def proj_polar(N,mag,color='k',simbolo='o',size=10):
'''
Generates a figure of a polar projection of estimates
input
N: int - number of prisms
mag: array - Matrix with shape (N x 3) containing intensity, declination and inclination
proj: array - list of projection values
return
Figure with polar projections of the estimates
'''
projections = []
for i in range(N):
projections.append(np.sqrt((np.cos(np.deg2rad(mag[i,1]))*np.cos(np.deg2rad(mag[i,2])))**2 +(np.cos(np.deg2rad(mag[i,1]))*np.sin(np.deg2rad(mag[i,2])))**2))
proj = np.array(projections)
for i in range(N):
if mag[i,1] >= 0.0:
mpl.plot(np.deg2rad(mag[i,2]), proj[i], marker=simbolo, ms=size,mec= color, mew=3, mfc= color, fillstyle='full')
else:
mpl.plot(np.deg2rad(mag[i,2]), proj[i], marker=simbolo, ms=size, mec= color, mew=3, fillstyle='none')
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
def plot_vnmo(cmp_gather, offsets, vnmo, dt, inc=70,
vmin=None, vmax=None, aspect='auto'):
r"""
Given nmo functions defined by t0 and vnmo, draw
it over the specified gather using `seismic_image`
Parameters:
* cmp_gather : 2D-array
traces of this gather from near to far-offset
(nsamples, ntraces)
* offsets : 1D-array
off-sets for each cmp in this gather
in the same sequence as ntraces
* vnmo : 1D-array
velocity parameter of all nmo functions for this cmp gather
must have same size as (nsamples)
* dt : float
sample rate
* inc: int
plotting option, step in time samples between hyperbolas
to avoid overlapping totally the seismic image bellow
* vmin, vmax : float
min and max values for imshow
* aspect : float
matplotlib imshow aspect parameter, ratio between axes
Returns:
* cmp_nmo : 2D array
nmo corrected cmp traces
"""
ns, nx = cmp_gather.shape
for i in range(0, ns, inc): # each (t0, vnmo) hyperbola
t0 = i*dt
t = np.sqrt(t0**2+(offsets/vnmo[i])**2)
mpl.seismic_image(cmp_gather, dt, aspect=aspect, vmin=vmin, vmax=vmax)
mpl.plot(range(nx), t, '+b')
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()
"""
GravMag: Generate synthetic gravity data on an irregular grid
"""
from fatiando import mesher, gridder, gravmag
from fatiando.vis import mpl
prisms = [mesher.Prism(-2000, 2000, -2000, 2000, 0, 2000, {'density':1000})]
xp, yp, zp = gridder.scatter((-5000, 5000, -5000, 5000), n=100, z=-100)
gz = gravmag.prism.gz(xp, yp, zp, prisms)
shape = (100,100)
mpl.axis('scaled')
mpl.title("gz produced by prism model on an irregular grid (mGal)")
mpl.plot(xp, yp, '.k', label='Grid points')
levels = mpl.contourf(xp, yp, gz, shape, 12, interp=True)
mpl.contour(xp, yp, gz, shape, levels, interp=True)
mpl.legend(loc='lower right', numpoints=1)
mpl.m2km()
mpl.show()
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.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)")
from fatiando.vis import mpl
verts = [(10000, 1.), (90000, 1.), (80000, 5000)]
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]), 1)
solver = inversion.gradient.levmarq(initial=(10000, 1000))
estimate, residuals = gravmag.basin2d.triangular(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')
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")
x, y = gridder.scatter((-2, 2, -2, 2), n=300, seed=1)
# And calculate 2D Gaussians on these points as sample data
def data(x, y):
return (utils.gaussian2d(x, y, -0.6, -1) -
utils.gaussian2d(x, y, 1.5, 1.5))
d = data(x, y)
# Extract a profile along the diagonal
p1, p2 = [-1.5, 0], [1.5, 1.5]
xp, yp, distance, dp = gridder.profile(x, y, d, p1, p2, 100)
dp_true = data(xp, yp)
mpl.figure()
mpl.subplot(2, 1, 2)
mpl.title("Irregular grid")
mpl.plot(xp, yp, '-k', label='Profile', linewidth=2)
mpl.contourf(x, y, d, (100, 100), 50, interp=True)
