DC Forward Simulation

Forward model two conductive spheres in a half-space and plot a pseudo-section. Assumes an infinite line source and measures along the center of the spheres.

INPUT: loc = Location of spheres [[x1, y1, z1], [x2, y2, z2]] radi = Radius of spheres [r1, r2] param = Conductivity of background and two spheres [m0, m1, m2] survey_type = survey type ‘pole-dipole’ or ‘dipole-dipole’ unitType = Data type “appResistivity” | “appConductivity” | “volt” Created by @fourndo

../../../_images/sphx_glr_plot_pseudo_section_001.png

Out:

Transmitter 0 of 9 -> Time:0.5852711200714111 sec

Transmitter 1 of 9 -> Time:0.5750536918640137 sec

Transmitter 2 of 9 -> Time:0.6389031410217285 sec

Transmitter 3 of 9 -> Time:0.5658323764801025 sec

Transmitter 4 of 9 -> Time:0.5030038356781006 sec

Transmitter 5 of 9 -> Time:0.47039198875427246 sec

Transmitter 6 of 9 -> Time:0.5218780040740967 sec

Transmitter 7 of 9 -> Time:0.5251367092132568 sec

Transmitter 8 of 9 -> Time:0.5094878673553467 sec
Transmitter 8 of 9
Forward completed
/Users/lindseyjh/git/python_symlinks/SimPEG/EM/Static/Utils/StaticUtils.py:420: MatplotlibDeprecationWarning:
The get_clim function was deprecated in Matplotlib 3.1 and will be removed in 3.3. Use ScalarMappable.get_clim instead.
  cmin, cmax = cbar.get_clim()
/Users/lindseyjh/git/simpeg/simpeg/examples/06-dc/plot_pseudo_section.py:255: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
  plt.show()

import time
import numpy as np
import scipy.sparse as sp
import matplotlib.pyplot as plt

from SimPEG import Mesh, Utils
from SimPEG.EM.Static.Utils import gen_DCIPsurvey
from SimPEG.EM.Static.Utils import convertObs_DC3D_to_2D
from SimPEG.EM.Static.Utils import plot_pseudoSection


def run(loc=None, sig=None, radi=None, param=None, survey_type='dipole-dipole',
        unitType='appConductivity', plotIt=True):

    assert survey_type in [
        'pole-dipole', 'dipole-dipole', 'pole-dipole', 'pole-pole'
        ], (
            """survey_type must be 'dipole-dipole' | 'pole-dipole' |
            'dipole-pole' | 'pole-pole'"""
            " not {}".format(survey_type)
    )

    assert unitType in ['appResistivity', 'appConductivity', 'volt'], (
        "Unit type (unitType) must be appResistivity or "
        "appConductivity or volt (potential)"
    )

    if loc is None:
        loc = np.c_[[-50., 0., -50.], [50., 0., -50.]]
    if sig is None:
        sig = np.r_[1e-2, 1e-1, 1e-3]
    if radi is None:
        radi = np.r_[25., 25.]
    if param is None:
        param = np.r_[30., 30., 5]

    dx = 5.

    hxind = [(dx, 15, -1.3), (dx, 75), (dx, 15, 1.3)]
    hyind = [(dx, 15, -1.3), (dx, 10), (dx, 15, 1.3)]
    hzind = [(dx, 15, -1.3), (dx, 15)]

    mesh = Mesh.TensorMesh([hxind, hyind, hzind], 'CCN')

    # Set background conductivity
    model = np.ones(mesh.nC) * sig[0]

    # First anomaly
    ind = Utils.ModelBuilder.getIndicesSphere(loc[:, 0], radi[0], mesh.gridCC)
    model[ind] = sig[1]

    # Second anomaly
    ind = Utils.ModelBuilder.getIndicesSphere(loc[:, 1], radi[1], mesh.gridCC)
    model[ind] = sig[2]

    # Get index of the center
    indy = int(mesh.nCy/2)

    # Plot the model for reference
    # Define core mesh extent
    xlim = 200
    zlim = 100

    # Then specify the end points of the survey. Let's keep it simple for now
    # and survey above the anomalies, top of the mesh
    ends = [(-175, 0), (175, 0)]
    ends = np.c_[np.asarray(ends), np.ones(2).T*mesh.vectorNz[-1]]

    # Snap the endpoints to the grid. Easier to create 2D section.
    indx = Utils.closestPoints(mesh, ends)
    locs = np.c_[
        mesh.gridCC[indx, 0],
        mesh.gridCC[indx, 1],
        np.ones(2).T*mesh.vectorNz[-1]
    ]

    # We will handle the geometry of the survey for you and create all the
    # combination of tx-rx along line
    survey = gen_DCIPsurvey(
        locs, dim=mesh.dim, survey_type=survey_type,
        a=param[0], b=param[1], n=param[2]
    )
    Tx = survey.srcList
    Rx = [src.rxList[0] for src in Tx]
    # Define some global geometry
    dl_len = np.sqrt(np.sum((locs[0, :] - locs[1, :])**2))
    dl_x = (Tx[-1].loc[0][1] - Tx[0].loc[0][0]) / dl_len
    dl_y = (Tx[-1].loc[1][1] - Tx[0].loc[1][0]) / dl_len

    # Set boundary conditions
    mesh.setCellGradBC('neumann')

    # Define the linear system needed for the DC problem. We assume an infitite
    # line source for simplicity.
    Div = mesh.faceDiv
    Grad = mesh.cellGrad
    Msig = Utils.sdiag(1./(mesh.aveF2CC.T*(1./model)))

