DC Analytic DipoleΒΆ

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

../../../_images/sphx_glr_plot_analytic_dipole_001.png

Out:

0.0646433348468

from __future__ import print_function
from SimPEG import Mesh, Utils
import numpy as np
import matplotlib.pyplot as plt
import SimPEG.EM.Static.DC as DC
try:
    from pymatsolver import Pardiso as Solver
except ImportError:
    from SimPEG import SolverLU as Solver


cs = 25.
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 = Mesh.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., ytemp, np.r_[0.])
xyz_rxN = Utils.ndgrid(xtemp+10., ytemp, np.r_[0.])
xyz_rxM = Utils.ndgrid(xtemp, ytemp, np.r_[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])
problem = DC.Problem3D_CC(mesh, Solver=Solver, sigma=sigma)
problem.pair(survey)

data = survey.dpred()


def DChalf(srclocP, srclocN, rxloc, sigma, I=1.):
    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.*np.pi)*(1/rP-1/rN)

data_anaP = DChalf(
    np.r_[-200, 0, 0.], np.r_[+200, 0, 0.], xyz_rxP, sighalf
)
data_anaN = DChalf(
    np.r_[-200, 0, 0.], np.r_[+200, 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))

Total running time of the script: ( 0 minutes 0.875 seconds)

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