mpl.colorbar(orientation='horizontal')
mpl.legend(loc='lower right')
mpl.subplot(2, 1, 1)
mpl.title('Profile')
mpl.plot(distance, dp, '.b', label='Extracted')
mpl.plot(distance, dp_true, '-k', label='True')
mpl.xlim(distance.min(), distance.max())
mpl.legend(loc='lower right')
mpl.show()
def data(x, y):
return utils.gaussian2d(x, y, -0.6, -1) - utils.gaussian2d(x, y, 1.5, 1.5)
z = data(x, y)
shape = (100, 100)
# First, we need to know the real data at the grid points
grdx, grdy = gridder.regular(area, shape)
grdz = data(grdx, grdy)
mpl.figure()
mpl.subplot(2, 2, 1)
mpl.axis("scaled")
mpl.title("True grid data")
mpl.plot(x, y, ".k", label="Data points")
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc="lower right", numpoints=1)
# Use the default interpolation (cubic)
grdx, grdy, grdz = gridder.interp(x, y, z, shape)
mpl.subplot(2, 2, 2)
mpl.axis("scaled")
mpl.title("Interpolated using cubic minimum-curvature")
mpl.plot(x, y, ".k", label="Data points")
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc="lower right", numpoints=1)
# Use the nearest neighbors interpolation
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
"""
t, u, seismograms = simulation.next()
mpl.title('time: %0.1f s' % (times[t]))
wavefield_plt.set_array(u[::-1]) # Revert the z axis so that 0 is top
# Make some synthetic gravity data from a simple prism model
model = [mesher.Prism(-4000, 0, -4000, -2000, 2000, 5000, {'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=-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()
# Get the iterator. This part only generates an iterator object. The actual
# computations take place at each iteration in the for loop below
dt = wavefd.maxdt(area, shape, svel.max())
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")
"""
from fatiando import mesher, gridder, utils, gravmag
from fatiando.vis import mpl
spheres = [mesher.Sphere(0, 0, 2000, 1000, {'density': 1000})]
# Create a set of points at 100m height
area = (-5000, 5000, -5000, 5000)
xp, yp, zp = gridder.scatter(area, 500, z=-100)
# Calculate the anomaly
gz = utils.contaminate(gravmag.sphere.gz(xp, yp, zp, spheres), 0.1)
gzz = utils.contaminate(gravmag.sphere.gzz(xp, yp, zp, spheres), 5.0)
# Plot
shape = (100, 100)
mpl.figure()
mpl.title("gz (mGal)")
mpl.axis('scaled')
mpl.plot(yp * 0.001, xp * 0.001, '.k')
mpl.contourf(yp * 0.001, xp * 0.001, gz, shape, 15, interp=True)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.figure()
mpl.title("gzz (Eotvos)")
mpl.axis('scaled')
mpl.plot(yp * 0.001, xp * 0.001, '.k')
mpl.contourf(yp * 0.001, xp * 0.001, gzz, shape, 15, interp=True)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.show()
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
"""
t, u, seismograms = simulation.next()
mpl.title('time: %0.1f s' % (times[t]))
wavefield_plt.set_array(u[::-1]) # Revert the z axis so that 0 is top
return (utils.gaussian2d(x, y, -0.6, -1) -
utils.gaussian2d(x, y, 1.5, 1.5))
z = data(x, y)
shape = (100, 100)
# First, we need to know the real data at the grid points
grdx, grdy = gridder.regular(area, shape)
grdz = data(grdx, grdy)
mpl.figure()
mpl.subplot(2, 2, 1)
mpl.axis('scaled')
mpl.title("True grid data")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the default interpolation (cubic)
grdx, grdy, grdz = gridder.interp(x, y, z, shape)
mpl.subplot(2, 2, 2)
mpl.axis('scaled')
mpl.title("Interpolated using cubic minimum-curvature")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the nearest neighbors interpolation
verts = [(10000, 1.), (90000, 1.), (90000, 7000), (10000, 3330)]
model = Polygon(verts, {'density': -100})
x = numpy.arange(0., 100000., 1000.)
