.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/generated/scripts_synth_data/single_survey_line_vertical_only.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_examples_generated_scripts_synth_data_single_survey_line_vertical_only.py: Inverting the vertical component of a single survey line for a thin plate ========================================================================= .. raw:: html .. GENERATED FROM PYTHON SOURCE LINES 13-18 |Open In Colab| .. |Open In Colab| image:: https://img.shields.io/badge/open%20in-Colab-b5e2fa?logo=googlecolab&style=flat-square&color=ffd670 :target: https://colab.research.google.com/github/inlab-geo/cofi-examples/blob/main/examples/airborne_em/airborne_em_single_line_transmitters_vertical_only.ipynb .. GENERATED FROM PYTHON SOURCE LINES 21-40 .. raw:: html .. raw:: html .. If you are running this notebook locally, make sure you’ve followed `steps here `__ to set up the environment. (This `environment.yml `__ file specifies a list of packages required to run the notebooks) .. GENERATED FROM PYTHON SOURCE LINES 40-52 .. code-block:: Python # -------------------------------------------------------- # # # # Uncomment below to set up environment on "colab" # # # # -------------------------------------------------------- # # !pip install -U cofi # !pip install git+https://github.com/JuergHauser/PyP223.git # !git clone https://github.com/inlab-geo/cofi-examples.git # %cd cofi-examples/examples/vtem_max .. GENERATED FROM PYTHON SOURCE LINES 54-59 .. code-block:: Python # If this notebook is run locally PyP223 needs to be installed separately by uncommenting the following line, # that is by removing the # and the white space between it and the exclamation mark. # !pip install git+https://github.com/JuergHauser/PyP223.git .. GENERATED FROM PYTHON SOURCE LINES 61-82 .. code-block:: Python import numpy import matplotlib.pyplot as plt from matplotlib.lines import Line2D import cofi from vtem_max_forward_lib import ( problem_setup, system_spec, survey_setup, true_model, ForwardWrapper, plot_transient, plot_predicted_profile, plot_observed_profile, plot_plate_faces, plot_plate_faces_single ) numpy.random.seed(42) .. GENERATED FROM PYTHON SOURCE LINES 87-98 Background ---------- This example inverts a single survey line of VTEM max data using the vertical component for a thin plate target. The dip azimuth of the plate is in the direction of the survey line and we only seek to recover the plate dip, the plate width and the location of the plate along the survey line. The forward problem and model setup is described `here <./thin_plate_inversion.ipynb>`__ and an example using the inline and vertical component is given `here <./single_survey_line.ipynb>`__. .. GENERATED FROM PYTHON SOURCE LINES 101-104 Problem definition ------------------ .. GENERATED FROM PYTHON SOURCE LINES 104-125 .. code-block:: Python tx_min = 115 tx_max = 281 tx_interval = 15 n_transmitters = (tx_max - tx_min - 1) // tx_interval + 1 tx = numpy.arange(tx_min, tx_max, tx_interval) transmitters_setup = { "tx": tx, # transmitter easting/x-position "ty": numpy.array([100]*n_transmitters), # transmitter northing/y-position "tz": numpy.array([50]*n_transmitters), # transmitter height/z-position "tazi": numpy.deg2rad(numpy.array([90]*n_transmitters)), # transmitter azimuth "tincl": numpy.deg2rad(numpy.array([6]*n_transmitters)), # transmitter inclination "rx": tx, # receiver easting/x-position "ry": numpy.array([100]*n_transmitters), # receiver northing/y-position "rz": numpy.array([50]*n_transmitters), # receiver height/z-position "trdx": numpy.array([0]*n_transmitters), # transmitter receiver separation inline "trdy": numpy.array([0]*n_transmitters), # transmitter receiver separation crossline "trdz": numpy.array([0]*n_transmitters), # transmitter receiver separation vertical } .. GENERATED FROM PYTHON SOURCE LINES 127-131 .. code-block:: Python forward = ForwardWrapper(true_model, problem_setup, system_spec, survey_setup, ["pdip", "peast", "ptop", "pwdth2"], data_returned=["vertical"]) .. rst-class:: sphx-glr-script-out .. code-block:: none ['pdip', 'peast', 'ptop', 'pwdth2'] .. GENERATED FROM PYTHON SOURCE LINES 133-137 .. code-block:: Python # check the order of parameters in a model vector forward.params_to_invert .. rst-class:: sphx-glr-script-out .. code-block:: none ['pdip', 'peast', 'ptop', 'pwdth2'] .. GENERATED FROM PYTHON SOURCE LINES 139-142 .. code-block:: Python true_param_value = numpy.array([60, 175, 30, 90]) .. GENERATED FROM PYTHON SOURCE LINES 147-150 True model ~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 150-168 .. code-block:: Python _, axes = plt.subplots(2, 2) axes[1,1].axis("off") plot_plate_faces( "plate_true", forward, true_param_value, axes[0,0], axes[0,1], axes[1,0], color="purple", label="True model" ) plt.tight_layout() point = Line2D([0], [0], label='Fiducial', marker='o', markersize=5, markeredgecolor='orange', markerfacecolor='orange', linestyle='') handles, labels = axes[1,0].get_legend_handles_labels() handles.extend([point]) axes[1,0].legend(handles=handles,bbox_to_anchor=(1.04, 0), loc="lower left") .. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_single_survey_line_vertical_only_001.png :alt: single survey line vertical only :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_single_survey_line_vertical_only_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 173-176 Generate synthetic data ~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 176-188 .. code-block:: Python # The data absolute_noise= 0.05 # create data and ad a realisation of the noise data_pred_true = forward(true_param_value) data_obs = data_pred_true + numpy.random.randn(len(data_pred_true))*absolute_noise # define data covariance matrix sigma=absolute_noise Cdinv=numpy.identity(len(data_obs))*(1.0/(sigma*sigma)) .. GENERATED FROM PYTHON SOURCE LINES 193-196 Parameter estimation -------------------- .. GENERATED FROM PYTHON SOURCE LINES 199-201 **Initialise a model for inversion** .. GENERATED FROM PYTHON SOURCE LINES 201-204 .. code-block:: Python init_param_value = numpy.array([50, 155, 35, 70]) .. GENERATED FROM PYTHON SOURCE LINES 209-211 **Define helper functions for CoFI** .. GENERATED FROM PYTHON SOURCE LINES 211-238 .. code-block:: Python def my_objective(model): dpred = forward(model) residual = dpred - data_obs return residual.T @ Cdinv @ residual def my_gradient(model): dpred = forward(model) jacobian = forward.jacobian(model, relative_step=0.1) residual = dpred - data_obs return jacobian.T @ Cdinv @ residual def my_hessian(model): jacobian = forward.jacobian(model) return jacobian.T @ Cdinv @ jacobian class PerIterationCallbackFunction: def __init__(self): self.x = None self.i = 0 def __call__(self, xk): print(f"Iteration #{self.i+1}") print(f" objective value: {my_problem.objective(xk)}") self.x = xk self.i += 1 .. GENERATED FROM PYTHON SOURCE LINES 243-245 **Define CoFI problem** .. GENERATED FROM PYTHON SOURCE LINES 245-252 .. code-block:: Python my_problem = cofi.BaseProblem() my_problem.set_objective(my_objective) my_problem.set_gradient(my_gradient) my_problem.set_hessian(my_hessian) my_problem.set_initial_model(init_param_value) .. GENERATED FROM PYTHON SOURCE LINES 257-259 **Define CoFI options** .. GENERATED FROM PYTHON SOURCE LINES 259-264 .. code-block:: Python my_options = cofi.InversionOptions() my_options.set_tool("scipy.optimize.minimize") my_options.set_params(method="Newton-CG",callback=PerIterationCallbackFunction()) .. GENERATED FROM PYTHON SOURCE LINES 269-271 **Run CoFI inversion** .. GENERATED FROM PYTHON SOURCE LINES 271-276 .. code-block:: Python my_inversion = cofi.Inversion(my_problem, my_options) my_result = my_inversion.run() print(my_result.model) .. rst-class:: sphx-glr-script-out .. code-block:: none Iteration #1 objective value: 542.0498961214748 Iteration #2 objective value: 507.0772320800675 Iteration #3 objective value: 504.0979188743853 Iteration #4 objective value: 503.20231017077174 Iteration #5 objective value: 502.54868940941464 [ 62.45323542 