def plot_data_inversion(self, ii, pred, fixed=False):
titles = ["Observed", "Predicted", "Normalized misfit"]
x = np.arange(10) + 1
y = np.arange(10) + 1
xy = utils.ndgrid(x, y)
fig, axs = plt.subplots(1, 3, figsize=(10, 3))
if fixed:
clim = (self.dobs.min(), self.dobs.max())
else:
clim = None
out = utils.plot2Ddata(xy, self.dobs, ax=axs[0], clim=clim)
plt.colorbar(out[0], ax=axs[0], fraction=0.02)
out = utils.plot2Ddata(xy, pred[ii], ax=axs[1], clim=clim)
plt.colorbar(out[0], ax=axs[1], fraction=0.02)
out = utils.plot2Ddata(xy, (pred[ii] - self.dobs) / self.uncertainty,
ax=axs[2],
clim=(-3, 3))
plt.colorbar(out[0], ax=axs[2], fraction=0.02, ticks=[-2, -1, 0, 1, 2])
for ii, ax in enumerate(axs):
ax.set_aspect(1)
ax.set_title(titles[ii])
ax.set_xlabel("Rx")
ax.set_ylabel("Tx")
plt.tight_layout()
plt.show()
def plot_magnetic_flux(self, itime):
bxy, xy = self.getSlices(
self.mesh, self.B, itime, normal="Z", loc=-100.5, isz=True
)
bxz, xz = self.getSlices(self.mesh, self.B, itime, normal="Y", loc=0.0)
label = "Magnetic flux density (T)"
plt.figure(figsize=(12, 5))
ax1 = plt.subplot(121)
ax2 = plt.subplot(122)
out_xy = utils.plot2Ddata(
xy, bxy, vec=False, ncontour=300, contourOpts={"cmap": "viridis"}, ax=ax1
)
vmin_xy, vmax_xy = out_xy[0].get_clim()
out_xz = utils.plot2Ddata(
xz, bxz, vec=True, ncontour=300, contourOpts={"cmap": "viridis"}, ax=ax2
)
vmin_xz, vmax_xz = out_xz[0].get_clim()
ax1.set_aspect("equal", adjustable="box")
ax2.set_aspect("equal", adjustable="box")
plt.colorbar(
out_xy[0],
ax=ax1,
format="%.1e",
ticks=np.linspace(vmin_xy, vmax_xy, 5),
fraction=0.02,
)
cb = plt.colorbar(
out_xz[0],
ax=ax2,
format="%.1e",
ticks=np.linspace(vmin_xz, vmax_xz, 5),
fraction=0.02,
)
cb.set_label(label)
ax1.set_title("")
ax1.set_xlabel("X (m)")
ax1.set_ylabel("Y (m)")
ax2.set_xlabel("X (m)")
ax2.set_ylabel("Z (m)")
ax1.set_xlim(self.xmin, self.xmax)
ax1.set_ylim(self.ymin, self.ymax)
ax2.set_xlim(self.xmin, self.xmax)
ax2.set_ylim(self.zmin, self.zmax)
ax1.plot(ax1.get_xlim(), np.zeros(2), "k--", lw=1)
ax2.plot(ax1.get_xlim(), np.zeros(2) - 100.0, "k--", lw=1)
ax2.plot(ax2.get_xlim(), np.zeros(2), "k-", lw=1)
ax2.plot(0, 30, "ro", ms=5)
title = ("Time at %.2f ms") % ((self.times[itime]) * 1e3)
ax1.set_title(title)
plt.tight_layout()
def plot_gravity(survey, data, ax=None, axlabels=True, colorbar=True,
ncontour=10, contour_opts={}):
"""
Shows a 2-D overhead map of a gravity survey
:param survey: survey instance
:param data: measurements
:param ax: optional matplotlib.axes.Axes instance (into subplot);
if None, create new set of axes and hit matplotlib.show() at the end
:return: nothing (yet)
"""
contourOpts = { 'cmap': 'bwr' }
contourOpts.update(contour_opts)
show = (ax is None)
if show:
fig = plt.figure(figsize=(6, 5))
ax = plt.gca()
locations = survey.receiver_locations
quadcont, axsub = plot2Ddata(
survey.receiver_locations, data, ax=ax,
ncontour=ncontour, contourOpts=contourOpts
)
if axlabels:
ax.set_title("Gravity Anomaly (Z-component)")
ax.set_xlabel("x (m)")
ax.set_ylabel("y (m)")
colorbar_label = "Anomaly (mgal)"
else:
colorbar_label = ""
if colorbar:
plt.colorbar(quadcont, format="%.0g", pad=0.03, label=colorbar_label)
if show:
plt.show()
def show_fdem_mag_map(fig, receiver_locations, mag_data):
"""
Parameters
----------
fig : matplotlib.figure.Figure
Empty figure.
receiver_locations : numpy.ndarray, shape(N*3)
See fdem_forward_simulation.fdem_forward_simulation receiver_locations.
mag_data : numpy.ndarray, shape(N*1)
See fdem_forward_simulation.fdem_forward_simulation mag_data.
Returns
-------
None.
"""
fig.clf()
mag_data_plotting = np.reshape(mag_data, (1, len(mag_data)))
v_max = np.max(mag_data_plotting)
v_min = np.min(mag_data_plotting)
ax1 = fig.add_axes([0.13, 0.12, 0.7, 0.8])
plot2Ddata(
receiver_locations[:, 0:2],
mag_data_plotting[0, :],
ax=ax1,
ncontour=30,
clim=(-v_max, v_max),
contourOpts={"cmap": "bwr"},
)
ax1.tick_params(width=0)
ax1.set_xlabel("x direction [m]")
ax1.set_ylabel("y direction [m]")
ax1.ticklabel_format(axis='y', style='sci', scilimits=(0, 0))
ax2 = fig.add_axes([0.85, 0.14, 0.03, 0.76])
norm = mpl.colors.Normalize(vmin=v_min, vmax=v_max)
cbar = mpl.colorbar.ColorbarBase(ax2,
norm=norm,
orientation="vertical",
cmap=mpl.cm.bwr)
cbar.set_label("Secondary field [T]", rotation=270, labelpad=15)
ax2.tick_params(width=0)
ax2.ticklabel_format(axis='y', style='sci', scilimits=(0, 0))
def plot_survey_data(self, percentage, floor, seed, add_noise, plot_type,
update):
self._percentage = percentage
self._floor = floor
self._seed = seed
self._dobs = self.add_noise()
self._data_prop.dobs = self._dobs.copy()
fig, axs = plt.subplots(1, 2, figsize=(8, 4))
out = self.mesh_prop.plotImage(1.0 / self.slowness_prop, ax=axs[0])
cb = plt.colorbar(out[0], ax=axs[0], fraction=0.02)
cb.set_label("Velocity (m/s)")
self.survey_prop.plot(ax=axs[0])
axs[0].set_title("Survey")
axs[0].set_xlabel("x (m)")
axs[0].set_ylabel("z (m)")
x = np.arange(10) + 1
y = np.arange(10) + 1
xy = utils.ndgrid(x, y)
if plot_type == "tx_rx_plane":
if add_noise:
out = utils.plot2Ddata(xy, self.dobs, ax=axs[1])
else:
out = utils.plot2Ddata(xy, self.pred, ax=axs[1])
axs[1].set_xlabel("Rx")
axs[1].set_ylabel("Tx")
axs[1].set_xticks(x)
axs[1].set_yticks(y)
cb = plt.colorbar(out[0], ax=axs[1], fraction=0.02)
cb.set_label("Traveltime (s)")
for ax in axs:
ax.set_aspect(1)
else:
if add_noise:
out = axs[1].hist(self.pred, edgecolor="k")
else:
out = axs[1].hist(self.dobs, edgecolor="k")
axs[1].set_ylabel("Count")
axs[1].set_xlabel("Travel time (s)")
axs[0].set_aspect(1)
plt.tight_layout()
plt.show()
dobs_mag = np.loadtxt(dir_path + "magnetic_data.obs")
# Define receiver locations and observed data
receiver_locations = dobs_grav[:, 0:3]
dobs_grav = dobs_grav[:, -1]
dobs_mag = dobs_mag[:, -1]
# Plot
mpl.rcParams.update({"font.size": 12})
# gravity data
fig = plt.figure(figsize=(7, 5))
ax1 = fig.add_axes([0.1, 0.1, 0.73, 0.85])
plot2Ddata(receiver_locations, dobs_grav, ax=ax1, contourOpts={"cmap": "bwr"})
ax1.set_title("Gravity Anomaly")
ax1.set_xlabel("x (m)")
ax1.set_ylabel("y (m)")
ax2 = fig.add_axes([0.8, 0.1, 0.03, 0.85])
norm = mpl.colors.Normalize(vmin=-np.max(np.abs(dobs_grav)),
vmax=np.max(np.abs(dobs_grav)))
cbar = mpl.colorbar.ColorbarBase(ax2,
norm=norm,
orientation="vertical",
cmap=mpl.cm.bwr,
format="%.1e")
cbar.set_label("$mgal$", rotation=270, labelpad=15, size=12)
# magnetic data
simulation = gravity.simulation.Simulation3DIntegral(
survey=survey,
mesh=mesh,
rhoMap=model_map,
actInd=ind_active,
store_sensitivities="forward_only",
)
# Compute predicted data for some model
dpred = simulation.dpred(model)
# Plot
fig = plt.figure(figsize=(7, 5))
ax1 = fig.add_axes([0.1, 0.1, 0.75, 0.85])
plot2Ddata(receiver_list[0].locations, dpred, ax=ax1, contourOpts={"cmap": "bwr"})
ax1.set_title("Gravity Anomaly (Z-component)")
ax1.set_xlabel("x (m)")
ax1.set_ylabel("y (m)")
ax2 = fig.add_axes([0.82, 0.1, 0.03, 0.85])
norm = mpl.colors.Normalize(vmin=-np.max(np.abs(dpred)), vmax=np.max(np.abs(dpred)))
cbar = mpl.colorbar.ColorbarBase(
ax2, norm=norm, orientation="vertical", cmap=mpl.cm.bwr, format="%.1e"
)
cbar.set_label("$mgal$", rotation=270, labelpad=15, size=12)
plt.show()
#######################################################
store_sensitivities="forward_only",
)
# Compute predicted data for some model
dpred = simulation.dpred(model)
n_data = len(dpred)
# Plot
fig = plt.figure(figsize=(13, 4))
v_max = np.max(np.abs(dpred))
ax1 = fig.add_axes([0.1, 0.15, 0.25, 0.78])
plot2Ddata(
receiver_list[0].locations,
dpred[0:n_data:3],
ax=ax1,
ncontour=30,
clim=(-v_max, v_max),
contourOpts={"cmap": "bwr"},
)
ax1.set_title("$dBz/dx$")
ax1.set_xlabel("x (m)")
ax1.set_ylabel("y (m)")
ax2 = fig.add_axes([0.36, 0.15, 0.25, 0.78])
cplot2 = plot2Ddata(
receiver_list[0].locations,
dpred[1:n_data:3],
ax=ax2,
ncontour=30,
clim=(-v_max, v_max),
contourOpts={"cmap": "bwr"},
def plot_magnetic_flux(self, itime):
bxy, xy = self.getSlices(self.mesh,
self.B,
itime,
normal="Z",
loc=-100.5)
byz, yz = self.getSlices(self.mesh, self.B, itime, normal="X", loc=0.0)
label = "Magnetic flux density (T)"
plt.figure(figsize=(12, 5))
ax1 = plt.subplot(121)
ax2 = plt.subplot(122)