z = numpy.zeros_like(x)
gz = utils.contaminate(talwani.gz(x, z, [model]), 0.5)
solver = basin2d.Trapezoidal(x, z, gz, verts[0:2],
density=-100).config('levmarq',
initial=[9000, 500]).fit()
estimate = solver.estimate_
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.title("Gravity anomaly")
mpl.plot(x, gz, 'ok', label='Observed')
mpl.plot(x, solver.predicted(), '-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")
"""
GravMag: Generate synthetic gravity data on an irregular grid
"""
from fatiando import mesher, gridder, gravmag
from fatiando.vis import mpl
prisms = [mesher.Prism(-2000, 2000, -2000, 2000, 0, 2000, {'density': 1000})]
xp, yp, zp = gridder.scatter((-5000, 5000, -5000, 5000), n=100, z=-100)
gz = gravmag.prism.gz(xp, yp, zp, prisms)
shape = (100, 100)
mpl.axis('scaled')
mpl.title("gz produced by prism model on an irregular grid (mGal)")
mpl.plot(xp, yp, '.k', label='Grid points')
levels = mpl.contourf(xp, yp, gz, shape, 12, interp=True)
mpl.contour(xp, yp, gz, shape, levels, interp=True)
mpl.legend(loc='lower right', numpoints=1)
mpl.m2km()
mpl.show()
from fatiando.gravmag import talwani, basin2d
from fatiando.vis import mpl
verts = [(10000, 1.), (90000, 1.), (90000, 7000), (10000, 3330)]
model = Polygon(verts, {'density':-100})
x = numpy.arange(0., 100000., 1000.)
z = numpy.zeros_like(x)
gz = utils.contaminate(talwani.gz(x, z, [model]), 0.5)
solver = basin2d.Trapezoidal(x, z, gz, verts[0:2], density=-100).config(
'levmarq', initial=[9000, 500]).fit()
estimate = solver.estimate_
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.title("Gravity anomaly")
mpl.plot(x, gz, 'ok', label='Observed')
mpl.plot(x, solver.predicted(), '-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()
depths = (-1e-15*(xs - 50000)**4 + 8000 -
3000*np.exp(-(xs - 70000)**2/(10000**2)))
depths -= depths.min() # Reduce depths to zero
props = {'density': -300}
model = Polygon(np.transpose([xs, depths]), props)
x = np.linspace(0, 100000, 100)
z = -100*np.ones_like(x)
data = utils.contaminate(talwani.gz(x, z, [model]), 0.5, seed=0)
# Make the solver using smoothness regularization and run the inversion
misfit = PolygonalBasinGravity(x, z, data, 50, props, top=0)
regul = Smoothness1D(misfit.nparams)
solver = misfit + 1e-4*regul
# This is a non-linear problem so we need to pick an initial estimate
initial = 3000*np.ones(misfit.nparams)
solver.config('levmarq', initial=initial).fit()
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.plot(x, data, 'ok', label='observed')
mpl.plot(x, solver[0].predicted(), '-r', linewidth=2, label='predicted')
mpl.legend()
ax = mpl.subplot(2, 1, 2)
mpl.polygon(model, fill='gray', alpha=0.5, label='True')
# The estimate_ property of our solver gives us the estimate basin as a polygon
# So we can directly pass it to plotting and forward modeling functions
mpl.polygon(solver.estimate_, style='o-r', label='Estimated')
ax.invert_yaxis()
mpl.legend()
mpl.show()
# Get the iterator for the simulation
dt = wavefd.maxdt(area, shape, pvel)
duration = 20
maxit = int(duration / dt)
stations = [[55000, 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_psv(lamb, mu, density, area, 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)')
mpl.ylabel('z (km)')
# Generate random points
x, y = gridder.scatter((-2, 2, -2, 2), n=300, seed=1)
# And calculate 2D Gaussians on these points as sample data
def data(x, y):
return (utils.gaussian2d(x, y, -0.6, -1)
- utils.gaussian2d(x, y, 1.5, 1.5))
d = data(x, y)
# Extract a profile along the diagonal
p1, p2 = [-1.5, 0], [1.5, 1.5]
xp, yp, distance, dp = gridder.profile(x, y, d, p1, p2, 100)
dp_true = data(xp, yp)
mpl.figure()
mpl.subplot(2, 1, 2)
mpl.title("Irregular grid")
mpl.plot(xp, yp, '-k', label='Profile', linewidth=2)
mpl.contourf(x, y, d, (100, 100), 50, interp=True)
mpl.colorbar(orientation='horizontal')
