.. 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_2_dcip2d.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_2_dcip2d.py: 2.5D Forward Simulation of a DCIP Line ====================================== Here we use the module *SimPEG.electromagnetics.static.resistivity* to predict DC resistivity data and the module *SimPEG.electromagnetics.static.induced_polarization* to predict IP data for a dipole-dipole survey. In this tutorial, we focus on the following: - How to define the survey - How to define the problem - How to predict DC resistivity data for a synthetic resistivity model - How to predict IP data for a synthetic chargeability model - How to include surface topography - The units of the models and resulting data This tutorial is split into two parts. First we create a resistivity model and predict DC resistivity data as measured voltages. Next we create a chargeability model and a background conductivity model to compute IP data defined as secondary potentials. We show how DC and IP in units of Volts can be plotted on pseudo-sections as apparent conductivities and apparent chargeabilities. .. GENERATED FROM PYTHON SOURCE LINES 28-31 Import modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 31-63 .. code-block:: default from discretize import TreeMesh from discretize.utils import mkvc, refine_tree_xyz, active_from_xyz from SimPEG.utils import model_builder from SimPEG.utils.io_utils.io_utils_electromagnetics import write_dcip2d_ubc from SimPEG import maps, data 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, plot_pseudosection, apparent_resistivity_from_voltage, ) import os import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt from matplotlib.colors import LogNorm 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 = 5 .. GENERATED FROM PYTHON SOURCE LINES 64-71 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 set of valleys that run North-South. .. GENERATED FROM PYTHON SOURCE LINES 71-85 .. code-block:: default x_topo, y_topo = np.meshgrid( np.linspace(-3000, 3000, 601), np.linspace(-3000, 3000, 101) ) z_topo = 40.0 * np.sin(2 * np.pi * x_topo / 800) - 40.0 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] # Create 2D topography. Since our 3D topography only changes in the x direction, # it is easy to define the 2D topography projected along the survey line. For # arbitrary topography and for an arbitrary survey orientation, the user must # define the 2D topography along the survey line. topo_2d = np.unique(topo_xyz[:, [0, 2]], axis=0) .. GENERATED FROM PYTHON SOURCE LINES 86-94 Create Dipole-Dipole Survey --------------------------- Here we define a single EW survey line that uses a dipole-dipole configuration. For the source, we must define the AB electrode locations. For the receivers we must define the MN electrode locations. Instead of creating the survey from scratch (see 1D example), we will use the *generat_dcip_survey_line* utility. .. GENERATED FROM PYTHON SOURCE LINES 94-118 .. code-block:: default # Define survey line parameters survey_type = "dipole-dipole" dimension_type = "2D" dc_data_type = "volt" end_locations = np.r_[-400.0, 400.0] station_separation = 40.0 num_rx_per_src = 10 # Generate source list for DC survey line source_list = generate_dcip_sources_line( survey_type, dc_data_type, dimension_type, end_locations, topo_xyz, num_rx_per_src, station_separation, ) # Define survey dc_survey = dc.survey.Survey(source_list) .. GENERATED FROM PYTHON SOURCE LINES 119-125 Create OcTree Mesh ------------------ Here, we create the OcTree mesh that will be used to predict both DC resistivity and IP data. .. GENERATED FROM PYTHON SOURCE LINES 125-172 .. code-block:: default dh = 4 # base cell width dom_width_x = 3200.0 # domain width x dom_width_z = 2400.0 # domain width z nbcx = 2 ** int(np.round(np.log(dom_width_x / dh) / np.log(2.0))) # num. base cells x 