def fwd_grav_fatiando():
"""
GravMag: 3D imaging using the migration method on synthetic gravity data
(more complex model + noisy data)
"""
# Make some synthetic gravity data from a simple prism model
za = 5000
zb = 7000
model = [mesher.Prism(-4000, 0, -4000, -2000, za, zb,
{'density': 1200})] #,
# mesher.Prism(-1000, 1000, -1000, 1000, 1000, 7000, {'density': -800}),
# mesher.Prism(2000, 4000, 3000, 4000, 0, 2000, {'density': 600})]
# Calculate on a scatter of points to show that migration doesn't need gridded
# data
# xp, yp, zp = gridder.scatter((-6000, 6000, -6000, 6000), 1000, z=0)
shape = (25, 25)
xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=0)
#gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.1)
gz = prism.gz(xp, yp, zp, model)
# Plot the data
shape = (50, 50)
mpl.figure()
mpl.axis('scaled')
mpl.contourf(yp, xp, gz, shape, 30, interp=True)
mpl.colorbar()
mpl.plot(yp, xp, '.k')
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
mpl.m2km()
mpl.show()
return xp, yp, zp, gz, shape, model
snapshot = int(0.004/dt) # Plot a snapshot of the simulation every 4 miliseconds
print "dt for simulation is ", dt
print "max iteration for simulation is ", maxit
print "duration for simulation is ", duration
simulation = wavefd.elastic_psv(lamb, mu, density, area, dt, maxit, sources,
stations, snapshot, padding=50, taper=0.01)
# This part makes an animation using matplotlibs animation API
fig = mpl.figure(figsize=(12, 5))
# Start with everything zero and grab the plot so that it can be updated later
mpl.imshow(pvel[::-1], extent=area, alpha=0.25)
wavefield = mpl.imshow(np.zeros(shape), extent=area, vmin=-10**-7, vmax=10**-7, alpha=0.75, cmap=mpl.cm.gray_r)
mpl.points(stations, '.k')
mpl.ylim(area[2:][::-1])
mpl.xlabel('x (km)')
mpl.ylabel('z (km)')
mpl.m2km()
times = np.linspace(0, maxit*dt, maxit)
# the only way for getting the feedback response of the seimograms
global seismograms
# This function updates the plot every few timesteps
def animate(i):
# Simulation will yield panels corresponding to P and S waves because
# xz2ps=True
t, ux, uz, xcomp, zcomp = simulation.next()
mpl.title('time: %0.3f s' % (times[t]))
# wavefield.set_array((p + s)[::-1])
wavefield.set_data(uz[::-1])
global seismograms
seismograms = zcomp
mesher.Prism(-1000, 1000, -1000, 1000, 1000, 7000, {'density': -800}),
mesher.Prism(2000, 4000, 3000, 4000, 0, 2000, {'density': 600})
]
# Calculate on a scatter of points to show that migration doesn't need gridded
# data
xp, yp, zp = gridder.scatter((-6000, 6000, -6000, 6000), 1000, z=-10)
gz = utils.contaminate(prism.gz(xp, yp, zp, model), 0.1)
# Plot the data
shape = (50, 50)
mpl.figure()
mpl.axis('scaled')
mpl.contourf(yp, xp, gz, shape, 30, interp=True)
mpl.colorbar()
mpl.plot(yp, xp, '.k')
mpl.xlabel('East (km)')
mpl.ylabel('North (km)')
mpl.m2km()
mpl.show()
mesh = imaging.migrate(xp, yp, zp, gz, 0, 10000, (30, 30, 30), power=0.8)
# Plot the results
myv.figure()
myv.prisms(model, 'density', style='wireframe', linewidth=2)
myv.prisms(mesh, 'density', edges=False)
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds)
myv.wall_north(axes.axes.bounds)
myv.show()
percent=True,
return_stddev=True)
# Assume that the thicknesses are unknown. In this case, use a mesh of many
# thin layers and invert for each slowness
thick = 10.
mesh = [thick] * int(sum(thickness) / thick)
solver = (LayeredStraight(tts, zp, mesh) + 5 * Smoothness1D(len(mesh))).fit()
velocity_ = solver.estimate_
mpl.figure(figsize=(12, 5))
mpl.subplot(1, 2, 1)
mpl.grid()
mpl.title("Vertical seismic profile")
mpl.plot(tts, zp, 'ok', label='Observed')
mpl.plot(solver[0].predicted(), zp, '-r', linewidth=3, label='Predicted')
mpl.legend(loc='upper right', numpoints=1)
mpl.xlabel("Travel-time (s)")
mpl.ylabel("Z (m)")
mpl.ylim(sum(mesh), 0)
mpl.subplot(1, 2, 2)
mpl.grid()
mpl.title("True velocity + smooth estimate")
mpl.layers(mesh, velocity_, '.-k', linewidth=2, label='Estimated')
mpl.layers(thickness, velocity, '--b', linewidth=2, label='True')
mpl.ylim(sum(mesh), 0)
mpl.xlim(0, 10000)
mpl.legend(loc='upper right', numpoints=1)
mpl.xlabel("Velocity (m/s)")
mpl.ylabel("Z (m)")
mpl.show()
"""
GravMag: 2D forward modeling with polygons
"""
