.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/tutorials/07-fdem/plot_fwd_2_fem_cyl.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_07-fdem_plot_fwd_2_fem_cyl.py: 3D Forward Simulation on a Cylindrical Mesh =========================================== Here we use the module *simpeg.electromagnetics.frequency_domain* to simulate the FDEM response for a borehole survey using a cylindrical mesh and radially symmetric conductivity model. For this tutorial, we focus on the following: - How to define the transmitters and receivers - How to define the survey - How to solve the FDEM problem on cylindrical meshes - The units of the conductivity/resistivity model and resulting data Please note that we have used a coarse mesh to shorten the time of the simulation. Proper discretization is required to simulate the fields at each frequency with sufficient accuracy. .. GENERATED FROM PYTHON SOURCE LINES 23-26 Import modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 26-47 .. code-block:: Python from discretize import CylindricalMesh from discretize.utils import mkvc from simpeg import maps import simpeg.electromagnetics.frequency_domain as fdem import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt try: from pymatsolver import Pardiso as Solver except ImportError: from simpeg import SolverLU as Solver write_file = False # sphinx_gallery_thumbnail_number = 2 .. GENERATED FROM PYTHON SOURCE LINES 48-55 Create Airborne Survey ---------------------- Here we define a x-offset borehole survey that consists of a single vertical line of source-receiver pairs which measred the secondary magnetic flux density over a range of frequencies. .. GENERATED FROM PYTHON SOURCE LINES 55-94 .. code-block:: Python # Frequencies being predicted (10 Hz to 10000 Hz) frequencies = np.logspace(1, 4, 16) # Defining transmitter locations xtx, ytx, ztx = np.meshgrid([0], [0], np.linspace(0, -500, 21)) source_locations = np.c_[mkvc(xtx), mkvc(ytx), mkvc(ztx)] ntx = np.size(xtx) # Define receiver locations xrx, yrx, zrx = np.meshgrid([100], [0], np.linspace(0, -500, 21)) receiver_locations = np.c_[mkvc(xrx), mkvc(yrx), mkvc(zrx)] source_list = [] # Create empty list to store sources # Each unique location and frequency defines a new transmitter for ii in range(ntx): # Define receivers of different types at each location. Real and imaginary # measurements require separate receivers. You can define the orientation of # the transmitters and receivers for different survey geometries. bzr_receiver = fdem.receivers.PointMagneticFluxDensitySecondary( receiver_locations[ii, :], "z", "real" ) bzi_receiver = fdem.receivers.PointMagneticFluxDensitySecondary( receiver_locations[ii, :], "z", "imag" ) receivers_list = [bzr_receiver, bzi_receiver] # must be a list for jj in range(len(frequencies)): # Must define the transmitter properties and associated receivers source_list.append( fdem.sources.MagDipole( receivers_list, frequencies[jj], source_locations[ii], orientation="z" ) ) # Define the survey survey = fdem.Survey(source_list) .. GENERATED FROM PYTHON SOURCE LINES 95-107 Create Cylindrical Mesh ----------------------- Here we create the cylindrical mesh that will be used for this tutorial example. We chose to design a coarser mesh to decrease the run time. When designing a mesh to solve practical frequency domain problems: - Your smallest cell size should be 10%-20% the size of your smallest skin depth - The thickness of your padding needs to be 2-3 times biggest than your largest skin depth - The skin depth is ~500*np.sqrt(rho/f) .. GENERATED FROM PYTHON SOURCE LINES 107-117 .. code-block:: Python hr = [(10.0, 30), (10.0, 10, 1.5)] # discretization in the radial direction hz = [ (10.0, 10, -1.5), (10.0, 200), (10.0, 10, 1.5), ] # discretization in vertical direction mesh = CylindricalMesh([hr, 1, hz], x0="00C") .. GENERATED FROM PYTHON SOURCE LINES 118-125 Create Conductivity/Resistivity Model and Mapping ------------------------------------------------- Here, we create the model that will be used to predict frequency domain data and the mapping from the model to the mesh. The model consists of several layers. For this example, we will have only flat topography. .. GENERATED FROM PYTHON SOURCE LINES 125-175 .. code-block:: Python # Conductivity in S/m (or resistivity in Ohm m) air_conductivity = 1e-8 background_conductivity = 1e-1 layer_conductivity_1 = 1e0 layer_conductivity_2 = 1e-2 # Find cells that are active in the forward modeling (cells below surface) ind_active = mesh.cell_centers[:, 