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)] hz = [(dh, nbcz)] mesh = TreeMesh([hx, hz], x0="CN") # Mesh refinement based on topography mesh = refine_tree_xyz( mesh, topo_xyz[:, [0, 2]], octree_levels=[0, 0, 4, 4], method="surface", finalize=False, ) # Mesh refinement near transmitters and receivers. First we need to obtain the # set of unique electrode locations. electrode_locations = np.c_[ dc_survey.locations_a, dc_survey.locations_b, dc_survey.locations_m, dc_survey.locations_n, ] unique_locations = np.unique( np.reshape(electrode_locations, (4 * dc_survey.nD, 2)), axis=0 ) mesh = refine_tree_xyz( mesh, unique_locations, octree_levels=[4, 4], method="radial", finalize=False ) # Refine core mesh region xp, zp = np.meshgrid([-600.0, 600.0], [-400.0, 0.0]) xyz = np.c_[mkvc(xp), mkvc(zp)] mesh = refine_tree_xyz( mesh, xyz, octree_levels=[0, 0, 2, 8], method="box", finalize=False ) mesh.finalize() .. rst-class:: sphx-glr-script-out .. code-block:: none /home/vsts/work/1/s/tutorials/06-ip/plot_fwd_2_dcip2d.py:138: 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/conda/envs/simpeg-test/lib/python3.8/site-packages/scipy/interpolate/_interpolate.py:698: RuntimeWarning: invalid value encountered in divide /home/vsts/work/1/s/tutorials/06-ip/plot_fwd_2_dcip2d.py:159: 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. /home/vsts/work/1/s/tutorials/06-ip/plot_fwd_2_dcip2d.py:166: DeprecationWarning: The box option is deprecated as of `0.9.0` please update your code to use the `TreeMesh.refine_bounding_box` functionality. It will be removed in a future version of discretize. .. GENERATED FROM PYTHON SOURCE LINES 173-181 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 sphere and a resistive sphere 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 181-230 .. code-block:: default # Define conductivity model in S/m (or resistivity model in Ohm m) air_conductivity = 1e-8 background_conductivity = 1e-2 conductor_conductivity = 1e-1 resistor_conductivity = 1e-3 # Find active cells in forward modeling (cell below surface) ind_active = active_from_xyz(mesh, topo_xyz[:, [0, 2]]) # Define mapping from model to active cells nC = int(ind_active.sum()) conductivity_map = maps.InjectActiveCells(mesh, ind_active, air_conductivity) # Define model conductivity_model = background_conductivity * np.ones(nC) ind_conductor = model_builder.getIndicesSphere(np.r_[-120.0, -160.0], 60.0, mesh.gridCC) ind_conductor = ind_conductor[ind_active] conductivity_model[ind_conductor] = conductor_conductivity ind_resistor = model_builder.getIndicesSphere(np.r_[120.0, -100.0], 60.0, mesh.gridCC) ind_resistor = ind_resistor[ind_active] conductivity_model[ind_resistor] = resistor_conductivity # Plot Conductivity Model fig = plt.figure(figsize=(9, 4)) plotting_map = maps.InjectActiveCells(mesh, ind_active, np.nan) norm = LogNorm(vmin=1e-3, vmax=1e-1) ax1 = fig.add_axes([0.14, 0.17, 0.68, 0.7]) mesh.plot_image( plotting_map * conductivity_model, ax=ax1, grid=False, pcolor_opts={"norm": norm} ) ax1.set_xlim(-600, 600) ax1.set_ylim(-600, 0) ax1.set_title("Conductivity Model") ax1.set_xlabel("x (m)") ax1.set_ylabel("z (m)") ax2 = fig.add_axes([0.84, 0.17, 0.03, 0.7]) cbar = mpl.colorbar.ColorbarBase(ax2, norm=norm, orientation="vertical") cbar.set_label(r"$\sigma$ (S/m)", rotation=270, labelpad=15, size=12) plt.show() .. image-sg:: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_001.png :alt: Conductivity Model :srcset: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 231-239 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 239-243 .. code-block:: default dc_survey.drape_electrodes_on_topography(mesh, ind_active, option="top") .. GENERATED FROM PYTHON SOURCE LINES 244-251 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 251-260 .. code-block:: default dc_simulation = dc.Simulation2DNodal( mesh, survey=dc_survey, sigmaMap=conductivity_map, solver=Solver ) # Predict the