.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/tutorials/06-ip/plot_fwd_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_tutorials_06-ip_plot_fwd_3_dcip3d.py: DC/IP Forward Simulation in 3D ============================== Here we use the module *SimPEG.electromagnetics.static.resistivity* to predict DC resistivity data on an OcTree mesh. Then we use the module *SimPEG.electromagnetics.static.induced_polarization* to predict IP data. In this tutorial, we focus on the following: - How to define the survey - How to definine a tree mesh based on the survey geometry - How to define the forward simulations - How to predict DC and IP for a synthetic conductivity model and a synthetic chargeability model - How to include surface topography - The units of the model and resulting data - Plotting DC and IP data in 3D In this case, we simulate dipole-dipole data for three East-West lines and two North-South lines. .. GENERATED FROM PYTHON SOURCE LINES 27-31 Import modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 31-70 .. code-block:: Python import os import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt from discretize import TreeMesh from discretize.utils import mkvc, refine_tree_xyz, active_from_xyz from SimPEG import maps, data from SimPEG.utils import model_builder from SimPEG.utils.io_utils.io_utils_electromagnetics import write_dcip_xyz 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 ( generate_dcip_sources_line, 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 try: from pymatsolver import Pardiso as Solver except ImportError: from SimPEG import SolverLU as Solver mpl.rcParams.update({"font.size": 16}) write_output = False # sphinx_gallery_thumbnail_number = 4 .. GENERATED FROM PYTHON SOURCE LINES 71-78 Defining Topography ------------------- Here we define surface topography as an (N, 3) numpy array. Topography could also be loaded from a file. In our case, our survey takes place within a circular depression. .. GENERATED FROM PYTHON SOURCE LINES 78-87 .. code-block:: Python x_topo, y_topo = np.meshgrid( np.linspace(-2100, 2100, 141), np.linspace(-2000, 2000, 141) ) s = np.sqrt(x_topo**2 + y_topo**2) z_topo = (1 / np.pi) * 140 * (-np.pi / 2 + np.arctan((s - 600.0) / 80.0)) x_topo, y_topo, z_topo = mkvc(x_topo), mkvc(y_topo), mkvc(z_topo) topo_xyz = np.c_[x_topo, y_topo, z_topo] .. GENERATED FROM PYTHON SOURCE LINES 88-99 Construct the DC Survey ----------------------- Here we define 5 DC lines that use a dipole-dipole electrode configuration; three lines along the East-West direction and 2 lines along the North-South direction. For each source, we must define the AB electrode locations. For each receiver we must define the MN electrode locations. Instead of creating the survey from scratch (see 1D example), we will use the *generat_dcip_sources_line* utility. This utility will give us the source list for a given DC/IP line. We can append the sources for multiple lines to create the survey. .. GENERATED FROM PYTHON SOURCE LINES 99-129 .. code-block:: Python # Define the parameters for each survey line survey_type = "dipole-dipole" dc_data_type = "volt" dimension_type = "3D" end_locations_list = [ np.r_[-1000.0, 1000.0, 0.0, 0.0], np.r_[-350.0, -350.0, -1000.0, 1000.0], np.r_[350.0, 350.0, -1000.0, 1000.0], ] station_separation = 100.0 num_rx_per_src = 8 # The source lists for each line can be appended to create the source # list for the whole survey. source_list = [] for ii in range(0, len(end_locations_list)): source_list += generate_dcip_sources_line( survey_type, dc_data_type, dimension_type, end_locations_list[ii], topo_xyz, num_rx_per_src, station_separation, ) # Define the survey dc_survey = dc.survey.Survey(source_list) .. GENERATED FROM PYTHON SOURCE LINES 130-136 Create OcTree Mesh ------------------ Here, we create the OcTree mesh that will be used to predict DC data. .. GENERATED FROM PYTHON SOURCE LINES 136-173 .. code-block:: Python # Defining domain side and minimum cell size 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_survey.locations_a, dc_survey.locations_b, dc_survey.locations_m, dc_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_fwd_3_dcip3d.py:154: 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_fwd_3_dcip3d.py:166: 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 174-182 Create Conductivity Model and Mapping for OcTree Mesh ----------------------------------------------------- Here we define the conductivity model that will be used to predict DC resistivity data. The model consists of a conductive block and a resistive block within a moderately conductive background. Note that you can carry through this work flow with a resistivity model if desired. .. GENERATED FROM PYTHON SOURCE LINES 182-240 .. code-block:: Python # Define conductivity model in S/m (or resistivity model in Ohm m) air_value = 1e-8 background_value = 1e-2 conductor_value = 1e-1 resistor_value = 1e-3 # Find active cells in forward modeling (cell below surface) ind_active = active_from_xyz(mesh, topo_xyz) # Define mapping from model to active cells nC = int(ind_active.sum()) conductivity_map = maps.InjectActiveCells(mesh, ind_active, air_value) # Define model 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, :] ) 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, :] ) conductivity_model[ind_resistor] = resistor_value # Plot Conductivity Model fig = plt.figure(figsize=(10, 4)) plotting_map = maps.InjectActiveCells(mesh, ind_active, np.nan) log_mod = np.log10(conductivity_model) ax1 = fig.add_axes([0.15, 0.15, 0.67, 0.75]) mesh.plot_slice( plotting_map * log_mod, ax=ax1, normal="Y", ind=int(len(mesh.h[1]) / 2), grid=True, clim=(np.log10(resistor_value), np.log10(conductor_value)), pcolor_opts={"cmap": mpl.cm.viridis}, ) ax1.set_title("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=np.log10(resistor_value), vmax=np.log10(conductor_value) ) 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) .. image-sg:: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_3_dcip3d_001.png :alt: Conductivity Model :srcset: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_3_dcip3d_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 241-250 Project Survey 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 250-253 .. code-block:: Python dc_survey.drape_electrodes_on_topography(mesh, ind_active, option="top") .. GENERATED FROM PYTHON SOURCE LINES 254-263 Predict DC Resistivity Data --------------------------- Here we predict DC resistivity data. If the keyword argument *sigmaMap* is defined, the simulation will expect a conductivity model. If the keyword argument *rhoMap* is defined, the simulation will expect a resistivity model. .. GENERATED FROM PYTHON SOURCE LINES 263-273 .. code-block:: Python # Define the DC simulation dc_simulation = dc.Simulation3DNodal( mesh, survey=dc_survey, sigmaMap=conductivity_map, solver=Solver ) # Predict the data by running the simulation. The data are the measured voltage # normalized by the source current in units of V/A. dpred_dc = dc_simulation.dpred(conductivity_model) .. GENERATED FROM PYTHON SOURCE LINES 274-285 Plot DC Data in 3D Pseudosection -------------------------------- Here we demonstrate how 3D DC resistivity data can be represented on a 3D pseudosection plot. To use this utility, you must have Python's *plotly* package. Here, we represent the data as apparent conductivities. The *plot_3d_pseudosection* utility allows the user to plot all pseudosection points, or plot the pseudosection plots that lie within some distance of one or more planes. .. GENERATED FROM PYTHON SOURCE LINES 285-339 .. code-block:: Python # Since the data are normalized voltage, we must convert predicted # to apparent conductivities. apparent_conductivity = 1 / apparent_resistivity_from_voltage( dc_survey, dpred_dc, ) # For large datasets or for surveys with unconventional electrode geometry, # interpretation can be challenging if we plot every datum. Here, we plot # 3 out of the 5 survey lines to better image anomalous structures. # To plot ALL of the data, simply remove the keyword argument *plane_points* # when calling *plot_3d_pseudosection*. plane_points = [] p1, p2, p3 = np.array([-1000, 0, 0]), np.array([1000, 0, 0]), np.array([0, 0, -1000]) plane_points.append([p1, p2, p3]) p1, p2, p3 = ( np.array([-350, -1000, 0]), np.array([-350, 1000, 0]), np.array([-350, 0, -1000]), ) plane_points.append([p1, p2, p3]) p1, p2, p3 = ( np.array([350, -1000, 0]), np.array([350, 1000, 0]), np.array([350, 0, -1000]), ) plane_points.append([p1, p2, p3]) if has_plotly: fig = plot_3d_pseudosection( dc_survey, apparent_conductivity, scale="log", units="S/m", plane_points=plane_points, plane_distance=15, ) 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=0.05, y=0, z=-0.4)), ) plotly.io.show(fig) else: print("INSTALL 'PLOTLY' TO VISUALIZE 3D PSEUDOSECTIONS") .. raw:: html :file: images/sphx_glr_plot_fwd_3_dcip3d_002.html .. GENERATED FROM PYTHON SOURCE LINES 340-347 Define IP Survey ---------------- In the same manner as before, we use the *generate_dcip_sources_lines* to generate an IP survey whose receivers define the data in terms of the apparent chargeability (V/V). .. GENERATED FROM PYTHON SOURCE LINES 347-369 .. code-block:: Python # Generate source list for IP survey lines ip_data_type = "apparent_chargeability" source_list = [] for ii in range(0, len(end_locations_list)): source_list += generate_dcip_sources_line( survey_type, ip_data_type, dimension_type, end_locations_list[ii], topo_xyz, num_rx_per_src, station_separation, ) # Define survey ip_survey = ip.survey.Survey(source_list, survey_type=survey_type) # Drape to discretized topography as before ip_survey.drape_electrodes_on_topography(mesh, ind_active, option="top") .. GENERATED FROM PYTHON SOURCE LINES 370-379 Create Chargeability Model and Mapping for OcTree Mesh ------------------------------------------------------ Here we define the chargeability model that will be used to predict IP data. Here we assume that the conductive sphere is also chargeable but the resistive sphere is not. Here, the chargeability model represents the intrinsic chargeability of the Earth (V/V). .. GENERATED FROM PYTHON SOURCE LINES 379-425 .. code-block:: Python # Define intrinsic chargeability model (V/V) air_value = 1e-8 background_value = 1e-6 chargeable_value = 1e-1 # Define mapping from model to active cells chargeability_map = maps.InjectActiveCells(mesh, ind_active, air_value) # Define model 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, :] ) chargeability_model[ind_chargeable] = chargeable_value # Plot Chargeability 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 * chargeability_model, ax=ax1, normal="Y", ind=int(len(mesh.h[1]) / 2), grid=True, clim=(background_value, chargeable_value), pcolor_opts={"cmap": mpl.cm.plasma}, ) ax1.set_title("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=background_value, vmax=chargeable_value) 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) .. image-sg:: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_3_dcip3d_003.png :alt: Chargeability Model :srcset: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_3_dcip3d_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 426-433 Predict IP Data --------------- Here we use a chargeability model and a background conductivity/resistivity model to predict IP data. .. GENERATED FROM PYTHON SOURCE LINES 433-448 .. code-block:: Python # We use the keyword argument *sigma* to define the background conductivity on # the mesh. We could use the keyword argument *rho* to accomplish the same thing # using a background resistivity model. ip_simulation = ip.Simulation3DNodal( mesh, survey=ip_survey, etaMap=chargeability_map, sigma=conductivity_map * conductivity_model, solver=Solver, ) # Run forward simulation and predicted IP data. The data are the voltage (V) dpred_ip = ip_simulation.dpred(chargeability_model) .. GENERATED FROM PYTHON SOURCE LINES 449-459 Plot IP Data in 3D Pseudosection -------------------------------- Here we demonstrate how 3D IP data can be represented on a 3D pseudosection plot. To use this utility, you must have Python's *plotly* package. Here, we represent the data as apparent chargeabilities. Since the IP data are already represented as apparent chargeabilities, we can plot the data directly. .. GENERATED FROM PYTHON SOURCE LINES 459-487 .. code-block:: Python if has_plotly: fig = plot_3d_pseudosection( ip_survey, dpred_ip, vlim=[0.0, np.max(dpred_ip)], scale="linear", units="V/V", plane_points=plane_points, plane_distance=15, 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=0.05, y=0, z=-0.4)), ) plotly.io.show(fig) else: print("INSTALL 'PLOTLY' TO VISUALIZE 3D PSEUDOSECTIONS") .. raw:: html :file: images/sphx_glr_plot_fwd_3_dcip3d_004.html .. GENERATED FROM PYTHON SOURCE LINES 488-491 Optional: Write Outputs ----------------------- .. GENERATED FROM PYTHON SOURCE LINES 491-575 .. code-block:: Python if write_output: dir_path = os.path.dirname(__file__).split(os.path.sep) dir_path.extend(["outputs"]) dir_path = os.path.sep.join(dir_path) + os.path.sep if not os.path.exists(dir_path): os.mkdir(dir_path) # Write topography fname = dir_path + "topo_xyz.txt" np.savetxt(fname, topo_xyz, fmt="%.4e") # Add 10% Gaussian noise to each datum np.random.seed(433) std = 0.1 * np.abs(dpred_dc) noise = std * np.random.randn(len(dpred_dc)) dobs = dpred_dc + noise # Create dictionary that stores line IDs N = int(dc_survey.nD / 3) lineID = np.r_[np.ones(N), 2 * np.ones(N), 3 * np.ones(N)] out_dict = {"LINEID": lineID} # Create a survey with the original electrode locations # and not the shifted ones source_list = [] for ii in range(0, len(end_locations_list)): source_list += generate_dcip_sources_line( survey_type, dc_data_type, dimension_type, end_locations_list[ii], topo_xyz, num_rx_per_src, station_separation, ) dc_survey_original = dc.survey.Survey(source_list) # Write out data at their original electrode locations (not shifted) data_obj = data.Data(dc_survey_original, dobs=dobs, standard_deviation=std) fname = dir_path + "dc_data.xyz" write_dcip_xyz( fname, data_obj, data_header="V/A", uncertainties_header="UNCERT", out_dict=out_dict, ) # Add Gaussian noise with a standard deviation of 5e-3 V/V np.random.seed(444) std = 5e-3 * np.ones_like(dpred_ip) noise = std * np.random.randn(len(dpred_ip)) dobs = dpred_ip + noise # Create a survey with the original electrode locations # and not the shifted ones. source_list = [] for ii in range(0, len(end_locations_list)): source_list += generate_dcip_sources_line( survey_type, ip_data_type, dimension_type, end_locations_list[ii], topo_xyz, num_rx_per_src, station_separation, ) ip_survey_original = ip.survey.Survey(source_list) # Write out data at their original electrode locations (not shifted) data_obj = data.Data(ip_survey, dobs=dobs, standard_deviation=std) fname = dir_path + "ip_data.xyz" write_dcip_xyz( fname, data_obj, data_header="APP_CHG", uncertainties_header="UNCERT", out_dict=out_dict, ) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 21.322 seconds) **Estimated memory usage:** 8 MB .. _sphx_glr_download_content_tutorials_06-ip_plot_fwd_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_fwd_3_dcip3d.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_fwd_3_dcip3d.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_