.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/examples/05-fdem/plot_0_fdem_analytic.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_05-fdem_plot_0_fdem_analytic.py: Simulation with Analytic FDEM Solutions ======================================= Here, the module *SimPEG.electromagnetics.analytics.FDEM* is used to simulate harmonic electric and magnetic field for both electric and magnetic dipole sources in a wholespace. .. GENERATED FROM PYTHON SOURCE LINES 13-16 Import modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 16-28 .. code-block:: default import numpy as np from SimPEG import utils from SimPEG.electromagnetics.analytics.FDEM import ( ElectricDipoleWholeSpace, MagneticDipoleWholeSpace, ) import matplotlib.pyplot as plt from matplotlib.colors import LogNorm .. GENERATED FROM PYTHON SOURCE LINES 29-37 Magnetic Fields for a Magnetic Dipole Source -------------------------------------------- Here, we compute the magnetic fields for a harmonic magnetic dipole source in the z direction. Based on the geometry of the problem, we expect magnetic fields in the x and z directions, but none in the y direction. .. GENERATED FROM PYTHON SOURCE LINES 37-94 .. code-block:: default # Defining electric dipole location and frequency source_location = np.r_[0, 0, 0] frequency = 1e3 # Defining observation locations (avoid placing observation at source) x = np.arange(-100.5, 100.5, step=1.0) y = np.r_[0] z = x observation_locations = utils.ndgrid(x, y, z) # Define wholespace conductivity sig = 1e-2 # Compute the fields Hx, Hy, Hz = MagneticDipoleWholeSpace( observation_locations, source_location, sig, frequency, moment="Z", fieldType="h", mu_r=1, eps_r=1, ) # Plot fig = plt.figure(figsize=(14, 5)) hxplt = Hx.reshape(x.size, z.size) hzplt = Hz.reshape(x.size, z.size) ax1 = fig.add_subplot(121) absH = np.sqrt(Hx.real ** 2 + Hy.real ** 2 + Hz.real ** 2) pc1 = ax1.pcolor(x, z, absH.reshape(x.size, z.size), norm=LogNorm()) ax1.streamplot(x, z, hxplt.real, hzplt.real, color="k", density=1) ax1.set_xlim([x.min(), x.max()]) ax1.set_ylim([z.min(), z.max()]) ax1.set_title("Real Component") ax1.set_xlabel("x") ax1.set_ylabel("z") cb1 = plt.colorbar(pc1, ax=ax1) cb1.set_label("Re[H] (A/m)") ax2 = fig.add_subplot(122) absH = np.sqrt(Hx.imag ** 2 + Hy.imag ** 2 + Hz.imag ** 2) pc2 = ax2.pcolor(x, z, absH.reshape(x.size, z.size), norm=LogNorm()) ax2.streamplot(x, z, hxplt.imag, hzplt.imag, color="k", density=1) ax2.set_xlim([x.min(), x.max()]) ax2.set_ylim([z.min(), z.max()]) ax2.set_title("Imaginary Component") ax2.set_xlabel("x") ax2.set_ylabel("z") cb2 = plt.colorbar(pc2, ax=ax2) cb2.set_label("Im[H] (A/m)") .. image-sg:: /content/examples/05-fdem/images/sphx_glr_plot_0_fdem_analytic_001.png :alt: Real Component, Imaginary Component :srcset: /content/examples/05-fdem/images/sphx_glr_plot_0_fdem_analytic_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 95-103 Electric Fields for a Magnetic Dipole Source -------------------------------------------- Here, we compute the electric fields for a harmonic magnetic dipole source in the y direction. Based on the geometry of the problem, we expect rotational electric fields in the x and z directions, but none in the y direction. .. GENERATED FROM PYTHON SOURCE LINES 103-160 .. code-block:: default # Defining electric dipole location and frequency source_location = np.r_[0, 0, 0] frequency = 1e3 # Defining observation locations (avoid placing observation at source) x = np.arange(-100.5, 100.5, step=1.0) y = np.r_[0] z = x observation_locations = utils.ndgrid(x, y, z) # Define wholespace conductivity sig = 1e-2 # Predict the fields Ex, Ey, Ez = MagneticDipoleWholeSpace( observation_locations, source_location, sig, frequency, moment="Y", fieldType="e", mu_r=1, eps_r=1, ) # Plot fig = plt.figure(figsize=(14, 5)) explt = Ex.reshape(x.size, z.size) ezplt = Ez.reshape(x.size, z.size) ax1 = fig.add_subplot(121) absE = np.sqrt(Ex.real ** 2 + Ey.real ** 2 + Ez.real ** 2) pc1 = ax1.pcolor(x, z, absE.reshape(x.size, z.size), norm=LogNorm()) ax1.streamplot(x, z, explt.real, ezplt.real, color="k", density=1) ax1.set_xlim([x.min(), x.max()]) ax1.set_ylim([z.min(), z.max()]) ax1.set_title("Real Component") ax1.set_xlabel("x") ax1.set_ylabel("z") cb1 = plt.colorbar(pc1, ax=ax1) cb1.set_label("Re[E] (V/m)") ax2 = fig.add_subplot(122) absE = np.sqrt(Ex.imag ** 2 + Ey.imag ** 2 + Ez.imag ** 2) pc2 = ax2.pcolor(x, z, absE.reshape(x.size, z.size), norm=LogNorm()) ax2.streamplot(x, z, explt.imag, ezplt.imag, color="k", density=1) ax2.set_xlim([x.min(), x.max()]) ax2.set_ylim([z.min(), z.max()]) ax2.set_title("Imaginary Component") ax2.set_xlabel("x") ax2.set_ylabel("z") cb2 = plt.colorbar(pc2, ax=ax2) cb2.set_label("Im[E] (V/m)") .. image-sg:: /content/examples/05-fdem/images/sphx_glr_plot_0_fdem_analytic_002.png :alt: Real Component, Imaginary Component :srcset: /content/examples/05-fdem/images/sphx_glr_plot_0_fdem_analytic_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 161-169 Electric Field from a Harmonic Electric Current Dipole Source ------------------------------------------------------------- Here, we compute the electric fields for a harmonic electric current dipole source in the z direction. Based on the geometry of the problem, we expect electric fields in the x and z directions, but none in the y direction. .. GENERATED FROM PYTHON SOURCE LINES 169-226 .. code-block:: default # Defining electric dipole location and frequency source_location = np.r_[0, 0, 0] frequency = 1e3 # Defining observation locations (avoid placing observation at source) x = np.arange(-100.5, 100.5, step=1.0) y = np.r_[0] z = x observation_locations = utils.ndgrid(x, y, z) # Define wholespace conductivity sig = 1e-2 # Predict the fields Ex, Ey, Ez = ElectricDipoleWholeSpace( observation_locations, source_location, sig, frequency, moment=[0, 0, 1], fieldType="e", mu_r=1, eps_r=1, ) # Plot fig = plt.figure(figsize=(14, 5)) explt = Ex.reshape(x.size, z.size) ezplt = Ez.reshape(x.size, z.size) ax1 = fig.add_subplot(121) absE = np.sqrt(Ex.real ** 2 + Ey.real ** 2 + Ez.real ** 2) pc1 = ax1.pcolor(x, z, absE.reshape(x.size, z.size), norm=LogNorm()) ax1.streamplot(x, z, explt.real, ezplt.real, color="k", density=1) ax1.set_xlim([x.min(), x.max()]) ax1.set_ylim([z.min(), z.max()]) ax1.set_title("Real Component") ax1.set_xlabel("x") ax1.set_ylabel("z") cb1 = plt.colorbar(pc1, ax=ax1) cb1.set_label("Re[E] (V/m)") ax2 = fig.add_subplot(122) absE = np.sqrt(Ex.imag ** 2 + Ey.imag ** 2 + Ez.imag ** 2) pc2 = ax2.pcolor(x, z, absE.reshape(x.size, z.size), norm=LogNorm()) ax2.streamplot(x, z, explt.imag, ezplt.imag, color="k", density=1) ax2.set_xlim([x.min(), x.max()]) ax2.set_ylim([z.min(), z.max()]) ax2.set_title("Imaginary Component") ax2.set_xlabel("x") ax2.set_ylabel("z") cb2 = plt.colorbar(pc2, ax=ax2) cb2.set_label("Im[E] (V/m)") .. image-sg:: /content/examples/05-fdem/images/sphx_glr_plot_0_fdem_analytic_003.png :alt: Real Component, Imaginary Component :srcset: /content/examples/05-fdem/images/sphx_glr_plot_0_fdem_analytic_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 227-235 Magnetic Field from a Harmonic Electric Dipole Source ----------------------------------------------------- Here, we compute the magnetic fields for a harmonic electric current dipole source in the y direction. Based on the geometry of the problem, we expect rotational magnetic fields in the x and z directions, but no fields in the y direction. .. GENERATED FROM PYTHON SOURCE LINES 235-290 .. code-block:: default # Defining electric dipole location and frequency source_location = np.r_[0, 0, 0] frequency = 1e3 # Defining observation locations (avoid placing observation at source) x = np.arange(-100.5, 100.5, step=1.0) y = np.r_[0] z = x observation_locations = utils.ndgrid(x, y, z) # Define wholespace conductivity sig = 1e-2 # Predict the fields Hx, Hy, Hz = ElectricDipoleWholeSpace( observation_locations, source_location, sig, frequency, moment=[0, 1, 0], fieldType="h", mu_r=1, eps_r=1, ) # Plot fig = plt.figure(figsize=(14, 5)) hxplt = Hx.reshape(x.size, z.size) hzplt = Hz.reshape(x.size, z.size) ax1 = fig.add_subplot(121) absH = np.sqrt(Hx.real ** 2 + Hy.real ** 2 + Hz.real ** 2) pc1 = ax1.pcolor(x, z, absH.reshape(x.size, z.size), norm=LogNorm()) ax1.streamplot(x, z, hxplt.real, hzplt.real, color="k", density=1) ax1.set_xlim([x.min(), x.max()]) ax1.set_ylim([z.min(), z.max()]) ax1.set_title("Real Component") ax1.set_xlabel("x") ax1.set_ylabel("z") cb1 = plt.colorbar(pc1, ax=ax1) cb1.set_label("Re[H] (A/m)") ax2 = fig.add_subplot(122) absH = np.sqrt(Hx.imag ** 2 + Hy.imag ** 2 + Hz.imag ** 2) pc2 = ax2.pcolor(x, z, absH.reshape(x.size, z.size), norm=LogNorm()) ax2.streamplot(x, z, hxplt.imag, hzplt.imag, color="k", density=1) ax2.set_xlim([x.min(), x.max()]) ax2.set_ylim([z.min(), z.max()]) ax2.set_title("Imaginary Component") ax2.set_xlabel("x") ax2.set_ylabel("z") cb2 = plt.colorbar(pc2, ax=ax2) cb2.set_label("Im[H] (A/m)") .. image-sg:: /content/examples/05-fdem/images/sphx_glr_plot_0_fdem_analytic_004.png :alt: Real Component, Imaginary Component :srcset: /content/examples/05-fdem/images/sphx_glr_plot_0_fdem_analytic_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 9.021 seconds) **Estimated memory usage:** 112 MB .. _sphx_glr_download_content_examples_05-fdem_plot_0_fdem_analytic.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_0_fdem_analytic.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_0_fdem_analytic.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_