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fm3d.py
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fm3d.py
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from SimPEG import DC, IP
from SimPEG import Maps, Utils
from SimPEG import Mesh
import matplotlib.pyplot as plt
from matplotlib import colors
import numpy as np
from time import clock
from pylab import hist
try:
from pymatsolver import Pardiso as Solver
except ImportError:
from SimPEG import SolverLU as Solver
def getRxData():
xyz = open("C:/Users/johnk/Projects/Seabridge/IdealizedStations_Rx.csv")
x = []
y = []
z = []
for line in xyz:
x_, y_, z_ = line.split(',')
x1_ = float(x_)
y1_ = float(y_)
dist = np.sqrt((x1_ - 374725.)**2 +
(y1_ - 6276216.)**2)
if dist > 160.:
x.append(float(x_))
y.append(float(y_))
z.append(float(z_))
xyz.close()
x1 = np.asarray(x)
y1 = np.asarray(y)
z1 = np.asarray(z)
rx_electrodes = np.c_[x1, y1, z1]
return rx_electrodes
def getTxData():
xyz = open("C:/Users/johnk/Projects/Seabridge/IdealizedStations_Tx.csv")
x = []
y = []
z = []
for line in xyz:
x_, y_, z_ = line.split(',')
x1_ = float(x_)
y1_ = float(y_)
dist = np.sqrt((x1_ - 374725.)**2 +
(y1_ - 6276216.)**2)
if dist > 160.:
x.append(float(x_))
y.append(float(y_))
z.append(float(z_))
xyz.close()
x.append(374739.0)
y.append(6276261.0)
z.append(1855.0)
x1 = np.asarray(x)
y1 = np.asarray(y)
z1 = np.asarray(z)
tx_electrodes = np.c_[x1, y1, z1]
return tx_electrodes
def generateSurvey(rx, tx, min_dipole_size, max_dipole_size):
"""
Generates a survey to through into a forward model
INPUT:
rx_dx = array of Rx x spacings
rx_dy = array of Rx y spacings
Tx_dx = array of Tx x spacings
Tx_dy = array of Tx y spacings
"""
SrcList = []
rx_length = rx.shape[0]
for idk in range(tx.shape[0]):
rx1 = []
rx2 = []
for idx in range(rx_length):
node1 = rx[idx, :]
for idj in range(idx, rx_length):
node2 = rx[idj, :]
dist = np.sqrt(np.sum((node1 - node2)**2))
distE = np.abs(node1[0] - tx[idk, 0])
if distE < 350:
if (min_dipole_size) < dist < (max_dipole_size):
rx1.append(node1)
rx2.append(node2)
# print(dist)
rx1 = np.asarray(rx1)
rx2 = np.asarray(rx2)
rxClass = DC.Rx.Dipole(rx1, rx2)
srcClass = DC.Src.Pole([rxClass], tx[idk, :])
SrcList.append(srcClass)
survey = DC.Survey(SrcList)
return survey
def run(plotIt=True, survey_type="pole-dipole"):
np.random.seed(1)
# Initiate I/O class for DC
IO = DC.IO()
# Obtain ABMN locations
fileName1 = "C:/Users/johnk/Projects/Seabridge/fmdataDC.con" # output mod
fileName1_ = "C:/Users/johnk/Projects/Seabridge/fmdataIP.chg" # output mod
fileName2 = "C:/Users/johnk/Projects/Seabridge/forwardmodel.msh" # in mesh
mesh = Mesh.TensorMesh._readUBC_3DMesh(fileName2) # Read in/create mesh
print("Starting forward modeling")
start = clock()
# Define model Background
rx = getRxData() # rx locations
tx = getTxData() # tx locations
survey_dc = generateSurvey(rx, tx, 45, 65) # create survey object
survey_dc.getABMN_locations() # get locations
# survey_dc = IO.from_ambn_locations_to_survey(
# survey_dc.a_locations, survey_dc.b_locations,
# survey_dc.m_locations, survey_dc.n_locations,
# survey_type, data_dc_type='volt', data_ip_type='volt'
# )
uniq = Utils.uniqueRows(np.vstack((survey_dc.a_locations,
survey_dc.b_locations,
survey_dc.m_locations,
survey_dc.n_locations)))
