# Set the parameters of the finite difference grid
velocity = np.zeros(shape)+6000.
velocity[100:,100:] = 0.
fc = 15.
sources = [wavefd.GaussSource(125*ds, 75*ds, area, shape, 1., fc)]
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
shape = (100,100)
xp, yp, zp = gridder.regular((-5000, 5000, -5000, 5000), shape, z=-150)
fields = [prism.potential(xp, yp, zp, model),
prism.gx(xp, yp, zp, model),
prism.gy(xp, yp, zp, model),
prism.gz(xp, yp, zp, model),
prism.gxx(xp, yp, zp, model),
prism.gxy(xp, yp, zp, model),
prism.gxz(xp, yp, zp, model),
prism.gyy(xp, yp, zp, model),
prism.gyz(xp, yp, zp, model),
prism.gzz(xp, yp, zp, model)]
titles = ['potential', 'gx', 'gy', 'gz',
'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz']
mpl.figure(figsize=(8, 9))
mpl.subplots_adjust(left=0.03, right=0.95, bottom=0.05, top=0.92, hspace=0.3)
mpl.suptitle("Potential fields produced by a 3 prism model")
for i, field in enumerate(fields):
mpl.subplot(4, 3, i + 3)
mpl.axis('scaled')
mpl.title(titles[i])
levels = mpl.contourf(yp*0.001, xp*0.001, field, shape, 15)
cb = mpl.colorbar()
mpl.contour(yp*0.001, xp*0.001, field, shape, levels, clabel=False, linewidth=0.1)
mpl.show()
myv.figure()
myv.prisms(model, prop='density')
axes = myv.axes(myv.outline())
myv.wall_bottom(axes.axes.bounds, opacity=0.2)
myv.wall_north(axes.axes.bounds)
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 * ((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,
gravmag.prism.potential(xp, yp, zp, prisms),
gravmag.prism.gx(xp, yp, zp, prisms),
gravmag.prism.gy(xp, yp, zp, prisms),
gravmag.prism.gz(xp, yp, zp, prisms),
gravmag.prism.gxx(xp, yp, zp, prisms),
gravmag.prism.gxy(xp, yp, zp, prisms),
gravmag.prism.gxz(xp, yp, zp, prisms),
gravmag.prism.gyy(xp, yp, zp, prisms),
gravmag.prism.gyz(xp, yp, zp, prisms),
gravmag.prism.gzz(xp, yp, zp, prisms)
]
titles = [
'potential', 'gx', 'gy', 'gz', 'gxx', 'gxy', 'gxz', 'gyy', 'gyz', 'gzz'
]
mpl.figure(figsize=(8, 9))
mpl.subplots_adjust(left=0.03, right=0.95, bottom=0.05, top=0.92, hspace=0.3)
mpl.suptitle("Potential fields produced by a 3 prism model")
for i, field in enumerate(fields):
mpl.subplot(4, 3, i + 3)
mpl.axis('scaled')
mpl.title(titles[i])
levels = mpl.contourf(yp * 0.001, xp * 0.001, field, shape, 15)
cb = mpl.colorbar()
mpl.contour(yp * 0.001,
xp * 0.001,
field,
shape,
levels,
clabel=False,
linewidth=0.1)
mpl.show()
shp = (70, 560)
nz, nx = shp # bellow load geologic model velociy model
vmodel = utils.fromimage('pinchout.bmp', ranges=[2500., 3500.], shape=shp)
twti = np.cumsum(ds / vmodel,
axis=0) * 2 # calculate irregular sampled twt times
twt = np.arange(0, np.max(twti) + 0.10, dt) # new twt times re-sampled to 4 ms
dnx = int(nx / disc)
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
gyz = utils.si2eotvos(transform.derivy(xp, yp, utils.mgal2si(gz), shape))
gzz = utils.si2eotvos(transform.derivz(xp, yp, utils.mgal2si(gz), shape))
gxz_true = prism.gxz(xp, yp, zp, model)
gyz_true = prism.gyz(xp, yp, zp, model)
gzz_true = prism.gzz(xp, yp, zp, model)
mpl.figure()
mpl.title("Original gravity anomaly")
mpl.axis('scaled')
mpl.contourf(xp, yp, gz, shape, 15)
mpl.colorbar(shrink=0.7)
mpl.m2km()
mpl.figure(figsize=(14, 10))
mpl.subplots_adjust(top=0.95, left=0.05, right=0.95)
mpl.subplot(2, 3, 1)
mpl.title("x deriv (contour) + true (color map)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gxz_true, shape, 12)
mpl.colorbar(shrink=0.7)
mpl.contour(yp, xp, gxz, shape, 12, color='k')
mpl.m2km()
mpl.subplot(2, 3, 2)
mpl.title("y deriv (contour) + true (color map)")
mpl.axis('scaled')
levels = mpl.contourf(yp, xp, gyz_true, shape, 12)
mpl.colorbar(shrink=0.7)
mpl.contour(yp, xp, gyz, shape, 12, color='k')
mpl.m2km()
mpl.subplot(2, 3, 3)
ds = 10. # depth increment
f = 30. # approximated frequency ricker wavelet (scipy a=1/(2.f.dt))
disc = 10 # space discretization
shp = (70, 560)
nz, nx = shp # bellow load geologic model velociy model
vmodel = utils.fromimage('pinchout.bmp', ranges=[2500., 3500.], shape=shp)
twti = np.cumsum(ds/vmodel, axis=0)*2 # calculate irregular sampled twt times
twt = np.arange(0, np.max(twti)+0.10, dt) # new twt times re-sampled to 4 ms
dnx = int(nx/disc)
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",
