.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "content/examples/02-gravity/plot_inv_grav_tiled.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_examples_02-gravity_plot_inv_grav_tiled.py: PF: Gravity: Tiled Inversion Linear =================================== Invert data in tiles. .. GENERATED FROM PYTHON SOURCE LINES 8-28 .. code-block:: Python import os import numpy as np import matplotlib.pyplot as plt from SimPEG.potential_fields import gravity from SimPEG import ( maps, data, data_misfit, regularization, optimization, inverse_problem, directives, inversion, ) from discretize.utils import mesh_builder_xyz, refine_tree_xyz, active_from_xyz from SimPEG import utils .. GENERATED FROM PYTHON SOURCE LINES 29-37 Setup ----- Define the survey and model parameters Create a global survey and mesh and simulate some data .. GENERATED FROM PYTHON SOURCE LINES 37-53 .. code-block:: Python # Create an array of observation points xr = np.linspace(-30.0, 30.0, 20) yr = np.linspace(-30.0, 30.0, 20) X, Y = np.meshgrid(xr, yr) # Move the observation points 5m above the topo Z = -np.exp((X**2 + Y**2) / 75**2) # Create a topo array topo = np.c_[utils.mkvc(X.T), utils.mkvc(Y.T), utils.mkvc(Z.T)] # Create station locations draped 0.1 m above topo rxLoc = np.c_[utils.mkvc(X.T), utils.mkvc(Y.T), utils.mkvc(Z.T) + 0.1] .. GENERATED FROM PYTHON SOURCE LINES 54-60 Divided and Conquer ------------------- Split the data set in two and create sub-problems .. GENERATED FROM PYTHON SOURCE LINES 60-90 .. code-block:: Python # Mesh parameters h = [5, 5, 5] padDist = np.ones((3, 2)) * 100 octree_levels = [8, 4] # Create tiles local_indices = [rxLoc[:, 0] <= 0, rxLoc[:, 0] > 0] local_surveys = [] local_meshes = [] for local_index in local_indices: receivers = gravity.receivers.Point(rxLoc[local_index, :]) srcField = gravity.sources.SourceField([receivers]) local_survey = gravity.survey.Survey(srcField) # Create a local mesh that covers all points, but refined on the local survey local_mesh = mesh_builder_xyz( topo, h, padding_distance=padDist, depth_core=100, mesh_type="tree" ) local_mesh = refine_tree_xyz( local_mesh, local_survey.receiver_locations, method="surface", octree_levels=octree_levels, finalize=True, ) local_surveys.append(local_survey) local_meshes.append(local_mesh) .. rst-class:: sphx-glr-script-out .. code-block:: none /home/vsts/work/1/s/examples/02-gravity/plot_inv_grav_tiled.py:79: DeprecationWarning: The surface option is deprecated as of `0.9.0` please update your code to use the `TreeMesh.refine_surface` functionality. It will be removed in a future version of discretize. .. GENERATED FROM PYTHON SOURCE LINES 91-97 Global Mesh ------------ Create a global mesh survey for simulation .. GENERATED FROM PYTHON SOURCE LINES 97-152 .. code-block:: Python mesh = mesh_builder_xyz( topo, h, padding_distance=padDist, depth_core=100, mesh_type="tree" ) # This guarantees that the local meshes are always coarser or equal for local_mesh in local_meshes: mesh.insert_cells( local_mesh.gridCC, local_mesh.cell_levels_by_index(np.arange(local_mesh.nC)), finalize=False, ) mesh.finalize() # Define an active cells from topo activeCells = active_from_xyz(mesh, topo) nC = int(activeCells.sum()) # We can now create a density model and generate data # Here a simple block in half-space # Get the indices of the magnetized block model = np.zeros(mesh.nC) ind = utils.model_builder.get_indices_block( np.r_[-10, -10, -30], np.r_[10, 10, -10], mesh.gridCC, )[0] # Assign magnetization values model[ind] = 0.3 # Remove air cells model = model[activeCells] # Create reduced identity map idenMap = maps.IdentityMap(nP=nC) # Create a global survey just for simulation of data receivers = gravity.receivers.Point(rxLoc) srcField = gravity.sources.SourceField([receivers]) survey = gravity.survey.Survey(srcField) # Create the forward simulation for the global dataset simulation = gravity.simulation.Simulation3DIntegral( survey=survey, mesh=mesh, rhoMap=idenMap, ind_active=activeCells ) # Compute linear forward operator and compute some data d = simulation.fields(model) # Add noise and uncertainties # We add some random Gaussian noise (1nT) synthetic_data = d + np.random.randn(len(d)) * 1e-3 wd = np.ones(len(synthetic_data)) * 1e-3 # Assign flat uncertainties .. GENERATED FROM PYTHON SOURCE LINES 153-158 Tiled misfits .. GENERATED FROM PYTHON SOURCE LINES 158-213 .. code-block:: Python local_misfits = [] for ii, local_survey in enumerate(local_surveys): tile_map = maps.TileMap(mesh, activeCells, local_meshes[ii]) local_actives = tile_map.local_active # Create the forward simulation simulation = gravity.simulation.Simulation3DIntegral( survey=local_survey, mesh=local_meshes[ii], rhoMap=tile_map, ind_active=local_actives, sensitivity_path=os.path.join("Inversion", f"Tile{ii}.zarr"), ) data_object = data.Data( local_survey, dobs=synthetic_data[local_indices[ii]], standard_deviation=wd[local_indices[ii]], ) local_misfits.append( data_misfit.L2DataMisfit(data=data_object, simulation=simulation) ) # Our global misfit global_misfit = local_misfits[0] + local_misfits[1] # Plot the model on different meshes fig = plt.figure(figsize=(12, 6)) for ii, local_misfit in enumerate(local_misfits): local_mesh = local_misfit.simulation.mesh local_map = local_misfit.simulation.rhoMap inject_local = maps.InjectActiveCells(local_mesh, local_map.local_active, np.nan) ax = plt.subplot(2, 2, ii + 1) local_mesh.plot_slice( inject_local * (local_map * model), normal="Y", ax=ax, grid=True ) ax.set_aspect("equal") ax.set_title(f"Mesh {ii+1}. Active cells {local_map.local_active.sum()}") # Create active map to go from reduce set to full inject_global = maps.InjectActiveCells(mesh, activeCells, np.nan) ax = plt.subplot(2, 1, 2) mesh.plot_slice(inject_global * model, normal="Y", ax=ax, grid=True) ax.set_title(f"Global Mesh. Active cells {activeCells.sum()}") ax.set_aspect("equal") plt.show() .. image-sg:: /content/examples/02-gravity/images/sphx_glr_plot_inv_grav_tiled_001.png :alt: Mesh 1. Active cells 1471, Mesh 2. Active cells 1197, Global Mesh. Active cells 2309 :srcset: /content/examples/02-gravity/images/sphx_glr_plot_inv_grav_tiled_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 214-220 Invert on the global mesh .. GENERATED FROM PYTHON SOURCE LINES 220-268 .. code-block:: Python # Create reduced identity map idenMap = maps.IdentityMap(nP=nC) # Create a regularization reg = regularization.Sparse(mesh, active_cells=activeCells, mapping=idenMap) m0 = np.ones(nC) * 1e-4 # Starting model # Add directives to the inversion opt = optimization.ProjectedGNCG( maxIter=100, lower=-1.0, upper=1.0, maxIterLS=20, maxIterCG=10, tolCG=1e-3 ) invProb = inverse_problem.BaseInvProblem(global_misfit, reg, opt) betaest = directives.BetaEstimate_ByEig(beta0_ratio=1e-1) # Here is where the norms are applied # Use a threshold parameter empirically based on the distribution of # model parameters update_IRLS = directives.Update_IRLS( f_min_change=1e-4, max_irls_iterations=0, coolEpsFact=1.5, beta_tol=1e-2, ) saveDict = directives.SaveOutputEveryIteration(save_txt=False) update_Jacobi = directives.UpdatePreconditioner() sensitivity_weights = directives.UpdateSensitivityWeights(every_iteration=False) inv = inversion.BaseInversion( invProb, directiveList=[update_IRLS, sensitivity_weights, betaest, update_Jacobi, saveDict], ) # Run the inversion mrec = inv.run(m0) # Plot the result ax = plt.subplot(1, 2, 1) mesh.plot_slice(inject_global * model, normal="Y", ax=ax, grid=True) ax.set_title("True") ax.set_aspect("equal") ax = plt.subplot(1, 2, 2) mesh.plot_slice(inject_global * mrec, normal="Y", ax=ax, grid=True) ax.set_title("Recovered") ax.set_aspect("equal") plt.show() .. image-sg:: /content/examples/02-gravity/images/sphx_glr_plot_inv_grav_tiled_002.png :alt: True, Recovered :srcset: /content/examples/02-gravity/images/sphx_glr_plot_inv_grav_tiled_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none SimPEG.InvProblem will set Regularization.reference_model to m0. SimPEG.InvProblem will set Regularization.reference_model to m0. SimPEG.InvProblem will set Regularization.reference_model to m0. SimPEG.InvProblem will set Regularization.reference_model to m0. SimPEG.InvProblem is setting bfgsH0 to the inverse of the eval2Deriv. ***Done using the default solver Pardiso and no solver_opts.*** model has any nan: 0 =============================== Projected GNCG =============================== # beta phi_d phi_m f |proj(x-g)-x| LS Comment ----------------------------------------------------------------------------- x0 has any nan: 0 0 2.15e+03 8.48e+04 0.00e+00 8.48e+04 4.80e+01 0 1 1.07e+03 1.03e+04 3.52e+00 1.41e+04 4.77e+01 0 2 5.36e+02 5.76e+03 6.52e+00 9.26e+03 4.76e+01 0 Skip BFGS 3 2.68e+02 2.80e+03 1.04e+01 5.58e+03 4.76e+01 0 Skip BFGS 4 1.34e+02 1.30e+03 1.42e+01 3.21e+03 4.73e+01 0 Skip BFGS 5 6.70e+01 6.74e+02 1.74e+01 1.84e+03 4.69e+01 0 Skip BFGS 6 3.35e+01 4.33e+02 1.99e+01 1.10e+03 4.63e+01 0 Skip BFGS Reached starting chifact with l2-norm regularization: Start IRLS steps... irls_threshold 0.07266071858039272 Reach maximum number of IRLS cycles: 0 ------------------------- STOP! ------------------------- 1 : |fc-fOld| = 0.0000e+00 <= tolF*(1+|f0|) = 8.4842e+03 1 : |xc-x_last| = 3.0084e-02 <= tolX*(1+|x0|) = 1.0048e-01 0 : |proj(x-g)-x| = 4.6325e+01 <= tolG = 1.0000e-01 0 : |proj(x-g)-x| = 4.6325e+01 <= 1e3*eps = 1.0000e-02 0 : maxIter = 100 <= iter = 7 ------------------------- DONE! ------------------------- .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 3.663 seconds) **Estimated memory usage:** 15 MB .. _sphx_glr_download_content_examples_02-gravity_plot_inv_grav_tiled.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_inv_grav_tiled.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_inv_grav_tiled.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_