.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/tutorials/03-gravity/plot_1a_gravity_anomaly.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_03-gravity_plot_1a_gravity_anomaly.py: Forward Simulation of Gravity Anomaly Data on a Tensor Mesh =========================================================== Here we use the module *SimPEG.potential_fields.gravity* to predict gravity anomaly data for a synthetic density contrast model. The simulation is carried out on a tensor mesh. For this tutorial, we focus on the following: - How to create gravity surveys - How to predict gravity anomaly data for a density contrast model - How to include surface topography - The units of the density contrast 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 gravity save_output = False # sphinx_gallery_thumbnail_number = 2 .. GENERATED FROM PYTHON SOURCE LINES 40-46 Defining Topography ------------------- Surface topography is defined as an (N, 3) numpy array. We create it here but the topography could also be loaded from a file. .. GENERATED FROM PYTHON SOURCE LINES 46-53 .. 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) topo_xyz = np.c_[x_topo, y_topo, z_topo] .. GENERATED FROM PYTHON SOURCE LINES 54-62 Defining the Survey ------------------- Here, we define survey that will be used for the forward simulation. Gravity surveys are simple to create. The user only needs an (N, 3) array to define the xyz locations of the observation locations, and a list of field components which are to be measured. .. GENERATED FROM PYTHON SOURCE LINES 62-89 .. 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]) + 5.0 receiver_locations = np.c_[x, y, z] # Define the component(s) of the field we want to simulate as strings within # a list. Here we simulate only the vertical component of gravity anomaly. components = ["gz"] # Use the observation locations and components to define the receivers. To # simulate data, the receivers must be defined as a list. receiver_list = gravity.receivers.Point(receiver_locations, components=components) receiver_list = [receiver_list] # Defining the source field. source_field = gravity.sources.SourceField(receiver_list=receiver_list) # Defining the survey survey = gravity.survey.Survey(source_field) .. GENERATED FROM PYTHON SOURCE LINES 90-96 Defining a Tensor Mesh ---------------------- Here, we create the tensor mesh that will be used to predict gravity anomaly data. .. GENERATED FROM PYTHON SOURCE LINES 96-103 .. 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 104-111 Density Contrast Model and Mapping on Tensor Mesh ------------------------------------------------- Here, we create the density contrast model that will be used to predict gravity anomaly data and the mapping from the model to the mesh. The model consists of a less dense block and a more dense sphere. .. GENERATED FROM PYTHON SOURCE LINES 111-175 .. code-block:: Python # Define density contrast values for each unit in g/cc background_density = 0.0 block_density = -0.2 sphere_density = 0.2 # Find the indices for the active mesh cells (e.g. cells below surface) ind_active = active_from_xyz(mesh, topo_xyz) # Define mapping from model to active cells. The model consists of a value for # each cell below the Earth's surface. nC = int(ind_active.sum()) model_map = maps.IdentityMap(nP=nC) # Define model. Models in SimPEG are vector arrays. model = background_density * np.ones(nC) # You could find the indicies of specific cells within the model and change their # value to add structures. ind_block = ( (mesh.gridCC[ind_active, 0] > -50.0) & (mesh.gridCC[ind_active, 0] < -20.0) & (mesh.gridCC[ind_active, 1] > -15.0) & (mesh.gridCC[ind_active, 1] < 15.0) & (mesh.gridCC[ind_active, 2] > -50.0) & (mesh.gridCC[ind_active, 2] < -30.0) ) model[ind_block] = block_density # You can also use SimPEG utilities to add structures to the model more concisely ind_sphere = model_builder.get_indices_sphere( np.r_[35.0, 0.0, -40.0], 15.0, mesh.gridCC ) ind_sphere = ind_sphere[ind_active] model[ind_sphere] = sphere_density # Plot Density Contrast 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)), pcolor_opts={"cmap": "viridis"}, ) 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", cmap=mpl.cm.viridis ) cbar.set_label("$g/cm^3$", rotation=270, labelpad=15, size=12) plt.show() .. image-sg:: /content/tutorials/03-gravity/images/sphx_glr_plot_1a_gravity_anomaly_001.png :alt: Model slice at y = 0 m :srcset: /content/tutorials/03-gravity/images/sphx_glr_plot_1a_gravity_anomaly_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 176-182 Simulation: Gravity Anomaly Data on Tensor Mesh ----------------------------------------------- Here we demonstrate how to predict gravity anomaly data using the integral formulation. .. GENERATED FROM PYTHON SOURCE LINES 184-188 Define the forward simulation. By setting the ``store_sensitivities`` keyword argument to ``"forward_only"``, we simulate the data without storing the sensitivities. .. GENERATED FROM PYTHON SOURCE LINES 188-198 .. code-block:: Python simulation = gravity.simulation.Simulation3DIntegral( survey=survey, mesh=mesh, rhoMap=model_map, ind_active=ind_active, store_sensitivities="forward_only", engine="choclo", ) .. GENERATED FROM PYTHON SOURCE LINES 199-206 .. tip:: Since SimPEG v0.21.0 we can use `Choclo `_ as the engine for running the gravity simulations, which results in faster and more memory efficient runs. Just pass ``engine="choclo"`` when constructing the simulation. .. GENERATED FROM PYTHON SOURCE LINES 208-211 Compute predicted data for some model SimPEG uses right handed coordinate where Z is positive upward. This causes gravity signals look "inconsistent" with density values in visualization. .. GENERATED FROM PYTHON SOURCE LINES 211-233 .. code-block:: Python dpred = simulation.dpred(model) # Plot fig = plt.figure(figsize=(7, 5)) ax1 = fig.add_axes([0.1, 0.1, 0.75, 0.85]) plot2Ddata(receiver_list[0].locations, dpred, ax=ax1, contourOpts={"cmap": "bwr"}) ax1.set_title("Gravity Anomaly (Z-component)") ax1.set_xlabel("x (m)") ax1.set_ylabel("y (m)") ax2 = fig.add_axes([0.82, 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, format="%.1e" ) cbar.set_label("$mgal$", rotation=270, labelpad=15, size=12) plt.show() .. image-sg:: /content/tutorials/03-gravity/images/sphx_glr_plot_1a_gravity_anomaly_002.png :alt: Gravity Anomaly (Z-component) :srcset: /content/tutorials/03-gravity/images/sphx_glr_plot_1a_gravity_anomaly_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 234-239 Optional: Exporting Results --------------------------- Write the data, topography and true model .. GENERATED FROM PYTHON SOURCE LINES 239-256 .. code-block:: Python if save_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 + "gravity_topo.txt" np.savetxt(fname, np.c_[topo_xyz], fmt="%.4e") np.random.seed(737) maximum_anomaly = np.max(np.abs(dpred)) noise = 0.01 * maximum_anomaly * np.random.randn(len(dpred)) fname = dir_path + "gravity_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 6.532 seconds) **Estimated memory usage:** 32 MB .. _sphx_glr_download_content_tutorials_03-gravity_plot_1a_gravity_anomaly.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_1a_gravity_anomaly.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_1a_gravity_anomaly.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_