.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/tutorials/05-dcr/plot_fwd_2_dcr2d.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_05-dcr_plot_fwd_2_dcr2d.py: DC Resistivity Forward Simulation in 2.5D ========================================= Here we use the module *SimPEG.electromagnetics.static.resistivity* to predict DC resistivity data and plot using a pseudosection. In this tutorial, we focus on the following: - How to define the survey - How to define the forward simulation - How to predict normalized voltage data for a synthetic conductivity model - How to include surface topography - The units of the model and resulting data .. GENERATED FROM PYTHON SOURCE LINES 20-23 Import modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 23-53 .. code-block:: Python 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.utils.static_utils import ( generate_dcip_sources_line, apparent_resistivity_from_voltage, plot_pseudosection, ) 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 write_output = False mpl.rcParams.update({"font.size": 16}) # sphinx_gallery_thumbnail_number = 3 .. GENERATED FROM PYTHON SOURCE LINES 54-61 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 61-75 .. code-block:: Python 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 76-84 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 84-107 .. code-block:: Python # Define survey line parameters survey_type = "dipole-dipole" dimension_type = "2D" 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, data_type, dimension_type, end_locations, topo_2d, num_rx_per_src, station_separation, ) # Define survey survey = dc.survey.Survey(source_list, survey_type=survey_type) .. GENERATED FROM PYTHON SOURCE LINES 108-113 Create Tree Mesh ------------------ Here, we create the Tree mesh that will be used to predict DC data. .. GENERATED FROM PYTHON SOURCE LINES 113-160 .. code-block:: Python 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_[ survey.locations_a, survey.locations_b, survey.locations_m, survey.locations_n, ] unique_locations = np.unique( np.reshape(electrode_locations, (4 * 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/05-dcr/plot_fwd_2_dcr2d.py:126: 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/05-dcr/plot_fwd_2_dcr2d.py:147: 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/05-dcr/plot_fwd_2_dcr2d.py:154: 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 161-169 Create Conductivity Model and Mapping for Tree Mesh ----------------------------------------------------- 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 169-219 .. code-block:: Python # 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.get_indices_sphere( 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.get_indices_sphere(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/05-dcr/images/sphx_glr_plot_fwd_2_dcr2d_001.png :alt: Conductivity Model :srcset: /content/tutorials/05-dcr/images/sphx_glr_plot_fwd_2_dcr2d_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 220-228 Project Survey to Discretized Topography ---------------------------------------- It is important that electrodes are not model 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 like on the discretized surface. .. GENERATED FROM PYTHON SOURCE LINES 228-232 .. code-block:: Python survey.drape_electrodes_on_topography(mesh, ind_active, option="top") .. GENERATED FROM PYTHON SOURCE LINES 233-240 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 240-249 .. code-block:: Python simulation = dc.simulation_2d.Simulation2DNodal( mesh, survey=survey, sigmaMap=conductivity_map, solver=Solver ) # Predict the data by running the simulation. The data are the raw voltage in # units of volts. dpred = simulation.dpred(conductivity_model) .. GENERATED FROM PYTHON SOURCE LINES 250-259 Plotting in Pseudo-Section -------------------------- Here, we demonstrate how to plot 2D 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 259-294 .. code-block:: Python # Plot voltages pseudo-section fig = plt.figure(figsize=(12, 5)) ax1 = fig.add_axes([0.1, 0.15, 0.75, 0.78]) plot_pseudosection( survey, dobs=np.abs(dpred), plot_type="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(survey, dpred) # 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( survey, dobs=apparent_conductivities, plot_type="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/05-dcr/images/sphx_glr_plot_fwd_2_dcr2d_002.png :alt: Normalized Voltages :srcset: /content/tutorials/05-dcr/images/sphx_glr_plot_fwd_2_dcr2d_002.png :class: sphx-glr-multi-img * .. image-sg:: /content/tutorials/05-dcr/images/sphx_glr_plot_fwd_2_dcr2d_003.png :alt: Apparent Conductivity :srcset: /content/tutorials/05-dcr/images/sphx_glr_plot_fwd_2_dcr2d_003.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 295-300 Optional: Write out dpred ------------------------- Write DC resistivity data, topography and true model .. GENERATED FROM PYTHON SOURCE LINES 300-336 .. 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) # Add 10% Gaussian noise to each datum np.random.seed(225) std = 0.05 * np.abs(dpred) dc_noise = std * np.random.randn(len(dpred)) dobs = dpred + 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, data_type, dimension_type, end_locations, topo_xyz, num_rx_per_src, station_separation, ) survey_original = dc.survey.Survey(source_list) # Write out data at their original electrode locations (not shifted) data_obj = data.Data(survey_original, dobs=dobs, standard_deviation=std) fname = dir_path + "dc_data.obs" write_dcip2d_ubc(fname, data_obj, "volt", "dobs") fname = dir_path + "topo_xyz.txt" np.savetxt(fname, topo_xyz, fmt="%.4e") .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 8.400 seconds) **Estimated memory usage:** 8 MB .. _sphx_glr_download_content_tutorials_05-dcr_plot_fwd_2_dcr2d.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_2_dcr2d.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_fwd_2_dcr2d.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_