditioner() directives_list = [ update_sensitivity_weighting, starting_beta, beta_schedule, save_iteration, target_misfit, update_jacobi, ] .. rst-class:: sphx-glr-script-out .. code-block:: none /home/vsts/work/1/s/simpeg/directives/_directives.py:1865: FutureWarning: SaveEveryIteration.save_txt has been deprecated, please use SaveEveryIteration.on_disk. It will be removed in version 0.26.0 of SimPEG. /home/vsts/work/1/s/simpeg/directives/_directives.py:1866: FutureWarning: SaveEveryIteration.save_txt has been deprecated, please use SaveEveryIteration.on_disk. It will be removed in version 0.26.0 of SimPEG. .. GENERATED FROM PYTHON SOURCE LINES 405-411 Running the DC Inversion ------------------------ To define the inversion object, we need to define the inversion problem and the set of directives. We can then run the inversion. .. GENERATED FROM PYTHON SOURCE LINES 411-420 .. code-block:: Python # Here we combine the inverse problem and the set of directives dc_inversion = inversion.BaseInversion( dc_inverse_problem, directiveList=directives_list ) # Run inversion recovered_conductivity_model = dc_inversion.run(starting_conductivity_model) .. rst-class:: sphx-glr-script-out .. code-block:: none Running inversion with SimPEG v0.25.0 ============================ Inexact Gauss Newton ============================ # beta phi_d phi_m f |proj(x-g)-x| LS Comment ----------------------------------------------------------------------------- 0 3.05e-02 4.29e+04 0.00e+00 4.29e+04 1 3.05e-02 1.05e+04 2.76e+05 1.89e+04 4.82e+03 0 2 3.05e-02 1.11e+04 2.52e+05 1.88e+04 2.42e+02 0 3 1.22e-02 5.30e+03 5.66e+05 1.22e+04 9.53e+02 0 4 1.22e-02 5.90e+03 5.11e+05 1.21e+04 1.38e+02 0 5 4.88e-03 2.45e+03 9.62e+05 7.15e+03 5.86e+02 0 6 4.88e-03 2.70e+03 9.05e+05 7.12e+03 7.37e+01 0 7 1.95e-03 1.01e+03 1.44e+06 3.82e+03 3.32e+02 0 8 1.95e-03 1.09e+03 1.39e+06 3.81e+03 3.65e+01 0 9 7.81e-04 3.87e+02 1.94e+06 1.90e+03 1.76e+02 0 10 7.81e-04 4.10e+02 1.90e+06 1.90e+03 1.73e+01 0 11 3.12e-04 1.45e+02 2.41e+06 8.98e+02 8.87e+01 0 ------------------------- STOP! ------------------------- 1 : |fc-fOld| = 1.0592e+02 <= tolF*(1+|f0|) = 4.2936e+03 1 : |xc-x_last| = 2.1517e+01 <= tolX*(1+|x0|) = 8.6952e+01 0 : |proj(x-g)-x| = 8.8748e+01 <= tolG = 1.0000e-01 0 : |proj(x-g)-x| = 8.8748e+01 <= 1e3*eps = 1.0000e-02 0 : maxIter = 15 <= iter = 11 ------------------------- DONE! ------------------------- .. GENERATED FROM PYTHON SOURCE LINES 421-424 Recreate True Conductivity Model -------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 424-441 .. code-block:: Python background_value = 1e-2 conductor_value = 1e-1 resistor_value = 1e-3 true_conductivity_model = background_value * np.ones(nC) ind_conductor = model_builder.get_indices_sphere( np.r_[-350.0, 0.0, -300.0], 160.0, mesh.cell_centers[ind_active, :] ) true_conductivity_model[ind_conductor] = conductor_value ind_resistor = model_builder.get_indices_sphere( np.r_[350.0, 0.0, -300.0], 160.0, mesh.cell_centers[ind_active, :] ) true_conductivity_model[ind_resistor] = resistor_value true_conductivity_model_log10 = np.log10(true_conductivity_model) .. GENERATED FROM PYTHON SOURCE LINES 442-445 Plotting True and Recovered Conductivity Model ---------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 445-507 .. code-block:: Python # Plot True Model fig = plt.figure(figsize=(10, 4)) plotting_map = maps.InjectActiveCells(mesh, ind_active, np.nan) ax1 = fig.add_axes([0.15, 0.15, 0.67, 0.75]) mesh.plot_slice( plotting_map * true_conductivity_model_log10, ax=ax1, normal="Y", ind=int(len(mesh.h[1]) / 2), grid=False, clim=(true_conductivity_model_log10.min(), true_conductivity_model_log10.max()), pcolor_opts={"cmap": mpl.cm.viridis}, ) ax1.set_title("True Conductivity Model") ax1.set_xlabel("x (m)") ax1.set_ylabel("z (m)") ax1.set_xlim([-1000, 1000]) ax1.set_ylim([-1000, 0]) ax2 = fig.add_axes([0.84, 0.15, 0.03, 0.75]) norm = mpl.colors.Normalize( vmin=true_conductivity_model_log10.min(), vmax=true_conductivity_model_log10.max() ) cbar = mpl.colorbar.ColorbarBase( ax2, cmap=mpl.cm.viridis, norm=norm, orientation="vertical", format="$10^{%.1f}$" ) cbar.set_label("Conductivity [S/m]", rotation=270, labelpad=15, size=12) # Plot recovered model recovered_conductivity_model_log10 = np.log10(np.exp(recovered_conductivity_model)) fig = plt.figure(figsize=(10, 4)) ax1 = fig.add_axes([0.15, 0.15, 0.67, 0.75]) mesh.plot_slice( plotting_map * recovered_conductivity_model_log10, ax=ax1, normal="Y", ind=int(len(mesh.h[1]) / 2), grid=False, clim=(true_conductivity_model_log10.min(), true_conductivity_model_log10.max()), pcolor_opts={"cmap": mpl.cm.viridis}, ) ax1.set_title("Recovered Conductivity Model") ax1.set_xlabel("x (m)") ax1.set_ylabel("z (m)") ax1.set_xlim([-1000, 1000]) ax1.set_ylim([-1000, 0]) ax2 = fig.add_axes([0.84, 0.15, 0.03, 0.75]) norm = mpl.colors.Normalize( vmin=true_conductivity_model_log10.min(), vmax=true_conductivity_model_log10.max() ) cbar = mpl.colorbar.ColorbarBase( ax2, cmap=mpl.cm.viridis, norm=norm, orientation="vertical", format="$10^{%.1f}$" ) cbar.set_label("Conductivity [S/m]", rotation=270, labelpad=15, size=12) plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /content/user-guide/tutorials/06-ip/images/sphx_glr_plot_inv_3_dcip3d_003.png :alt: True Conductivity Model :srcset: /content/user-guide/tutorials/06-ip/images/sphx_glr_plot_inv_3_dcip3d_003.png :class: sphx-glr-multi-img * .. image-sg:: /content/user-guide/tutorials/06-ip/images/sphx_glr_plot_inv_3_dcip3d_004.png :alt: Recovered Conductivity Model :srcset: /content/user-guide/tutorials/06-ip/images/sphx_glr_plot_inv_3_dcip3d_004.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 508-515 Plotting Normalized Data Misfit or Predicted DC Data ---------------------------------------------------- To see how well the recovered model reproduces the observed data, it is a good idea to compare the predicted and observed data. Here, we accomplish this by plotting the normalized misfit. .. GENERATED FROM PYTHON SOURCE LINES 515-550 .. code-block:: Python # Predicted data from recovered model dpred_dc = dc_inverse_problem.dpred # Compute the normalized data misfit dc_normalized_misfit = (dc_data.dobs - dpred_dc) / dc_data.standard_deviation if has_plotly: # Plot IP Data fig = plot_3d_pseudosection( dc_data.survey, dc_normalized_misfit, scale="linear", units="", vlim=[-2, 2], plane_distance=15, ) fig.update_layout( title_text="Normalized Data Misfit", title_x=0.5, title_font_size=24, width=650, height=500, scene_camera=dict( center=dict(x=0, y=0, z=-0.4), eye=dict(x=1.5, y=-1.5, z=1.8) ), ) plotly.io.show(fig) else: print("INSTALL 'PLOTLY' TO VISUALIZE 3D PSEUDOSECTIONS") .. raw:: html :file: images/sphx_glr_plot_inv_3_dcip3d_005.html .. GENERATED FROM PYTHON SOURCE LINES 551-560 Starting/Reference Model for IP Inversion ----------------------------------------- Here, we would create starting and/or reference models for the IP inversion as well as the mapping from the model space to the active cells. Starting and reference models can be a constant background value or contain a-priori structures. Here, the starting model is the 1e-6 V/V. .. GENERATED FROM PYTHON SOURCE LINES 560-575 .. code-block:: Python # Define chargeability model in V/V air_chargeability = 0.0 background_chargeability = 1e-6 active_map = maps.InjectActiveCells(mesh, ind_active, air_chargeability) nC = int(ind_active.sum()) chargeability_map = active_map # Define starting model starting_chargeability_model = background_chargeability * np.ones(nC) .. GENERATED FROM PYTHON SOURCE LINES 576-585 Define the Physics of the IP Simulation --------------------------------------- Here, we define the physics of the IP problem. For the chargeability, we require a mapping from the model space to the entire mesh. For the background conductivity/resistivity, we require the conductivity/resistivity on the entire mesh. .. GENERATED