2] < 0 # Define mapping from model to active cells model_map = maps.InjectActiveCells(mesh, ind_active, air_conductivity) # Define the model model = background_conductivity * np.ones(ind_active.sum()) ind = (mesh.cell_centers[ind_active, 2] > -200.0) & ( mesh.cell_centers[ind_active, 2] < -0 ) model[ind] = layer_conductivity_1 ind = (mesh.cell_centers[ind_active, 2] > -400.0) & ( mesh.cell_centers[ind_active, 2] < -200 ) model[ind] = layer_conductivity_2 # Plot Conductivity Model mpl.rcParams.update({"font.size": 14}) fig = plt.figure(figsize=(5, 6)) plotting_map = maps.InjectActiveCells(mesh, ind_active, np.nan) log_model = np.log10(model) ax1 = fig.add_axes([0.14, 0.1, 0.6, 0.85]) mesh.plot_image( plotting_map * log_model, ax=ax1, grid=False, clim=(np.log10(layer_conductivity_2), np.log10(layer_conductivity_1)), ) ax1.set_title("Conductivity Model") ax2 = fig.add_axes([0.76, 0.1, 0.05, 0.85]) norm = mpl.colors.Normalize( vmin=np.log10(layer_conductivity_2), vmax=np.log10(layer_conductivity_1) ) cbar = mpl.colorbar.ColorbarBase( ax2, norm=norm, orientation="vertical", format="$10^{%.1f}$" ) cbar.set_label("Conductivity [S/m]", rotation=270, labelpad=15, size=12) .. image-sg:: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_2_fem_cyl_001.png :alt: Conductivity Model :srcset: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_2_fem_cyl_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 176-185 Simulation: Predicting FDEM Data -------------------------------- Here we define the formulation for solving Maxwell's equations. Since we are measuring the magnetic flux density and working with a conductivity model, the EB formulation is the most natural. We must also remember to define the mapping for the conductivity model. If you defined a resistivity model, use the kwarg *rhoMap* instead of *sigmaMap* .. GENERATED FROM PYTHON SOURCE LINES 185-190 .. code-block:: Python simulation = fdem.simulation.Simulation3DMagneticFluxDensity( mesh, survey=survey, sigmaMap=model_map, solver=Solver ) .. GENERATED FROM PYTHON SOURCE LINES 191-196 Predict and Plot Data --------------------- Here we show how the simulation is used to predict data. .. GENERATED FROM PYTHON SOURCE LINES 196-232 .. code-block:: Python # Compute predicted data for the given model. dpred = simulation.dpred(model) # Data are organized by transmitter location, then component, then frequency. We had nFreq # transmitters and each transmitter had 2 receivers (real and imaginary component). So # first we will pick out the real and imaginary data bz_real = dpred[0 : len(dpred) : 2] bz_imag = dpred[1 : len(dpred) : 2] # Then we will will reshape the data. bz_real = np.reshape(bz_real, (ntx, len(frequencies))) bz_imag = np.reshape(bz_imag, (ntx, len(frequencies))) # Plot secondary field along the profile at f = 10000 Hz fig = plt.figure(figsize=(5, 5)) ax1 = fig.add_axes([0.2, 0.15, 0.75, 0.75]) frequencies_index = 0 ax1.plot(bz_real[:, frequencies_index], receiver_locations[:, -1], "b-", lw=3) ax1.plot(bz_imag[:, frequencies_index], receiver_locations[:, -1], "b--", lw=3) ax1.set_xlabel("Bz secondary [T]") ax1.set_ylabel("Elevation [m]") ax1.set_title("Response at 10000 Hz") ax1.legend(["Real", "Imaginary"], loc="upper right") # Plot FEM response for all frequencies fig = plt.figure(figsize=(5, 5)) ax1 = fig.add_axes([0.2, 0.15, 0.75, 0.75]) location_index = 0 ax1.semilogx(frequencies, bz_real[location_index, :], "b-", lw=3) ax1.semilogx(frequencies, bz_imag[location_index, :], "b--", lw=3) ax1.set_xlim((np.min(frequencies), np.max(frequencies))) ax1.set_xlabel("Frequency [Hz]") ax1.set_ylabel("Bz secondary [T]") ax1.set_title("Response at Smallest Offset") ax1.legend(["Real", "Imaginary"], loc="upper left") .. rst-class:: sphx-glr-horizontal * .. image-sg:: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_2_fem_cyl_002.png :alt: Response at 10000 Hz :srcset: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_2_fem_cyl_002.png :class: sphx-glr-multi-img * .. image-sg:: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_2_fem_cyl_003.png :alt: Response at Smallest Offset :srcset: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_2_fem_cyl_003.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 9.489 seconds) **Estimated memory usage:** 9 MB .. _sphx_glr_download_content_tutorials_07-fdem_plot_fwd_2_fem_cyl.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_fem_cyl.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_fwd_2_fem_cyl.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_