import numpy
from fatiando import utils, mesher
from fatiando.gravmag import talwani
from fatiando.vis import mpl
# Notice that the last two number are switched.
# This way, the z axis in the plots points down.
area = (-5000, 5000, 5000, 0)
axes = mpl.figure().gca()
mpl.xlabel("X")
mpl.ylabel("Z")
mpl.axis('scaled')
polygons = [mesher.Polygon(mpl.draw_polygon(area, axes),
{'density': 500})]
xp = numpy.arange(-4500, 4500, 100)
zp = numpy.zeros_like(xp)
gz = talwani.gz(xp, zp, polygons)
mpl.figure()
mpl.axis('scaled')
mpl.subplot(2, 1, 1)
mpl.title(r"Gravity anomaly produced by the model")
mpl.plot(xp, gz, '-k', linewidth=2)
mpl.ylabel("mGal")
mpl.xlim(-5000, 5000)
mpl.subplot(2, 1, 2)
mpl.polygon(polygons[0], 'o-k', linewidth=2, fill='k', alpha=0.5)
mpl.xlabel("X")
0.02,
percent=True,
return_stddev=True)
# Preparing for the inversion
p, residuals = climsig.iabrupt(temp, zp)
est_amp, est_age = p
mpl.figure(figsize=(12, 5))
mpl.subplot(1, 2, 1)
mpl.title("Climate signal (abrupt)")
mpl.plot(temp, zp, 'ok', label='Observed')
mpl.plot(temp - residuals, zp, '--r', linewidth=3, label='Predicted')
mpl.legend(loc='lower right', numpoints=1)
mpl.xlabel("Temperature (C)")
mpl.ylabel("Z")
mpl.ylim(100, 0)
ax = mpl.subplot(1, 2, 2)
ax2 = mpl.twinx()
mpl.title("Age and amplitude")
width = 0.3
ax.bar([1 - width], [age], width, color='b', label="True")
ax.bar([1], [est_age], width, color='r', label="Estimate")
ax2.bar([2 - width], [amp], width, color='b')
ax2.bar([2], [est_amp], width, color='r')
ax.legend(loc='upper center', numpoints=1)
ax.set_ylabel("Age (years)")
ax2.set_ylabel("Amplitude (C)")
ax.set_xticks([1, 2])
ax.set_xticklabels(['Age', 'Amplitude'])
ax.set_ylim(0, 70)
# fetch sample SEGY data, near-offset marmousi data
url = "http://dl.dropboxusercontent.com/" \
"s/i287ci4ww3w7gdt/marmousi_nearoffset.segy"
urllib.urlretrieve(url, 'marmousi_nearoffset.segy')
# We'll use the ObsPy library to load the SEGY data"
segyfile = segy.readSEGY('marmousi_nearoffset.segy')
# turn ObsPy Stream in a matrix of traces
# first dimension time, second dimension traces
ntraces = len(segyfile.traces)
nsamples = len(segyfile.traces[0].data)
mtraces = np.zeros((nsamples, ntraces))
i = 0
for tr in segyfile.traces:
mtraces[:, i] = tr.data[:]
i += 1
# make plots
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.ylabel('time (seconds)')
mpl.title("Seismic wiggle plot", fontsize=13, family='sans-serif',
weight='bold')
# plot using wiggle
mpl.seismic_wiggle(mtraces, scale=10**-4)
mpl.subplot(2, 1, 2)
mpl.ylabel('time (seconds)')
mpl.title("Seismic image plot", fontsize=13, family='sans-serif',
weight='bold')
# plot using image
mpl.seismic_image(mtraces, aspect='auto')
mpl.show()
mpl.points(src, '*y')
initial = mpl.pick_points(area, mpl.gca(), marker='*', color='b')
if len(initial) > 1:
print "Don't be greedy! Pick only one point"
sys.exit()
# Fit using many different solvers
levmarq = [e for e in solver.levmarq(initial=initial[0], iterate=True)]
steepest = [e for e in solver.steepest(initial=initial[0], iterate=True)]
newton = [e for e in solver.newton(initial=initial[0], iterate=True)]
ACO_R = [e for e in solver.acor(bounds=area, maxit=100, iterate=True)]
# Make a map of the objective function
shape = (100, 100)
xs, ys = gridder.regular(area, shape)
obj = [solver.value(numpy.array([x, y])) for x, y in zip(xs, ys)]
mpl.figure()
mpl.title('Epicenter + %d recording stations' % (len(recs)))
mpl.axis('scaled')
mpl.contourf(xs, ys, obj, shape, 60)
mpl.points(recs, '^r')
mpl.points(initial, '*w')
mpl.points(levmarq, '.-k', label="Levemeber-Marquardt")
mpl.points(newton, '.-r', label="Newton")
mpl.points(steepest, '.-m', label="Steepest descent")
mpl.points(ACO_R, '.-c', label="Ant Colony")
mpl.points(src, '*y')
mpl.set_area(area)
mpl.legend(loc='lower right', shadow=True, numpoints=1, prop={'size': 12})
mpl.xlabel("X")
mpl.ylabel("Y")
mpl.show()
zp = numpy.arange(0, 100, 1)
temp, error = utils.contaminate(climsig.abrupt(amp, age, zp),
0.02, percent=True, return_stddev=True)
# Preparing for the inversion assuming that the change was LINEAR
p, residuals = climsig.ilinear(temp, zp)
est_amp, est_age = p
mpl.figure(figsize=(12,5))
mpl.subplot(1, 2, 1)
mpl.title("Climate signal\n(true is abrupt but inverted using linear)")
mpl.plot(temp, zp, 'ok', label='Observed')
mpl.plot(temp - residuals, zp, '--r', linewidth=3, label='Predicted')
mpl.legend(loc='lower right', numpoints=1)
mpl.xlabel("Temperature (C)")
mpl.ylabel("Z")
mpl.ylim(100, 0)
ax = mpl.subplot(1, 2, 2)
ax2 = mpl.twinx()