data by running the simulation. The data are the raw voltage in # units of volts. dpred_dc = dc_simulation.dpred(conductivity_model) .. GENERATED FROM PYTHON SOURCE LINES 261-270 Plotting DC Data in Pseudo-Section ---------------------------------- Here, we demonstrate how to plot 2D DC data in pseudo-section. First, we plot the voltages in pseudo-section as a scatter plot. This allows us to visualize the pseudo-sensitivity locations for our survey. Next, we plot the apparent conductivities in pseudo-section as a filled contour plot. .. GENERATED FROM PYTHON SOURCE LINES 270-306 .. code-block:: default # Plot voltages pseudo-section fig = plt.figure(figsize=(12, 5)) ax1 = fig.add_axes([0.1, 0.15, 0.75, 0.78]) plot_pseudosection( dc_survey, dpred_dc, "scatter", ax=ax1, scale="log", cbar_label="V/A", scatter_opts={"cmap": mpl.cm.viridis}, ) ax1.set_title("Normalized Voltages") plt.show() # Get apparent conductivities from volts and survey geometry apparent_conductivities = 1 / apparent_resistivity_from_voltage(dc_survey, dpred_dc) # Plot apparent conductivity pseudo-section fig = plt.figure(figsize=(12, 5)) ax1 = fig.add_axes([0.1, 0.15, 0.75, 0.78]) plot_pseudosection( dc_survey, apparent_conductivities, "contourf", ax=ax1, scale="log", cbar_label="S/m", mask_topography=True, contourf_opts={"levels": 20, "cmap": mpl.cm.viridis}, ) ax1.set_title("Apparent Conductivity") plt.show() .. rst-class:: sphx-glr-horizontal * .. image-sg:: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_002.png :alt: Normalized Voltages :srcset: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_002.png :class: sphx-glr-multi-img * .. image-sg:: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_003.png :alt: Apparent Conductivity :srcset: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_003.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 307-313 Define IP Survey ---------------- The geometry of the survey was defined earlier. We will define the IP data as apparent chargeability in V/V. .. GENERATED FROM PYTHON SOURCE LINES 313-332 .. code-block:: default # Generate source list for IP survey line ip_data_type = "apparent_chargeability" source_list = generate_dcip_sources_line( survey_type, ip_data_type, dimension_type, end_locations, topo_xyz, num_rx_per_src, station_separation, ) # Define survey ip_survey = ip.survey.Survey(source_list, survey_type=survey_type) # Drape over discrete topography ip_survey.drape_electrodes_on_topography(mesh, ind_active, option="top") .. GENERATED FROM PYTHON SOURCE LINES 333-340 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 is defined as mV/V. .. GENERATED FROM PYTHON SOURCE LINES 340-388 .. code-block:: default # Define chargeability model as intrinsic chargeability (V/V). air_chargeability = 0.0 background_chargeability = 1e-6 sphere_chargeability = 1e-1 # Find active cells in forward modeling (cells below surface) ind_active = active_from_xyz(mesh, topo_xyz[:, [0, 2]]) # Define mapping from model to active cells nC = int(ind_active.sum()) chargeability_map = maps.InjectActiveCells(mesh, ind_active, air_chargeability) # Define chargeability model chargeability_model = background_chargeability * np.ones(nC) ind_chargeable = model_builder.getIndicesSphere( np.r_[-120.0, -160.0], 60.0, mesh.gridCC ) ind_chargeable = ind_chargeable[ind_active] chargeability_model[ind_chargeable] = sphere_chargeability # Plot Chargeability Model fig = plt.figure(figsize=(9, 4)) ax1 = fig.add_axes([0.14, 0.17, 0.68, 0.7]) mesh.plot_image( plotting_map * chargeability_model, ax=ax1, grid=False, clim=(background_chargeability, sphere_chargeability), pcolor_opts={"cmap": mpl.cm.plasma}, ) ax1.set_xlim(-600, 600) ax1.set_ylim(-600, 0) ax1.set_title("Intrinsic Chargeability") ax1.set_xlabel("x (m)") ax1.set_ylabel("z (m)") ax2 = fig.add_axes([0.84, 0.17, 0.03, 0.7]) norm = mpl.colors.Normalize(vmin=background_chargeability, vmax=sphere_chargeability) cbar = mpl.colorbar.ColorbarBase( ax2, norm=norm, orientation="vertical", cmap=mpl.cm.plasma ) cbar.set_label("Intrinsic Chargeability (V/V)", rotation=270, labelpad=15, size=12) plt.show() .. image-sg:: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_004.png :alt: Intrinsic Chargeability :srcset: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 389-395 Predict IP Data --------------- Here we use a chargeability model and a background conductivity/resistivity model to predict IP data. .. GENERATED FROM PYTHON SOURCE LINES 395-411 .. code-block:: default # 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. simulation_ip = ip.Simulation2DNodal( 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 = simulation_ip.dpred(chargeability_model) .. GENERATED FROM PYTHON SOURCE LINES 412-418 Plot 2D IP Data in Pseudosection -------------------------------- We want to plot apparent chargeability. To accomplish this, we must normalize the IP voltage by the DC voltage. This is then multiplied by 1000 so that our apparent chargeability is in units mV/V. .. GENERATED FROM PYTHON SOURCE LINES 418-456 .. code-block:: default fig = plt.figure(figsize=(12, 11)) # Plot apparent conductivity ax1 = fig.add_axes([0.1, 0.58, 0.7, 0.35]) cax1 = fig.add_axes([0.82, 0.58, 0.025, 0.35]) plot_pseudosection( dc_survey, apparent_conductivities, "contourf", ax=ax1, cax=cax1, scale="log", cbar_label="S/m", mask_topography=True, contourf_opts={"levels": 20, "cmap": mpl.cm.viridis}, ) ax1.set_title("Apparent Conductivity") # Plot apparent chargeability ax2 = fig.add_axes([0.1, 0.08, 0.7, 0.35]) cax2 = fig.add_axes([0.82, 0.08, 0.025, 0.35]) plot_pseudosection( ip_survey, dpred_ip, "contourf", ax=ax2, cax=cax2, scale="linear", cbar_label="V/V", mask_topography=True, contourf_opts={"levels": 20, "cmap": mpl.cm.plasma}, ) ax2.set_title("Apparent Chargeability (V/V)") plt.show() .. image-sg:: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_005.png :alt: Apparent Conductivity, Apparent Chargeability (V/V) :srcset: /content/tutorials/06-ip/images/sphx_glr_plot_fwd_2_dcip2d_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 457-460 Write Outputs (Optional) ------------------------ .. GENERATED FROM PYTHON SOURCE LINES 460-521 .. code-block:: default 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 5% Gaussian noise to each DC datum np.random.seed(225) std = 0.05 * np.abs(dpred_dc) dc_noise = std * np.random.rand(len(dpred_dc)) dobs = dpred_dc + dc_noise # Create a survey with the original electrode locations # and not the shifted ones # Generate source list for DC survey line source_list = generate_dcip_sources_line( survey_type, dc_data_type, dimension_type, end_locations, 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.obs" write_dcip2d_ubc(fname, data_obj, "volt", "dobs") # Add Gaussian noise equal to 5e-3 V/V std = 5e-3 * np.ones_like(dpred_ip) ip_noise = std * np.random.rand(len(dpred_ip)) dobs = dpred_ip + ip_noise # Create a survey with the original electrode locations # and not the shifted ones # Generate source list for DC survey line source_list = generate_dcip_sources_line( survey_type, ip_data_type, dimension_type, end_locations, topo_xyz, num_rx_per_src, station_separation, ) ip_survey_original = dc.survey.Survey(source_list) # Write out data at their original electrode locations (not shifted) data_obj = data.Data(ip_survey_original, dobs=dobs, standard_deviation=std) fname = dir_path + "ip_data.obs" write_dcip2d_ubc(fname, data_obj, "apparent_chargeability", "dobs") .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 12.270 seconds) **Estimated memory usage:** 9 MB .. _sphx_glr_download_content_tutorials_06-ip_plot_fwd_2_dcip2d.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_fwd_2_dcip2d.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_fwd_2_dcip2d.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_