"""
Seismic: 2D straight-ray tomography using smoothness regularization
"""
import numpy as np
from fatiando.mesher import SquareMesh
from fatiando.seismic import ttime2d, srtomo
from fatiando.inversion.regularization import Smoothness2D, LCurve
from fatiando.vis import mpl
from fatiando import utils
area = (0, 500000, 0, 500000)
shape = (30, 30)
model = SquareMesh(area, shape)
vel = 4000 * np.ones(shape)
vel[5:25, 5:25] = 10000
model.addprop('vp', vel.ravel())
# Make some travel time data and add noise
seed = 0 # Set the random seed so that points are the same every time
src_loc = utils.random_points(area, 80, seed=seed)
rec_loc = utils.circular_points(area, 30, random=True, seed=seed)
srcs, recs = utils.connect_points(src_loc, rec_loc)
tts = ttime2d.straight(model, 'vp', srcs, recs)
tts, error = utils.contaminate(tts,
0.02,
percent=True,
return_stddev=True,
seed=seed)
# Make the mesh
mesh = SquareMesh(area, shape)
# and run the inversion
"""
import numpy as np
import matplotlib.pyplot as plt
from fatiando.mesher import SquareMesh
from fatiando.seismic import ttime2d, srtomo
from fatiando.inversion import Smoothness2D, Damping, TotalVariation2D
from fatiando import utils, gridder
# First, we'll create a simple model with a high velocity square in the middle
area = (0, 500000, 0, 500000)
shape = (30, 30)
model = SquareMesh(area, shape)
vel = 4000 * np.ones(shape)
vel[5:25, 5:25] = 10000
model.addprop('vp', vel.ravel())
# Make some noisy travel time data using straight-rays
# Set the random seed so that points are the same every time we run this script
seed = 0
src_loc_x, src_loc_y = gridder.scatter(area, 80, seed=seed)
src_loc = np.transpose([src_loc_x, src_loc_y])
rec_loc_x, rec_loc_y = gridder.circular_scatter(area, 30,
random=True, seed=seed)
rec_loc = np.transpose([rec_loc_x, rec_loc_y])
srcs = [src for src in src_loc for _ in rec_loc]
recs = [rec for _ in src_loc for rec in rec_loc]
tts = ttime2d.straight(model, 'vp', srcs, recs)
# Use 2% random noise to corrupt the data
tts = utils.contaminate(tts, 0.02, percent=True, seed=seed)
"""
Seismic: 2D straight-ray tomography using smoothness regularization
"""
import numpy as np
from fatiando.mesher import SquareMesh
from fatiando.seismic import ttime2d, srtomo
from fatiando.inversion.regularization import Smoothness2D, LCurve
from fatiando.vis import mpl
from fatiando import utils
area = (0, 500000, 0, 500000)
shape = (30, 30)
model = SquareMesh(area, shape)
vel = 4000 * np.ones(shape)
vel[5:25, 5:25] = 10000
model.addprop('vp', vel.ravel())
# Make some travel time data and add noise
seed = 0 # Set the random seed so that points are the same every time
src_loc = utils.random_points(area, 80, seed=seed)
rec_loc = utils.circular_points(area, 30, random=True, seed=seed)
srcs, recs = utils.connect_points(src_loc, rec_loc)
tts = ttime2d.straight(model, 'vp', srcs, recs)
tts, error = utils.contaminate(tts, 0.02, percent=True, return_stddev=True,
seed=seed)
# Make the mesh
mesh = SquareMesh(area, shape)
# and run the inversion
misfit = srtomo.SRTomo(tts, srcs, recs, mesh)
regularization = Smoothness2D(mesh.shape)
# Will use the l-curve criterion to find the best regularization parameter
# Make some travel time data and add noise
seed = 0 # Set the random seed so that points are the same everythime
src_loc = utils.random_points(area, 80, seed=seed)
rec_loc = utils.circular_points(area, 30, random=True, seed=seed)