mpl.title("Age and amplitude")
width = 0.3
ax.bar([1 - width], [age], width, color='b', label="True")
ax.bar([1], [est_age], width, color='r', label="Estimate")
ax2.bar([2 - width], [amp], width, color='b')
ax2.bar([2], [est_amp], width, color='r')
ax.legend(loc='upper center', numpoints=1)
ax.set_ylabel("Age (years)")
ax2.set_ylabel("Amplitude (C)")
ax.set_xticks([1, 2])
ax.set_xticklabels(['Age', 'Amplitude'])
ax.set_ylim(0, 150)
taper=0.01)
# This part makes an animation using matplotlibs animation API
fig = mpl.figure(figsize=(12, 5))
# Start with everything zero and grab the plot so that it can be updated later
mpl.imshow(pvel[::-1], extent=area, alpha=0.25)
wavefield = mpl.imshow(np.zeros(shape),
extent=area,
vmin=-10**-7,
vmax=10**-7,
alpha=0.75,
cmap=mpl.cm.gray_r)
mpl.points(stations, '.k')
mpl.ylim(area[2:][::-1])
mpl.xlabel('x (km)')
mpl.ylabel('z (km)')
mpl.m2km()
times = np.linspace(0, maxit * dt, maxit)
# the only way for getting the feedback response of the seimograms
global seismograms
# This function updates the plot every few timesteps
def animate(i):
# Simulation will yield panels corresponding to P and S waves because
# xz2ps=True
t, ux, uz, xcomp, zcomp = simulation.next()
mpl.title('time: %0.3f s' % (times[t]))
# wavefield.set_array((p + s)[::-1])
wavefield.set_data(uz[::-1])
global seismograms
duration = 250
maxit = int(duration / dt)
stations = [[100000, 0], [700000, 0]]
snapshots = int(1.0 / dt)
simulation = wavefd.elastic_sh(mu, density, area, dt, maxit, sources, stations, snapshots, padding=70, taper=0.005)
# This part makes an animation using matplotlibs animation API
background = svel * 5 * 10 ** -7
fig = mpl.figure(figsize=(10, 8))
mpl.subplots_adjust(right=0.98, left=0.11, hspace=0.3, top=0.93)
mpl.subplot(3, 1, 1)
mpl.title("Seismogram 1")
seismogram1, = mpl.plot([], [], "-k")
mpl.xlim(0, duration)
mpl.ylim(-0.1, 0.1)
mpl.ylabel("Amplitude")
mpl.subplot(3, 1, 2)
mpl.title("Seismogram 2")
seismogram2, = mpl.plot([], [], "-k")
mpl.xlim(0, duration)
mpl.ylim(-0.1, 0.1)
mpl.ylabel("Amplitude")
ax = mpl.subplot(3, 1, 3)
mpl.title("time: 0.0 s")
wavefield = mpl.imshow(background, extent=area, cmap=mpl.cm.gray_r, vmin=-0.005, vmax=0.005)
mpl.points(stations, "^b", size=8)
mpl.text(750000, 20000, "Crust")
mpl.text(740000, 100000, "Mantle")
fig.text(0.82, 0.33, "Seismometer 2")
fig.text(0.16, 0.33, "Seismometer 1")
mpl.ylim(area[2:][::-1])
"""
Gridding: Load a Surfer ASCII grid file
"""
from fatiando import datasets, gridder
from fatiando.vis import mpl
# Fetching Bouguer anomaly model data (Surfer ASCII grid file)"
# Will download the archive and save it with the default name
archive = datasets.fetch_bouguer_alps_egm()
# Load the GRD file and convert in three numpy-arrays (x, y, bouguer)
x, y, bouguer, shape = gridder.load_surfer(archive, fmt="ascii")
mpl.figure()
mpl.axis("scaled")
mpl.title("Data loaded from a Surfer ASCII grid file")
mpl.contourf(y, x, bouguer, shape, 15, cmap=mpl.cm.RdBu_r)
cb = mpl.colorbar()
cb.set_label("mGal")
mpl.xlabel("y points to East (km)")
mpl.ylabel("x points to North (km)")
mpl.m2km()
mpl.show()
mpl.points(src, '*y')
initial = mpl.pick_points(area, mpl.gca(), marker='*', color='b')
if len(initial) > 1:
print "Don't be greedy! Pick only one point"
sys.exit()
estimate = solver.config('levmarq', initial=initial[0]).fit().estimate_
mpl.figure(figsize=(10, 4))
mpl.subplot(1, 2, 1)
mpl.title('Epicenter + %d recording stations' % (len(recs)))
mpl.axis('scaled')
mpl.points(src, '*y', label="True")
mpl.points(recs, '^r', label="Stations")
mpl.points(initial, '*b', label="Initial")
mpl.points([estimate], '*g', label="Estimate")
mpl.set_area(area)
mpl.legend(loc='lower right', shadow=True, numpoints=1, prop={'size': 12})
mpl.xlabel("X")
mpl.ylabel("Y")
ax = mpl.subplot(1, 2, 2)
mpl.title('Travel-time residuals + error bars')
s = numpy.arange(len(traveltime)) + 1
width = 0.3
mpl.bar(s - width, traveltime, width, color='g', label="Observed", yerr=error)
mpl.bar(s, solver.predicted(), width, color='r', label="Predicted")
ax.set_xticks(s)
mpl.legend(loc='upper right', shadow=True, prop={'size': 12})
mpl.xlabel("Station number")
mpl.ylabel("Travel-time residual")
mpl.show()
utils.contaminate(gravmag.prism.gxx(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gxy(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gxz(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gyy(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gyz(x, y, z, model), noise),
utils.contaminate(gravmag.prism.gzz(x, y, z, model), noise)
]
with open('data.txt', 'w') as f:
f.write(logger.header(comment='#'))
f.write("# Noise corrupted gz and tensor components:\n")
f.write("# noise = %g Eotvos\n" % (noise))
f.write("# noise = %g mGal\n" % (noisegz))
f.write("# coordinates are in meters\n")
f.write("# gz in mGal and tensor in Eotvos\n")
f.write("# x y z height gz gxx gxy gxz gyy gyz gzz\n")
numpy.savetxt(f, numpy.transpose(data))
# Show it
mpl.figure(figsize=(10, 9))
names = "z height gz gxx gxy gxz gyy gyz gzz".split()
for i, comp in enumerate(data[2:]):
mpl.subplot(3, 3, i + 1)
mpl.axis('scaled')
mpl.title(names[i])
levels = mpl.contourf(y * 0.001, x * 0.001, comp, shape, 8)
mpl.contour(y * 0.001, x * 0.001, comp, shape, levels)
if i == 3:
mpl.ylabel('North = x (km)')
if i == 7:
mpl.xlabel('East = y (km)')
mpl.show()
twtvmodel = np.zeros((len(twt), dnx)) # velocity model in time and discretized
for i in xrange(0, nx, disc): # set the time re-sample velocity model
twtvmodel[:, int(i/disc)] = np.interp(twt, twti[:, i], vmodel[:, i])
zimp = np.ones(twtvmodel.shape)*1000.*twtvmodel # create impedance z = rho*v
rc = (zimp[1:]-zimp[:-1])/(zimp[1:]+zimp[:-1]) # calculate reflection coefs
fig = mpl.figure(figsize=(11, 7)) # plottings
mpl.subplots_adjust(right=0.98, left=0.11, hspace=0.4, top=0.93, bottom=0.13)
mpl.subplot2grid((3, 4), (0, 0), colspan=4) # plot rc model
mpl.title("Zero-offset section reflection coefficients",
fontsize=13, family='sans-serif', weight='bold')
rcs = utils.matrix2stream(rc.transpose(), header={'delta': dt})
mpl.seismic_wiggle(rcs, normalize=True, scale=1.5, ranges=[0, nx]) # rc model
wavelet = signal.ricker(255, 1/(2*f*dt)) # create wavelet
samples = signal.filtfilt(wavelet, np.ones(len(wavelet)),
rc, axis=0, padlen=len(twt)-2) # convolve rc*wavelet
mpl.ylabel('twt (s)')
mpl.subplot2grid((3, 4), (1, 0), colspan=4) # plot zero-offset traces
traces = utils.matrix2stream(samples.transpose(), header={'delta': dt})
mpl.seismic_image(traces, cmap=mpl.pyplot.cm.jet, aspect='auto', ranges=[0, nx])
mpl.seismic_wiggle(traces, ranges=[0, nx], normalize=True)
mpl.ylabel('twt (s)')
mpl.title("Zero-offset section amplitude",
fontsize=13, family='sans-serif', weight='bold')
ax = mpl.subplot2grid((3, 4), (2, 0), colspan=4) # plot vmodel
mpl.imshow(vmodel, extent=[0, nx, nz*ds, 0],
cmap=mpl.pyplot.cm.bwr, aspect='auto', origin='upper')
ax.autoscale(False)
mpl.ylabel('depth (m)')
stations = [[i, 0] for i in xrange(0, nx, disc)]
mpl.points(stations, '^k', size=7) # zero-offset station points
mpl.text(250, 120, '2900 m/s') # model velocities
from fatiando import utils
from fatiando.geothermal.climsig import linear, SingleChange
from fatiando.vis import mpl
# Generating synthetic data
amp = 5.43
age = 78.2
# along a well at these depths
zp = numpy.arange(0, 100, 1)
temp, error = utils.contaminate(linear(amp, age, zp), 0.02,
percent=True, return_stddev=True)
# Preparing for the inversion
data = SingleChange(temp, zp, mode='linear').config('levmarq', initial=[1, 1])
amp_, age_ = data.fit().estimate_
print "Linear change in temperature"
print " true: amp=%.3f age=%.3f" % (amp, age)
print " estimated: amp=%.3f age=%.3f" % (amp_, age_)
mpl.figure(figsize=(4, 5))
mpl.title("Residual well temperature")
mpl.plot(temp, zp, 'ok', label='Observed')
mpl.plot(data.predicted(), zp, '--r', linewidth=3, label='Predicted')
mpl.legend(loc='lower right', numpoints=1)
mpl.xlabel("Temperature (C)")
mpl.ylabel("Z (m)")
mpl.ylim(100, 0)
mpl.show()
mesher.Prism(-4000, -3000, -4000, -3000, 0, 2000,
{'magnetization': 2}), # a scalar magnetization means only induced
mesher.Prism(-1000, 1000, -1000, 1000, 0, 2000,
{'magnetization': 1}),
# This prism will have magnetization in a different direction
mesher.Prism(2000, 4000, 3000, 4000, 0, 2000,
{'magnetization': utils.ang2vec(3, -10, 45)})] # induced + remanent
# Create a regular grid at 100m height
shape = (200, 200)
area = bounds[:4]
xp, yp, zp = gridder.regular(area, shape, z=-500)
# Calculate the anomaly for a given regional field
tf = prism.tf(xp, yp, zp, model, inc, dec)
# Plot
mpl.figure()
mpl.title("Total-field anomaly (nT)")
mpl.axis('scaled')
mpl.contourf(yp, xp, tf, shape, 15)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.m2km()
mpl.show()
# Show the prisms
myv.figure()
myv.prisms(model, 'magnetization')
myv.axes(myv.outline(bounds), ranges=[i * 0.001 for i in bounds])
myv.wall_north(bounds)
myv.wall_bottom(bounds)
myv.show()
Seismic: Invert vertical seismic profile (VSP) traveltimes for the velocity
of a layered model.
"""
import numpy
from fatiando import utils
from fatiando.seismic.profile import layered_straight_ray, LayeredStraight
from fatiando.inversion.regularization import Damping
from fatiando.vis import mpl
# The limits in velocity and depths, respectively
area = (0, 10000, 0, 100)
vmin, vmax, zmin, zmax = area
# Use the interactive functions of mpl to draw a layered model
figure = mpl.figure()
mpl.xlabel("Velocity (m/s)")
mpl.ylabel("Depth (m)")
thickness, velocity = mpl.draw_layers(area, figure.gca())
# Make some synthetic noise-corrupted travel-time data
zp = numpy.arange(zmin + 0.5, zmax, 0.5)
tts, error = utils.contaminate(
layered_straight_ray(thickness, velocity, zp),
0.02, percent=True, return_stddev=True)
# Make the solver and run the inversion using damping regularization
# (assumes known thicknesses of the layers)
solver = (LayeredStraight(tts, zp, thickness) +
0.1 * Damping(len(thickness))).fit()
velocity_ = solver.estimate_
# Plot the results
mpl.figure(figsize=(12, 5))
mpl.subplot(1, 2, 1)
mpl.subplot(2, 2, 4)
mpl.title('z component')
zseismogram, = mpl.plot([], [], '-k')
mpl.xlim(0, duration)
mpl.ylim(-10**(-3), 10**(-3))
mpl.subplot(1, 2, 1)
# Start with everything zero and grab the plot so that it can be updated later
wavefield = mpl.imshow(np.zeros(shape),
extent=area,
vmin=-10**-6,
vmax=10**-6,
cmap=mpl.cm.gray_r)
mpl.points(stations, '^k')
mpl.ylim(area[2:][::-1])
mpl.xlabel('x (km)')
mpl.ylabel('z (km)')
mpl.m2km()
times = np.linspace(0, maxit * dt, maxit)
# This function updates the plot every few timesteps
def animate(i):
# Simulation will yield panels corresponding to P and S waves because
# xz2ps=True
t, p, s, xcomp, zcomp = simulation.next()
mpl.title('time: %0.1f s' % (times[t]))
wavefield.set_array((p + s)[::-1])
xseismogram.set_data(times[:t + 1], xcomp[0][:t + 1])
zseismogram.set_data(times[:t + 1], zcomp[0][:t + 1])
return wavefield, xseismogram, zseismogram
fig = mpl.figure(figsize=(11, 7)) # plottings
mpl.subplots_adjust(right=0.98, left=0.11, hspace=0.4, top=0.93, bottom=0.13)
mpl.subplot2grid((3, 4), (0, 0), colspan=4) # plot rc model
mpl.title("Zero-offset section reflection coefficients",
fontsize=13,
family='sans-serif',
weight='bold')
rcs = utils.matrix2stream(rc.transpose(), header={'delta': dt})
mpl.seismic_wiggle(rcs, normalize=True, scale=1.5, ranges=[0, nx]) # rc model
wavelet = signal.ricker(255, 1 / (2 * f * dt)) # create wavelet
samples = signal.filtfilt(wavelet,
np.ones(len(wavelet)),
rc,
axis=0,
padlen=len(twt) - 2) # convolve rc*wavelet
mpl.ylabel('twt (s)')
mpl.subplot2grid((3, 4), (1, 0), colspan=4) # plot zero-offset traces
traces = utils.matrix2stream(samples.transpose(), header={'delta': dt})
mpl.seismic_image(traces,
cmap=mpl.pyplot.cm.jet,
aspect='auto',
ranges=[0, nx])
mpl.seismic_wiggle(traces, ranges=[0, nx], normalize=True)
mpl.ylabel('twt (s)')
mpl.title("Zero-offset section amplitude",
fontsize=13,
family='sans-serif',
weight='bold')
ax = mpl.subplot2grid((3, 4), (2, 0), colspan=4) # plot vmodel
mpl.imshow(vmodel,
extent=[0, nx, nz * ds, 0],
log.info("Generating synthetic data")
verts = [(10000, 1.), (90000, 1.), (90000, 7000), (10000, 3330)]
model = mesher.Polygon(verts, {'density':-100})
xp = numpy.arange(0., 100000., 1000.)
zp = numpy.zeros_like(xp)
gz = utils.contaminate(gravmag.talwani.gz(xp, zp, [model]), 0.5)
log.info("Preparing for the inversion")
solver = inversion.gradient.levmarq(initial=(9000, 500))
estimate, residuals = gravmag.basin2d.trapezoidal(xp, zp, gz, verts[0:2], -100,
solver)
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.title("Gravity anomaly")
mpl.plot(xp, gz, 'ok', label='Observed')
mpl.plot(xp, gz - residuals, '-r', linewidth=2, label='Predicted')
mpl.legend(loc='lower left', numpoints=1)
mpl.ylabel("mGal")
mpl.xlim(0, 100000)
mpl.subplot(2, 1, 2)
mpl.polygon(estimate, 'o-r', linewidth=2, fill='r', alpha=0.3,
label='Estimated')
mpl.polygon(model, '--k', linewidth=2, label='True')
mpl.legend(loc='lower left', numpoints=1)
mpl.xlabel("X")
mpl.ylabel("Z")
mpl.set_area((0, 100000, 10000, -500))
mpl.show()
noise = 0.1 # 0.1 mGal noise
gz = utils.contaminate(polyprism.gz(xp, yp, zp, model), noise)
# Create a mesh
mesh = PrismMesh(bounds, (25, 50, 50))
# Wrap the data so that harvester can read it
data = [harvester.Gz(xp, yp, zp, gz)]
# Plot the data and pick the location of the seeds
mpl.figure()
mpl.suptitle("Pick the seeds (polygon is the true source)")
mpl.axis("scaled")
levels = mpl.contourf(yp, xp, gz, shape, 12)
mpl.colorbar()
mpl.polygon(model[0], xy2ne=True)
mpl.xlabel("Horizontal coordinate y (km)")
mpl.ylabel("Horizontal coordinate x (km)")
seedx, seedy = mpl.pick_points(area, mpl.gca(), xy2ne=True).T
# Set the right density and depth
locations = [[x, y, 1500, {"density": 1000}] for x, y in zip(seedx, seedy)]
mpl.show()
# Make the seed and set the compactness regularizing parameter mu
seeds = harvester.sow(locations, mesh)
# Run the inversion
estimate, predicted = harvester.harvest(data, seeds, mesh, compactness=0.05, threshold=0.0005)
# Put the estimated density values in the mesh
mesh.addprop("density", estimate["density"])
# Plot the adjustment and the result
mpl.figure()
mpl.title("True: color | Predicted: contour")
mpl.axis("scaled")
levels = mpl.contourf(yp, xp, gz, shape, 12)
print "dt for simulation is ", dt
print "max iteration for simulation is ", maxit
print "duration for simulation is ", duration
# TODO implement 2D esg version with abs condition
simulation = wavefd.scalar3_esg(pvel, density, area, dt, maxit, sources,
stations, snapshot, padding=50, taper=0.01)
# This part makes an animation using matplotlibs animation API
fig = mpl.figure(figsize=(12, 5))
# Start with everything zero and grab the plot so that it can be updated later
mpl.imshow(pvel[0][::-1], extent=area[:4], alpha=0.25)
wavefield = mpl.imshow(np.zeros(shape[1:]), extent=area[:4], vmin=-10**-7, vmax=10**-7, alpha=0.75, cmap=mpl.cm.gray_r)
mpl.points([ stations[i][:2] for i in range(len(stations))], '.k')
mpl.ylim(area[2:4][::-1])
mpl.xlabel('x (km)')
mpl.ylabel('z (km)')
mpl.m2km()
times = np.linspace(0, maxit*dt, maxit)
# the only way for getting the feedback response of the seimograms
global seismograms
# This function updates the plot every few timesteps
def animate(i):
# t, pressure, seismograms
t, u, zcomp = simulation.next()
mpl.title('time: %0.3f s' % (times[t]))
# wavefield.set_array((p + s)[::-1])
wavefield.set_data(u[0][::-1])
global seismograms
seismograms = zcomp
return wavefield, seismograms
mpl.points(src, '*y')
initial = mpl.pick_points(area, mpl.gca(), marker='*', color='b')
if len(initial) > 1:
print "Don't be greedy! Pick only one point"
sys.exit()
# Fit using many different solvers
levmarq = [e for e in solver.levmarq(initial=initial[0], iterate=True)]
steepest = [e for e in solver.steepest(initial=initial[0], iterate=True)]
newton = [e for e in solver.newton(initial=initial[0], iterate=True)]
ACO_R = [e for e in solver.acor(bounds=area, maxit=100, iterate=True)]
# Make a map of the objective function
shape = (100, 100)
xs, ys = gridder.regular(area, shape)
obj = [solver.value(numpy.array([x, y])) for x, y in zip(xs, ys)]
mpl.figure()
mpl.title('Epicenter + %d recording stations' % (len(recs)))
mpl.axis('scaled')
mpl.contourf(xs, ys, obj, shape, 60)
mpl.points(recs, '^r')
mpl.points(initial, '*w')
mpl.points(levmarq, '.-k', label="Levemeber-Marquardt")
mpl.points(newton, '.-r', label="Newton")
mpl.points(steepest, '.-m', label="Steepest descent")
mpl.points(ACO_R, '.-c', label="Ant Colony")
mpl.points(src, '*y')
mpl.set_area(area)
mpl.legend(loc='lower right', shadow=True, numpoints=1, prop={'size':12})
mpl.xlabel("X")
mpl.ylabel("Y")
mpl.show()
model = [Prism(250, 750, 250, 750, 200, 700, {'density':1000})]
# and generate synthetic data from it
shape = (25, 25)
bounds = [0, 1000, 0, 1000, 0, 1000]
area = bounds[0:4]
xp, yp, zp = gridder.regular(area, shape, z=-1)
noise = 0.1 # 0.1 mGal noise
gz = utils.contaminate(gm.prism.gz(xp, yp, zp, model), noise)
# plot the data
mpl.figure()
mpl.title("Synthetic gravity anomaly (mGal)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gz, shape, 12)
mpl.colorbar()
mpl.xlabel('Horizontal coordinate y (km)')
mpl.ylabel('Horizontal coordinate x (km)')
mpl.m2km()
mpl.show()
# Inversion setup
# Create a mesh
mesh = PrismMesh(bounds, (25, 25, 25))
# Wrap the data so that harvester can use it
data = [gm.harvester.Gz(xp, yp, zp, gz)]
# Make the seed
seeds = gm.harvester.sow([[500, 500, 450, {'density':1000}]], mesh)
# Run the inversioin
estimate, predicted = gm.harvester.harvest(data, seeds, mesh,
compactness=0.5, threshold=0.0005)
# Put the estimated density values in the mesh
noise = 0.1 # 0.1 mGal noise
gz = utils.contaminate(gm.polyprism.gz(xp, yp, zp, model), noise)
# Create a mesh
mesh = PrismMesh(bounds, (25, 50, 50))
# Wrap the data so that harvester can read it
data = [gm.harvester.Gz(xp, yp, zp, gz)]
# Plot the data and pick the location of the seeds
mpl.figure()
mpl.suptitle("Pick the seeds (polygon is the true source)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gz, shape, 12)
mpl.colorbar()
mpl.polygon(model[0], xy2ne=True)
mpl.xlabel('Horizontal coordinate y (km)')
mpl.ylabel('Horizontal coordinate x (km)')
seedx, seedy = mpl.pick_points(area, mpl.gca(), xy2ne=True).T
# Set the right density and depth
locations = [[x, y, 1500, {'density': 1000}] for x, y in zip(seedx, seedy)]
mpl.show()
# Make the seed and set the compactness regularizing parameter mu
seeds = gm.harvester.sow(locations, mesh)
# Run the inversion
estimate, predicted = gm.harvester.harvest(data,
seeds,
mesh,
compactness=0.05,
threshold=0.0005)
# Put the estimated density values in the mesh
mesh.addprop('density', estimate['density'])
# Plot the adjustment and the result
Seismic: Invert vertical seismic profile (VSP) traveltimes for the velocity
of a layered model.
