.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "gallery/comparisons/magnetic_field.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_gallery_comparisons_magnetic_field.py: 6. Magnetic field due to an el. source ====================================== The solver emg3d returns the electric field in x-, y-, and z-direction. Using Farady's law of induction we can obtain the magnetic field from it. Faraday's law of induction in the frequency domain can be written as, in its differential form, .. math:: :label: faraday \nabla \times \mathbf{E} = \rm{i}\omega \mathbf{B} = \rm{i}\omega\mu\mathbf{H}\, . This is exactly what we do in this example, for a rotated finite length bipole in a homogeneous VTI fullspace, and compare it to the semi-analytical solution of empymod. (The code empymod is an open-source code which can model CSEM responses for a layered medium including VTI electrical anisotropy, see emsig.xyz _.) .. GENERATED FROM PYTHON SOURCE LINES 23-29 .. code-block:: default import emg3d import empymod import numpy as np import matplotlib.pyplot as plt .. GENERATED FROM PYTHON SOURCE LINES 31-36 Full-space model for a finite length, finite strength, rotated bipole --------------------------------------------------------------------- In order to shorten the build-time of the gallery we use a coarse model. Set coarse_model = False to obtain a result of higher accuracy. .. GENERATED FROM PYTHON SOURCE LINES 36-39 .. code-block:: default coarse_model = True .. GENERATED FROM PYTHON SOURCE LINES 40-42 Survey and model parameters  .. GENERATED FROM PYTHON SOURCE LINES 42-68 .. code-block:: default # Receiver coordinates if coarse_model: x = (np.arange(256))*20-2550 else: x = (np.arange(1025))*5-2560 rx = np.repeat([x, ], np.size(x), axis=0) ry = rx.transpose() frx, fry = rx.ravel(), ry.ravel() rz = -400.0 azimuth = 30 elevation = 10 # Source coordinates, frequency, and strength source = emg3d.TxElectricDipole( coordinates=[-50, 50, -30, 30, -320., -280.], # [x1, x2, y1, y2, z1, z2] strength=3.3, # A ) frequency = 0.8 # Hz # Model parameters h_res = 1. # Horizontal resistivity aniso = np.sqrt(2.) # Anisotropy v_res = h_res*aniso**2 # Vertical resistivity .. GENERATED FROM PYTHON SOURCE LINES 69-73 empymod  Note: The coordinate system of empymod is positive z down, for emg3d it is positive z up. We have to switch therefore src_z, rec_z, and elevation. .. GENERATED FROM PYTHON SOURCE LINES 73-89 .. code-block:: default # Compute epm = empymod.bipole( src=np.r_[source.coordinates[:4], -source.coordinates[4:]], rec=[frx, fry, -rz, azimuth, -elevation], depth=[], res=h_res, aniso=aniso, strength=source.strength, srcpts=5, freqtime=frequency, htarg={'pts_per_dec': -1}, mrec=True, verb=3, ).reshape(np.shape(rx)) .. rst-class:: sphx-glr-script-out .. code-block:: none :: empymod START :: v2.2.0 depth [m] : res [Ohm.m] : 1 aniso [-] : 1.41421 epermH [-] : 1 epermV [-] : 1 mpermH [-] : 1 mpermV [-] : 1 > MODEL IS A FULLSPACE direct field : Comp. in wavenumber domain frequency [Hz] : 0.8 Hankel : DLF (Fast Hankel Transform) > Filter : Key 201 (2009) > DLF type : Lagged Convolution