srcs, recs = utils.connect_points(src_loc, rec_loc)
tts = ttime2d.straight(model, 'vp', srcs, recs)
tts, error = utils.contaminate(tts, 0.01, percent=True, return_stddev=True)
# Make the mesh
mesh = SquareMesh(area, shape)
# and run the inversion
start = time.time()
tomo = srtomo.SRTomo(tts, srcs, recs, mesh) + 10**6*Damping(mesh.size)
estimate = tomo.fit().estimate_
residuals = tomo.residuals()
print "time: %g s" % (time.time() - start)
mesh.addprop('vp', estimate)
# Calculate and print the standard deviation of the residuals
# it should be close to the data error if the inversion was able to fit the data
print "Assumed error: %g" % (error)
print "Standard deviation of residuals: %g" % (numpy.std(residuals))
mpl.figure(figsize=(14, 5))
mpl.subplot(1, 2, 1)
mpl.axis('scaled')
mpl.title('Vp synthetic model of the Earth')
mpl.squaremesh(model, prop='vp', cmap=mpl.cm.seismic)
cb = mpl.colorbar()
cb.set_label('Velocity')
mpl.points(src_loc, '*y', label="Sources")
mpl.points(rec_loc, '^r', label="Receivers")
"""
import numpy as np
import matplotlib.pyplot as plt
from fatiando.mesher import SquareMesh
from fatiando.seismic import ttime2d, srtomo
from fatiando.inversion import Smoothness2D, Damping, TotalVariation2D
from fatiando import utils, gridder
# First, we'll create a simple model with a high velocity square in the middle
area = (0, 500000, 0, 500000)
shape = (30, 30)
model = SquareMesh(area, shape)
vel = 4000 * np.ones(shape)
vel[5:25, 5:25] = 10000
model.addprop('vp', vel.ravel())
# Make some noisy travel time data using straight-rays
# Set the random seed so that points are the same every time we run this script
seed = 0
src_loc_x, src_loc_y = gridder.scatter(area, 80, seed=seed)
src_loc = np.transpose([src_loc_x, src_loc_y])
rec_loc_x, rec_loc_y = gridder.circular_scatter(area,
30,
random=True,
seed=seed)
rec_loc = np.transpose([rec_loc_x, rec_loc_y])
srcs = [src for src in src_loc for _ in rec_loc]
recs = [rec for _ in src_loc for rec in rec_loc]
tts = ttime2d.straight(model, 'vp', srcs, recs)
# Use 2% random noise to corrupt the data
src_loc = utils.random_points(area, 80, seed=seed)
rec_loc = utils.circular_points(area, 30, random=True, seed=seed)
srcs, recs = utils.connect_points(src_loc, rec_loc)
tts = ttime2d.straight(model, 'vp', srcs, recs)
tts, error = utils.contaminate(tts, 0.01, percent=True, return_stddev=True)
# Make the mesh
mesh = SquareMesh(area, shape)
# and run the inversion
tomo = (srtomo.SRTomo(tts, srcs, recs, mesh) +
1*TotalVariation2D(10**-8, mesh.shape))
# Since Total Variation is a non-linear function, then the tomography becomes
# non-linear. So we need to configure fit to use the Levemberg-Marquardt
# algorithm, a gradient descent method, that requires an initial estimate
tomo.config('levmarq', initial=0.0005*numpy.ones(mesh.size)).fit()
residuals = tomo.residuals()
mesh.addprop('vp', tomo.estimate_)
# Calculate and print the standard deviation of the residuals
# it should be close to the data error if the inversion was able to fit the data
print "Assumed error: %f" % (error)
print "Standard deviation of residuals: %f" % (numpy.std(residuals))
mpl.figure(figsize=(14, 5))
mpl.subplot(1, 2, 1)
mpl.axis('scaled')
mpl.title('Vp synthetic model of the Earth')
mpl.squaremesh(model, prop='vp', vmin=vmin, vmax=vmax,
cmap=mpl.cm.seismic)
cb = mpl.colorbar()
cb.set_label('Velocity')
mpl.points(src_loc, '*y', label="Sources")