vmin, vmax = abs(np.r_[byz]).min(), abs(np.r_[byz]).max()
out_yz = utils.plot2Ddata(yz,
byz,
vec=True,
ncontour=20,
contourOpts={"cmap": "viridis"},
ax=ax2)
vmin, vmax = out_yz[0].get_clim()
utils.plot2Ddata(
xy,
bxy,
vec=True,
ncontour=20,
contourOpts={
"cmap": "viridis",
"vmin": vmin,
"vmax": vmax
},
ax=ax1,
)
ax1.set_aspect("equal", adjustable="box")
ax2.set_aspect("equal", adjustable="box")
plt.colorbar(
out_yz[0],
ax=ax1,
format="%.1e",
ticks=np.linspace(vmin, vmax, 5),
fraction=0.02,
)
cb = plt.colorbar(
out_yz[0],
ax=ax2,
format="%.1e",
ticks=np.linspace(vmin, vmax, 5),
fraction=0.02,
)
cb.set_label(label)
ax1.set_title("")
ax1.set_xlabel("X (m)")
ax1.set_ylabel("Y (m)")
ax2.set_xlabel("Y (m)")
ax2.set_ylabel("Z (m)")
ax1.set_xlim(self.xmin, self.xmax)
ax1.set_ylim(self.ymin, self.ymax)
ax2.set_xlim(self.xmin, self.xmax)
ax2.set_ylim(self.zmin, self.zmax)
ax1.plot(ax1.get_xlim(), np.zeros(2), "k--", lw=1)
ax2.plot(ax1.get_xlim(), np.zeros(2) - 100.0, "k--", lw=1)
title = ("Time at %.2f ms") % ((self.times[itime]) * 1e3)
ax1.set_title(title)
plt.tight_layout()
def run(plotIt=True, saveFig=False, cleanup=True):
"""
Run 1D inversions for a single sounding of the RESOLVE and SkyTEM
bookpurnong data
:param bool plotIt: show the plots?
:param bool saveFig: save the figure
:param bool cleanup: remove the downloaded results
"""
downloads, directory = download_and_unzip_data()
resolve = h5py.File(os.path.sep.join([directory, "booky_resolve.hdf5"]),
"r")
skytem = h5py.File(os.path.sep.join([directory, "booky_skytem.hdf5"]), "r")
river_path = resolve["river_path"].value
# Choose a sounding location to invert
xloc, yloc = 462100.0, 6196500.0
rxind_skytem = np.argmin(
abs(skytem["xy"][:, 0] - xloc) + abs(skytem["xy"][:, 1] - yloc))
rxind_resolve = np.argmin(
abs(resolve["xy"][:, 0] - xloc) + abs(resolve["xy"][:, 1] - yloc))
# Plot both resolve and skytem data on 2D plane
fig = plt.figure(figsize=(13, 6))
title = ["RESOLVE In-phase 400 Hz", "SkyTEM High moment 156 $\mu$s"]
ax1 = plt.subplot(121)
ax2 = plt.subplot(122)
axs = [ax1, ax2]
out_re = utils.plot2Ddata(
resolve["xy"],
resolve["data"][:, 0],
ncontour=100,
contourOpts={"cmap": "viridis"},
ax=ax1,
)
vmin, vmax = out_re[0].get_clim()
cb_re = plt.colorbar(out_re[0],
ticks=np.linspace(vmin, vmax, 3),
ax=ax1,
fraction=0.046,
pad=0.04)
temp_skytem = skytem["data"][:, 5].copy()
temp_skytem[skytem["data"][:, 5] > 7e-10] = 7e-10
out_sky = utils.plot2Ddata(
skytem["xy"][:, :2],
temp_skytem,
ncontour=100,
contourOpts={
"cmap": "viridis",
"vmax": 7e-10
},
ax=ax2,
)
vmin, vmax = out_sky[0].get_clim()
cb_sky = plt.colorbar(
out_sky[0],
ticks=np.linspace(vmin, vmax * 0.99, 3),
ax=ax2,
format="%.1e",
fraction=0.046,
pad=0.04,
)
cb_re.set_label("Bz (ppm)")
cb_sky.set_label("dB$_z$ / dt (V/A-m$^4$)")
for i, ax in enumerate(axs):
xticks = [460000, 463000]
yticks = [6195000, 6198000, 6201000]
ax.set_xticks(xticks)
ax.set_yticks(yticks)
ax.plot(xloc, yloc, "wo")
ax.plot(river_path[:, 0], river_path[:, 1], "k", lw=0.5)
ax.set_aspect("equal")
if i == 1:
ax.plot(skytem["xy"][:, 0],
skytem["xy"][:, 1],
"k.",
alpha=0.02,
ms=1)
ax.set_yticklabels([str(" ") for f in yticks])
else:
ax.plot(resolve["xy"][:, 0],
resolve["xy"][:, 1],
"k.",
alpha=0.02,
ms=1)
ax.set_yticklabels([str(f) for f in yticks])
ax.set_ylabel("Northing (m)")
ax.set_xlabel("Easting (m)")
ax.set_title(title[i])
ax.axis("equal")
# plt.tight_layout()
if saveFig is True:
fig.savefig("resolve_skytem_data.png", dpi=600)
# ------------------ Mesh ------------------ #
# Step1: Set 2D cylindrical mesh
cs, ncx, ncz, npad = 1.0, 10.0, 10.0, 20
hx = [(cs, ncx), (cs, npad, 1.3)]
npad = 12
temp = np.logspace(np.log10(1.0), np.log10(12.0), 19)
temp_pad = temp[-1] * 1.3**np.arange(npad)
hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad]
mesh = discretize.CylMesh([hx, 1, hz], "00C")
active = mesh.vectorCCz < 0.0
# Step2: Set a SurjectVertical1D mapping
# Note: this sets our inversion model as 1D log conductivity
# below subsurface
active = mesh.vectorCCz < 0.0
actMap = maps.InjectActiveCells(mesh, active, np.log(1e-8), nC=mesh.nCz)
mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap
sig_half = 1e-1
sig_air = 1e-8
sigma = np.ones(mesh.nCz) * sig_air
sigma[active] = sig_half
# Initial and reference model
m0 = np.log(sigma[active])
# ------------------ RESOLVE Forward Simulation ------------------ #
# Step3: Invert Resolve data
# Bird height from the surface
b_height_resolve = resolve["src_elevation"].value
src_height_resolve = b_height_resolve[rxind_resolve]
# Set Rx (In-phase and Quadrature)
rxOffset = 7.86
bzr = FDEM.Rx.PointMagneticFluxDensitySecondary(
np.array([[rxOffset, 0.0, src_height_resolve]]),
orientation="z",
component="real",
)
bzi = FDEM.Rx.PointMagneticFluxDensity(
np.array([[rxOffset, 0.0, src_height_resolve]]),
orientation="z",
component="imag",
)
# Set Source (In-phase and Quadrature)
frequency_cp = resolve["frequency_cp"].value
freqs = frequency_cp.copy()
srcLoc = np.array([0.0, 0.0, src_height_resolve])
srcList = [
FDEM.Src.MagDipole([bzr, bzi], freq, srcLoc, orientation="Z")
for freq in freqs
]
# Set FDEM survey (In-phase and Quadrature)
survey = FDEM.Survey(srcList)
prb = FDEM.Simulation3DMagneticFluxDensity(mesh,
sigmaMap=mapping,
Solver=Solver)
prb.survey = survey
# ------------------ RESOLVE Inversion ------------------ #
# Primary field
bp = -mu_0 / (4 * np.pi * rxOffset**3)
# Observed data
cpi_inds = [0, 2, 6, 8, 10]
cpq_inds = [1, 3, 7, 9, 11]
dobs_re = (np.c_[resolve["data"][rxind_resolve, :][cpi_inds],
resolve["data"][rxind_resolve, :][cpq_inds], ].flatten() *
bp * 1e-6)
# Uncertainty
relative = np.repeat(np.r_[np.ones(3) * 0.1, np.ones(2) * 0.15], 2)
floor = 20 * abs(bp) * 1e-6
std = abs(dobs_re) * relative + floor
# Data Misfit
data_resolve = data.Data(dobs=dobs_re,
survey=survey,
standard_deviation=std)
dmisfit = data_misfit.L2DataMisfit(simulation=prb, data=data_resolve)
# Regularization
regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]])
reg = regularization.Simple(regMesh, mapping=maps.IdentityMap(regMesh))
# Optimization
opt = optimization.InexactGaussNewton(maxIter=5)
# statement of the inverse problem
invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt)
# Inversion directives and parameters
target = directives.TargetMisfit() # stop when we hit target misfit
invProb.beta = 2.0
inv = inversion.BaseInversion(invProb, directiveList=[target])
reg.alpha_s = 1e-3
reg.alpha_x = 1.0
reg.mref = m0.copy()
opt.LSshorten = 0.5
opt.remember("xc")
# run the inversion
mopt_re = inv.run(m0)
dpred_re = invProb.dpred
# ------------------ SkyTEM Forward Simulation ------------------ #
# Step4: Invert SkyTEM data
# Bird height from the surface
b_height_skytem = skytem["src_elevation"].value
src_height = b_height_skytem[rxind_skytem]
srcLoc = np.array([0.0, 0.0, src_height])
# Radius of the source loop
area = skytem["area"].value
radius = np.sqrt(area / np.pi)
rxLoc = np.array([[radius, 0.0, src_height]])
# Parameters for current waveform
t0 = skytem["t0"].value
times = skytem["times"].value
waveform_skytem = skytem["waveform"].value
offTime = t0
times_off = times - t0
# Note: we are Using theoretical VTEM waveform,
# but effectively fits SkyTEM waveform
peakTime = 1.0000000e-02
a = 3.0
dbdt_z = TDEM.Rx.PointMagneticFluxTimeDerivative(
locations=rxLoc, times=times_off[:-3] + offTime,
orientation="z") # vertical db_dt
rxList = [dbdt_z] # list of receivers
srcList = [
TDEM.Src.CircularLoop(
rxList,
loc=srcLoc,
radius=radius,
orientation="z",
waveform=TDEM.Src.VTEMWaveform(offTime=offTime,
peakTime=peakTime,
a=3.0),
)
]
# solve the problem at these times
timeSteps = [
(peakTime / 5, 5),
((offTime - peakTime) / 5, 5),
(1e-5, 5),
(5e-5, 5),
(1e-4, 10),
(5e-4, 15),
]
prob = TDEM.Simulation3DElectricField(mesh,
time_steps=timeSteps,
sigmaMap=mapping,
Solver=Solver)
survey = TDEM.Survey(srcList)
prob.survey = survey
src = srcList[0]
rx = src.receiver_list[0]
wave = []
for time in prob.times:
wave.append(src.waveform.eval(time))
wave = np.hstack(wave)
out = prob.dpred(m0)
# plot the waveform
fig = plt.figure(figsize=(5, 3))
times_off = times - t0
plt.plot(waveform_skytem[:, 0], waveform_skytem[:, 1], "k.")
plt.plot(prob.times, wave, "k-", lw=2)
plt.legend(("SkyTEM waveform", "Waveform (fit)"), fontsize=10)
for t in rx.times:
plt.plot(np.ones(2) * t, np.r_[-0.03, 0.03], "k-")
plt.ylim(-0.1, 1.1)
plt.grid(True)
plt.xlabel("Time (s)")
plt.ylabel("Normalized current")
if saveFig:
fig.savefig("skytem_waveform", dpi=200)
# Observed data
dobs_sky = skytem["data"][rxind_skytem, :-3] * area
# ------------------ SkyTEM Inversion ------------------ #
# Uncertainty
relative = 0.12
floor = 7.5e-12
std = abs(dobs_sky) * relative + floor
# Data Misfit
data_sky = data.Data(dobs=-dobs_sky, survey=survey, standard_deviation=std)
dmisfit = data_misfit.L2DataMisfit(simulation=prob, data=data_sky)
# Regularization
regMesh = discretize.TensorMesh([mesh.hz[mapping.maps[-1].indActive]])
reg = regularization.Simple(regMesh, mapping=maps.IdentityMap(regMesh))
# Optimization
opt = optimization.InexactGaussNewton(maxIter=5)
# statement of the inverse problem
invProb = inverse_problem.BaseInvProblem(dmisfit, reg, opt)
# Directives and Inversion Parameters
target = directives.TargetMisfit()
invProb.beta = 20.0
inv = inversion.BaseInversion(invProb, directiveList=[target])
reg.alpha_s = 1e-1
reg.alpha_x = 1.0
opt.LSshorten = 0.5
opt.remember("xc")
reg.mref = mopt_re # Use RESOLVE model as a reference model
# run the inversion
mopt_sky = inv.run(m0)
dpred_sky = invProb.dpred
# Plot the figure from the paper
plt.figure(figsize=(12, 8))
fs = 13 # fontsize
matplotlib.rcParams["font.size"] = fs
ax0 = plt.subplot2grid((2, 2), (0, 0), rowspan=2)
ax1 = plt.subplot2grid((2, 2), (0, 1))
ax2 = plt.subplot2grid((2, 2), (1, 1))
# Recovered Models
sigma_re = np.repeat(np.exp(mopt_re), 2, axis=0)
sigma_sky = np.repeat(np.exp(mopt_sky), 2, axis=0)
z = np.repeat(mesh.vectorCCz[active][1:], 2, axis=0)
z = np.r_[mesh.vectorCCz[active][0], z, mesh.vectorCCz[active][-1]]
ax0.semilogx(sigma_re, z, "k", lw=2, label="RESOLVE")
ax0.semilogx(sigma_sky, z, "b", lw=2, label="SkyTEM")
ax0.set_ylim(-50, 0)
# ax0.set_xlim(5e-4, 1e2)
ax0.grid(True)
ax0.set_ylabel("Depth (m)")
ax0.set_xlabel("Conducivity (S/m)")
ax0.legend(loc=3)
ax0.set_title("(a) Recovered Models")
# RESOLVE Data
ax1.loglog(frequency_cp,
dobs_re.reshape((5, 2))[:, 0] / bp * 1e6,
"k-",
label="Obs (real)")
ax1.loglog(
frequency_cp,
dobs_re.reshape((5, 2))[:, 1] / bp * 1e6,
"k--",
label="Obs (imag)",
)
ax1.loglog(
frequency_cp,
dpred_re.reshape((5, 2))[:, 0] / bp * 1e6,
"k+",
ms=10,
markeredgewidth=2.0,
label="Pred (real)",
)
ax1.loglog(
frequency_cp,
dpred_re.reshape((5, 2))[:, 1] / bp * 1e6,
"ko",
ms=6,
markeredgecolor="k",
markeredgewidth=0.5,
label="Pred (imag)",
)
ax1.set_title("(b) RESOLVE")
ax1.set_xlabel("Frequency (Hz)")
ax1.set_ylabel("Bz (ppm)")
ax1.grid(True)
ax1.legend(loc=3, fontsize=11)
# SkyTEM data
ax2.loglog(times_off[3:] * 1e6, dobs_sky / area, "b-", label="Obs")
ax2.loglog(
times_off[3:] * 1e6,
-dpred_sky / area,
"bo",
ms=4,
markeredgecolor="k",
markeredgewidth=0.5,
label="Pred",
)
ax2.set_xlim(times_off.min() * 1e6 * 1.2, times_off.max() * 1e6 * 1.1)
ax2.set_xlabel("Time ($\mu s$)")
ax2.set_ylabel("dBz / dt (V/A-m$^4$)")
ax2.set_title("(c) SkyTEM High-moment")
ax2.grid(True)
ax2.legend(loc=3)
a3 = plt.axes([0.86, 0.33, 0.1, 0.09], facecolor=[0.8, 0.8, 0.8, 0.6])
a3.plot(prob.times * 1e6, wave, "k-")
a3.plot(rx.times * 1e6,
np.zeros_like(rx.times),
"k|",
markeredgewidth=1,
markersize=12)
a3.set_xlim([prob.times.min() * 1e6 * 0.75, prob.times.max() * 1e6 * 1.1])
a3.set_title("(d) Waveform", fontsize=11)
a3.set_xticks([prob.times.min() * 1e6, t0 * 1e6, prob.times.max() * 1e6])
a3.set_yticks([])
# a3.set_xticklabels(['0', '2e4'])
a3.set_xticklabels(["-1e4", "0", "1e4"])
plt.tight_layout()
if saveFig:
plt.savefig("booky1D_time_freq.png", dpi=600)
if plotIt:
plt.show()
resolve.close()
skytem.close()
if cleanup:
print(os.path.split(directory)[:-1])
os.remove(
os.path.sep.join(directory.split()[:-1] +
["._bookpurnong_inversion"]))
os.remove(downloads)
shutil.rmtree(directory)
n_loc = locations.shape[0]
dpred = np.reshape(dpred, (n_loc, n_times))
# Plot
fig = plt.figure(figsize=(13, 5))
# Index for what time channel you would like to see the data map.
time_index = 10
v_max = np.max(np.abs(dpred[:, time_index]))
v_min = np.min(np.abs(dpred[:, time_index]))
ax11 = fig.add_axes([0.12, 0.1, 0.33, 0.85])
plot2Ddata(
locations[:, 0:2],
-dpred[:, time_index],
ax=ax11,
ncontour=30,
clim=(v_min, v_max),
contourOpts={"cmap": "magma_r"},
)
ax11.set_xlabel("x (m)")
ax11.set_ylabel("y (m)")
titlestr = "- dBz/dt at t=" + "{:.1e}".format(time_channels[time_index]) + " s"
ax11.set_title(titlestr)
ax12 = fig.add_axes([0.46, 0.1, 0.02, 0.85])
norm1 = mpl.colors.Normalize(vmin=v_min, vmax=v_max)
cbar1 = mpl.colorbar.ColorbarBase(ax12,
norm=norm1,
orientation="vertical",
cmap=mpl.cm.magma_r)
cbar1.set_label("$T/s$", rotation=270, labelpad=15, size=12)
def plotField(
self,
Field="B",
view="vec",
scale="linear",
itime=0,
Geometry=True,
Scenario=None,
Fixed=False,
vmin=None,
vmax=None,
):
# Printout for null cases
if (Field == "B") & (view == "y"):
print(
"Think about the problem geometry. There is NO By in this case."
)
elif (Field == "dBdt") & (view == "y"):
print(
"Think about the problem geometry. There is NO dBy/dt in this case."
)
elif (Field == "E") & (view == "x") | (Field == "E") & (view == "z"):
print(
"Think about the problem geometry. There is NO Ex or Ez in this case. Only Ey."
)
elif (Field == "J") & (view == "x") | (Field == "J") & (view == "z"):
print(
"Think about the problem geometry. There is NO Jx or Jz in this case. Only Jy."
)
elif (Field == "E") & (view == "vec"):
print(
"Think about the problem geometry. E only has components along y. Vector plot not possible"
)
elif (Field == "J") & (view == "vec"):
print(
"Think about the problem geometry. J only has components along y. Vector plot not possible"
)
elif Field == "Model":
plt.figure(figsize=(7, 6))
ax = plt.subplot(111)
if Scenario == "Sphere":
model2D, mapping2D = self.getCoreModel("Sphere")
elif Scenario == "Layer":
model2D, mapping2D = self.getCoreModel("Layer")
if Fixed:
clim = (np.log10(vmin), np.log10(vmax))
else:
clim = None
out = self.mesh2D.plotImage(np.log10(mapping2D * model2D),
ax=ax,
clim=clim)
cb = plt.colorbar(out[0], ax=ax, format="$10^{%.1f}$")
cb.set_label("$\sigma$ (S/m)")
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Depth (m)")
ax.set_title("Conductivity Model")
plt.show()
else:
plt.figure(figsize=(10, 6))
ax = plt.subplot(111)
vec = False
if view == "vec":
tname = "Vector "
title = tname + Field + "-field"
elif view == "amp":
tname = "|"
title = tname + Field + "|-field"
else:
title = Field + view + "-field"
if Field == "B":
label = "Magnetic field (T)"
if view == "vec":
vec = True
val = np.c_[self.Bx, self.Bz]
elif view == "x":
val = self.Bx
elif view == "z":
val = self.Bz
else:
return
elif Field == "dBdt":
label = "Time derivative of magnetic field (T/s)"
if view == "vec":
vec = True
val = np.c_[self.dBxdt, self.dBzdt]
elif view == "x":
val = self.dBxdt
elif view == "z":
val = self.dBzdt
else:
return
elif Field == "E":
label = "Electric field (V/m)"
if view == "y":
val = self.Ey
else:
return
elif Field == "J":
label = "Current density (A/m$^2$)"
if view == "y":
val = self.Jy
else:
return
if Fixed:
if scale == "log":
vmin, vmax = (np.log10(vmin), np.log10(vmax))
out = ax.scatter(np.zeros(3) - 1000,
np.zeros(3),
c=np.linspace(vmin, vmax, 3))
utils.plot2Ddata(
self.mesh2D.gridCC,
val,
vec=vec,
ax=ax,
contourOpts={
"cmap": "viridis",
"vmin": vmin,
"vmax": vmax
},
ncontour=200,
scale=scale,
)
else:
out = utils.plot2Ddata(
self.mesh2D.gridCC,
val,
vec=vec,
ax=ax,
contourOpts={"cmap": "viridis"},
ncontour=200,
scale=scale,
)[0]
if scale == "linear":
cb = plt.colorbar(out, ax=ax, format="%.2e")
elif scale == "log":
cb = plt.colorbar(out, ax=ax, format="$10^{%.1f}$")
else:
raise Exception("We consdier only linear and log scale!")
cb.set_label(label)
xmax = self.mesh2D.gridCC[:, 0].max()
if Geometry:
if Scenario == "Layer":
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.srcLoc[2],
"w-",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z0,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z1,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z2,
"w--",
lw=1)
ax.plot(0, self.srcLoc[2], "ko", ms=4)
ax.plot(self.rxLoc[0, 0], self.srcLoc[2], "ro", ms=4)
elif Scenario == "Sphere":
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.srcLoc[2],
"k-",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z0,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z1,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * (self.z1 - self.h),
"w--",
lw=1)
Phi = np.linspace(0, 2 * np.pi, 41)
ax.plot(
self.R * np.cos(Phi),
self.z2 + self.R * np.sin(Phi),
"w--",
lw=1,
)
ax.plot(0, self.srcLoc[2], "ko", ms=4)
ax.plot(self.rxLoc[0, 0], self.srcLoc[2], "ro", ms=4)
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Depth (m)")
title = (title + "\nt = " +
"{:.2e}".format(self.sim.times[itime] * 1e3) + " ms")
ax.set_title(title)
ax.set_xlim(-190, 190)
ax.set_ylim(-190, 190)
plt.show()
# Load topography
xyz_topo = np.loadtxt(str(topo_filename))
# Load field data
dobs = np.loadtxt(str(data_filename))
# Define receiver locations and observed data
receiver_locations = dobs[:, 0:3]
dobs = dobs[:, -1]
# Plot
mpl.rcParams.update({"font.size": 12})
fig = plt.figure(figsize=(7, 5))
ax1 = fig.add_axes([0.1, 0.1, 0.73, 0.85])
plot2Ddata(receiver_locations, dobs, ax=ax1, contourOpts={"cmap": "bwr"})
ax1.set_title("Gravity Anomaly")
ax1.set_xlabel("x (m)")
ax1.set_ylabel("y (m)")
ax2 = fig.add_axes([0.8, 0.1, 0.03, 0.85])
norm = mpl.colors.Normalize(vmin=-np.max(np.abs(dobs)),
vmax=np.max(np.abs(dobs)))
cbar = mpl.colorbar.ColorbarBase(ax2,
norm=norm,
orientation="vertical",
cmap=mpl.cm.bwr,
format="%.1e")
cbar.set_label("$mgal$", rotation=270, labelpad=15, size=12)
plt.show()
def run(plotIt=True, saveIt=False, saveFig=False, cleanup=True):
"""
Download and plot the Bookpurnong data. Here, we parse the data into a
dictionary that can be easily saved and loaded into other worflows (for
later on when we are doing the inversion)
:param bool plotIt: show the Figures?
:param bool saveIt: re-save the parsed data?
:param bool saveFig: save the matplotlib figures?
:param bool cleanUp: remove the downloaded and saved data?
"""
downloads, directory = download_and_unzip_data()
# data are in a directory inside bookpurnong_inversion
data_directory = os.path.sep.join([directory, "bookpurnong_data"])
# Load RESOLVE (2008)
header_resolve = "Survey Date Flight fid utctime helicopter_easting helicopter_northing gps_height bird_easting bird_northing bird_gpsheight elevation bird_height bird_roll bird_pitch bird_yaw em[0] em[1] em[2] em[3] em[4] em[5] em[6] em[7] em[8] em[9] em[10] em[11] Line "
header_resolve = header_resolve.split()
resolve = np.loadtxt(
os.path.sep.join([data_directory, "Bookpurnong_Resolve_Exported.XYZ"]),
skiprows=8,
)
# Omit the cross lines
resolve = resolve[(resolve[:, -1] > 30002) & (resolve[:, -1] < 38000), :]
dat_header_resolve = "CPI400_F CPQ400_F CPI1800_F CPQ1800_F CXI3300_F CXQ3300_F CPI8200_F CPQ8200_F CPI40k_F CPQ40k_F CPI140k_F CPQ140k_F "
dat_header_resolve = dat_header_resolve.split()
xyz_resolve = resolve[:, 8:11]
data_resolve = resolve[:, 16:-1]
line_resolve = np.unique(resolve[:, -1])
# Load SkyTEM (2006)
fid = open(
os.path.sep.join(
[data_directory, "SK655CS_Bookpurnong_ZX_HM_TxInc_newDTM.txt"]
),
"rb",
)
lines = fid.readlines()
fid.close()
header_skytem = lines[0].split()
info_skytem = []
data_skytem = []
for i, line in enumerate(lines[1:]):
if len(line.split()) != 65:
info_skytem.append(np.array(line.split()[:16], dtype="O"))
data_skytem.append(np.array(line.split()[16 : 16 + 24], dtype="float"))
else:
info_skytem.append(np.array(line.split()[:16], dtype="O"))
data_skytem.append(np.array(line.split()[17 : 17 + 24], dtype="float"))
info_skytem = np.vstack(info_skytem)
data_skytem = np.vstack(data_skytem)
lines_skytem = info_skytem[:, 1].astype(float)
line_skytem = np.unique(lines_skytem)
inds = lines_skytem < 2026
info_skytem = info_skytem[inds, :]
data_skytem = data_skytem[inds, :].astype(float)
xyz_skytem = info_skytem[:, [13, 12]].astype(float)
lines_skytem = info_skytem[:, 1].astype(float)
line_skytem = np.unique(lines_skytem)
# Load path of Murray River
river_path = np.loadtxt(os.path.sep.join([directory, "MurrayRiver.txt"]))
# Plot the data
nskip = 40
fig = plt.figure(figsize=(12 * 0.8, 6 * 0.8))
title = ["Resolve In-phase 400 Hz", "SkyTEM High moment 156 $\mu$s"]
ax1 = plt.subplot(121)
ax2 = plt.subplot(122)
axs = [ax1, ax2]
out_re = utils.plot2Ddata(
xyz_resolve[::nskip, :2],
data_resolve[::nskip, 0],
ncontour=100,
contourOpts={"cmap": "viridis"},
ax=ax1,
)
vmin, vmax = out_re[0].get_clim()
cb_re = plt.colorbar(
out_re[0], ticks=np.linspace(vmin, vmax, 3), ax=ax1, fraction=0.046, pad=0.04
)
temp_skytem = data_skytem[:, 5].copy()
temp_skytem[data_skytem[:, 5] > 7e-10] = 7e-10
out_sky = utils.plot2Ddata(
xyz_skytem[:, :2],
temp_skytem,
ncontour=100,
contourOpts={"cmap": "viridis", "vmax": 7e-10},
ax=ax2,
)
vmin, vmax = out_sky[0].get_clim()
cb_sky = plt.colorbar(
out_sky[0],
ticks=np.linspace(vmin, vmax, 3),
ax=ax2,
format="%.1e",
fraction=0.046,
pad=0.04,
)
cb_re.set_label("Bz (ppm)")
cb_sky.set_label("Voltage (V/A-m$^4$)")
for i, ax in enumerate(axs):
xticks = [460000, 463000]
yticks = [6195000, 6198000, 6201000]
ax.set_xticks(xticks)
ax.set_yticks(yticks)
ax.plot(river_path[:, 0], river_path[:, 1], "k", lw=0.5)
ax.set_aspect("equal")
if i == 1:
ax.plot(xyz_skytem[:, 0], xyz_skytem[:, 1], "k.", alpha=0.02, ms=1)
ax.set_yticklabels([str(" ") for f in yticks])
else:
ax.plot(xyz_resolve[:, 0], xyz_resolve[:, 1], "k.", alpha=0.02, ms=1)
ax.set_yticklabels([str(f) for f in yticks])
ax.set_ylabel("Northing (m)")
ax.set_xlabel("Easting (m)")
ax.set_title(title[i])
plt.tight_layout()
if plotIt:
plt.show()
if saveFig:
fig.savefig("bookpurnong_data.png")
cs, ncx, ncz, npad = 1.0, 10.0, 10.0, 20
hx = [(cs, ncx), (cs, npad, 1.3)]
npad = 12
temp = np.logspace(np.log10(1.0), np.log10(12.0), 19)
temp_pad = temp[-1] * 1.3 ** np.arange(npad)
hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad]
mesh = discretize.CylMesh([hx, 1, hz], "00C")
active = mesh.vectorCCz < 0.0
dobs_re = np.load(os.path.sep.join([directory, "dobs_re_final.npy"]))
dpred_re = np.load(os.path.sep.join([directory, "dpred_re_final.npy"]))
mopt_re = np.load(os.path.sep.join([directory, "mopt_re_final.npy"]))
# Down sample resolve data
nskip = 40
inds_resolve = np.r_[np.array(range(0, data_resolve.shape[0] - 1, nskip)), 16730]
booky_resolve = {
"data": data_resolve[inds_resolve, :],
"data_header": dat_header_resolve,
"line": resolve[:, -1][inds_resolve],
"xy": xyz_resolve[:, :2][inds_resolve],
"src_elevation": resolve[:, 12][inds_resolve],
"ground_elevation": resolve[:, 11][inds_resolve],
"dobs": dobs_re,
"dpred": dpred_re,
"mopt": mopt_re,
"z": mesh.vectorCCz[active],
"frequency_cp": np.r_[382, 1822, 7970, 35920, 130100],
"frequency_cx": np.r_[3258.0],
"river_path": river_path,
}
area = 314.0
waveform = np.loadtxt(os.path.sep.join([directory, "skytem_hm.wf"]))
times = np.loadtxt(os.path.sep.join([directory, "skytem_hm.tc"]))
booky_skytem = {
"data": data_skytem,
"data_header": header_skytem[17 : 17 + 24],
"line": lines_skytem,
"xy": xyz_skytem,
"src_elevation": info_skytem[:, 10].astype(float),
"ground_elevation": info_skytem[:, 15].astype(float),
"area": area,
"radius": np.sqrt(area / np.pi),
"t0": 0.01004,
"waveform": waveform,
"times": times,
}
if saveIt:
save_dict_to_hdf5(
os.path.sep.join([directory, "booky_resolve.hdf5"]), booky_resolve
)
save_dict_to_hdf5(
os.path.sep.join([directory, "booky_skytem.hdf5"]), booky_skytem
)
if cleanup:
os.remove(downloads)
shutil.rmtree(directory)
def plotField(
self,
Field="B",
ComplexNumber="real",
view="vec",
scale="linear",
Frequency=100,
Geometry=True,
Scenario=None,
):
# Printout for null cases
if (Field == "B") & (view == "y"):
print(
"Think about the problem geometry. There is NO By in this case."
)
elif (Field == "E") & (view == "x") | (Field == "E") & (view == "z"):
print(
"Think about the problem geometry. There is NO Ex or Ez in this case. Only Ey."
)
elif (Field == "J") & (view == "x") | (Field == "J") & (view == "z"):
print(
"Think about the problem geometry. There is NO Jx or Jz in this case. Only Jy."
)
elif (Field == "E") & (view == "vec"):
print(
"Think about the problem geometry. E only has components along y. Vector plot not possible"
)
elif (Field == "J") & (view == "vec"):
print(
"Think about the problem geometry. J only has components along y. Vector plot not possible"
)
elif (view == "vec") & (ComplexNumber == "Amp") | (view == "vec") & (
ComplexNumber == "Phase"):
print(
"Cannot show amplitude or phase when vector plot selected. Set 'AmpDir=None' to see amplitude or phase."
)
elif Field == "Model":
plt.figure(figsize=(7, 6))
ax = plt.subplot(111)
if Scenario == "Sphere":
model2D, mapping2D = self.getCoreModel("Sphere")
elif Scenario == "Layer":
model2D, mapping2D = self.getCoreModel("Layer")
out = self.mesh2D.plotImage(np.log10(mapping2D * model2D), ax=ax)
cb = plt.colorbar(out[0], ax=ax, format="$10^{%.1f}$")
cb.set_label("$\sigma$ (S/m)")
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Depth (m)")
ax.set_title("Conductivity Model")
plt.show()
else:
plt.figure(figsize=(10, 6))
ax = plt.subplot(111)
vec = False
if view == "vec":
tname = "Vector "
title = tname + Field + "-field"
elif view == "amp":
tname = "|"
title = tname + Field + "|-field"
else:
if ComplexNumber == "real":
tname = "Re("
elif ComplexNumber == "imag":
tname = "Im("
elif ComplexNumber == "amplitude":
tname = "Amp("
elif ComplexNumber == "phase":
tname = "Phase("
title = tname + Field + view + ")-field"
if Field == "B":
label = "Magnetic field (T)"
if view == "vec":
vec = True
if ComplexNumber == "real":
val = np.c_[self.Bx.real, self.Bz.real]
elif ComplexNumber == "imag":
val = np.c_[self.Bx.imag, self.Bz.imag]
else:
return
elif view == "x":
if ComplexNumber == "real":
val = self.Bx.real
elif ComplexNumber == "imag":
val = self.Bx.imag
elif ComplexNumber == "amplitude":
val = abs(self.Bx)
elif ComplexNumber == "phase":
val = np.angle(self.Bx)
elif view == "z":
if ComplexNumber == "real":
val = self.Bz.real
elif ComplexNumber == "imag":
val = self.Bz.imag
elif ComplexNumber == "amplitude":
val = abs(self.Bz)
elif ComplexNumber == "phase":
val = np.angle(self.Bz)
else:
return
elif Field == "E":
label = "Electric field (V/m)"
if view == "y":
if ComplexNumber == "real":
val = self.Ey.real
elif ComplexNumber == "imag":
val = self.Ey.imag
elif ComplexNumber == "amplitude":
val = abs(self.Ey)
elif ComplexNumber == "phase":
val = np.angle(self.Ey)
else:
return
elif Field == "J":
label = "Current density (A/m$^2$)"
if view == "y":
if ComplexNumber == "real":
val = self.Jy.real
elif ComplexNumber == "imag":
val = self.Jy.imag
elif ComplexNumber == "amplitude":
val = abs(self.Jy)
elif ComplexNumber == "phase":
val = np.angle(self.Jy)
else:
return
out = utils.plot2Ddata(
self.mesh2D.gridCC,
val,
vec=vec,
ax=ax,
contourOpts={"cmap": "viridis"},
ncontour=200,
scale=scale,
)
cb = plt.colorbar(out[0], ax=ax, format="%.2e")
cb.set_label(label)
xmax = self.mesh2D.gridCC[:, 0].max()
if Geometry:
if Scenario == "Layer":
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.srcLoc[2],
"w-",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z0,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z1,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z2,
"w--",
lw=1)
ax.plot(0, self.srcLoc[2], "ko", ms=4)
ax.plot(self.rxLoc[0, 0], self.srcLoc[2], "ro", ms=4)
elif Scenario == "Sphere":
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.srcLoc[2],
"k-",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z0,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * self.z1,
"w--",
lw=1)
ax.plot(np.r_[-xmax, xmax],
np.ones(2) * (self.z1 - self.h),
"w--",
lw=1)
Phi = np.linspace(0, 2 * np.pi, 41)
ax.plot(
self.R * np.cos(Phi),
self.z2 + self.R * np.sin(Phi),
"w--",
lw=1,
)
ax.plot(0, self.srcLoc[2], "ko", ms=4)
ax.plot(self.rxLoc[0, 0], self.srcLoc[2], "ro", ms=4)
ax.set_xlabel("Distance (m)")
ax.set_ylabel("Depth (m)")
title = title + "\nf = " + "{:.2e}".format(Frequency) + " Hz"
ax.set_title(title)
plt.show()
dobs_imag = dobs[:, 5]
# Plot the data
unique_frequencies = np.unique(frequencies)
frequency_index = 0
k = frequencies == unique_frequencies[frequency_index]
fig = plt.figure(figsize=(10, 4))
# Real Component
v_max = np.max(np.abs(dobs_real[k]))
ax1 = fig.add_axes([0.05, 0.05, 0.35, 0.9])
plot2Ddata(
receiver_locations[k, 0:2],
dobs_real[k],
ax=ax1,
ncontour=30,
clim=(-v_max, v_max),
contourOpts={"cmap": "RdBu_r"},
)
ax1.set_title("Re[$B_z$] at 200 Hz")
ax2 = fig.add_axes([0.41, 0.05, 0.02, 0.9])
norm = mpl.colors.Normalize(vmin=-v_max, vmax=v_max)
cbar = mpl.colorbar.ColorbarBase(ax2,
norm=norm,
orientation="vertical",
cmap=mpl.cm.RdBu_r)
cbar.set_label("$T$", rotation=270, labelpad=15, size=12)
# Imaginary Component
v_max = np.max(np.abs(dobs_imag[k]))
bz_imag = dpred[1:len(dpred):2]
# Then we will will reshape the data for plotting.
bz_real_plotting = np.reshape(bz_real, (len(frequencies), ntx))
bz_imag_plotting = np.reshape(bz_imag, (len(frequencies), ntx))
fig = plt.figure(figsize=(10, 4))
# Real Component
frequencies_index = 0
v_max = np.max(np.abs(bz_real_plotting[frequencies_index, :]))
ax1 = fig.add_axes([0.05, 0.05, 0.35, 0.9])
plot2Ddata(
receiver_locations[:, 0:2],
bz_real_plotting[frequencies_index, :],
ax=ax1,
ncontour=30,
clim=(-v_max, v_max),
contourOpts={"cmap": "bwr"},
)
ax1.set_title("Re[$B_z$] at 100 Hz")
ax2 = fig.add_axes([0.41, 0.05, 0.02, 0.9])
norm = mpl.colors.Normalize(vmin=-v_max, vmax=v_max)
cbar = mpl.colorbar.ColorbarBase(ax2,
norm=norm,
orientation="vertical",
cmap=mpl.cm.bwr)
cbar.set_label("$T$", rotation=270, labelpad=15, size=12)
# Imaginary Component
v_max = np.max(np.abs(bz_imag_plotting[frequencies_index, :]))
def run(plotIt=True, cleanAfterRun=True):
# Start by downloading files from the remote repository
# directory where the downloaded files are
url = "https://storage.googleapis.com/simpeg/Chile_GRAV_4_Miller/Chile_GRAV_4_Miller.tar.gz"
downloads = download(url, overwrite=True)
basePath = downloads.split(".")[0]
# unzip the tarfile
tar = tarfile.open(downloads, "r")
tar.extractall()
tar.close()
input_file = basePath + os.path.sep + "LdM_input_file.inp"
# %% User input
# Plotting parameters, max and min densities in g/cc
vmin = -0.6
vmax = 0.6
# weight exponent for default weighting
wgtexp = 3.0
# %%
# Read in the input file which included all parameters at once
# (mesh, topo, model, survey, inv param, etc.)
driver = GravityDriver_Inv(input_file)
# %%
# Now we need to create the survey and model information.
# Access the mesh and survey information
mesh = driver.mesh #
survey = driver.survey
data_object = driver.data
# [survey, data_object] = driver.survey
# define gravity survey locations
rxLoc = survey.source_field.receiver_list[0].locations
# define gravity data and errors
d = data_object.dobs
# Get the active cells
active = driver.activeCells
nC = len(active) # Number of active cells
# Create active map to go from reduce set to full
activeMap = maps.InjectActiveCells(mesh, active, -100)
# Create static map
static = driver.staticCells
dynamic = driver.dynamicCells
staticCells = maps.InjectActiveCells(None,
dynamic,
driver.m0[static],
nC=nC)
mstart = driver.m0[dynamic]
# Get index of the center
midx = int(mesh.nCx / 2)
# %%
# Now that we have a model and a survey we can build the linear system ...
# Create the forward model operator
simulation = gravity.simulation.Simulation3DIntegral(survey=survey,
mesh=mesh,
rhoMap=staticCells,
actInd=active)
# %% Create inversion objects
reg = regularization.Sparse(mesh,
indActive=active,
mapping=staticCells,
gradientType="total")
reg.mref = driver.mref[dynamic]
reg.norms = np.c_[0.0, 1.0, 1.0, 1.0]
# reg.norms = driver.lpnorms
# Specify how the optimization will proceed
opt = optimization.ProjectedGNCG(
maxIter=20,
lower=driver.bounds[0],
upper=driver.bounds[1],
maxIterLS=10,
maxIterCG=20,
tolCG=1e-4,
)
# Define misfit function (obs-calc)
dmis = data_misfit.L2DataMisfit(data=data_object, simulation=simulation)
# create the default L2 inverse problem from the above objects
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt)
# Specify how the initial beta is found
betaest = directives.BetaEstimate_ByEig(beta0_ratio=1e-2)
# IRLS sets up the Lp inversion problem
# Set the eps parameter parameter in Line 11 of the
# input file based on the distribution of model (DEFAULT = 95th %ile)
IRLS = directives.Update_IRLS(f_min_change=1e-4,
max_irls_iterations=40,
coolEpsFact=1.5,
beta_tol=5e-1)
# Preconditioning refreshing for each IRLS iteration
update_Jacobi = directives.UpdatePreconditioner()
sensitivity_weights = directives.UpdateSensitivityWeights()
# Create combined the L2 and Lp problem
inv = inversion.BaseInversion(
invProb,
directiveList=[sensitivity_weights, IRLS, update_Jacobi, betaest])
# %%
# Run L2 and Lp inversion
mrec = inv.run(mstart)
if cleanAfterRun:
os.remove(downloads)
shutil.rmtree(basePath)
# %%
if plotIt:
# Plot observed data
# The sign of the data is flipped here for the change of convention
# between Cartesian coordinate system (internal SimPEG format that
# expects "positive up" gravity signal) and traditional gravity data
# conventions (positive down). For example a traditional negative
# gravity anomaly is described as "positive up" in Cartesian coordinates
# and hence the sign needs to be flipped for use in SimPEG.
plot2Ddata(rxLoc, -d)
# %%
# Write output model and data files and print misfit stats.
# reconstructing l2 model mesh with air cells and active dynamic cells
L2out = activeMap * invProb.l2model
# reconstructing lp model mesh with air cells and active dynamic cells
Lpout = activeMap * mrec
# %%
# Plot out sections and histograms of the smooth l2 model.
# The ind= parameter is the slice of the model from top down.
yslice = midx + 1
L2out[L2out == -100] = np.nan # set "air" to nan
plt.figure(figsize=(10, 7))
plt.suptitle("Smooth Inversion: Depth weight = " + str(wgtexp))
ax = plt.subplot(221)
dat1 = mesh.plotSlice(
L2out,
ax=ax,
normal="Z",
ind=-16,
clim=(vmin, vmax),
pcolorOpts={"cmap": "bwr"},
)
plt.plot(
np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]),
c="gray",
linestyle="--",
)
plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color="k", s=1)
plt.title("Z: " + str(mesh.vectorCCz[-16]) + " m")
plt.xlabel("Easting (m)")
plt.ylabel("Northing (m)")
plt.gca().set_aspect("equal", adjustable="box")
cb = plt.colorbar(dat1[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label("Density (g/cc$^3$)")
ax = plt.subplot(222)
dat = mesh.plotSlice(
L2out,
ax=ax,
normal="Z",
ind=-27,
clim=(vmin, vmax),
pcolorOpts={"cmap": "bwr"},
)
plt.plot(
np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]),
c="gray",
linestyle="--",
)
plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color="k", s=1)
plt.title("Z: " + str(mesh.vectorCCz[-27]) + " m")
plt.xlabel("Easting (m)")
plt.ylabel("Northing (m)")
plt.gca().set_aspect("equal", adjustable="box")
cb = plt.colorbar(dat1[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label("Density (g/cc$^3$)")
ax = plt.subplot(212)
mesh.plotSlice(
L2out,
ax=ax,
normal="Y",
ind=yslice,
clim=(vmin, vmax),
pcolorOpts={"cmap": "bwr"},
)
plt.title("Cross Section")
plt.xlabel("Easting(m)")
plt.ylabel("Elevation")
plt.gca().set_aspect("equal", adjustable="box")
cb = plt.colorbar(
dat1[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4),
cmap="bwr",
)
cb.set_label("Density (g/cc$^3$)")
# %%
# Make plots of Lp model
yslice = midx + 1
Lpout[Lpout == -100] = np.nan # set "air" to nan
plt.figure(figsize=(10, 7))
plt.suptitle("Compact Inversion: Depth weight = " + str(wgtexp) +
": $\epsilon_p$ = " + str(round(reg.eps_p, 1)) +
": $\epsilon_q$ = " + str(round(reg.eps_q, 2)))
ax = plt.subplot(221)
dat = mesh.plotSlice(
Lpout,
ax=ax,
normal="Z",
ind=-16,
clim=(vmin, vmax),
pcolorOpts={"cmap": "bwr"},
)
plt.plot(
np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]),
c="gray",
linestyle="--",
)
plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color="k", s=1)
plt.title("Z: " + str(mesh.vectorCCz[-16]) + " m")
plt.xlabel("Easting (m)")
plt.ylabel("Northing (m)")
plt.gca().set_aspect("equal", adjustable="box")
cb = plt.colorbar(dat[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label("Density (g/cc$^3$)")
ax = plt.subplot(222)
dat = mesh.plotSlice(
Lpout,
ax=ax,
normal="Z",
ind=-27,
clim=(vmin, vmax),
pcolorOpts={"cmap": "bwr"},
)
plt.plot(
np.array([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
np.array([mesh.vectorCCy[yslice], mesh.vectorCCy[yslice]]),
c="gray",
linestyle="--",
)
plt.scatter(rxLoc[0:, 0], rxLoc[0:, 1], color="k", s=1)
plt.title("Z: " + str(mesh.vectorCCz[-27]) + " m")
plt.xlabel("Easting (m)")
plt.ylabel("Northing (m)")
plt.gca().set_aspect("equal", adjustable="box")
cb = plt.colorbar(dat[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label("Density (g/cc$^3$)")
ax = plt.subplot(212)
dat = mesh.plotSlice(
Lpout,
ax=ax,
normal="Y",
ind=yslice,
clim=(vmin, vmax),
pcolorOpts={"cmap": "bwr"},
)
plt.title("Cross Section")
plt.xlabel("Easting (m)")
plt.ylabel("Elevation (m)")
plt.gca().set_aspect("equal", adjustable="box")
cb = plt.colorbar(dat[0],
orientation="vertical",
ticks=np.linspace(vmin, vmax, 4))
cb.set_label("Density (g/cc$^3$)")
# Predict data for a given model
dpred = simulation.dpred(model)
# Data were organized by location, then by time channel
dpred_plotting = np.reshape(dpred, (n_tx**2, n_times))
# Plot
fig = plt.figure(figsize=(10, 4))
# dB/dt at early time
v_max = np.max(np.abs(dpred_plotting[:, 0]))
ax11 = fig.add_axes([0.05, 0.05, 0.35, 0.9])
plot2Ddata(
receiver_locations[:, 0:2],
dpred_plotting[:, 0],
ax=ax11,
ncontour=30,
clim=(-v_max, v_max),
contourOpts={"cmap": "bwr"},
)
ax11.set_title("dBz/dt at 0.0001 s")
ax12 = fig.add_axes([0.42, 0.05, 0.02, 0.9])
norm1 = mpl.colors.Normalize(vmin=-v_max, vmax=v_max)
cbar1 = mpl.colorbar.ColorbarBase(ax12,
norm=norm1,
orientation="vertical",
cmap=mpl.cm.bwr)
cbar1.set_label("$T/s$", rotation=270, labelpad=15, size=12)
# dB/dt at later times
v_max = np.max(np.abs(dpred_plotting[:, -1]))
def run(runIt=False, plotIt=True, saveIt=False, saveFig=False, cleanup=True):
"""
Run the bookpurnong 1D stitched RESOLVE inversions.
:param bool runIt: re-run the inversions? Default downloads and plots saved results
:param bool plotIt: show the plots?
:param bool saveIt: save the re-inverted results?
:param bool saveFig: save the figure
:param bool cleanup: remove the downloaded results
"""
# download the data
downloads, directory = download_and_unzip_data()
# Load resolve data
resolve = h5py.File(os.path.sep.join([directory, "booky_resolve.hdf5"]),
"r")
river_path = resolve["river_path"][()] # River path
nSounding = resolve["data"].shape[0] # the # of soundings
# Bird height from surface
b_height_resolve = resolve["src_elevation"][()]
# fetch the frequencies we are considering
cpi_inds = [0, 2, 6, 8, 10] # Indices for HCP in-phase
cpq_inds = [1, 3, 7, 9, 11] # Indices for HCP quadrature
frequency_cp = resolve["frequency_cp"][()]
# build a mesh
cs, ncx, ncz, npad = 1.0, 10.0, 10.0, 20
hx = [(cs, ncx), (cs, npad, 1.3)]
npad = 12
temp = np.logspace(np.log10(1.0), np.log10(12.0), 19)
temp_pad = temp[-1] * 1.3**np.arange(npad)
hz = np.r_[temp_pad[::-1], temp[::-1], temp, temp_pad]
mesh = discretize.CylMesh([hx, 1, hz], "00C")
active = mesh.vectorCCz < 0.0
# survey parameters
rxOffset = 7.86 # tx-rx separation
bp = -mu_0 / (4 * np.pi * rxOffset**3) # primary magnetic field
# re-run the inversion
if runIt:
# set up the mappings - we are inverting for 1D log conductivity
# below the earth's surface.
actMap = maps.InjectActiveCells(mesh,
active,
np.log(1e-8),
nC=mesh.nCz)
mapping = maps.ExpMap(mesh) * maps.SurjectVertical1D(mesh) * actMap
# build starting and reference model
sig_half = 1e-1
sig_air = 1e-8
sigma = np.ones(mesh.nCz) * sig_air
sigma[active] = sig_half
m0 = np.log(1e-1) * np.ones(active.sum()) # starting model
mref = np.log(1e-1) * np.ones(active.sum()) # reference model
# initalize empty lists for storing inversion results
mopt_re = [] # recovered model
dpred_re = [] # predicted data
dobs_re = [] # observed data
# downsample the data for the inversion
nskip = 40
# set up a noise model
# 10% for the 3 lowest frequencies, 15% for the two highest
relative = np.repeat(np.r_[np.ones(3) * 0.1, np.ones(2) * 0.15], 2)
floor = abs(20 * bp * 1e-6) # floor of 20ppm
# loop over the soundings and invert each
for rxind in range(nSounding):
# convert data from ppm to magnetic field (A/m^2)
dobs = (np.c_[resolve["data"][rxind, :][cpi_inds].astype(float),
resolve["data"][
rxind, :][cpq_inds].astype(float), ].flatten() *
bp * 1e-6)
# perform the inversion
src_height = b_height_resolve[rxind].astype(float)
mopt, dpred, dobs = resolve_1Dinversions(
mesh,
dobs,
src_height,
frequency_cp,
m0,
mref,
mapping,
relative=relative,
floor=floor,
)
# add results to our list
mopt_re.append(mopt)
dpred_re.append(dpred)
dobs_re.append(dobs)
# save results
mopt_re = np.vstack(mopt_re)
dpred_re = np.vstack(dpred_re)
dobs_re = np.vstack(dobs_re)
if saveIt:
np.save("mopt_re_final", mopt_re)
np.save("dobs_re_final", dobs_re)
np.save("dpred_re_final", dpred_re)
mopt_re = resolve["mopt"][()]
dobs_re = resolve["dobs"][()]
dpred_re = resolve["dpred"][()]
sigma = np.exp(mopt_re)
indz = -7 # depth index
# so that we can visually compare with literature (eg Viezzoli, 2010)
cmap = "jet"
# dummy figure for colobar
fig = plt.figure()
out = plt.scatter(np.ones(3),
np.ones(3),
c=np.linspace(-2, 1, 3),
cmap=cmap)
plt.close(fig)
# plot from the paper
fs = 13 # fontsize
# matplotlib.rcParams['font.size'] = fs
plt.figure(figsize=(13, 7))
ax0 = plt.subplot2grid((2, 3), (0, 0), rowspan=2, colspan=2)
ax1 = plt.subplot2grid((2, 3), (0, 2))
ax2 = plt.subplot2grid((2, 3), (1, 2))
# titles of plots
title = [
("(a) Recovered model, %.1f m depth") %
(-mesh.vectorCCz[active][indz]),
"(b) Obs (Real 400 Hz)",
"(c) Pred (Real 400 Hz)",
]
temp = sigma[:, indz]
tree = cKDTree(list(zip(resolve["xy"][:, 0], resolve["xy"][:, 1])))
d, d_inds = tree.query(list(zip(resolve["xy"][:, 0], resolve["xy"][:, 1])),
k=20)
w = 1.0 / (d + 100.0)**2.0
w = utils.sdiag(1.0 / np.sum(w, axis=1)) * (w)
xy = resolve["xy"]
temp = (temp.flatten()[d_inds] * w).sum(axis=1)
utils.plot2Ddata(
xy,
temp,
ncontour=100,
scale="log",
dataloc=False,
contourOpts={
"cmap": cmap,
"vmin": 1e-2,
"vmax": 1e1
},
ax=ax0,
)
ax0.plot(resolve["xy"][:, 0], resolve["xy"][:, 1], "k.", alpha=0.02, ms=1)
cb = plt.colorbar(out,
ax=ax0,
ticks=np.linspace(-2, 1, 4),
format="$10^{%.1f}$")
cb.set_ticklabels(["0.01", "0.1", "1", "10"])
cb.set_label("Conductivity (S/m)")
ax0.plot(river_path[:, 0], river_path[:, 1], "k-", lw=0.5)
# plot observed and predicted data
freq_ind = 0
axs = [ax1, ax2]
temp_dobs = dobs_re[:, freq_ind].copy()
ax1.plot(river_path[:, 0], river_path[:, 1], "k-", lw=0.5)
inf = temp_dobs / abs(bp) * 1e6
print(inf.min(), inf.max())
out = utils.plot2Ddata(
resolve["xy"][()],
temp_dobs / abs(bp) * 1e6,
ncontour=100,
scale="log",
dataloc=False,
ax=ax1,
contourOpts={"cmap": "viridis"},
)
vmin, vmax = out[0].get_clim()
print(vmin, vmax)
cb = plt.colorbar(
out[0],
ticks=np.logspace(np.log10(vmin), np.log10(vmax), 3),
ax=ax1,
format="%.1e",
fraction=0.046,
pad=0.04,
)
cb.set_label("Bz (ppm)")
temp_dpred = dpred_re[:, freq_ind].copy()
# temp_dpred[mask_:_data] = np.nan
ax2.plot(river_path[:, 0], river_path[:, 1], "k-", lw=0.5)
utils.plot2Ddata(
resolve["xy"][()],
temp_dpred / abs(bp) * 1e6,
ncontour=100,
scale="log",
dataloc=False,
contourOpts={
"vmin": vmin,
"vmax": vmax,
"cmap": "viridis"
},
ax=ax2,
)
cb = plt.colorbar(
out[0],
ticks=np.logspace(np.log10(vmin), np.log10(vmax), 3),
ax=ax2,
format="%.1e",
fraction=0.046,
pad=0.04,
)
cb.set_label("Bz (ppm)")
for i, ax in enumerate([ax0, ax1, ax2]):
xticks = [460000, 463000]
yticks = [6195000, 6198000, 6201000]
xloc, yloc = 462100.0, 6196500.0
ax.set_xticks(xticks)
ax.set_yticks(yticks)
# ax.plot(xloc, yloc, 'wo')
ax.plot(river_path[:, 0], river_path[:, 1], "k", lw=0.5)
ax.set_aspect("equal")
ax.plot(resolve["xy"][:, 0],
resolve["xy"][:, 1],
"k.",
alpha=0.02,
ms=1)
ax.set_yticklabels([str(f) for f in yticks])
ax.set_ylabel("Northing (m)")
ax.set_xlabel("Easting (m)")
ax.set_title(title[i])
plt.tight_layout()
if plotIt:
plt.show()
if saveFig is True:
fig.savefig("obspred_resolve.png", dpi=200)
resolve.close()
if cleanup:
os.remove(downloads)
shutil.rmtree(directory)
def run(plotIt=True):
# Create a mesh
dx = 5.0
hxind = [(dx, 5, -1.3), (dx, 15), (dx, 5, 1.3)]
hyind = [(dx, 5, -1.3), (dx, 15), (dx, 5, 1.3)]
hzind = [(dx, 5, -1.3), (dx, 7), (3.5, 1), (2, 5)]
mesh = TensorMesh([hxind, hyind, hzind], "CCC")
# Get index of the center
midx = int(mesh.nCx / 2)
midy = int(mesh.nCy / 2)
# Lets create a simple Gaussian topo and set the active cells
[xx, yy] = np.meshgrid(mesh.vectorNx, mesh.vectorNy)
zz = -np.exp((xx ** 2 + yy ** 2) / 75 ** 2) + mesh.vectorNz[-1]
# We would usually load a topofile
topo = np.c_[utils.mkvc(xx), utils.mkvc(yy), utils.mkvc(zz)]
# Go from topo to array of indices of active cells
actv = utils.surface2ind_topo(mesh, topo, "N")
actv = np.where(actv)[0]
nC = len(actv)
# Create and array of observation points
xr = np.linspace(-30.0, 30.0, 20)