electrode_locations = uniq[0] # assign
actinds = Utils.surface2ind_topo(mesh,
electrode_locations,
method='cubic') # active indicies
survey_dc.drapeTopo(mesh, actinds) # drape topo
# =============================================================================
# create sphere for ice representation
x0 = (np.max(mesh.gridCC[:, 0]) +
np.min(mesh.gridCC[:, 0])) / 2. + 50 # x0 center point of sphere
y0 = (np.max(mesh.gridCC[:, 1]) +
np.min(mesh.gridCC[:, 1])) / 2. - 50 # y0 center point of sphere
z0 = 2350 # x0 center point of sphere
# (np.max(mesh.gridCC[:, 2]) + np.min(mesh.gridCC[:, 2])) / 2.
r0 = 500 # radius of sphere
print(x0, y0, z0)
csph = (np.sqrt((mesh.gridCC[:, 0] - x0)**2. +
(mesh.gridCC[:, 1] - y0)**2. +
(mesh.gridCC[:, 2] - z0)**2.)) < r0 # indicies of sphere
# sphere done =================================================================
# ============================================================================
# Create model
mx = np.ones(mesh.nC) * 0.020 # chargeability
sigma = np.ones(mesh.nC) * 1. / 15000.
# create dipping structure parameters
theta = 45. * np.pi / 180. # dipping angle
x0_d = 374700.
x1_d = 375000.
y0_d = 6275850.
y0_1d = 500. * np.sin(theta) + y0_d
y1_d = 6275900.
y1_1d = 500. * np.sin(theta) + y1_d
z0_d = 1860.
z1_d = z0_d - (500. * np.cos(theta))
m_ = (z0_d - z1_d) / (y0_1d - y0_d) # slope of dip
# loop through mesh and assign dipping structure conductivity
for idx in range(mesh.nC):
if z1_d <= mesh.gridCC[idx, 2] <= z0_d:
if (x0_d <= mesh.gridCC[idx, 0] <= x1_d):
yslope1 = y0_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
yslope2 = y1_d + (1. / m_) * (mesh.gridCC[idx, 2] - z0_d)
if yslope1 <= mesh.gridCC[idx, 1] <= yslope2:
mx[idx] = 0.03
sigma[idx] = 1. / 300.
# mx[csph] = ((0.025) *
# np.ones_like(mx[csph])) # set sphere values
mx[~actinds] = 1. / 1e8 # flag air values
# sigma[csph] = ((5000.) *
# np.ones_like(sigma[csph])) # set sphere values
sigma[~actinds] = 1. / 1e8 # flag air values
rho = 1. / sigma
stop = clock()
print(stop)
# plot results
# Show the true conductivity model
if plotIt:
ncy = mesh.nCy
ncz = mesh.nCz
ncx = mesh.nCx
mtrue = mx
print(mtrue.min(), mtrue.max())
clim = [0, 0.04]
fig, ax = plt.subplots(2, 2, figsize=(12, 6))
ax = Utils.mkvc(ax)
dat = mesh.plotSlice(((mx)), ax=ax[0], normal='Z', clim=clim,
ind=int(ncz / 2), pcolorOpts={"cmap": "jet"})
ax[0].plot(rx[:, 0], rx[:, 1], 'or')
ax[0].plot(tx[:, 0], tx[:, 1], 'dk')
mesh.plotSlice(((mx)), ax=ax[1], normal='Y', clim=clim,
ind=int(ncy / 2 + 2), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)), ax=ax[2], normal='X', clim=clim,
ind=int(ncx / 2 + 4), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mx)), ax=ax[3], normal='X', clim=clim,
ind=int(ncx / 2 + 8), pcolorOpts={"cmap": "jet"})
cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
cb = plt.colorbar(dat[0], ax=cbar_ax)
fig.subplots_adjust(right=0.85)
cb.set_label('V/V')
cbar_ax.axis('off')
plt.show()
mtrue = 1. / sigma
print(mtrue.min(), mtrue.max())
clim = [0, 20000]
fig, ax = plt.subplots(2, 2, figsize=(12, 6))
ax = Utils.mkvc(ax)
dat = mesh.plotSlice(((mtrue)), ax=ax[0], normal='Z', clim=clim,
ind=int(ncz / 2 - 4), pcolorOpts={"cmap": "jet"})
ax[0].plot(rx[:, 0], rx[:, 1], 'or')
ax[0].plot(tx[:, 0], tx[:, 1], 'dk')
mesh.plotSlice(((mtrue)), ax=ax[1], normal='Y', clim=clim,
