.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "gallery/tutorials/mapping.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_tutorials_mapping.py: 02. Model property mapping ========================== Physical rock properties (and their units) can be a tricky thing. And emg3d is no difference in this respect. It was first developed for oil and gas, having resistive bodies in mind. You will therefore find that the documentation often talks about resistivity (Ohm.m). However, internally the computation is carried out in conductivities (S/m), so resistivities are converted into conductivities internally. For the simple forward model this is not a big issue, as the output is simply the electromagnetic field. However, moving over to optimization makes things more complicated, as the gradient of the misfit function, for instance, depends on the parametrization. Since emg3d v0.12.0 it is therefore possible to define a :class:emg3d.models.Model in different ways, thanks to different maps, defined with the parameter mapping. Currently implemented are six different maps: - 'Resistivity': :math:\rho (Ohm.m), the default; - 'LgResistivity': :math:\log_{10}(\rho); - 'LnResistivity': :math:\log_e(\rho); - 'Conductivity': :math:\sigma (S/m); - 'LgConductivity': :math:\log_{10}(\sigma); - 'LnConductivity': :math:\log_e(\sigma). We take here the model from :ref:sphx_glr_gallery_tutorials_total_vs_ps_field.py and map it once as 'LgResistivity' and once as 'LgConductivity', and verify that the resulting electric field is the same. .. GENERATED FROM PYTHON SOURCE LINES 34-39 .. code-block:: default import emg3d import numpy as np import matplotlib.pyplot as plt plt.style.use('bmh') .. GENERATED FROM PYTHON SOURCE LINES 40-42 Survey ------ .. GENERATED FROM PYTHON SOURCE LINES 42-49 .. code-block:: default src = [0, 0, -1950, 0, 0] # x-dir. source at the origin, 50 m above seafloor off = np.arange(5, 81)*100 # Offsets rec = [off, off*0, -2000] # In-line receivers on the seafloor res = [0.3, 1] # 1D resistivities (Ohm.m): [water, background] freq = 1.0 # Frequency (Hz) .. GENERATED FROM PYTHON SOURCE LINES 50-55 Mesh ---- We create quite a coarse grid (100 m minimum cell width), to have reasonable fast computation times. .. GENERATED FROM PYTHON SOURCE LINES 55-67 .. code-block:: default grid = emg3d.construct_mesh( frequency=freq, min_width_limits=100.0, properties=[res[0], res[1], res[1], res[0]], center=(src[0], src[1], -2000), domain=([-100, 8100], [-500, 500], [-3500, -1500]), center_on_edge=True, verb=0, ) grid .. raw:: html
 MESH EXTENT CELL WIDTH FACTOR dir nC TensorMesh 73,728 cells x 96 -3,303.39 11,303.39 100.00 996.95 1.39 y 24 -3,703.39 3,703.39 100.00 996.95 1.39 z 32 -7,512.73 240.89 100.00 1,344.36 1.45

.. GENERATED FROM PYTHON SOURCE LINES 68-70 Define resistivities -------------------- .. GENERATED FROM PYTHON SOURCE LINES 70-82 .. code-block:: default # Layered_background res_x = np.ones(grid.n_cells)*res[0] # Water resistivity res_x[grid.cell_centers[:, 2] < -2000] = res[1] # Background resistivity # Include the target xx = (grid.cell_centers[:, 0] >= 0) & (grid.cell_centers[:, 0] <= 6000) yy = abs(grid.cell_centers[:, 1]) <= 500 zz = (grid.cell_centers[:, 2] > -3500)*(grid.cell_centers[:, 2] < -3000) res_x[xx*yy*zz] = 100. # Target resistivity .. GENERATED FROM PYTHON SOURCE LINES 83-85 Create LgResistivity and