yr = np.linspace(-30.0, 30.0, 20)
X, Y = np.meshgrid(xr, yr)
# Move the observation points 5m above the topo
Z = -np.exp((X ** 2 + Y ** 2) / 75 ** 2) + mesh.vectorNz[-1] + 0.1
# Create a GRAVsurvey
rxLoc = np.c_[utils.mkvc(X.T), utils.mkvc(Y.T), utils.mkvc(Z.T)]
rxLoc = gravity.receivers.Point(rxLoc)
srcField = gravity.sources.SourceField([rxLoc])
survey = gravity.survey.Survey(srcField)
# We can now create a density model and generate data
# Here a simple block in half-space
model = np.zeros((mesh.nCx, mesh.nCy, mesh.nCz))
model[(midx - 5) : (midx - 1), (midy - 2) : (midy + 2), -10:-6] = 0.75
model[(midx + 1) : (midx + 5), (midy - 2) : (midy + 2), -10:-6] = -0.75
model = utils.mkvc(model)
model = model[actv]
# Create active map to go from reduce set to full
actvMap = maps.InjectActiveCells(mesh, actv, -100)
# Create reduced identity map
idenMap = maps.IdentityMap(nP=nC)
# Create the forward simulation
simulation = gravity.simulation.Simulation3DIntegral(
survey=survey, mesh=mesh, rhoMap=idenMap, actInd=actv
)
# Compute linear forward operator and compute some data
d = simulation.fields(model)
# Add noise and uncertainties
# We add some random Gaussian noise (1nT)
synthetic_data = d + np.random.randn(len(d)) * 1e-3
wd = np.ones(len(synthetic_data)) * 1e-3 # Assign flat uncertainties
data_object = data.Data(survey, dobs=synthetic_data, noise_floor=wd)
m0 = np.ones(nC) * 1e-4 # Starting model
# Create sensitivity weights from our linear forward operator
rxLoc = survey.source_field.receiver_list[0].locations
# Create a regularization
reg = regularization.Sparse(mesh, indActive=actv, mapping=idenMap)
reg.norms = np.c_[0, 0, 0, 0]
# Data misfit function
dmis = data_misfit.L2DataMisfit(data=data_object, simulation=simulation)
dmis.W = utils.sdiag(1 / wd)
# Add directives to the inversion
opt = optimization.ProjectedGNCG(
maxIter=100, lower=-1.0, upper=1.0, maxIterLS=20, maxIterCG=10, tolCG=1e-3
)
invProb = inverse_problem.BaseInvProblem(dmis, reg, opt)
betaest = directives.BetaEstimate_ByEig(beta0_ratio=1e-1)
# Here is where the norms are applied
# Use pick a threshold parameter empirically based on the distribution of
# model parameters
update_IRLS = directives.Update_IRLS(
f_min_change=1e-4, max_irls_iterations=30, coolEpsFact=1.5, beta_tol=1e-2,
)
saveDict = directives.SaveOutputEveryIteration(save_txt=False)
update_Jacobi = directives.UpdatePreconditioner()
sensitivity_weights = directives.UpdateSensitivityWeights(everyIter=False)
inv = inversion.BaseInversion(
invProb,
directiveList=[
update_IRLS,
sensitivity_weights,
betaest,
update_Jacobi,
saveDict,
],
)
# Run the inversion
mrec = inv.run(m0)
if plotIt:
# Here is the recovered susceptibility model
ypanel = midx
zpanel = -7
m_l2 = actvMap * invProb.l2model
m_l2[m_l2 == -100] = np.nan
m_lp = actvMap * mrec
m_lp[m_lp == -100] = np.nan
m_true = actvMap * model
m_true[m_true == -100] = np.nan
vmin, vmax = mrec.min(), mrec.max()
# Plot the data
plot2Ddata(rxLoc, data_object.dobs)
plt.figure()
# Plot L2 model
ax = plt.subplot(321)
mesh.plotSlice(
m_l2, ax=ax, normal="Z", ind=zpanel, grid=True, clim=(vmin, vmax)
)
plt.plot(
([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]),
color="w",
)
plt.title("Plan l2-model.")
plt.gca().set_aspect("equal")
plt.ylabel("y")
ax.xaxis.set_visible(False)
plt.gca().set_aspect("equal", adjustable="box")
# Vertical section
ax = plt.subplot(322)
mesh.plotSlice(m_l2, ax=ax, normal="Y", ind=midx, grid=True, clim=(vmin, vmax))
plt.plot(
([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]),
color="w",
)
plt.title("E-W l2-model.")
plt.gca().set_aspect("equal")
ax.xaxis.set_visible(False)
plt.ylabel("z")
plt.gca().set_aspect("equal", adjustable="box")
# Plot Lp model
ax = plt.subplot(323)
mesh.plotSlice(
m_lp, ax=ax, normal="Z", ind=zpanel, grid=True, clim=(vmin, vmax)
)
plt.plot(
([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]),
color="w",
)
plt.title("Plan lp-model.")
plt.gca().set_aspect("equal")
ax.xaxis.set_visible(False)
plt.ylabel("y")
plt.gca().set_aspect("equal", adjustable="box")
# Vertical section
ax = plt.subplot(324)
mesh.plotSlice(m_lp, ax=ax, normal="Y", ind=midx, grid=True, clim=(vmin, vmax))
plt.plot(
([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]),
color="w",
)
plt.title("E-W lp-model.")
plt.gca().set_aspect("equal")
ax.xaxis.set_visible(False)
plt.ylabel("z")
plt.gca().set_aspect("equal", adjustable="box")
# Plot True model
ax = plt.subplot(325)
mesh.plotSlice(
m_true, ax=ax, normal="Z", ind=zpanel, grid=True, clim=(vmin, vmax)
)
plt.plot(
([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCy[ypanel], mesh.vectorCCy[ypanel]]),
color="w",
)
plt.title("Plan true model.")
plt.gca().set_aspect("equal")
plt.xlabel("x")
plt.ylabel("y")
plt.gca().set_aspect("equal", adjustable="box")
# Vertical section
ax = plt.subplot(326)
mesh.plotSlice(
m_true, ax=ax, normal="Y", ind=midx, grid=True, clim=(vmin, vmax)
)
plt.plot(
([mesh.vectorCCx[0], mesh.vectorCCx[-1]]),
([mesh.vectorCCz[zpanel], mesh.vectorCCz[zpanel]]),
color="w",
)
plt.title("E-W true model.")
plt.gca().set_aspect("equal")
plt.xlabel("x")
plt.ylabel("z")
plt.gca().set_aspect("equal", adjustable="box")
# Plot convergence curves
fig, axs = plt.figure(), plt.subplot()
axs.plot(saveDict.phi_d, "k", lw=2)
axs.plot(
np.r_[update_IRLS.iterStart, update_IRLS.iterStart],
np.r_[0, np.max(saveDict.phi_d)],
"k:",
)
twin = axs.twinx()
twin.plot(saveDict.phi_m, "k--", lw=2)
axs.text(
update_IRLS.iterStart,
np.max(saveDict.phi_d) / 2.0,
"IRLS Steps",
va="bottom",
ha="center",
rotation="vertical",
size=12,
bbox={"facecolor": "white"},
)
axs.set_ylabel("$\phi_d$", size=16, rotation=0)
axs.set_xlabel("Iterations", size=14)
twin.set_ylabel("$\phi_m$", size=16, rotation=0)
normal="Z",
ind=int(-10),
grid=True,
pcolorOpts={"cmap": "Greys"},
ax=ax[0],
)
mm = utils.plot2Ddata(
data_grav.survey.receiver_locations,
-data_grav.dobs,
ax=ax[0],
level=True,
nx=20,
ny=20,
dataloc=True,
ncontour=12,
shade=True,
contourOpts={
"cmap": "Blues_r",
"alpha": 0.8
},
levelOpts={
"colors": "k",
"linewidths": 0.5,
"linestyles": "dashed"
},
)
ax[0].set_aspect(1)
ax[0].set_title(
"Gravity data values and locations,\nwith mesh and geology overlays",
fontsize=16)
plt.colorbar(mm[0], cax=ax[2], orientation="horizontal")
ax[2].set_aspect(0.05)
actInd=ind_active,
store_sensitivities="forward_only",
)
# Compute predicted data for a susceptibility model
dpred = simulation.dpred(model)
# Plot
fig = plt.figure(figsize=(6, 5))
v_max = np.max(np.abs(dpred))
ax1 = fig.add_axes([0.1, 0.1, 0.8, 0.85])
plot2Ddata(
receiver_list[0].locations,
dpred,
ax=ax1,
ncontour=30,
clim=(-v_max, v_max),
contourOpts={"cmap": "bwr"},
)
ax1.set_title("TMI Anomaly")
ax1.set_xlabel("x (m)")
ax1.set_ylabel("y (m)")
ax2 = fig.add_axes([0.87, 0.1, 0.03, 0.85])
norm = mpl.colors.Normalize(vmin=-np.max(np.abs(dpred)),
vmax=np.max(np.abs(dpred)))
cbar = mpl.colorbar.ColorbarBase(ax2,
norm=norm,
orientation="vertical",
cmap=mpl.cm.bwr)
cbar.set_label("$nT$", rotation=270, labelpad=15, size=12)