"""
import numpy
from fatiando import utils
from fatiando.seismic.profile import layered_straight_ray, LayeredStraight
from fatiando.inversion.regularization import Damping
from fatiando.vis import mpl
# The limits in velocity and depths, respectively
area = (0, 10000, 0, 100)
vmin, vmax, zmin, zmax = area
# Use the interactive functions of mpl to draw a layered model
figure = mpl.figure()
mpl.xlabel("Velocity (m/s)")
mpl.ylabel("Depth (m)")
thickness, velocity = mpl.draw_layers(area, figure.gca())
# Make some synthetic noise-corrupted travel-time data
zp = numpy.arange(zmin + 0.5, zmax, 0.5)
tts, error = utils.contaminate(layered_straight_ray(thickness, velocity, zp),
0.02,
percent=True,
return_stddev=True)
# Make the solver and run the inversion using damping regularization
# (assumes known thicknesses of the layers)
solver = (LayeredStraight(tts, zp, thickness) +
0.1 * Damping(len(thickness))).fit()
velocity_ = solver.estimate_
# Plot the results
mpl.figure(figsize=(12, 5))
stations,
snapshots,
padding=70,
taper=0.005,
xz2ps=True)
# This part makes an animation using matplotlibs animation API
background = 10**-5 * ((density - density.min()) / density.max())
fig = mpl.figure(figsize=(10, 8))
mpl.subplots_adjust(right=0.98, left=0.11, hspace=0.3, top=0.93)
mpl.subplot(3, 1, 1)
mpl.title('x seismogram')
xseismogram, = mpl.plot([], [], '-k')
mpl.xlim(0, duration)
mpl.ylim(-0.05, 0.05)
mpl.ylabel('Amplitude')
mpl.subplot(3, 1, 2)
mpl.title('z seismogram')
zseismogram, = mpl.plot([], [], '-k')
mpl.xlim(0, duration)
mpl.ylim(-0.05, 0.05)
mpl.ylabel('Amplitude')
ax = mpl.subplot(3, 1, 3)
mpl.title('time: 0.0 s')
wavefield = mpl.imshow(background,
extent=area,
cmap=mpl.cm.gray_r,
vmin=-0.00001,
vmax=0.00001)
mpl.points(stations, '^b', size=8)
mpl.text(500000, 20000, 'Crust')
maxit = int(duration/dt)
stations = [[75*ds, 125*ds]] # x, z coordinate of the seismometer
snapshots = 3 # every 3 iterations plots one
simulation = wavefd.scalar(velocity, area, dt, maxit, sources, stations, snapshots)
# This part makes an animation using matplotlibs animation API
background = (velocity-4000)*10**-1
fig = mpl.figure(figsize=(8, 6))
mpl.subplots_adjust(right=0.98, left=0.11, hspace=0.5, top=0.93)
mpl.subplot2grid((4, 3), (0,0), colspan=3,rowspan=3)
wavefield = mpl.imshow(np.zeros_like(velocity), extent=area, cmap=mpl.cm.gray_r,
vmin=-1000, vmax=1000)
mpl.points(stations, '^b', size=8)
mpl.ylim(area[2:][::-1])
mpl.xlabel('x (km)')
mpl.ylabel('z (km)')
mpl.m2km()
mpl.subplot2grid((4,3), (3,0), colspan=3)
seismogram1, = mpl.plot([],[],'-k')
mpl.xlim(0, duration)
mpl.ylim(-200, 200)
mpl.ylabel('Amplitude')
times = np.linspace(0, dt*maxit, maxit)
# This function updates the plot every few timesteps
def animate(i):
t, u, seismogram = simulation.next()
seismogram1.set_data(times[:t+1], seismogram[0][:t+1])
wavefield.set_array(background[::-1]+u[::-1])
return wavefield, seismogram1
anim = animation.FuncAnimation(fig, animate, frames=maxit/snapshots, interval=1)
mpl.show()
"""
Gridding: Load a Surfer ASCII grid file
"""
from fatiando import datasets, gridder
from fatiando.vis import mpl
# Fetching Bouguer anomaly model data (Surfer ASCII grid file)"
# Will download the archive and save it with the default name
archive = datasets.fetch_bouguer_alps_egm()
# Load the GRD file and convert in three numpy-arrays (y, x, bouguer)
y, x, bouguer, shape = gridder.load_surfer(archive, fmt='ascii')
mpl.figure()
mpl.axis('scaled')
mpl.title("Data loaded from a Surfer ASCII grid file")
mpl.contourf(y, x, bouguer, shape, 15)
cb = mpl.colorbar()
cb.set_label('mGal')
mpl.xlabel('y points to East (km)')
mpl.ylabel('x points to North (km)')
mpl.m2km()
mpl.show()
gxz = utils.contaminate(gm.prism.gxz(xp, yp, zp, model), noise)
gyy = utils.contaminate(gm.prism.gyy(xp, yp, zp, model), noise)
gyz = utils.contaminate(gm.prism.gyz(xp, yp, zp, model), noise)
gzz = utils.contaminate(gm.prism.gzz(xp, yp, zp, model), noise)
tensor = [gxx, gxy, gxz, gyy, gyz, gzz]
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
# plot the data
mpl.figure()
for i in xrange(len(tensor)):
mpl.subplot(2, 3, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, tensor[i], shape, 30)
mpl.colorbar()
mpl.xlabel('y (km)')
mpl.ylabel('x (km)')
mpl.m2km()
mpl.show()
# Inversion setup
# Create a mesh
mesh = PrismMesh(bounds, (30, 30, 30))
# Wrap the data so that harvester can use it
data = [gm.harvester.Gxx(xp, yp, zp, gxx),
gm.harvester.Gxy(xp, yp, zp, gxy),
gm.harvester.Gxz(xp, yp, zp, gxz),
gm.harvester.Gyy(xp, yp, zp, gyy),
gm.harvester.Gyz(xp, yp, zp, gyz),
gm.harvester.Gzz(xp, yp, zp, gzz)]
# Make the seeds
seeds = gm.harvester.sow([
"""
Gridding: Load a Surfer ASCII grid file
"""