    A = Div*Msig*Grad

    # Change one corner to deal with nullspace
    A[0, 0] = 1
    A = sp.csc_matrix(A)

    # We will solve the system iteratively, so a pre-conditioner is helpful
    # This is simply a Jacobi preconditioner (inverse of the main diagonal)
    dA = A.diagonal()
    P = sp.spdiags(1/dA, 0, A.shape[0], A.shape[0])

    # Now we can solve the system for all the transmitters
    # We want to store the data
    data = []

    # There is probably a more elegant way to do this,
    # but we can just for-loop through the transmitters
    for ii in range(len(Tx)):

        start_time = time.time()  # Let's time the calculations

        # print("Transmitter %i / %i\r" % (ii+1, len(Tx)))

        # Select dipole locations for receiver
        rxloc_M = np.asarray(Rx[ii].locs[0])
        rxloc_N = np.asarray(Rx[ii].locs[1])

        # For usual cases 'dipole-dipole' or "gradient"
        if survey_type == 'pole-dipole':
            # Create an "inifinity" pole
            tx = np.squeeze(Tx[ii].loc[:, 0:1])
            tinf = tx + np.array([dl_x, dl_y, 0])*dl_len*2
            inds = Utils.closestPoints(mesh, np.c_[tx, tinf].T)
            RHS = (
                mesh.getInterpolationMat(np.asarray(Tx[ii]).T, 'CC').T *
                ([-1] / mesh.vol[inds])
            )
        else:
            inds = Utils.closestPoints(mesh, np.asarray(Tx[ii].loc))
            RHS = (
                mesh.getInterpolationMat(np.asarray(Tx[ii].loc), 'CC').T *
                ([-1, 1] / mesh.vol[inds])
            )

        # Iterative Solve
        Ainvb = sp.linalg.bicgstab(P*A, P*RHS, tol=1e-5)

        # We now have the potential everywhere
        phi = Utils.mkvc(Ainvb[0])

        # Solve for phi on pole locations
        P1 = mesh.getInterpolationMat(rxloc_M, 'CC')
        P2 = mesh.getInterpolationMat(rxloc_N, 'CC')

        # Compute the potential difference
        dtemp = (P1*phi - P2*phi)*np.pi

        data.append(dtemp)
        print('\rTransmitter {0} of {1} -> Time:{2} sec'.format(
            ii, len(Tx), time.time() - start_time)
        )

    print('Transmitter {0} of {1}'.format(ii, len(Tx)))
    print('Forward completed')

    # Let's just convert the 3D format into 2D (distance along line) and plot
    survey2D = convertObs_DC3D_to_2D(survey, np.ones(survey.nSrc), 'Xloc')
    survey2D.dobs = np.hstack(data)

    if not plotIt:
        return

    fig = plt.figure(figsize=(7, 7))
    ax = plt.subplot(2, 1, 1, aspect='equal')
    # Plot the location of the spheres for reference
    circle1 = plt.Circle(
        (loc[0, 0], loc[2, 0]), radi[0], color='w', fill=False, lw=3
    )
    circle2 = plt.Circle(
        (loc[0, 1], loc[2, 1]), radi[1], color='k', fill=False, lw=3
    )
    ax.add_artist(circle1)
    ax.add_artist(circle2)

    dat = mesh.plotSlice(
        np.log10(model), ax=ax, normal='Y',
        ind=indy, grid=True, clim=np.log10([sig.min(), sig.max()])
    )

    ax.set_title('3-D model')
    plt.gca().set_aspect('equal', adjustable='box')
    plt.scatter(Tx[0].loc[0][0], Tx[0].loc[0][2], s=40, c='g', marker='v')
    plt.scatter(Rx[0].locs[0][:, 0], Rx[0].locs[0][:, 1], s=40, c='y')
    plt.xlim([-xlim, xlim])
    plt.ylim([-zlim, mesh.vectorNz[-1]+dx])

    pos = ax.get_position()
    ax.set_position([pos.x0, pos.y0 + 0.025, pos.width, pos.height])
    pos = ax.get_position()
    # the parameters are the specified position you set
    cbarax = fig.add_axes(
        [pos.x0, pos.y0 + 0.025,  pos.width, pos.height * 0.04]
    )
    cb = fig.colorbar(
        dat[0],
        cax=cbarax,
        orientation="horizontal",
        ax=ax,
        ticks=np.linspace(np.log10(sig.min()), np.log10(sig.max()), 3),
        format="$10^{%.1f}$"
    )
    cb.set_label("Conductivity (S/m)", size=12)
    cb.ax.tick_params(labelsize=12)

    # Second plot for the predicted apparent resistivity data
    ax2 = plt.subplot(2, 1, 2, aspect='equal')

    # Plot the location of the spheres for reference
    circle1 = plt.Circle(
        (loc[0, 0], loc[2, 0]), radi[0], color='w', fill=False, lw=3
    )
    circle2 = plt.Circle(
        (loc[0, 1], loc[2, 1]), radi[1], color='k', fill=False, lw=3
    )
    ax2.add_artist(circle1)
    ax2.add_artist(circle2)

    # Add the pseudo section
    dat = plot_pseudoSection(
        survey2D, ax2, survey_type=survey_type, data_type=unitType
    )
    ax2.set_title('Apparent Conductivity data')

    plt.ylim([-zlim, mesh.vectorNz[-1]+dx])

    return fig, ax

if __name__ == '__main__':
    run()
    plt.show()

Total running time of the script: ( 0 minutes 5.557 seconds)

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