Loop over : Frequencies Source(s) : 1 bipole(s) > intpts : 5 > length [m] : 123.288 > strength[A] : 3.3 > x_c [m] : 0 > y_c [m] : 0 > z_c [m] : 300 > azimuth [°] : 30.9638 > dip [°] : -18.9318 Receiver(s) : 65536 dipole(s) > x [m] : -2550 - 2550 : 65536 [min-max; #] > y [m] : -2550 - 2550 : 65536 [min-max; #] > z [m] : 400 > azimuth [°] : 30 > dip [°] : -10 Required ab's : 14 24 34 15 25 35 16 26 36 :: empymod END; runtime = 0:00:00.671096 :: 40 kernel call(s) .. GENERATED FROM PYTHON SOURCE LINES 90-92 emg3d  .. GENERATED FROM PYTHON SOURCE LINES 92-114 .. code-block:: default if coarse_model: min_width_limits = 40 stretching = [1.045, 1.045] else: min_width_limits = 20 stretching = [1.03, 1.045] # Create stretched grid grid = emg3d.construct_mesh( frequency=frequency, properties=h_res, center=source.center, domain=([-2500, 2500], [-2500, 2500], [-2900, 2100]), min_width_limits=min_width_limits, stretching=stretching, lambda_from_center=True, lambda_factor=0.8, center_on_edge=False, ) grid .. raw:: html
 MESH EXTENT CELL WIDTH FACTOR dir nC TensorMesh 512,000 cells x 80 -4,155.20 4,378.72 40.00 223.51 1.04 y 80 -4,155.20 4,378.72 40.00 223.51 1.04 z 80 -4,566.91 3,752.18 40.00 214.73 1.04

.. GENERATED FROM PYTHON SOURCE LINES 115-123 .. code-block:: default # Define the model model = emg3d.Model( grid, property_x=h_res, property_z=v_res, mapping='Resistivity') # Compute the electric field efield = emg3d.solve_source(model, source, frequency, verb=4, plain=True) .. rst-class:: sphx-glr-script-out .. code-block:: none :: emg3d START :: 21:47:20 :: v1.8.0 MG-cycle : 'F' sslsolver : False semicoarsening : False [0] tol : 1e-06 linerelaxation : False [0] maxit : 50 nu_{i,1,c,2} : 0, 2, 1, 2 verb : 4 Original grid : 80 x 80 x 80 => 512,000 cells Coarsest grid : 5 x 5 x 5 => 125 cells Coarsest level : 4 ; 4 ; 4 [hh:mm:ss] rel. error [abs. error, last/prev] l s h_ 2h_ \ / 4h_ \ /\ / 8h_ \ /\ / \ / 16h_ \/\/ \/ \/ [21:47:23] 3.602e-02 after 1 F-cycles [3.540e-05, 0.036] 0 0 [21:47:25] 3.766e-03 after 2 F-cycles [3.701e-06, 0.105] 0 0 [21:47:28] 5.020e-04 after 3 F-cycles [4.933e-07, 0.133] 0 0 [21:47:30] 7.497e-05 after 4 F-cycles [7.367e-08, 0.149] 0 0 [21:47:33] 1.211e-05 after 5 F-cycles [1.190e-08, 0.162] 0 0 [21:47:35] 2.223e-06 after 6 F-cycles [2.184e-09, 0.184] 0 0 [21:47:38] 6.236e-07 after 7 F-cycles [6.128e-10, 0.281] 0 0 > CONVERGED > MG cycles : 7 > Final rel. error : 6.236e-07 :: emg3d END :: 21:47:38 :: runtime = 0:00:18 .. GENERATED FROM PYTHON SOURCE LINES 124-126 Compute magnetic field :math:H from the electric field -------------------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 126-132 .. code-block:: default hfield = emg3d.get_magnetic_field(model, efield) # Get responses at receivers e3d = hfield.get_receiver((rx, ry, rz, azimuth, elevation)) .. GENERATED FROM PYTHON SOURCE LINES 133-135 Plot  .. GENERATED FROM PYTHON SOURCE LINES 135-192 .. code-block:: default # Start figure. a_kwargs = {'cmap': "viridis", 'vmin': -10, 'vmax': -4, 'shading': 'nearest'} e_kwargs = {'cmap': plt.cm.get_cmap("RdBu_r", 8), 'vmin': -2, 'vmax': 2, 'shading': 