FROM PYTHON SOURCE LINES 585-594 .. code-block:: Python ip_simulation = ip.Simulation3DNodal( mesh, survey=ip_survey, etaMap=chargeability_map, sigma=conductivity_map * recovered_conductivity_model, storeJ=True, ) .. GENERATED FROM PYTHON SOURCE LINES 595-600 Define IP Inverse Problem ------------------------- Here we define the inverse problem in the same manner as the DC inverse problem. .. GENERATED FROM PYTHON SOURCE LINES 600-625 .. code-block:: Python # Define the data misfit (Here we use weighted L2-norm) ip_data_misfit = data_misfit.L2DataMisfit(data=ip_data, simulation=ip_simulation) # Define the regularization (model objective function) ip_regularization = regularization.WeightedLeastSquares( mesh, active_cells=ind_active, mapping=maps.IdentityMap(nP=nC), alpha_s=0.01, alpha_x=1, alpha_y=1, alpha_z=1, ) # Define how the optimization problem is solved. ip_optimization = optimization.ProjectedGNCG( maxIter=15, lower=0.0, upper=10, cg_maxiter=30, cg_rtol=1e-3 ) # Here we define the inverse problem that is to be solved ip_inverse_problem = inverse_problem.BaseInvProblem( ip_data_misfit, ip_regularization, ip_optimization ) .. GENERATED FROM PYTHON SOURCE LINES 626-631 Define IP Inversion Directives ------------------------------ Here we define the directives in the same manner as the DC inverse problem. .. GENERATED FROM PYTHON SOURCE LINES 631-649 .. code-block:: Python update_sensitivity_weighting = directives.UpdateSensitivityWeights(threshold_value=1e-3) starting_beta = directives.BetaEstimate_ByEig(beta0_ratio=1e2) beta_schedule = directives.BetaSchedule(coolingFactor=2.5, coolingRate=1) save_iteration = directives.SaveOutputEveryIteration(save_txt=False) target_misfit = directives.TargetMisfit(chifact=1.0) update_jacobi = directives.UpdatePreconditioner() directives_list = [ update_sensitivity_weighting, starting_beta, beta_schedule, save_iteration, target_misfit, update_jacobi, ] .. rst-class:: sphx-glr-script-out .. code-block:: none /home/vsts/work/1/s/simpeg/directives/_directives.py:1865: FutureWarning: SaveEveryIteration.save_txt has been deprecated, please use SaveEveryIteration.on_disk. It will be removed in version 0.26.0 of SimPEG. /home/vsts/work/1/s/simpeg/directives/_directives.py:1866: FutureWarning: SaveEveryIteration.save_txt has been deprecated, please use SaveEveryIteration.on_disk. It will be removed in version 0.26.0 of SimPEG. .. GENERATED FROM PYTHON SOURCE LINES 650-653 Running the IP Inversion ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 653-662 .. code-block:: Python # Here we combine the inverse problem and the set of directives ip_inversion = inversion.BaseInversion( ip_inverse_problem, directiveList=directives_list ) # Run inversion recovered_chargeability_model = ip_inversion.run(starting_chargeability_model) .. rst-class:: sphx-glr-script-out .. code-block:: none Running inversion with SimPEG v0.25.0 ================================================= Projected GNCG ================================================= # beta phi_d phi_m f |proj(x-g)-x| LS iter_CG CG |Ax-b|/|b| CG |Ax-b| Comment ----------------------------------------------------------------------------------------------------------------- 0 2.22e+01 7.47e+03 0.00e+00 7.47e+03 0 inf inf 1 2.22e+01 2.02e+02 2.75e+01 8.15e+02 9.87e+02 0 10 9.35e-04 1.25e+01 ------------------------- STOP! ------------------------- 0 : |fc-fOld| = 6.6536e+03 <= tolF*(1+|f0|) = 7.4694e+02 0 : |xc-x_last| = 1.4542e+00 <= tolX*(1+|x0|) = 1.0002e-01 0 : |proj(x-g)-x| = 9.8690e+02 <= tolG = 1.0000e-01 0 : |proj(x-g)-x| = 9.8690e+02 <= 1e3*eps = 1.0000e-02 0 : maxIter = 15 <= iter = 1 ------------------------- DONE! ------------------------- .. GENERATED FROM PYTHON SOURCE LINES 663-666 Recreate True Chargeability Model --------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 666-677 .. code-block:: Python background_value = 1e-6 chargeable_value = 1e-1 true_chargeability_model = background_value * np.ones(nC) ind_chargeable = model_builder.get_indices_sphere( np.r_[-350.0, 0.0, -300.0], 160.0, mesh.cell_centers[ind_active, :] ) true_chargeability_model[ind_chargeable] = chargeable_value .. GENERATED FROM PYTHON SOURCE LINES 678-681 Plot True and Recovered Chargeability Model -------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 681-741 .. code-block:: Python # Plot True Model fig = plt.figure(figsize=(10, 4)) plotting_map = maps.InjectActiveCells(mesh, ind_active, np.nan) ax1 = fig.add_axes([0.15, 0.15, 0.67, 0.75]) mesh.plot_slice( plotting_map * true_chargeability_model, ax=ax1, normal="Y", ind=int(len(mesh.h[1]) / 2), grid=False, clim=(true_chargeability_model.min(), true_chargeability_model.max()), pcolor_opts={"cmap": mpl.cm.plasma}, ) ax1.set_title("True Chargeability Model") ax1.set_xlabel("x (m)") ax1.set_ylabel("z (m)") ax1.set_xlim([-1000, 1000]) ax1.set_ylim([-1000, 0]) ax2 = fig.add_axes([0.84, 0.15, 0.03, 0.75]) norm = mpl.colors.Normalize( vmin=true_chargeability_model.min(), vmax=true_chargeability_model.max() ) cbar = mpl.colorbar.ColorbarBase( ax2, cmap=mpl.cm.plasma, norm=norm, orientation="vertical", format="%.2f" ) cbar.set_label("Intrinsic Chargeability [V/V]", rotation=270, labelpad=15, size=12) # Plot Recovered Model fig = plt.figure(figsize=(10, 4)) ax1 = fig.add_axes([0.15, 0.15, 0.67, 0.75]) mesh.plot_slice( plotting_map * recovered_chargeability_model, ax=ax1, normal="Y", ind=int(len(mesh.h[1]) / 2), grid=False, clim=(true_chargeability_model.min(), true_chargeability_model.max()), pcolor_opts={"cmap": mpl.cm.plasma}, ) ax1.set_title("Recovered Chargeability Model") ax1.set_xlabel("x (m)") ax1.set_ylabel("z (m)") ax1.set_xlim([-1000, 1000]) ax1.set_ylim([-1000, 0]) ax2 = fig.add_axes([0.84, 0.15, 0.03, 0.75]) norm = mpl.colors.Normalize( vmin=true_chargeability_model.min(), vmax=true_chargeability_model.max() ) cbar = mpl.colorbar.ColorbarBase( ax2, cmap=mpl.cm.plasma, norm=norm, orientation="vertical", format="%.2f" ) cbar.set_label("Intrinsic Chargeability [V/V]", rotation=270, labelpad=15, size=12) plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /content/user-guide/tutorials/06-ip/images/sphx_glr_plot_inv_3_dcip3d_006.png :alt: True Chargeability Model :srcset: /content/user-guide/tutorials/06-ip/images/sphx_glr_plot_inv_3_dcip3d_006.png :class: sphx-glr-multi-img * .. image-sg:: /content/user-guide/tutorials/06-ip/images/sphx_glr_plot_inv_3_dcip3d_007.png :alt: Recovered Chargeability Model :srcset: /content/user-guide/tutorials/06-ip/images/sphx_glr_plot_inv_3_dcip3d_007.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 742-745 Plotting Normalized Data Misfit or Predicted IP Data ---------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 745-778 .. code-block:: Python # Predicted data from recovered model dpred_ip = ip_inverse_problem.dpred # Normalized misfit ip_normalized_misfit = (ip_data.dobs - dpred_ip) / ip_data.standard_deviation if has_plotly: fig = plot_3d_pseudosection( ip_data.survey, ip_normalized_misfit, scale="linear", units="", vlim=[-2, 2], plane_distance=15, marker_opts={"colorscale": "plasma"}, ) fig.update_layout( title_text="Normalized Data Misfit", title_x=0.5, title_font_size=24, width=650, height=500, scene_camera=dict( center=dict(x=0, y=0, z=-0.4), eye=dict(x=1.5, y=-1.5, z=1.8) ), ) plotly.io.show(fig) else: print("INSTALL 'PLOTLY' TO VISUALIZE 3D PSEUDOSECTIONS") .. raw:: html :file: images/sphx_glr_plot_inv_3_dcip3d_008.html .. rst-class:: sphx-glr-timing **Total running time of the script:** (4 minutes 15.483 seconds) **Estimated memory usage:** 414 MB .. _sphx_glr_download_content_user-guide_tutorials_06-ip_plot_inv_3_dcip3d.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_inv_3_dcip3d.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_inv_3_dcip3d.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_inv_3_dcip3d.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_