.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/Datapoints/plot_tempest_datapoint.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_Datapoints_plot_tempest_datapoint.py: Tempest Datapoint Class ----------------------- .. GENERATED FROM PYTHON SOURCE LINES 7-15 Credits: We would like to thank Ross Brodie at Geoscience Australia for his airborne time domain forward modeller https://github.com/GeoscienceAustralia/ga-aem For ground-based time domain data, we are using Dieter Werthmuller's python package Empymod https://empymod.github.io/ Thanks to Dieter for his help getting Empymod ready for incorporation into GeoBIPy .. GENERATED FROM PYTHON SOURCE LINES 17-54 .. code-block:: Python from os.path import join import numpy as np import h5py import matplotlib.pyplot as plt from geobipy import TempestData # from geobipy import TemDataPoint from geobipy import RectilinearMesh1D from geobipy import Model from geobipy import StatArray from geobipy import Distribution from geobipy import get_prng dataFolder = "..//..//supplementary//data//" # dataFolder = "source//examples//supplementary//Data" # Obtaining a tempest datapoint from a dataset # ++++++++++++++++++++++++++++++++++++++++++++ # More often than not, our observed data is stored in a file on disk. # We can read in a dataset and pull datapoints from it. # # For more information about the time domain data set, see :ref:`Time domain dataset` # The data file name dataFile = dataFolder + 'tempest_saline_clay.csv' # The EM system file name systemFile = dataFolder + 'Tempest.stm' # Prepare the dataset so that we can read a point at a time. Dataset = TempestData._initialize_sequential_reading(dataFile, systemFile) # Get a datapoint from the file. tdp = Dataset._read_record(0) plt.figure() tdp.plot() prng = get_prng(seed=146100583096709124601953385843316024947) .. image-sg:: /examples/Datapoints/images/sphx_glr_plot_tempest_datapoint_001.png :alt: Time Domain EM Data :srcset: /examples/Datapoints/images/sphx_glr_plot_tempest_datapoint_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) self.n_components=2, self.nTimes=array([15]) .. GENERATED FROM PYTHON SOURCE LINES 55-57 Using a tempest domain datapoint ++++++++++++++++++++++++++++++++ .. GENERATED FROM PYTHON SOURCE LINES 59-60 We can define a 1D layered earth model, and use it to predict some data .. GENERATED FROM PYTHON SOURCE LINES 60-67 .. code-block:: Python par = StatArray(np.r_[0.01, 0.1, 1.], "Conductivity", "$\frac{S}{m}$") mod = Model(mesh=RectilinearMesh1D(edges=np.r_[0.0, 50.0, 75.0, np.inf]), values=par) par = StatArray(np.logspace(-3, 3, 30), "Conductivity", "$\frac{S}{m}$") e = np.linspace(0, 350, 31); e[-1] = np.inf mod = Model(mesh=RectilinearMesh1D(edges=e), values=par) .. GENERATED FROM PYTHON SOURCE LINES 68-69 Forward model the data .. GENERATED FROM PYTHON SOURCE LINES 69-108 .. code-block:: Python tdp.forward(mod) print('primary', tdp.primary_field) print('sx', tdp.secondary_field[:15]) print('sz', tdp.secondary_field[15:]) # #%% # plt.figure() # plt.subplot(121) # _ = mod.pcolor(transpose=True) # plt.subplot(122) # _ = tdp.plot() # _ = tdp.plot_predicted() # plt.tight_layout() # plt.suptitle('Model and response') # #%% # # plt.figure() # # tdp.plotDataResidual(xscale='log') # # plt.title('data residual') # #%% # # Compute the sensitivity matrix for a given model J = tdp.sensitivity(mod) # plt.figure() # _ = np.abs(J).pcolor(equalize=True, log=10, flipY=True) print('J', J) # print('J shape', J.shape) # print('sx 0', J[:16, 0]) tdp.fm_dlogc(mod) print('new primary', tdp.primary_field) print('sx', tdp.secondary_field[:15]) print('sz', tdp.secondary_field[15:]) print('new J', tdp.sensitivity_matrix) .. rst-class:: sphx-glr-script-out .. code-block:: none primary [34.27253219 17.55503397] sx [4.46362582 2.52720951 2.10544857 1.76862398 1.52893914 1.38117676 1.19246619 1.10920301 0.94437018 0.81202664 0.67054942 0.4124596 0.34346631 0.27359586 0.19875285] sz [6.47100177 4.53101158 3.87594468 3.43396174 3.10487058 2.80230168 2.59759025 2.34406113 2.09040444 1.83288007 1.59137993 1.34037776 1.05345525 0.79969548 0.56994112] J [[ 1.13463137e-01 1.49920887e-01 1.76789170e-01 1.79809001e-01 1.49232157e-01 9.28385121e-02 3.82492975e-02 8.70404368e-03 7.17305034e-04 -2.13238764e-04 -3.69663472e-04 -5.69915094e-04 -8.66319388e-04 -1.29165072e-03 -1.87152454e-03 -2.59562194e-03 -3.36123923e-03 -3.90030818e-03 -3.77459399e-03 -2.64263369e-03 -8.86540172e-04 2.51618719e-04 2.30305587e-04 -6.44400641e-06 -7.48897278e-06 7.03319747e-07 -1.06012557e-08 -1.01809840e-09 1.13341751e-11 7.27489718e-13] [ 2.09383016e-02 3.20412212e-02 4.74815387e-02 6.68394476e-02 8.66127424e-02 9.82359342e-02 9.01124001e-02 5.92842924e-02 2.34205425e-02 4.15453831e-03 -1.09167097e-04 -5.65296487e-04 -8.64759189e-04 -1.28934957e-03 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2.90072503e-03 4.49316096e-03 6.89992517e-03 1.04683047e-02 1.56072826e-02 2.26762962e-02 3.16873527e-02 4.17028524e-02 4.99874496e-02 5.17013957e-02 4.21733381e-02 2.28200440e-02 3.82984440e-03 -6.33720101e-03 -1.00245588e-02 -1.15046567e-02 -1.09214085e-02 -7.50193333e-03 -2.45576522e-03 7.34156901e-04 6.50341911e-04 -1.99157631e-05 -2.13290962e-05 2.03378663e-06 -3.03475874e-08 -2.99444288e-09 3.05612182e-11 2.21589868e-12] [ 6.85874915e-04 1.07682023e-03 1.68386072e-03 2.61987206e-03 4.04914185e-03 6.20161303e-03 9.37821632e-03 1.39243312e-02 2.01215828e-02 2.79102957e-02 3.63473409e-02 4.28853433e-02 4.32376197e-02 3.36297749e-02 1.60073986e-02 -4.06785684e-04 -8.80728389e-03 -1.13318343e-02 -1.09066424e-02 -7.63408387e-03 -2.65456561e-03 6.28266935e-04 6.52593634e-04 -1.03896087e-05 -2.20113234e-05 1.98192000e-06 -2.40851870e-08 -3.30993214e-09 4.26225630e-11 2.14448663e-12] [ 3.97492384e-04 6.25157499e-04 9.79921161e-04 1.52970807e-03 2.37536579e-03 3.66271307e-03 5.59386199e-03 8.42905152e-03 1.24572773e-02 1.78898983e-02 2.45996014e-02 3.16300164e-02 3.65896683e-02 3.56805170e-02 2.59498079e-02 9.86642743e-03 -4.10943284e-03 -1.04067976e-02 -1.08453857e-02 -7.81980250e-03 -2.94955068e-03 4.61942047e-04 6.51481607e-04 4.26410089e-06 -2.28927981e-05 1.88642473e-06 -1.40539393e-08 -3.78496662e-09 6.10881749e-11 2.02231492e-12] [ 2.28080390e-04 3.59214465e-04 5.64123292e-04 8.82901267e-04 1.37590272e-03 2.13229122e-03 3.28010534e-03 4.99495403e-03 7.49889373e-03 1.10291699e-02 1.57351196e-02 2.14354311e-02 2.71796318e-02 3.07485869e-02 2.88194031e-02 1.91824631e-02 4.74579200e-03 -6.62815391e-03 -1.02522566e-02 -8.05421115e-03 -3.38560057e-03 1.94539854e-04 6.38800599e-04 2.69696365e-05 -2.38478094e-05 1.69920478e-06 2.54712999e-09 -4.50079969e-09 8.97509521e-11 1.79896722e-12] [ 1.29157970e-04 2.03638462e-04 3.20279179e-04 5.02283991e-04 7.84929060e-04 1.22110741e-03 1.88855988e-03 2.89810780e-03 4.40002044e-03 6.58049511e-03 9.62949036e-03 1.36425076e-02 1.83983022e-02 2.29735567e-02 2.53448895e-02 2.26700994e-02 1.34473467e-02 9.93070247e-04 -7.36015610e-03 -7.99203352e-03 -3.99599890e-03 -2.35776594e-04 5.92920699e-04 6.10047295e-05 -2.42531710e-05 1.31928881e-06 3.00943322e-08 -5.52361380e-09 1.33382890e-10 1.36385417e-12] [ 7.20880061e-05 1.13758034e-04 1.79138645e-04 2.81407647e-04 4.40747144e-04 6.87743061e-04 1.06807700e-03 1.64853558e-03 2.52359197e-03 3.81977707e-03 5.69034409e-03 8.28314284e-03 1.16486754e-02 1.55401010e-02 1.90830522e-02 2.04784376e-02 1.73880609e-02 9.00684847e-03 -1.02276636e-03 -6.16193045e-03 -4.55276841e-03 -9.05861401e-04 4.62099921e-04 1.06772207e-04 -2.22070456e-05 5.69979180e-07 7.14251079e-08 -6.62044639e-09 1.91310127e-10 4.83737910e-13] [ 3.95655826e-05 6.25753935e-05 9.87713313e-05 1.55544424e-04 2.44279987e-04 3.82372569e-04 5.96103961e-04 9.24568516e-04 1.42459850e-03 2.17591241e-03 3.28383735e-03 4.87272362e-03 7.05478183e-03 9.84575428e-03 1.29883829e-02 1.56762996e-02 1.63521364e-02 1.31874963e-02 6.03082080e-03 -1.38179333e-03 -3.86761777e-03 -1.71060819e-03 1.49403391e-04 1.48327671e-04 -1.36249992e-05 -6.68291558e-07 1.10857913e-07 -6.33418159e-09 2.26727066e-10 -1.05451995e-12] [ 1.60007270e-05 3.08385747e-05 5.05626410e-05 8.02783444e-05 1.26736452e-04 1.99365944e-04 3.12397549e-04 4.87311178e-04 7.55978090e-04 1.16456467e-03 1.77748717e-03 2.67915445e-03 3.96768519e-03 5.72788161e-03 7.96032467e-03 1.04376098e-02 1.24913986e-02 1.28874625e-02 1.02847605e-02 4.83824498e-03 -3.09434558e-04 -1.64870226e-03 -4.15885174e-04 1.11378943e-04 7.62988405e-06 -1.95004388e-06 8.68582964e-08 -1.28316523e-09 1.11041966e-10 -2.41585978e-12]] .. GENERATED FROM PYTHON SOURCE LINES 109-111 Attaching statistical descriptors to the tempest datapoint ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ .. GENERATED FROM PYTHON SOURCE LINES 111-125 .. code-block:: Python from numpy.random import Generator from numpy.random import PCG64DXSM generator = PCG64DXSM(seed=0) prng = Generator(generator) # Set relative errors for the primary fields, and secondary fields. tdp.relative_error = np.r_[0.001, 0.001] # Set the additive errors for tdp.additive_error = np.hstack([[0.011474, 0.012810, 0.008507, 0.005154, 0.004742, 0.004477, 0.004168, 0.003539, 0.003352, 0.003213, 0.003161, 0.003122, 0.002587, 0.002038, 0.002201], [0.007383, 0.005693, 0.005178, 0.003659, 0.003426, 0.003046, 0.003095, 0.003247, 0.002775, 0.002627, 0.002460, 0.002178, 0.001754, 0.001405, 0.001283]]) # Define a multivariate log normal distribution as the prior on the predicted data. tdp.predictedData.prior = Distribution('MvLogNormal', tdp.data[tdp.active], tdp.std[tdp.active]**2.0, prng=prng) .. GENERATED FROM PYTHON SOURCE LINES 126-127 This allows us to evaluate the likelihood of the predicted data .. GENERATED FROM PYTHON SOURCE LINES 127-131 .. code-block:: Python print(tdp.likelihood(log=True)) # Or the misfit print(tdp.data_misfit()) .. rst-class:: sphx-glr-script-out .. code-block:: none -36389.6500813217 72940.71365767403 .. GENERATED FROM PYTHON SOURCE LINES 132-133 Plot the misfits for a range of half space conductivities .. GENERATED FROM PYTHON SOURCE LINES 133-138 .. code-block:: Python plt.figure() plt.subplot(1, 2, 1) _ = tdp.plot_halfspace_responses(-6.0, 4.0, 200) plt.title("Halfspace responses") .. image-sg:: /examples/Datapoints/images/sphx_glr_plot_tempest_datapoint_002.png :alt: Halfspace responses :srcset: /examples/Datapoints/images/sphx_glr_plot_tempest_datapoint_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(0.5, 1.0, 'Halfspace responses') .. GENERATED FROM PYTHON SOURCE LINES 139-140 We can perform a quick search for the best fitting half space .. GENERATED FROM PYTHON SOURCE LINES 140-161 .. code-block:: Python halfspace = tdp.find_best_halfspace() print('Best half space conductivity is {} $S/m$'.format(halfspace.values)) plt.subplot(1, 2, 2) _ = tdp.plot() _ = tdp.plot_predicted() plt.figure() tdp.plot_secondary_field() tdp.plot_predicted_secondary_field() # #%% # # We can attach priors to the height of the datapoint, # # the relative error multiplier, and the additive error noise floor # Define the distributions used as priors. relative_prior = Distribution('Uniform', min=np.r_[0.01, 0.01], max=np.r_[0.5, 0.5], prng=prng) receiver_x_prior = Distribution('Uniform', min=np.float64(tdp.receiver.x) - 1.0, max=np.float64(tdp.receiver.x) + 1.0, prng=prng) receiver_z_prior = Distribution('Uniform', min=np.float64(tdp.receiver.z) - 1.0, max=np.float64(tdp.receiver.z) + 1.0, prng=prng) receiver_pitch_prior = Distribution('Uniform', min=tdp.receiver.pitch - 5.0, max=tdp.receiver.pitch + 5.0, prng=prng) tdp.set_priors(relative_error_prior=relative_prior, receiver_x_prior=receiver_x_prior, receiver_z_prior=receiver_z_prior, receiver_pitch_prior=receiver_pitch_prior, prng=prng) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /examples/Datapoints/images/sphx_glr_plot_tempest_datapoint_003.png :alt: Time Domain EM Data :srcset: /examples/Datapoints/images/sphx_glr_plot_tempest_datapoint_003.png :class: sphx-glr-multi-img * .. image-sg:: /examples/Datapoints/images/sphx_glr_plot_tempest_datapoint_004.png :alt: plot tempest datapoint :srcset: /examples/Datapoints/images/sphx_glr_plot_tempest_datapoint_004.png :class: sphx-glr-multi-img .. rst-class:: sphx-glr-script-out .. code-block:: none Best half space conductivity is [0.01830738] $S/m$ /Users/nfoks/codes/repositories/geobipy/documentation_source/source/examples/Datapoints/plot_tempest_datapoint.py:156: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.) receiver_x_prior = Distribution('Uniform', min=np.float64(tdp.receiver.x) - 1.0, max=np.float64(tdp.receiver.x) + 1.0, prng=prng) /Users/nfoks/codes/repositories/geobipy/documentation_source/source/examples/Datapoints/plot_tempest_datapoint.py:157: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.) receiver_z_prior = Distribution('Uniform', min=np.float64(tdp.receiver.z) - 1.0, max=np.float64(tdp.receiver.z) + 1.0, prng=prng) .. GENERATED FROM PYTHON SOURCE LINES 162-163 In order to perturb our solvable parameters, we need to attach proposal distributions .. GENERATED FROM PYTHON SOURCE LINES 163-173 .. code-block:: Python relative_proposal = Distribution('MvNormal', mean=tdp.relative_error, variance=2.5e-4, prng=prng) receiver_x_proposal = Distribution('Normal', mean=tdp.receiver.x, variance = 0.01, prng=prng) receiver_z_proposal = Distribution('Normal', mean=tdp.receiver.z, variance = 0.01, prng=prng) receiver_pitch_proposal = Distribution('Normal', mean=tdp.receiver.pitch, variance = 0.01, prng=prng) tdp.set_proposals(relative_error_proposal=relative_proposal, receiver_x_proposal=receiver_x_proposal, receiver_z_proposal=receiver_z_proposal, receiver_pitch_proposal=receiver_pitch_proposal, solve_additive_error=True, additive_error_proposal_variance=1e-4, prng=prng) .. GENERATED FROM PYTHON SOURCE LINES 174-175 With priors set we can auto generate the posteriors .. GENERATED FROM PYTHON SOURCE LINES 175-177 .. code-block:: Python tdp.set_posteriors() .. GENERATED FROM PYTHON SOURCE LINES 178-180 Perturb the datapoint and record the perturbations Note we are not using the priors to accept or reject perturbations. .. GENERATED FROM PYTHON SOURCE LINES 180-184 .. code-block:: Python for i in range(10): tdp.perturb() tdp.update_posteriors() plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.659 seconds) .. _sphx_glr_download_examples_Datapoints_plot_tempest_datapoint.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_tempest_datapoint.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_tempest_datapoint.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_tempest_datapoint.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_