172.06155342 27.54374975 88.66921388] .. GENERATED FROM PYTHON SOURCE LINES 281-284 Plotting -------- .. GENERATED FROM PYTHON SOURCE LINES 287-290 Data ~~~~ .. GENERATED FROM PYTHON SOURCE LINES 290-302 .. code-block:: Python idx_to_plot = numpy.arange(8, 20) # subset of numpy.arange(0, 44) _, (ax1) = plt.subplots(1, 1, figsize=(12,4)) plot_predicted_profile(true_param_value, forward, "Data from true model", gate_idx=idx_to_plot, ax=ax1, cmp='vertical', color="purple") plot_predicted_profile(init_param_value, forward, "Data from starting model", gate_idx=idx_to_plot, ax=ax1,cmp='vertical', color="green", linestyle=":") plot_predicted_profile(my_result.model, forward, "Data from MAP model", gate_idx=idx_to_plot, ax=ax1, cmp='vertical',color="red", linestyle="-.") ax1.legend(bbox_to_anchor=(1.04, 0), loc="lower left") plt.tight_layout() .. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_single_survey_line_vertical_only_002.png :alt: single survey line vertical only :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_single_survey_line_vertical_only_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 307-310 Model ~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 310-334 .. code-block:: Python _, axes = plt.subplots(2, 2) axes[1,1].axis("off") plot_plate_faces( "plate_true", forward, true_param_value, axes[0,0], axes[0,1], axes[1,0], color="purple", label="True model" ) plot_plate_faces( "plate_init", forward, init_param_value, axes[0,0], axes[0,1], axes[1,0], color="green", label="Starting model" ) plot_plate_faces( "plate_inverted", forward, my_result.model, axes[0,0], axes[0,1], axes[1,0], color="red", label="MAP solution", linestyle="dotted" ) plt.tight_layout() point = Line2D([0], [0], label='Fiducial', marker='o', markersize=5, markeredgecolor='orange', markerfacecolor='orange', linestyle='') handles, labels = axes[1,0].get_legend_handles_labels() handles.extend([point]) axes[1,0].legend(handles=handles,bbox_to_anchor=(1.04, 0), loc="lower left") .. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_single_survey_line_vertical_only_003.png :alt: single survey line vertical only :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_single_survey_line_vertical_only_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 336-343 .. code-block:: Python _, ax = plt.subplots(1, 1) plot_plate_faces_single("plate_true", "xz", forward, true_param_value, ax, color="purple", label="True model") plot_plate_faces_single("plate_init", "xz", forward, init_param_value, ax, color="green", label="Starting model") plot_plate_faces_single("plate_inverted", "xz", forward, my_result.model, ax, color="red", label="MAP solution", linestyle="dotted") ax.legend(); .. image-sg:: /examples/generated/scripts_synth_data/images/sphx_glr_single_survey_line_vertical_only_004.png :alt: single survey line vertical only :srcset: /examples/generated/scripts_synth_data/images/sphx_glr_single_survey_line_vertical_only_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. GENERATED FROM PYTHON SOURCE LINES 348-361 -------------- Watermark ========= .. raw:: html .. raw:: html .. GENERATED FROM PYTHON SOURCE LINES 361-367 .. code-block:: Python watermark_list = ["cofi", "numpy", "scipy", "matplotlib"] for pkg in watermark_list: pkg_var = __import__(pkg) print(pkg, getattr(pkg_var, "__version__")) .. rst-class:: sphx-glr-script-out .. code-block:: none cofi 0.2.11 numpy 2.3.5 scipy 1.17.0 matplotlib 3.10.8 .. GENERATED FROM PYTHON SOURCE LINES 368-368 sphinx_gallery_thumbnail_number = -1 .. rst-class:: sphx-glr-timing **Total running time of the script:** (1 minutes 9.065 seconds) .. _sphx_glr_download_examples_generated_scripts_synth_data_single_survey_line_vertical_only.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: single_survey_line_vertical_only.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: single_survey_line_vertical_only.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: single_survey_line_vertical_only.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_