.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/tutorials/08-tdem/plot_fwd_2_tem_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_08-tdem_plot_fwd_2_tem_cyl.py: 3D Forward Simulation for Transient Response on a Cylindrical Mesh ================================================================== Here we use the module *SimPEG.electromagnetics.time_domain* to simulate the transient response for borehole survey using a cylindrical mesh and a radially symmetric conductivity. For this tutorial, we focus on the following: - How to define the transmitters and receivers - How to define the transmitter waveform for a step-off - How to define the time-stepping - How to define the survey - How to solve TDEM problems on a cylindrical mesh - The units of the conductivity/resistivity model and resulting data Please note that we have used a coarse mesh larger time-stepping to shorten the time of the simulation. Proper discretization in space and time is required to simulate the fields at each time channel with sufficient accuracy. .. GENERATED FROM PYTHON SOURCE LINES 25-28 Import Modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 28-49 .. code-block:: default from discretize import CylindricalMesh from discretize.utils import mkvc from SimPEG import maps import SimPEG.electromagnetics.time_domain as tdem 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 50-58 Defining the Waveform --------------------- Under *SimPEG.electromagnetic.time_domain.sources* there are a multitude of waveforms that can be defined (VTEM, Ramp-off etc...). Here we simulate the response due to a step off waveform where the off-time begins at t=0. Other waveforms are discuss in the OcTree simulation example. .. GENERATED FROM PYTHON SOURCE LINES 58-62 .. code-block:: default waveform = tdem.sources.StepOffWaveform(off_time=0.0) .. GENERATED FROM PYTHON SOURCE LINES 63-72 Create Airborne Survey ---------------------- Here we define the survey used in our simulation. For time domain simulations, we must define the geometry of the source and its waveform. For the receivers, we define their geometry, the type of field they measure and the time channels at which they measure the field. For this example, the survey consists of a borehold survey with a coincident loop geometry. .. GENERATED FROM PYTHON SOURCE LINES 72-109 .. code-block:: default # Observation times for response (time channels) time_channels = np.logspace(-4, -2, 11) # Defining transmitter locations xtx, ytx, ztx = np.meshgrid([0], [0], np.linspace(0, -500, 26) - 2.5) source_locations = np.c_[mkvc(xtx), mkvc(ytx), mkvc(ztx)] ntx = np.size(xtx) # Define receiver locations xrx, yrx, zrx = np.meshgrid([0], [0], np.linspace(0, -500, 26) - 2.5) receiver_locations = np.c_[mkvc(xrx), mkvc(yrx), mkvc(zrx)] source_list = [] # Create empty list to store sources # Each unique location defines a new transmitter for ii in range(ntx): # Define receivers at each location. dbzdt_receiver = tdem.receivers.PointMagneticFluxTimeDerivative( receiver_locations[ii, :], time_channels, "z" ) receivers_list = [ dbzdt_receiver ] # Make a list containing all receivers even if just one # Must define the transmitter properties and associated receivers source_list.append( tdem.sources.CircularLoop( receivers_list, location=source_locations[ii], waveform=waveform, radius=10.0, ) ) survey = tdem.Survey(source_list) .. GENERATED FROM PYTHON SOURCE LINES 110-122 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 time domain problems: - Your smallest cell size should be 10%-20% the size of your smallest diffusion distance - The thickness of your padding needs to be 2-3 times biggest than your largest diffusion distance - The diffusion distance is ~1260*np.sqrt(rho*t) .. GENERATED FROM PYTHON SOURCE LINES 122-128 .. code-block:: default hr = [(5.0, 40), (5.0, 15, 1.5)] hz = [(5.0, 15, -1.5), (5.0, 300), (5.0, 15, 1.5)] mesh = CylindricalMesh([hr, 1, hz], x0="00C") .. GENERATED FROM PYTHON SOURCE LINES 129-136 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 136-185 .. code-block:: default # 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([0.20, 0.1, 0.54, 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/08-tdem/images/sphx_glr_plot_fwd_2_tem_cyl_001.png :alt: Conductivity Model :srcset: /content/tutorials/08-tdem/images/sphx_glr_plot_fwd_2_tem_cyl_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 186-191 Define the Time-Stepping ------------------------ Stuff about time-stepping and some rule of thumb for step-off waveform .. GENERATED FROM PYTHON SOURCE LINES 191-195 .. code-block:: default time_steps = [(5e-06, 20), (0.0001, 20), (0.001, 21)] .. GENERATED FROM PYTHON SOURCE LINES 196-205 Define the Simulation --------------------- Here we define the formulation for solving Maxwell's equations. Since we are measuring the time-derivative of 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. Use *rhoMap* instead of *sigmaMap* if you defined a resistivity model. .. GENERATED FROM PYTHON SOURCE LINES 205-213 .. code-block:: default simulation = tdem.simulation.Simulation3DMagneticFluxDensity( mesh, survey=survey, sigmaMap=model_map, solver=Solver ) # Set the time-stepping for the simulation simulation.time_steps = time_steps .. GENERATED FROM PYTHON SOURCE LINES 214-218 Predict Data and Plot --------------------- .. GENERATED FROM PYTHON SOURCE LINES 218-247 .. code-block:: default # Data are organized by transmitter, then by # receiver then by observation time. dBdt data are in T/s. dpred = simulation.dpred(model) # Plot the response dpred = np.reshape(dpred, (ntx, len(time_channels))) # TDEM Profile fig = plt.figure(figsize=(5, 5)) ax1 = fig.add_axes([0.15, 0.15, 0.8, 0.75]) for ii in range(0, len(time_channels)): ax1.semilogx( -dpred[:, ii], receiver_locations[:, -1], "k", lw=2 ) # -ve sign to plot -dBz/dt ax1.set_xlabel("-dBz/dt [T/s]") ax1.set_ylabel("Elevation [m]") ax1.set_title("Airborne TDEM Profile") # Response for all time channels fig = plt.figure(figsize=(5, 5)) ax1 = fig.add_axes([0.15, 0.15, 0.8, 0.75]) ax1.loglog(time_channels, -dpred[0, :], "b", lw=2) ax1.loglog(time_channels, -dpred[-1, :], "r", lw=2) ax1.set_xlim((np.min(time_channels), np.max(time_channels))) ax1.set_xlabel("time [s]") ax1.set_ylabel("-dBz/dt [T/s]") ax1.set_title("Decay Curve") ax1.legend(["First Sounding", "Last Sounding"], loc="upper right") .. rst-class:: sphx-glr-horizontal * .. image-sg:: /content/tutorials/08-tdem/images/sphx_glr_plot_fwd_2_tem_cyl_002.png :alt: Airborne TDEM Profile :srcset: /content/tutorials/08-tdem/images/sphx_glr_plot_fwd_2_tem_cyl_002.png :class: sphx-glr-multi-img * .. image-sg:: /content/tutorials/08-tdem/images/sphx_glr_plot_fwd_2_tem_cyl_003.png :alt: Decay Curve :srcset: /content/tutorials/08-tdem/images/sphx_glr_plot_fwd_2_tem_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 38.366 seconds) **Estimated memory usage:** 9 MB .. _sphx_glr_download_content_tutorials_08-tdem_plot_fwd_2_tem_cyl.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_tem_cyl.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_fwd_2_tem_cyl.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_