.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/examples/06-tdem/plot_fwd_tdem_inductive_src_permeable_target.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code .. rst-class:: sphx-glr-example-title .. _sphx_glr_content_examples_06-tdem_plot_fwd_tdem_inductive_src_permeable_target.py: EM: TDEM: Permeable Target, Inductive Source ============================================ In this example, we demonstrate 2 approaches for simulating TDEM data when a permeable target is present in the simulation domain. In the first, we use a step-on waveform (QuarterSineRampOnWaveform) and look at the magnetic flux at a late on-time. In the second, we solve the magnetostatic problem to compute the initial magnetic flux so that a step-off waveform may be used. A cylindrically symmetric mesh is employed and a circular loop source is used .. GENERATED FROM PYTHON SOURCE LINES 13-29 .. code-block:: default import discretize import numpy as np import matplotlib.pyplot as plt from matplotlib.colors import LogNorm from scipy.constants import mu_0 try: from pymatsolver import Pardiso as Solver except ImportError: from SimPEG import SolverLU as Solver import time from SimPEG.electromagnetics import time_domain as TDEM from SimPEG import utils, maps, Report .. GENERATED FROM PYTHON SOURCE LINES 30-35 Model Parameters ---------------- Here, we define our simulation parameters. The target has a relative permeability of 100 :math:`\mu_0` .. GENERATED FROM PYTHON SOURCE LINES 35-45 .. code-block:: default target_mur = 100 # permeability of the target target_l = 500 # length of target target_r = 50 # radius of the target sigma_back = 1e-5 # conductivity of the background radius_loop = 100 # radius of the transmitter loop .. GENERATED FROM PYTHON SOURCE LINES 46-50 Mesh ---- Next, we create a cylindrically symmteric tensor mesh .. GENERATED FROM PYTHON SOURCE LINES 50-78 .. code-block:: default csx = 5.0 # core cell size in the x-direction csz = 5.0 # core cell size in the z-direction domainx = 100 # use a uniform cell size out to a radius of 100m # padding parameters npadx, npadz = 15, 15 # number of padding cells pfx = 1.4 # expansion factor for the padding to infinity in the x-direction pfz = 1.4 # expansion factor for the padding to infinity in the z-direction ncz = int(target_l / csz) # number of z cells in the core region # create the cyl mesh mesh = discretize.CylindricalMesh( [ [(csx, int(domainx / csx)), (csx, npadx, pfx)], 1, [(csz, npadz, -pfz), (csz, ncz), (csz, npadz, pfz)], ] ) # put the origin at the top of the target mesh.x0 = [0, 0, -mesh.h[2][: npadz + ncz].sum()] # plot the mesh mesh.plot_grid() .. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_fwd_tdem_inductive_src_permeable_target_001.png :alt: plot fwd tdem inductive src permeable target :srcset: /content/examples/06-tdem/images/sphx_glr_plot_fwd_tdem_inductive_src_permeable_target_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 79-80 Assign physical properties on the mesh .. GENERATED FROM PYTHON SOURCE LINES 80-92 .. code-block:: default mur_model = np.ones(mesh.nC) # find the indices of the target x_inds = mesh.gridCC[:, 0] < target_r z_inds = (mesh.gridCC[:, 2] <= 0) & (mesh.gridCC[:, 2] >= -target_l) mur_model[x_inds & z_inds] = target_mur mu_model = mu_0 * mur_model sigma = np.ones(mesh.nC) * sigma_back .. GENERATED FROM PYTHON SOURCE LINES 93-94 Plot the models .. GENERATED FROM PYTHON SOURCE LINES 94-117 .. code-block:: default xlim = np.r_[-200, 200] # x-limits in meters zlim = np.r_[-1.5 * target_l, 10.0] # z-limits in meters. (z-positive up) fig, ax = plt.subplots(1, 1, figsize=(6, 5)) # plot the permeability plt.colorbar( mesh.plot_image( mur_model, ax=ax, pcolor_opts={"norm": LogNorm()}, # plot on a log-scale mirror=True, )[0], ax=ax, ) ax.plot(np.r_[radius_loop], np.r_[0.0], "wo", markersize=8) ax.plot(np.r_[-radius_loop], np.r_[0.0], "wx", markersize=8) ax.set_title("Relative permeability", fontsize=13) ax.set_xlim(xlim) ax.set_ylim(zlim) .. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_fwd_tdem_inductive_src_permeable_target_002.png :alt: Relative permeability :srcset: /content/examples/06-tdem/images/sphx_glr_plot_fwd_tdem_inductive_src_permeable_target_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none (-750.0, 10.0) .. GENERATED FROM PYTHON SOURCE LINES 118-124 Waveform for the Long On-Time Simulation ---------------------------------------- Here, we define our time-steps for the simulation where we will use a waveform with a long on-time to reach a steady-state magnetic field and define a quarter-sine ramp-on waveform as our transmitter waveform .. GENERATED FROM PYTHON SOURCE LINES 124-153 .. code-block:: default ramp = [ (1e-5, 20), (1e-4, 20), (3e-4, 20), (1e-3, 20), (3e-3, 20), (1e-2, 20), (3e-2, 20), (1e-1, 20), (3e-1, 20), (1, 50), ] time_mesh = discretize.TensorMesh([ramp]) # define an off time past when we will simulate to keep the transmitter on off_time = 100 quarter_sine = TDEM.Src.QuarterSineRampOnWaveform( ramp_on=np.r_[0.0, 3], ramp_off=off_time - np.r_[1.0, 0] ) # evaluate the waveform at each time in the simulation quarter_sine_plt = [quarter_sine.eval(t) for t in time_mesh.gridN] fig, ax = plt.subplots(1, 1, figsize=(6, 4)) ax.plot(time_mesh.gridN, quarter_sine_plt) ax.plot(time_mesh.gridN, np.zeros(time_mesh.nN), "k|", markersize=2) ax.set_title("quarter sine waveform") .. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_fwd_tdem_inductive_src_permeable_target_003.png :alt: quarter sine waveform :srcset: /content/examples/06-tdem/images/sphx_glr_plot_fwd_tdem_inductive_src_permeable_target_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(0.5, 1.0, 'quarter sine waveform') .. GENERATED FROM PYTHON SOURCE LINES 154-159 Sources for the 2 simulations ----------------------------- We use two sources, one for the magnetostatic simulation and one for the ramp on simulation. .. GENERATED FROM PYTHON SOURCE LINES 159-180 .. code-block:: default # For the magnetostatic simulation. The default waveform is a step-off src_magnetostatic = TDEM.Src.CircularLoop( [], location=np.r_[0.0, 0.0, 0.0], orientation="z", radius=100, ) # For the long on-time simulation. We use the ramp-on waveform src_ramp_on = TDEM.Src.CircularLoop( [], location=np.r_[0.0, 0.0, 0.0], orientation="z", radius=100, waveform=quarter_sine, ) src_list_magnetostatic = [src_magnetostatic] src_list_ramp_on = [src_ramp_on] .. GENERATED FROM PYTHON SOURCE LINES 181-186 Create the simulations ---------------------- To simulate magnetic flux data, we use the b-formulation of Maxwell's equations .. GENERATED FROM PYTHON SOURCE LINES 186-205 .. code-block:: default survey_magnetostatic = TDEM.Survey(source_list=src_list_magnetostatic) survey_ramp_on = TDEM.Survey(src_list_ramp_on) prob_magnetostatic = TDEM.Simulation3DMagneticFluxDensity( mesh=mesh, survey=survey_magnetostatic, sigmaMap=maps.IdentityMap(mesh), time_steps=ramp, solver=Solver, ) prob_ramp_on = TDEM.Simulation3DMagneticFluxDensity( mesh=mesh, survey=survey_ramp_on, sigmaMap=maps.IdentityMap(mesh), time_steps=ramp, solver=Solver, ) .. GENERATED FROM PYTHON SOURCE LINES 206-208 Run the long on-time simulation ------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 208-221 .. code-block:: default t = time.time() print("--- Running Long On-Time Simulation ---") prob_ramp_on.mu = mu_model fields = prob_ramp_on.fields(sigma) print(" ... done. Elapsed time {}".format(time.time() - t)) print("\n") # grab the last time-step in the simulation b_ramp_on = utils.mkvc(fields[:, "b", -1]) .. rst-class:: sphx-glr-script-out .. code-block:: none --- Running Long On-Time Simulation --- ... done. Elapsed time 1.5786447525024414 .. GENERATED FROM PYTHON SOURCE LINES 222-224 Compute Magnetostatic Fields from the step-off source ----------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 224-230 .. code-block:: default prob_magnetostatic.mu = mu_model prob_magnetostatic.model = sigma b_magnetostatic = src_magnetostatic.bInitial(prob_magnetostatic) .. GENERATED FROM PYTHON SOURCE LINES 231-233 Plot the results ----------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 233-295 .. code-block:: default def plotBFieldResults( ax=None, clim_min=None, clim_max=None, max_depth=1.5 * target_l, max_r=100, top=10.0, view="magnetostatic", ): if ax is None: plt.subplots(1, 1, figsize=(6, 7)) assert view.lower() in ["magnetostatic", "late_ontime", "diff"] xlim = max_r * np.r_[-1, 1] # x-limits in meters zlim = np.r_[-max_depth, top] # z-limits in meters. (z-positive up) clim = None if clim_max is not None and clim_max != 0.0: clim = clim_max * np.r_[-1, 1] if clim_min is not None and clim_min != 0.0: clim[0] = clim_min if view == "magnetostatic": plotme = b_magnetostatic elif view == "late_ontime": plotme = b_ramp_on elif view == "diff": plotme = b_magnetostatic - b_ramp_on cb = plt.colorbar( mesh.plot_image( plotme, view="vec", v_type="F", ax=ax, range_x=xlim, range_y=zlim, sample_grid=np.r_[np.diff(xlim) / 100.0, np.diff(zlim) / 100.0], mirror=True, pcolor_opts={"norm": LogNorm()}, )[0], ax=ax, ) ax.set_title("{}".format(view), fontsize=13) ax.set_xlim(xlim) ax.set_ylim(zlim) cb.update_ticks() return ax fig, ax = plt.subplots(1, 3, figsize=(12, 5)) for a, v in zip(ax, ["magnetostatic", "late_ontime", "diff"]): a = plotBFieldResults(ax=a, clim_min=1e-15, clim_max=1e-7, view=v, max_r=200) plt.tight_layout() .. image-sg:: /content/examples/06-tdem/images/sphx_glr_plot_fwd_tdem_inductive_src_permeable_target_004.png :alt: magnetostatic, late_ontime, diff :srcset: /content/examples/06-tdem/images/sphx_glr_plot_fwd_tdem_inductive_src_permeable_target_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 296-299 Print the version of SimPEG and dependencies -------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 299-302 .. code-block:: default plt.show() Report() .. raw:: html
Thu Nov 10 06:27:56 2022 UTC
OS Linux CPU(s) 2 Machine x86_64
Architecture 64bit RAM 6.8 GiB Environment Python
File system ext4
Python 3.7.12 | packaged by conda-forge | (default, Oct 26 2021, 06:08:21) [GCC 9.4.0]
SimPEG 0.18.1 discretize 0.8.2 pymatsolver 0.2.0
vectormath Module not found properties Module not found numpy 1.21.6
scipy 1.7.3 cython Module not found IPython 7.33.0
matplotlib 3.5.3 ipywidgets 8.0.2


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