'nearest'} fig, axs = plt.subplots(2, 3, figsize=(10, 5.5), sharex=True, sharey=True, subplot_kw={'box_aspect': 1}) ((ax1, ax2, ax3), (ax4, ax5, ax6)) = axs x3 = x/1000 # km # Plot Re(data) ax1.set_title(r"(a) |Re(empymod)|") cf0 = ax1.pcolormesh(x3, x3, np.log10(epm.real.amp()), **a_kwargs) ax2.set_title(r"(b) |Re(emg3d)|") ax2.pcolormesh(x3, x3, np.log10(e3d.real.amp()), **a_kwargs) ax3.set_title(r"(c) Error real part") rel_error = 100*np.abs((epm.real - e3d.real) / epm.real) cf2 = ax3.pcolormesh(x3, x3, np.log10(rel_error), **e_kwargs) # Plot Im(data) ax4.set_title(r"(d) |Im(empymod)|") ax4.pcolormesh(x3, x3, np.log10(epm.imag.amp()), **a_kwargs) ax5.set_title(r"(e) |Im(emg3d)|") ax5.pcolormesh(x3, x3, np.log10(e3d.imag.amp()), **a_kwargs) ax6.set_title(r"(f) Error imaginary part") rel_error = 100*np.abs((epm.imag - e3d.imag) / epm.imag) ax6.pcolormesh(x3, x3, np.log10(rel_error), **e_kwargs) # Colorbars fig.colorbar(cf0, ax=axs[0, :], label=r"$\log_{10}$ Amplitude (A/m)") cbar = fig.colorbar(cf2, ax=axs[1, :], label=r"Relative Error") cbar.set_ticks([-2, -1, 0, 1, 2]) cbar.ax.set_yticklabels([r"$0.01\,\%$", r"$0.1\,\%$", r"$1\,\%$", r"$10\,\%$", r"$100\,\%$"]) ax1.set_xlim(min(x3), max(x3)) ax1.set_ylim(min(x3), max(x3)) # Axis label fig.text(0.4, 0.05, "Inline Offset (km)", fontsize=14) fig.text(0.05, 0.3, "Crossline Offset (km)", rotation=90, fontsize=14) fig.suptitle(r'Diffusive Fullspace, $H$-field', y=1, fontsize=20) print(f"- Source: {source}") print(f"- Frequency: {frequency} Hz") print(f"- Magnetic receivers: z={rz} m; θ={azimuth}°, φ={elevation}°") fig.show() .. image-sg:: /gallery/comparisons/images/sphx_glr_magnetic_field_001.png :alt: Diffusive Fullspace, $H$-field, (a) |Re(empymod)|, (b) |Re(emg3d)|, (c) Error real part, (d) |Im(empymod)|, (e) |Im(emg3d)|, (f) Error imaginary part :srcset: /gallery/comparisons/images/sphx_glr_magnetic_field_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none - Source: TxElectricDipole: 3.3 A; e1={-50.0; -30.0; -320.0} m; e2={50.0; 30.0; -280.0} m - Frequency: 0.8 Hz - Magnetic receivers: z=-400.0 m; θ=30°, φ=10° .. GENERATED FROM PYTHON SOURCE LINES 193-194 .. code-block:: default emg3d.Report() .. raw:: html
 Wed Aug 31 21:47:40 2022 CEST OS Linux CPU(s) 4 Machine x86_64 Architecture 64bit RAM 15.5 GiB Environment Python File system ext4 Python 3.9.12 | packaged by conda-forge | (main, Mar 24 2022, 23:22:55) [GCC 10.3.0] numpy 1.22.4 scipy 1.9.0 numba 0.55.2 emg3d 1.8.0 empymod 2.2.0 xarray 2022.6.0 discretize 0.8.2 h5py 3.7.0 matplotlib 3.4.3 tqdm 4.64.0 IPython 8.4.0 Intel(R) oneAPI Math Kernel Library Version 2022.0-Product Build 20211112 for Intel(R) 64 architecture applications

.. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 21.690 seconds) **Estimated memory usage:** 112 MB .. _sphx_glr_download_gallery_comparisons_magnetic_field.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:Download Python source code: magnetic_field.py  .. container:: sphx-glr-download sphx-glr-download-jupyter :download:Download Jupyter notebook: magnetic_field.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery `_