MT: 3D: Forward

Forward model 3D MT data.

Test script to use SimPEG.NSEM platform to forward model impedance and tipper synthetic data.

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Out:

/Users/josephcapriotti/codes/simpeg/examples/07-nsem/plot_fwd_nsem_MTTipper3D.py:125: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
  plt.show()

import discretize
from SimPEG.electromagnetics import natural_source as NSEM
from SimPEG import utils
import numpy as np
import matplotlib.pyplot as plt

try:
    from pymatsolver import Pardiso as Solver
except:
    from SimPEG import Solver


def run(plotIt=True):
    """
        MT: 3D: Forward
        ===============

        Forward model 3D MT data.

    """

    # Make a mesh
    M = discretize.TensorMesh(
        [
            [(100, 9, -1.5), (100.0, 13), (100, 9, 1.5)],
            [(100, 9, -1.5), (100.0, 13), (100, 9, 1.5)],
            [(50, 10, -1.6), (50.0, 10), (50, 6, 2)],
        ],
        x0=["C", "C", -14926.8217],
    )
    # Setup the model
    conds = [1, 1e-2]
    sig = utils.model_builder.defineBlock(
        M.gridCC, [-100, -100, -350], [100, 100, -150], conds
    )
    sig[M.gridCC[:, 2] > 0] = 1e-8
    sig[M.gridCC[:, 2] < -1000] = 1e-1
    sigBG = np.zeros(M.nC) + conds[1]
    sigBG[M.gridCC[:, 2] > 0] = 1e-8
    if plotIt:
        collect_obj, line_obj = M.plotSlice(np.log10(sig), grid=True, normal="X")
        color_bar = plt.colorbar(collect_obj)

    # Setup the the survey object
    # Receiver locations
    rx_x, rx_y = np.meshgrid(np.arange(-600, 601, 100), np.arange(-600, 601, 100))
    rx_loc = np.hstack(
        (utils.mkvc(rx_x, 2), utils.mkvc(rx_y, 2), np.zeros((np.prod(rx_x.shape), 1)))
    )

    # Make a receiver list
    rxList = []
    for rx_orientation in ["xx", "xy", "yx", "yy"]:
        rxList.append(NSEM.Rx.Point3DImpedance(rx_loc, rx_orientation, "real"))
        rxList.append(NSEM.Rx.Point3DImpedance(rx_loc, rx_orientation, "imag"))
    for rx_orientation in ["zx", "zy"]:
        rxList.append(NSEM.Rx.Point3DTipper(rx_loc, rx_orientation, "real"))
        rxList.append(NSEM.Rx.Point3DTipper(rx_loc, rx_orientation, "imag"))

    # Source list
    srcList = [
        NSEM.Src.Planewave_xy_1Dprimary(rxList, freq) for freq in np.logspace(4, -2, 13)
    ]
    # Survey MT
    survey = NSEM.Survey(srcList)

    # Setup the problem object
    problem = NSEM.Simulation3DPrimarySecondary(
        M, survey=survey, solver=Solver, sigma=sig, sigmaPrimary=sigBG
    )

    # Calculate the data
    # data = problem.make_synthetic_data(relative_error=0.1, add_noise=True)
    data = NSEM.Data(survey=survey, dobs=problem.dpred())
    # Add standard deviation to the data - 10% relative error and 0 floor
    data.relative_error = 0.1
    data.noise_floor = 0.0

    # Add plots
    if plotIt:
        # Plot the data
        # On and off diagonal (on left and right axis, respectively)
        fig, axes = plt.subplots(2, 1, figsize=(7, 5))
        plt.subplots_adjust(right=0.8)
        [(ax.invert_xaxis(), ax.set_xscale("log")) for ax in axes]
        ax_r, ax_p = axes
        ax_r.set_yscale("log")
        ax_r.set_ylabel("Apparent resistivity [xy-yx]")
        ax_r_on = ax_r.twinx()
        ax_r_on.set_yscale("log")
        ax_r_on.set_ylabel("Apparent resistivity [xx-yy]")
        ax_p.set_ylabel("Apparent phase")
        ax_p.set_xlabel("Frequency [Hz]")
        # Start plotting
        ax_r = data.plot_app_res(
            np.array([-200, 0]), components=["xy", "yx"], ax=ax_r, errorbars=True
        )
        ax_r_on = data.plot_app_res(
            np.array([-200, 0]), components=["xx", "yy"], ax=ax_r_on, errorbars=True
        )
        ax_p = data.plot_app_phs(
            np.array([-200, 0]),
            components=["xx", "xy", "yx", "yy"],
            ax=ax_p,
            errorbars=True,
        )
        ax_p.legend(bbox_to_anchor=(1.05, 1), loc=2)


if __name__ == "__main__":

    do_plots = True
    run(do_plots)
    if do_plots:
        plt.show()