ind=int(ncy / 2), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mtrue)), ax=ax[2], normal='X', clim=clim,
ind=int(ncx / 2 + 4), pcolorOpts={"cmap": "jet"})
mesh.plotSlice(((mtrue)), ax=ax[3], normal='X', clim=clim,
ind=int(ncx / 2 + 8), pcolorOpts={"cmap": "jet"})
cbar_ax = fig.add_axes([0.82, 0.15, 0.05, 0.7])
cb = plt.colorbar(dat[0], ax=cbar_ax)
fig.subplots_adjust(right=0.85)
cb.set_label('rho')
cbar_ax.axis('off')
plt.show()
# Use Exponential Map: m = log(rho)
actmap = Maps.InjectActiveCells(
mesh, indActive=actinds, valInactive=np.log(1e8)
)
mapping = Maps.ExpMap(mesh) * actmap
# Generate mtrue_dc for resistivity
mtrue_dc = np.log(rho[actinds])
# Generate 3D DC problem
# "CC" means potential is defined at center
prb = DC.Problem3D_CC(
mesh, rhoMap=mapping, storeJ=False,
Solver=Solver
)
# Pair problem with survey
try:
prb.pair(survey_dc)
except:
survey_dc.unpair()
prb.pair(survey_dc)
# Make synthetic DC data with 5% Gaussian noise
dtrue_dc = survey_dc.makeSyntheticData(mtrue_dc, std=0.05, force=True)
IO.data_dc = dtrue_dc
# Generate mtrue_ip for chargability
mtrue_ip = mx[actinds]
# Generate 3D DC problem
# "CC" means potential is defined at center
prb_ip = IP.Problem3D_CC(
mesh, etaMap=actmap, storeJ=False, rho=rho,
Solver=Solver
)
survey_ip = IP.from_dc_to_ip_survey(survey_dc, dim="3D")
prb_ip.pair(survey_ip)
dtrue_ip = survey_ip.makeSyntheticData(mtrue_ip, std=0.05)
IO.data_ip = dtrue_ip
# Show apparent resisitivty histogram
# if plotIt:
# fig = plt.figure(figsize=(10, 4))
# ax1 = plt.subplot(121)
# out = hist(np.log10(abs(IO.voltages)), bins=20)
# ax1.set_xlabel("log10 DC voltage (V)")
# ax2 = plt.subplot(122)
# out = hist(IO.apparent_resistivity, bins=20)
# ax2.set_xlabel("Apparent Resistivity ($\Omega$m)")
# plt.tight_layout()
# plt.show()
# Set initial model based upon histogram
m0_dc = np.ones(actmap.nP) * np.log(10000.)
# Set uncertainty
# floor
eps_dc = 10**(-3.2)
# percentage
std_dc = 0.05
mopt_dc, pred_dc = DC.run_inversion(
m0_dc, survey_dc, actinds, mesh, std_dc, eps_dc,
use_sensitivity_weight=False)
# Convert obtained inversion model to resistivity
# rho = M(m), where M(.) is a mapping
rho_est = mapping * mopt_dc
# rho_est[~actinds] = np.nan
rho_true = rho.copy()
rho_true[~actinds] = np.nan
# write data to file
out_file = open(fileName1, "w")
for i in range(rho_est.size):
out_file.write("%0.5e\n" % rho_est[i])
# Set initial model based upon histogram
m0_ip = np.ones(actmap.nP) * 1e-10
# Set uncertainty
# floor
eps_ip = 10**(-4)
# percentage
std_ip = 0.05
# Clean sensitivity function formed with true resistivity
prb_ip._Jmatrix = None
# Input obtained resistivity to form sensitivity
prb_ip.rho = mapping * mopt_dc
mopt_ip, _ = IP.run_inversion(
m0_ip, survey_ip, actinds, mesh, std_ip, eps_ip,
upper=np.Inf, lower=0.,
use_sensitivity_weight=False)
# Convert obtained inversion model to chargeability
# charg = M(m), where M(.) is a mapping for cells below topography
charg_est = actmap * mopt_ip
# charg_est[~actinds] = np.nan
charg_true = charg.copy()
charg_true[~actinds] = np.nan
# write IP data to file
out_file = open(fileName1_, "w")
for i in range(charg_est.size):
out_file.write("%0.5e\n" % charg_est[i])
if __name__ == '__main__':
survey_type = 'pole-dipole'
run(survey_type=survey_type, plotIt=True)