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()
dt = wavefd.scalar_maxdt(area, shape, np.max(velocity))
duration = 2.5
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
maxit = int(duration/dt)
stations = [[2200+i*dx, 0] for i in range(220)] # x, z coordinate of the seismometers
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])
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()
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.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(thickness), 0)
mpl.subplot(1, 2, 2)
mpl.grid()
mpl.title("Velocity profile")
mpl.layers(thickness, velocity_, 'o-k', linewidth=2, label='Estimated')
mpl.layers(thickness, velocity, '--b', linewidth=2, label='True')
mpl.ylim(zmax, zmin)
mpl.xlim(vmin, vmax)
leg = mpl.legend(loc='upper right', numpoints=1)
leg.get_frame().set_alpha(0.5)
mpl.xlabel("Velocity (m/s)")
mpl.ylabel("Z (m)")
mpl.show()
dt,
maxit,
sources,
stations,
snapshot,
padding=50,
taper=0.01,
xz2ps=True)
# This part makes an animation using matplotlibs animation API
fig = mpl.figure(figsize=(12, 5))
mpl.subplot(2, 2, 2)
mpl.title('x component')
xseismogram, = mpl.plot([], [], '-k')
mpl.xlim(0, duration)
mpl.ylim(-10**(-3), 10**(-3))
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)')
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)
ax2.set_ylim(0, 4)
sources,
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)
0.02, 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.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()
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])
maxit = int(duration / dt)
stations = [[50000, 0]] # x, z coordinate of the seismometer
snapshot = int(0.5 / dt) # Plot a snapshot of the simulation every 0.5 seconds
simulation = wavefd.elastic_sh(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=(14, 5))
ax = mpl.subplot(1, 2, 2)
mpl.title('Wavefield')
# Start with everything zero and grab the plot so that it can be updated later
wavefield_plt = mpl.imshow(np.zeros(shape), extent=area, vmin=-10 ** (-5),
vmax=10 ** (-5), cmap=mpl.cm.gray_r)
mpl.points(stations, '^b')
mpl.xlim(area[:2])
mpl.ylim(area[2:][::-1])
mpl.xlabel('x (km)')
mpl.ylabel('z (km)')
mpl.subplot(1, 2, 1)
seismogram_plt, = mpl.plot([], [], '-k')
mpl.xlim(0, duration)
mpl.ylim(-10 ** (-4), 10 ** (-4))
mpl.xlabel('time (s)')
mpl.ylabel('Amplitude')
times = np.linspace(0, duration, maxit)
# Update the plot everytime the simulation yields
def animate(i):
"""
Grab the iteration number, displacment panel and seismograms
maxit = int(duration/dt)
stations = [[550000, 0]]
snapshots = int(1./dt)
simulation = wavefd.elastic_psv(lamb, mu, density, area, dt, maxit, sources,
stations, snapshots, padding=70, taper=0.005, xz2ps=True)
# This part makes an animation using matplotlibs animation API
background = 10**-5*((pvel - pvel.min())/pvel.max())
fig = mpl.figure(figsize=(10, 8))
mpl.subplots_adjust(right=0.98, left=0.11, hspace=0.3, top=0.93)
mpl.subplot(2, 1, 1)
mpl.title('x seismogram')
xseismogram, = mpl.plot([],[],'-k')
mpl.xlim(0, duration)
mpl.ylim(-0.05, 0.05)
mpl.ylabel('Amplitude')
ax = mpl.subplot(2, 1, 2)
mpl.title('time: 0.0 s')
wavefield = mpl.imshow(density, extent=area, cmap=mpl.cm.gray_r,
vmin=-0.00001, vmax=0.00001)
mpl.points(stations, '^b', size=8)
#mpl.text(500000, 20000, 'Crust')
#mpl.text(500000, 60000, 'Mantle')
fig.text(0.8, 0.5, 'Seismometer')
mpl.xlim(area[:2])
mpl.ylim(area[2:][::-1])
mpl.xlabel('x (km)')
mpl.ylabel('z (km)')
mpl.m2km()
times = np.linspace(0, dt*maxit, maxit)
dt = wavefd.maxdt(area, shape, svel.max())
duration = 250
maxit = int(duration / dt)
stations = [[100000, 0], [700000, 0]]
snapshots = int(1. / 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
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(np.zeros_like(density), extent=area, cmap=mpl.cm.gray_r,
vmin=-0.005, vmax=0.005)
mpl.points(stations, '^b', size=8)
fig.text(0.82, 0.33, 'Seismometer 2')
fig.text(0.16, 0.33, 'Seismometer 1')
mpl.ylim(area[2:][::-1])
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.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(thickness), 0)
mpl.subplot(1, 2, 2)
mpl.grid()
mpl.title("Velocity profile")
mpl.layers(thickness, velocity_, 'o-k', linewidth=2, label='Estimated')
mpl.layers(thickness, velocity, '--b', linewidth=2, label='True')
mpl.ylim(zmax, zmin)
mpl.xlim(vmin, vmax)
leg = mpl.legend(loc='upper right', numpoints=1)
leg.get_frame().set_alpha(0.5)
mpl.xlabel("Velocity (m/s)")
mpl.ylabel("Z (m)")
mpl.show()
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)
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])