from fatiando import datasets, gridder
from fatiando.vis import mpl
# Fetching Bouguer anomaly model data (Surfer ASCII grid file)"
# Will download the archive and save it with the default name
archive = datasets.fetch_bouguer_alps_egm()
# Load the GRD file and convert in three numpy-arrays (x, y, bouguer)
x, y, bouguer, shape = gridder.load_surfer(archive, fmt='ascii')
mpl.figure()
mpl.axis('scaled')
mpl.title("Data loaded from a Surfer ASCII grid file")
mpl.contourf(y, x, bouguer, shape, 15, cmap=mpl.cm.RdBu_r)
cb = mpl.colorbar()
cb.set_label('mGal')
mpl.xlabel('y points to East (km)')
mpl.ylabel('x points to North (km)')
mpl.m2km()
mpl.show()
print 'Estimated magnetization (intensity, inclination, declination)'
for e in solver.estimate_:
print e
# Plot the fit and the normalized histogram of the residuals
mpl.figure(figsize=(14, 5))
mpl.subplot(1, 2, 1)
mpl.title("Total Field Anomaly (nT)", fontsize=14)
mpl.axis('scaled')
nlevels = mpl.contour(y, x, tf, (50, 50), 15, interp=True, color='r',
label='Observed', linewidth=2.0)
mpl.contour(y, x, solver.predicted(), (50, 50), nlevels, interp=True,
color='b', label='Predicted', style='dashed', linewidth=2.0)
mpl.legend(loc='upper left', shadow=True, prop={'size': 13})
mpl.xlabel('East y (m)', fontsize=14)
mpl.ylabel('North x (m)', fontsize=14)
mpl.subplot(1, 2, 2)
residuals_mean = numpy.mean(solver.residuals())
residuals_std = numpy.std(solver.residuals())
# Each residual is subtracted from the mean and the resulting
# difference is divided by the standard deviation
s = (solver.residuals() - residuals_mean) / residuals_std
mpl.hist(s, bins=21, range=None, normed=True, weights=None,
cumulative=False, bottom=None, histtype='bar', align='mid',
orientation='vertical', rwidth=None, log=False,
color=None, label=None)
mpl.xlim(-4, 4)
mpl.title("mean = %.3f std = %.3f" % (residuals_mean, residuals_std),
fontsize=14)
mpl.ylabel("P(z)", fontsize=14)
mpl.xlabel("z", fontsize=14)
gxz = utils.contaminate(gm.prism.gxz(xp, yp, zp, model), noise)
gyy = utils.contaminate(gm.prism.gyy(xp, yp, zp, model), noise)
gyz = utils.contaminate(gm.prism.gyz(xp, yp, zp, model), noise)
gzz = utils.contaminate(gm.prism.gzz(xp, yp, zp, model), noise)
tensor = [gxx, gxy, gxz, gyy, gyz, gzz]
titles = ['gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
# plot the data
mpl.figure()
for i in xrange(len(tensor)):
mpl.subplot(2, 3, i + 1)
mpl.title(titles[i])
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, tensor[i], shape, 30)
mpl.colorbar()
mpl.xlabel('y (km)')
mpl.ylabel('x (km)')
mpl.m2km()
mpl.show()
# Inversion setup
# Create a mesh
mesh = PrismMesh(bounds, (30, 30, 30))
# Wrap the data so that harvester can use it
data = [
gm.harvester.Gxx(xp, yp, zp, gxx),
gm.harvester.Gxy(xp, yp, zp, gxy),
gm.harvester.Gxz(xp, yp, zp, gxz),
gm.harvester.Gyy(xp, yp, zp, gyy),
gm.harvester.Gyz(xp, yp, zp, gyz),
gm.harvester.Gzz(xp, yp, zp, gzz)
]
initial = mpl.pick_points(area, mpl.gca(), marker='*', color='b')
if len(initial) > 1:
print "Don't be greedy! Pick only one point"
sys.exit()
estimate = solver.config('levmarq', initial=initial[0]).fit().estimate_
mpl.figure(figsize=(10,4))
mpl.subplot(1, 2, 1)
mpl.title('Epicenter + %d recording stations' % (len(recs)))
mpl.axis('scaled')
mpl.points(src, '*y', label="True")
mpl.points(recs, '^r', label="Stations")
mpl.points(initial, '*b', label="Initial")
mpl.points([estimate], '*g', label="Estimate")
mpl.set_area(area)
mpl.legend(loc='lower right', shadow=True, numpoints=1, prop={'size':12})
mpl.xlabel("X")
mpl.ylabel("Y")
ax = mpl.subplot(1, 2, 2)
mpl.title('Travel-time residuals + error bars')
s = numpy.arange(len(traveltime)) + 1
width = 0.3
mpl.bar(s - width, traveltime, width, color='g', label="Observed",
yerr=error)
mpl.bar(s, solver.predicted(), width, color='r', label="Predicted")
ax.set_xticks(s)
mpl.legend(loc='upper right', shadow=True, prop={'size':12})
mpl.xlabel("Station number")
mpl.ylabel("Travel-time residual")
mpl.show()
interp=True,
color='r',
label='Observed',
linewidth=2.0)
mpl.contour(y,
x,
solver.predicted(), (50, 50),
nlevels,
interp=True,
color='b',
label='Predicted',
style='dashed',
linewidth=2.0)
mpl.legend(loc='upper left', shadow=True, prop={'size': 13})
mpl.xlabel('East y (m)', fontsize=14)
mpl.ylabel('North x (m)', fontsize=14)
mpl.subplot(1, 2, 2)
residuals_mean = numpy.mean(solver.residuals())
residuals_std = numpy.std(solver.residuals())
# Each residual is subtracted from the mean and the resulting
# difference is divided by the standard deviation
s = (solver.residuals() - residuals_mean) / residuals_std
mpl.hist(s,
bins=21,
range=None,
normed=True,
weights=None,
cumulative=False,
bottom=None,
histtype='bar',
align='mid',