.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/tutorials/07-fdem/plot_fwd_1_em1dfm.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_07-fdem_plot_fwd_1_em1dfm.py: 1D Forward Simulation for a Single Sounding =========================================== Here we use the module *SimPEG.electromangetics.frequency_domain_1d* to predict frequency domain data for a single sounding over a 1D layered Earth. In this tutorial, we focus on the following: - Defining receivers, sources and the survey - How to predict total field, secondary field or ppm data - The units of the model and resulting data - Defining and running the 1D simulation for a single sounding Our survey geometry consists of a vertical magnetic dipole source located 30 m above the Earth's surface. The receiver is offset 10 m horizontally from the source. .. GENERATED FROM PYTHON SOURCE LINES 22-25 Import Modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 25-41 .. code-block:: Python import numpy as np import os from matplotlib import pyplot as plt from discretize import TensorMesh from SimPEG import maps from SimPEG.electromagnetics import frequency_domain as fdem from SimPEG.utils import plot_1d_layer_model plt.rcParams.update({"font.size": 16}) write_output = False # sphinx_gallery_thumbnail_number = 2 .. GENERATED FROM PYTHON SOURCE LINES 42-50 Create Survey ------------- Here we demonstrate a general way to define the receivers, sources and survey. For this tutorial, the source is a vertical magnetic dipole that will be used to simulate data at a number of frequencies. The receivers measure real and imaginary ppm data. .. GENERATED FROM PYTHON SOURCE LINES 50-99 .. code-block:: Python # Frequencies being observed in Hz frequencies = np.array([382, 1822, 7970, 35920, 130100], dtype=float) # Define a list of receivers. The real and imaginary components are defined # as separate receivers. receiver_location = np.array([10.0, 0.0, 30.0]) receiver_orientation = "z" # "x", "y" or "z" data_type = "ppm" # "secondary", "total" or "ppm" receiver_list = [] receiver_list.append( fdem.receivers.PointMagneticFieldSecondary( receiver_location, orientation=receiver_orientation, data_type=data_type, component="real", ) ) receiver_list.append( fdem.receivers.PointMagneticFieldSecondary( receiver_location, orientation=receiver_orientation, data_type=data_type, component="imag", ) ) # Define the source list. A source must be defined for each frequency. source_location = np.array([0.0, 0.0, 30.0]) source_orientation = "z" # "x", "y" or "z" moment = 1.0 # dipole moment source_list = [] for freq in frequencies: source_list.append( fdem.sources.MagDipole( receiver_list=receiver_list, frequency=freq, location=source_location, orientation=source_orientation, moment=moment, ) ) # Define a 1D FDEM survey survey = fdem.survey.Survey(source_list) .. GENERATED FROM PYTHON SOURCE LINES 100-112 Defining a 1D Layered Earth Model --------------------------------- Here, we define the layer thicknesses and electrical conductivities for our 1D simulation. If we have N layers, we define N electrical conductivity values and N-1 layer thicknesses. The lowest layer is assumed to extend to infinity. If the Earth is a halfspace, the thicknesses can be defined by an empty array, and the physical property values by an array of length 1. In this case, we have a more conductive layer within a background halfspace. This can be defined as a 3 layered Earth model. .. GENERATED FROM PYTHON SOURCE LINES 112-137 .. code-block:: Python # Physical properties background_conductivity = 1e-1 layer_conductivity = 1e0 # Layer thicknesses thicknesses = np.array([20.0, 40.0]) n_layer = len(thicknesses) + 1 # physical property model (conductivity model) model = background_conductivity * np.ones(n_layer) model[1] = layer_conductivity # Define a mapping from model parameters to conductivities model_mapping = maps.IdentityMap(nP=n_layer) # Plot conductivity model thicknesses_for_plotting = np.r_[thicknesses, 40.0] mesh_for_plotting = TensorMesh([thicknesses_for_plotting]) fig = plt.figure(figsize=(6, 5)) ax = fig.add_axes([0.15, 0.15, 0.8, 0.75]) plot_1d_layer_model(thicknesses_for_plotting, model, ax=ax, show_layers=False) plt.gca().invert_yaxis() .. image-sg:: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_1_em1dfm_001.png :alt: plot fwd 1 em1dfm :srcset: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_1_em1dfm_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 138-148 Define the Forward Simulation, Predict Data and Plot ---------------------------------------------------- Here we define the simulation and predict the 1D FDEM sounding data. The simulation requires the user define the survey, the layer thicknesses and a mapping from the model to the conductivities of the layers. When using the *SimPEG.electromagnetics.frequency_domain_1d* module, predicted data are organized by source, then by receiver, then by frequency. .. GENERATED FROM PYTHON SOURCE LINES 148-169 .. code-block:: Python # Define the simulation simulation = fdem.Simulation1DLayered( survey=survey, thicknesses=thicknesses, sigmaMap=model_mapping, ) # Predict sounding data dpred = simulation.dpred(model) # Plot sounding data fig = plt.figure(figsize=(6, 6)) ax = fig.add_axes([0.15, 0.15, 0.8, 0.75]) ax.semilogx(frequencies, np.abs(dpred[0::2]), "k-o", lw=3, ms=10) ax.semilogx(frequencies, np.abs(dpred[1::2]), "k:o", lw=3, ms=10) ax.set_xlabel("Frequency (Hz)") ax.set_ylabel("|Hs/Hp| (ppm)") ax.set_title("Secondary Magnetic Field as ppm") ax.legend(["Real", "Imaginary"]) .. image-sg:: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_1_em1dfm_002.png :alt: Secondary Magnetic Field as ppm :srcset: /content/tutorials/07-fdem/images/sphx_glr_plot_fwd_1_em1dfm_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 170-175 Optional: Export Data --------------------- Write the predicted data. Note that noise has been added. .. GENERATED FROM PYTHON SOURCE LINES 175-195 .. code-block:: Python if write_output: dir_path = os.path.dirname(__file__).split(os.path.sep) dir_path.extend(["outputs"]) dir_path = os.path.sep.join(dir_path) + os.path.sep if not os.path.exists(dir_path): os.mkdir(dir_path) np.random.seed(222) noise = 0.05 * np.abs(dpred) * np.random.randn(len(dpred)) dpred += noise fname = dir_path + "em1dfm_data.txt" np.savetxt( fname, np.c_[frequencies, dpred[0 : len(frequencies)], dpred[len(frequencies) :]], fmt="%.4e", header="FREQUENCY HZ_REAL HZ_IMAG", ) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 2.913 seconds) **Estimated memory usage:** 8 MB .. _sphx_glr_download_content_tutorials_07-fdem_plot_fwd_1_em1dfm.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_fwd_1_em1dfm.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_fwd_1_em1dfm.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_