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plot_pseudo_section.py
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plot_pseudo_section.py
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"""
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
"""
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()