mpl.legend(loc='lower right')
mpl.subplot(2, 1, 1)
mpl.title('Profile')
mpl.plot(distance, dp, '.b', label='Extracted')
mpl.plot(distance, dp_true, '-k', label='True')
mpl.xlim(distance.min(), distance.max())
mpl.legend(loc='lower right')
mpl.show()
# And calculate 2D Gaussians on these points as sample data
def data(x, y):
return (utils.gaussian2d(x, y, -0.6, -1)
- utils.gaussian2d(x, y, 1.5, 1.5))
z = data(x, y)
shape = (100, 100)
# First, we need to know the real data at the grid points
grdx, grdy = gridder.regular(area, shape)
grdz = data(grdx, grdy)
mpl.figure()
mpl.subplot(2, 2, 1)
mpl.axis('scaled')
mpl.title("True grid data")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the default interpolation (cubic)
grdx, grdy, grdz = gridder.interp(x, y, z, shape)
mpl.subplot(2, 2, 2)
mpl.axis('scaled')
mpl.title("Interpolated using cubic minimum-curvature")
mpl.plot(x, y, '.k', label='Data points')
mpl.contourf(grdx, grdy, grdz, shape, 50)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
# Use the nearest neighbors interpolation
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")
mpl.ylabel("Z")
mpl.set_area(area)
mpl.show()
tts, error = utils.contaminate(
layered_straight_ray(thickness, velocity, zp),
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)")
from fatiando.geothermal.climsig import abrupt, SingleChange
from fatiando.vis import mpl
# Generating synthetic data using an ABRUPT model
amp = 3
age = 54
# along a well at these depths
zp = numpy.arange(0, 100, 1)
temp, error = utils.contaminate(abrupt(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 "Trying to invert an abrupt change as linear"
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()
# Generating synthetic data using an ABRUPT model
amp = 3
age = 54
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)")
points2pad = raw_input("\nAmmount of spectrum points (default = "+
str(default_spectrum_points) + ", 0 means no padding): ")
if points2pad == "":
points2pad = default_spectrum_points
else:
points2pad = int(points2pad)
points2pad *= 2
# Seleccion de la ventana
bool_plot = False
while bool_plot == False:
fig, (ax1,ax2) = plt.subplots(1,2)
ax2.set_aspect('equal')
if tmp_exists == True:
mpl.plot(x_last_point,y_last_point,'o',color='w')
if outfile_exists == True:
mpl.plot(x_done_points[:-1],y_done_points[:-1],'o',color='k')
mpl.plot(x_done_points[-1],y_done_points[-1],'s',color='k')
mpl.contourf(x,y,anomaly,shape,50,interp=False)
mpl.colorbar()
window = WindowConstruction(x,y,shape,anomaly,ax2,ax1,points2pad)
mpl.show()
if window.x_center != None:
bool_plot = True
# Recupero los datos de la ventana
x_center, y_center = window.x_center, window.y_center
width = 2*window.half_width
print "(x,y)=",(x_center,y_center),"Width:",width
density,
area,
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')
"""
Gridding: Generate and plot irregular grids (scatter)
"""
from fatiando import gridder, utils
from fatiando.vis import mpl
# Generate random points
x, y = gridder.scatter((-2, 2, -2, 2), n=200)
# And calculate a 2D Gaussian on these points
z = utils.gaussian2d(x, y, 1, 1)
mpl.axis('scaled')
mpl.title("Irregular grid")
mpl.plot(x, y, '.k', label='Grid points')
# Make a filled contour plot and tell the function to automatically interpolate
# the data on a 100x100 grid
mpl.contourf(x, y, z, (100, 100), 50, interp=True)
mpl.colorbar()
mpl.legend(loc='lower right', numpoints=1)
mpl.show()
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()
# Plot the layer and the fit
mpl.figure(figsize=(14, 4))
mpl.suptitle('Observed data (black) | Predicted by layer (red)')
mpl.subplot(1, 3, 1)
mpl.axis('scaled')
mpl.title('Layer (kg.m^-3)')
mpl.pcolor(layer.y, layer.x, layer.props['density'], layer.shape)
mpl.colorbar().set_label(r'Density $kg.m^{-3}$')
mpl.m2km()