LgConductivity models ------------------------------------------------------ .. GENERATED FROM PYTHON SOURCE LINES 85-115 .. code-block:: default # Create log10-res model model_lg_res = emg3d.Model( grid, property_x=np.log10(res_x), mapping='LgResistivity') # Create log10-con model model_lg_con = emg3d.Model( grid, property_x=np.log10(1/res_x), mapping='LgConductivity') # Plot the models fig, axs = plt.subplots(figsize=(9, 6), nrows=1, ncols=2) # log10-res f0 = grid.plot_slice(model_lg_res.property_x, v_type='CC', normal='Y', ax=axs[0], clim=[-2, 2]) axs[0].set_title(r'Resistivity (Ohm.m); $\log_{10}$-scale') axs[0].set_xlim([-1000, 8000]) axs[0].set_ylim([-4000, -1500]) # log10-con f1 = grid.plot_slice(model_lg_con.property_x, v_type='CC', normal='Y', ax=axs[1], clim=[-2, 2]) axs[1].set_title(r'Conductivity (S/m); $\log_{10}$-scale') axs[1].set_xlim([-1000, 8000]) axs[1].set_ylim([-4000, -1500]) plt.tight_layout() fig.colorbar(f0[0], ax=axs, orientation='horizontal', fraction=0.05) plt.show() .. image-sg:: /gallery/tutorials/images/sphx_glr_mapping_001.png :alt: Resistivity (Ohm.m); $\log_{10}$-scale, Conductivity (S/m); $\log_{10}$-scale :srcset: /gallery/tutorials/images/sphx_glr_mapping_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 116-118 Compute electric fields ----------------------- .. GENERATED FROM PYTHON SOURCE LINES 118-133 .. code-block:: default source = emg3d.TxElectricDipole(coordinates=src) solver_opts = { 'source': source, 'frequency': freq, 'verb': 1, } efield_lg_res = emg3d.solve_source(model_lg_res, **solver_opts) efield_lg_con = emg3d.solve_source(model_lg_con, **solver_opts) # Extract responses at receiver locations. rec_lg_res = efield_lg_res.get_receiver((*rec, 0, 0)) rec_lg_con = efield_lg_con.get_receiver((*rec, 0, 0)) .. rst-class:: sphx-glr-script-out .. code-block:: none :: emg3d :: 8.9e-07; 1(4); 0:00:05; CONVERGED :: emg3d :: 8.9e-07; 1(4); 0:00:05; CONVERGED .. GENERATED FROM PYTHON SOURCE LINES 134-136 Compare the two results ----------------------- .. GENERATED FROM PYTHON SOURCE LINES 136-160 .. code-block:: default plt.figure() plt.title('Comparison') # Log_10(resistivity)-model. plt.plot(off/1e3, rec_lg_res.real, 'C0', label=r'$\Re[\log_{10}(\rho)]$-model') plt.plot(off/1e3, rec_lg_res.imag, 'C1-', label=r'$\Im[\log_{10}(\rho)]$-model') # Log_10(conductivity)-model. plt.plot(off/1e3, rec_lg_con.real, 'C2-.', label=r'$\Re[\log_{10}(\sigma)]$-model') plt.plot(off/1e3, rec_lg_con.imag, 'C3-.', label=r'$\Im[\log_{10}(\sigma)]$-model') plt.xlabel('Offset (km)') plt.ylabel('$E_x$ (V/m)') plt.yscale('symlog', linthresh=1e-17) plt.legend() plt.tight_layout() plt.show() .. image-sg:: /gallery/tutorials/images/sphx_glr_mapping_002.png :alt: Comparison :srcset: /gallery/tutorials/images/sphx_glr_mapping_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 161-163 .. code-block:: default emg3d.Report() .. raw:: html
 Wed Aug 31 21:25:16 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 12.046 seconds) **Estimated memory usage:** 45 MB .. _sphx_glr_download_gallery_tutorials_mapping.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-python :download:Download Python source code: mapping.py  .. container:: sphx-glr-download sphx-glr-download-jupyter :download:Download Jupyter notebook: mapping.ipynb  .. only:: html .. rst-class:: sphx-glr-signature Gallery generated by Sphinx-Gallery _