.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/tutorials/04-magnetics/plot_2a_magnetics_induced.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_04-magnetics_plot_2a_magnetics_induced.py: Forward Simulation of Total Magnetic Intensity Data =================================================== Here we use the module *SimPEG.potential_fields.magnetics* to predict magnetic data for a magnetic susceptibility model. We simulate the data on a tensor mesh. For this tutorial, we focus on the following: - How to define the survey - How to predict magnetic data for a susceptibility model - How to include surface topography - The units of the physical property model and resulting data .. GENERATED FROM PYTHON SOURCE LINES 18-21 Import Modules -------------- .. GENERATED FROM PYTHON SOURCE LINES 21-39 .. code-block:: Python import numpy as np from scipy.interpolate import LinearNDInterpolator import matplotlib as mpl import matplotlib.pyplot as plt import os from discretize import TensorMesh from discretize.utils import mkvc, active_from_xyz from SimPEG.utils import plot2Ddata, model_builder from SimPEG import maps from SimPEG.potential_fields import magnetics write_output = False # sphinx_gallery_thumbnail_number = 2 .. GENERATED FROM PYTHON SOURCE LINES 40-46 Topography ---------- Surface topography is defined as an (N, 3) numpy array. We create it here but topography could also be loaded from a file. .. GENERATED FROM PYTHON SOURCE LINES 46-52 .. code-block:: Python [x_topo, y_topo] = np.meshgrid(np.linspace(-200, 200, 41), np.linspace(-200, 200, 41)) z_topo = -15 * np.exp(-(x_topo**2 + y_topo**2) / 80**2) x_topo, y_topo, z_topo = mkvc(x_topo), mkvc(y_topo), mkvc(z_topo) xyz_topo = np.c_[x_topo, y_topo, z_topo] .. GENERATED FROM PYTHON SOURCE LINES 53-61 Defining the Survey ------------------- Here, we define survey that will be used for the simulation. Magnetic surveys are simple to create. The user only needs an (N, 3) array to define the xyz locations of the observation locations, the list of field components which are to be modeled and the properties of the Earth's field. .. GENERATED FROM PYTHON SOURCE LINES 61-97 .. code-block:: Python # Define the observation locations as an (N, 3) numpy array or load them. x = np.linspace(-80.0, 80.0, 17) y = np.linspace(-80.0, 80.0, 17) x, y = np.meshgrid(x, y) x, y = mkvc(x.T), mkvc(y.T) fun_interp = LinearNDInterpolator(np.c_[x_topo, y_topo], z_topo) z = fun_interp(np.c_[x, y]) + 10 # Flight height 10 m above surface. receiver_locations = np.c_[x, y, z] # Define the component(s) of the field we want to simulate as a list of strings. # Here we simulation total magnetic intensity data. components = ["tmi"] # Use the observation locations and components to define the receivers. To # simulate data, the receivers must be defined as a list. receiver_list = magnetics.receivers.Point(receiver_locations, components=components) receiver_list = [receiver_list] # Define the inducing field H0 = (intensity [nT], inclination [deg], declination [deg]) inclination = 90 declination = 0 strength = 50000 source_field = magnetics.sources.UniformBackgroundField( receiver_list=receiver_list, amplitude=strength, inclination=inclination, declination=declination, ) # Define the survey survey = magnetics.survey.Survey(source_field) .. GENERATED FROM PYTHON SOURCE LINES 98-103 Defining a Tensor Mesh ---------------------- Here, we create the tensor mesh that will be used for the forward simulation. .. GENERATED FROM PYTHON SOURCE LINES 103-111 .. code-block:: Python dh = 5.0 hx = [(dh, 5, -1.3), (dh, 40), (dh, 5, 1.3)] hy = [(dh, 5, -1.3), (dh, 40), (dh, 5, 1.3)] hz = [(dh, 5, -1.3), (dh, 15)] mesh = TensorMesh([hx, hy, hz], "CCN") .. GENERATED FROM PYTHON SOURCE LINES 112-119 Defining a Susceptibility Model ------------------------------- Here, we create the model that will be used to predict magnetic data and the mapping from the model to the mesh. The model consists of a susceptible sphere in a less susceptible host. .. GENERATED FROM PYTHON SOURCE LINES 119-164 .. code-block:: Python # Define susceptibility values for each unit in SI background_susceptibility = 0.0001 sphere_susceptibility = 0.01 # Find cells that are active in the forward modeling (cells below surface) ind_active = active_from_xyz(mesh, xyz_topo) # Define mapping from model to active cells nC = int(ind_active.sum()) model_map = maps.IdentityMap(nP=nC) # model is a vlue for each active cell # Define model. Models in SimPEG are vector arrays model = background_susceptibility * np.ones(ind_active.sum()) ind_sphere = model_builder.get_indices_sphere( np.r_[0.0, 0.0, -45.0], 15.0, mesh.cell_centers ) ind_sphere = ind_sphere[ind_active] model[ind_sphere] = sphere_susceptibility # Plot Model fig = plt.figure(figsize=(9, 4)) plotting_map = maps.InjectActiveCells(mesh, ind_active, np.nan) ax1 = fig.add_axes([0.1, 0.12, 0.73, 0.78]) mesh.plot_slice( plotting_map * model, normal="Y", ax=ax1, ind=int(mesh.shape_cells[1] / 2), grid=True, clim=(np.min(model), np.max(model)), ) ax1.set_title("Model slice at y = 0 m") ax1.set_xlabel("x (m)") ax1.set_ylabel("z (m)") ax2 = fig.add_axes([0.85, 0.12, 0.05, 0.78]) norm = mpl.colors.Normalize(vmin=np.min(model), vmax=np.max(model)) cbar = mpl.colorbar.ColorbarBase(ax2, norm=norm, orientation="vertical") cbar.set_label("Magnetic Susceptibility (SI)", rotation=270, labelpad=15, size=12) plt.show() .. image-sg:: /content/tutorials/04-magnetics/images/sphx_glr_plot_2a_magnetics_induced_001.png :alt: Model slice at y = 0 m :srcset: /content/tutorials/04-magnetics/images/sphx_glr_plot_2a_magnetics_induced_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 165-171 Simulation: TMI Data for a Susceptibility Model ----------------------------------------------- Here we demonstrate how to predict magnetic data for a magnetic susceptibility model using the integral formulation. .. GENERATED FROM PYTHON SOURCE LINES 171-213 .. code-block:: Python # Define the forward simulation. By setting the 'store_sensitivities' keyword # argument to "forward_only", we simulate the data without storing the sensitivities simulation = magnetics.simulation.Simulation3DIntegral( survey=survey, mesh=mesh, model_type="scalar", chiMap=model_map, ind_active=ind_active, store_sensitivities="forward_only", ) # Compute predicted data for a susceptibility model dpred = simulation.dpred(model) # Plot fig = plt.figure(figsize=(6, 5)) v_max = np.max(np.abs(dpred)) ax1 = fig.add_axes([0.1, 0.1, 0.8, 0.85]) plot2Ddata( receiver_list[0].locations, dpred, ax=ax1, ncontour=30, clim=(-v_max, v_max), contourOpts={"cmap": "bwr"}, ) ax1.set_title("TMI Anomaly") ax1.set_xlabel("x (m)") ax1.set_ylabel("y (m)") ax2 = fig.add_axes([0.87, 0.1, 0.03, 0.85]) norm = mpl.colors.Normalize(vmin=-np.max(np.abs(dpred)), vmax=np.max(np.abs(dpred))) cbar = mpl.colorbar.ColorbarBase( ax2, norm=norm, orientation="vertical", cmap=mpl.cm.bwr ) cbar.set_label("$nT$", rotation=270, labelpad=15, size=12) plt.show() .. image-sg:: /content/tutorials/04-magnetics/images/sphx_glr_plot_2a_magnetics_induced_002.png :alt: TMI Anomaly :srcset: /content/tutorials/04-magnetics/images/sphx_glr_plot_2a_magnetics_induced_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 214-219 Optional: Export Data --------------------- Write the data and topography .. GENERATED FROM PYTHON SOURCE LINES 219-236 .. 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) fname = dir_path + "magnetics_topo.txt" np.savetxt(fname, np.c_[xyz_topo], fmt="%.4e") np.random.seed(211) maximum_anomaly = np.max(np.abs(dpred)) noise = 0.02 * maximum_anomaly * np.random.randn(len(dpred)) fname = dir_path + "magnetics_data.obs" np.savetxt(fname, np.c_[receiver_locations, dpred + noise], fmt="%.4e") .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 8.364 seconds) **Estimated memory usage:** 8 MB .. _sphx_glr_download_content_tutorials_04-magnetics_plot_2a_magnetics_induced.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_2a_magnetics_induced.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_2a_magnetics_induced.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_