def test_general():
"""
General test of the class SRTomo, as it is in the docs of this class.
"""
model = SquareMesh((0, 10, 0, 10), shape=(2, 1), props={'vp': [2., 5.]})
src = (5, 0)
srcs = [src, src]
recs = [(0, 0), (5, 10)]
ttimes = ttime2d.straight(model, 'vp', srcs, recs)
mesh = SquareMesh((0, 10, 0, 10), shape=(2, 1))
tomo = srtomo.SRTomo(ttimes, srcs, recs, mesh)
assert_array_almost_equal(tomo.fit().estimate_, np.array([2., 5.]), 9)
def test_jacobian():
"""
srtomo.SRTomo.jacobian return the jacobian of the model provided. In this
simple model, the jacobian can be easily calculated.
"""
model = SquareMesh((0, 10, 0, 10), shape=(2, 1), props={'vp': [2., 5.]})
src = (5, 0)
srcs = [src, src]
recs = [(0, 0), (5, 10)]
ttimes = ttime2d.straight(model, 'vp', srcs, recs)
mesh = SquareMesh((0, 10, 0, 10), shape=(2, 1))
tomo = srtomo.SRTomo(ttimes, srcs, recs, mesh)
assert_array_almost_equal(tomo.jacobian().todense(),
np.array([[5., 0.], [5., 5.]]), 9)
def test_predicted():
"""
Test to verify srtomo.SRTomo.predicted function. Given the correct
parameters, this function must return the result of the forward data.
"""
model = SquareMesh((0, 10, 0, 10), shape=(2, 1), props={'vp': [2., 5.]})
src = (5, 0)
srcs = [src, src]
recs = [(0, 0), (5, 10)]
ttimes = ttime2d.straight(model, 'vp', srcs, recs)
mesh = SquareMesh((0, 10, 0, 10), shape=(2, 1))
tomo = srtomo.SRTomo(ttimes, srcs, recs, mesh)
# The parameter used inside the class is slowness, so 1/vp.
tomo.p_ = np.array([1. / 2., 1. / 5.])
assert_array_almost_equal(tomo.predicted(), ttimes, 9)
"""
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
refraction (Snell's Law). Results can be significantly distorted,
particularly on highly heterogeneous media.
"""
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)
"""
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
Seismic: 2D straight-ray tomography using damping regularization
Uses synthetic data and a model generated from an image file.
"""
import urllib
import time
import numpy
from fatiando.mesher import SquareMesh
from fatiando.seismic import ttime2d, srtomo
from fatiando.inversion.regularization import Damping
from fatiando.vis import mpl
from fatiando import utils
area = (0, 500000, 0, 500000)
shape = (30, 30)
model = SquareMesh(area, shape)
# Fetch the image from the online docs
urllib.urlretrieve(
'http://fatiando.readthedocs.org/en/latest/_static/logo.png', 'logo.png')
model.img2prop('logo.png', 4000, 10000, 'vp')
# 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
This simple tomography is implemented in the
:class:`~fatiando.seismic.srtomo.SRTomo` class. The example below uses 3 forms
of regularization to invert a synthetic data-set.
"""
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]
regularization
Uses synthetic data and a model generated from an image file.
"""
import urllib
from os import path
import numpy
from fatiando.mesher import SquareMesh
from fatiando.seismic import ttime2d, srtomo
from fatiando.inversion.regularization import TotalVariation2D
from fatiando.vis import mpl
from fatiando import utils
area = (0, 100000, 0, 100000)
shape = (20, 20)
model = SquareMesh(area, shape)
# Fetch the image from the online docs
urllib.urlretrieve(
'http://fatiando.readthedocs.org/en/latest/_static/logo.png', 'logo.png')
vmin, vmax = 4000, 10000
model.img2prop('logo.png', vmin, vmax, 'vp')
# 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)