mpl.subplot(1, 3, 2)
mpl.axis('scaled')
mpl.title('Fit gz (mGal)')
levels = mpl.contour(y1, x1, gz, shape, 15, color='k', interp=True)
mpl.contour(y1, x1, solver.predicted()[0], shape, levels, color='r',
interp=True)
mpl.plot(y1, x1, 'xk', label='Data points')
mpl.legend()
mpl.m2km()
mpl.subplot(1, 3, 3)
mpl.axis('scaled')
mpl.title('Fit gzz (Eotvos)')
levels = mpl.contour(y2, x2, gzz, shape, 10, color='k', interp=True)
mpl.contour(y2, x2, solver.predicted()[1], shape, levels, color='r',
interp=True)
mpl.plot(y2, x2, 'xk', label='Data points')
mpl.legend()
mpl.m2km()
mpl.figure()
mpl.suptitle('Interpolated gz at ground level')
mpl.subplot(1, 2, 1)
amp = 3
age = 54
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
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)")
"""
GravMag: Forward modeling of the gravity anomaly using spheres (calculate on
random points)
"""
from fatiando import logger, mesher, gridder, utils, gravmag
from fatiando.vis import mpl
log = logger.get()
log.info(logger.header())
log.info(__doc__)
spheres = [mesher.Sphere(0, 0, -2000, 1000, {'density':1000})]
# Create a set of points at 100m height
area = (-5000, 5000, -5000, 5000)
xp, yp, zp = gridder.scatter(area, 500, z=-100)
# Calculate the anomaly
gz = utils.contaminate(gravmag.sphere.gz(xp, yp, zp, spheres), 0.1)
# Plot
shape = (100, 100)
mpl.figure()
mpl.title("gz (mGal)")
mpl.axis('scaled')
mpl.plot(yp*0.001, xp*0.001, '.k')
mpl.contourf(yp*0.001, xp*0.001, gz, shape, 15, interp=True)
mpl.colorbar()
mpl.xlabel('East y (km)')
mpl.ylabel('North x (km)')
mpl.show()
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")
mpl.ylabel("Z")
mpl.set_area(area)
mpl.show()
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,
mesher.Prism(-4000, 0, -4000, -2000, 2000, 5000, {'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=-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()
mpl.title('Layer (kg.m^-3)')
mpl.pcolor(layer.y, layer.x, layer.props['density'], layer.shape)
mpl.colorbar().set_label(r'Density $kg.m^{-3}$')
mpl.m2km()
mpl.subplot(1, 3, 2)
mpl.axis('scaled')
mpl.title('Fit gz (mGal)')
levels = mpl.contour(y1, x1, gz, shape, 15, color='k', interp=True)
mpl.contour(y1,
x1,
solver.predicted()[0],
shape,
levels,
color='r',
interp=True)
mpl.plot(y1, x1, 'xk', label='Data points')
mpl.legend()
mpl.m2km()
mpl.subplot(1, 3, 3)
mpl.axis('scaled')
mpl.title('Fit gzz (Eotvos)')
levels = mpl.contour(y2, x2, gzz, shape, 10, color='k', interp=True)
mpl.contour(y2,
x2,
solver.predicted()[1],
shape,
levels,
color='r',
interp=True)
mpl.plot(y2, x2, 'xk', label='Data points')
mpl.legend()
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()
x = np.linspace(0, 100000, 100)
z = -100*np.ones_like(x)
data = utils.contaminate(talwani.gz(x, z, [model]), 0.5, seed=0)
# Make the solver using smoothness regularization and run the inversion
misfit = PolygonalBasinGravity(x, z, data, 50, props, top=0)
regul = Smoothness1D(misfit.nparams)
solver = misfit + 1e-4*regul
# This is a non-linear problem so we need to pick an initial estimate
initial = 3000*np.ones(misfit.nparams)
solver.config('levmarq', initial=initial).fit()
mpl.figure()
mpl.subplot(2, 1, 1)
mpl.plot(x, data, 'ok', label='Gravity Data')
mpl.plot(x, solver[0].predicted(), '-r', linewidth=2, label='predicted Gravity')
mpl.legend()
ax = mpl.subplot(2, 1, 2)
mpl.polygon(model, fill='gray', alpha=0.5, label='Polygon')
# The estimate_ property of our solver gives us the estimate basin as a polygon
# So we can directly pass it to plotting and forward modeling functions
mpl.polygon(solver.estimate_, style='o-r', label='Inverted')
ax.invert_yaxis()
mpl.legend()
mpl.show()
# columns = ['data','depths']
# values = np.array([data,depths])
# df = pd.DataFrame(data=values.T,columns=columns, index = xs)
# df.to_csv('Fatiando_2DBasin_forGMSYS.csv')
