DC Analytic Dipole

Comparison of the analytic and numerical solution for a direct current resistivity dipole in 3D.

/home/vsts/work/1/s/simpeg/simulation.py:197: DefaultSolverWarning:

Using the default solver: Pardiso.

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/usr/share/miniconda/envs/simpeg-test/lib/python3.10/site-packages/pymatsolver/solvers.py:415: FutureWarning:

In Future pymatsolver v0.4.0, passing a vector of shape (n, 1) to the solve method will return an array with shape (n, 1), instead of always returning a flattened array. This is to be consistent with numpy.linalg.solve broadcasting.

0.06464333484677041

import discretize
from simpeg import utils
import numpy as np
import matplotlib.pyplot as plt
from simpeg.electromagnetics.static import resistivity as DC


cs = 25.0
hx = [(cs, 7, -1.3), (cs, 21), (cs, 7, 1.3)]
hy = [(cs, 7, -1.3), (cs, 21), (cs, 7, 1.3)]
hz = [(cs, 7, -1.3), (cs, 20)]
mesh = discretize.TensorMesh([hx, hy, hz], "CCN")
sighalf = 1e-2
sigma = np.ones(mesh.nC) * sighalf
xtemp = np.linspace(-150, 150, 21)
ytemp = np.linspace(-150, 150, 21)
xyz_rxP = utils.ndgrid(xtemp - 10.0, ytemp, np.r_[0.0])
xyz_rxN = utils.ndgrid(xtemp + 10.0, ytemp, np.r_[0.0])
xyz_rxM = utils.ndgrid(xtemp, ytemp, np.r_[0.0])


rx = DC.Rx.Dipole(xyz_rxP, xyz_rxN)
src = DC.Src.Dipole([rx], np.r_[-200, 0, -12.5], np.r_[+200, 0, -12.5])
survey = DC.Survey([src])
sim = DC.Simulation3DCellCentered(mesh, survey=survey, sigma=sigma, bc_type="Neumann")

data = sim.dpred()


def DChalf(srclocP, srclocN, rxloc, sigma, I=1.0):
    rp = (srclocP.reshape([1, -1])).repeat(rxloc.shape[0], axis=0)
    rn = (srclocN.reshape([1, -1])).repeat(rxloc.shape[0], axis=0)
    rP = np.sqrt(((rxloc - rp) ** 2).sum(axis=1))
    rN = np.sqrt(((rxloc - rn) ** 2).sum(axis=1))
    return I / (sigma * 2.0 * np.pi) * (1 / rP - 1 / rN)


data_anaP = DChalf(np.r_[-200, 0, 0.0], np.r_[+200, 0, 0.0], xyz_rxP, sighalf)
data_anaN = DChalf(np.r_[-200, 0, 0.0], np.r_[+200, 0, 0.0], xyz_rxN, sighalf)
data_ana = data_anaP - data_anaN
Data_ana = data_ana.reshape((21, 21), order="F")
Data = data.reshape((21, 21), order="F")
X = xyz_rxM[:, 0].reshape((21, 21), order="F")
Y = xyz_rxM[:, 1].reshape((21, 21), order="F")


fig, ax = plt.subplots(1, 2, figsize=(12, 5))
vmin = np.r_[data, data_ana].min()
vmax = np.r_[data, data_ana].max()
dat0 = ax[0].contourf(X, Y, Data_ana, 60, vmin=vmin, vmax=vmax)
dat1 = ax[1].contourf(X, Y, Data, 60, vmin=vmin, vmax=vmax)
plt.colorbar(dat0, orientation="horizontal", ax=ax[0])
plt.colorbar(dat1, orientation="horizontal", ax=ax[1])
ax[0].set_title("Analytic")
ax[1].set_title("Computed")

print(np.linalg.norm(data - data_ana) / np.linalg.norm(data_ana))
plt.show()

Estimated memory usage: 292 MB