def test_traveltime_table():
"""Compare analytical and eikonal traveltimes in homogenous medium
"""
# 2d
trav_ana, trav_srcs_ana, trav_recs_ana =\
_traveltime_table(z, x, s2d, r2d, v0, mode='analytic')
trav_eik, trav_srcs_eik, trav_recs_eik = \
_traveltime_table(z, x, s2d, r2d, v0*np.ones((PAR['nx'], PAR['nz'])),
mode='eikonal')
assert_array_almost_equal(trav_srcs_ana, trav_srcs_eik, decimal=2)
assert_array_almost_equal(trav_recs_ana, trav_recs_ana, decimal=2)
assert_array_almost_equal(trav_ana, trav_eik, decimal=2)
# 3d
trav_ana, trav_srcs_ana, trav_recs_ana = \
_traveltime_table(z, x, s3d, r3d, v0, y=y, mode='analytic')
trav_eik, trav_srcs_eik, trav_recs_eik = \
_traveltime_table(z, x, s3d, r3d,
v0 * np.ones((PAR['ny'], PAR['nx'], PAR['nz'])),
y=y, mode='eikonal')
assert_array_almost_equal(trav_srcs_ana, trav_srcs_eik, decimal=2)
assert_array_almost_equal(trav_recs_ana, trav_recs_eik, decimal=2)
assert_array_almost_equal(trav_ana, trav_eik, decimal=2)
def test_demigration2d(par):
"""Dot-test for Demigration operator"""
vel = v0 * np.ones((PAR["nx"], PAR["nz"]))
if par["mode"] == "byot":
trav, _, _ = _traveltime_table(z, x, s2d, r2d, v0, mode="analytic")
else:
trav = None
if skfmm_enabled or par["mode"] != "eikonal":
Dop = Demigration(
z,
x,
t,
s2d,
r2d,
vel if par["mode"] == "eikonal" else v0,
wav,
wavc,
y=None,
trav=trav,
mode=par["mode"],
)
assert dottest(Dop, PAR["nsx"] * PAR["nrx"] * PAR["nt"],
PAR["nz"] * PAR["nx"])
def test_traveltime_ana():
"""Check analytical traveltimes in homogenous medium for horizontal and
vertical paths
"""
src = np.array([100, 0])[:, np.newaxis]
_, trav_srcs_ana, trav_recs_ana = \
_traveltime_table(np.arange(0, 200, 1), np.arange(0, 200, 1),
src, src, v0, mode='analytic')
assert trav_srcs_ana[0, 0] == 100 / v0
assert trav_recs_ana[0, 0] == 100 / v0
def test_demigration2d(par):
"""Dot-test for Demigration operator
"""
vel = v0 * np.ones((PAR['nx'], PAR['nz']))
if par['mode'] == 'byot':
trav, _, _ = \
_traveltime_table(z, x, s2d, r2d, v0, mode='analytic')
else:
trav = None
Dop = Demigration(z, x, t, s2d, r2d,
vel if par['mode'] == 'eikonal' else v0, wav, wavc,
y=None, trav=trav, mode=par['mode'])
assert dottest(Dop, PAR['nsx']*PAR['nrx']*PAR['nt'], PAR['nz']*PAR['nx'])
def test_traveltime_table():
"""Compare analytical and eikonal traveltimes in homogenous medium"""
if skfmm_enabled:
# 2d
trav_ana, trav_srcs_ana, trav_recs_ana = _traveltime_table(
z, x, s2d, r2d, v0, mode="analytic")
trav_eik, trav_srcs_eik, trav_recs_eik = _traveltime_table(
z,
x,
s2d,
r2d,
v0 * np.ones((PAR["nx"], PAR["nz"])),
mode="eikonal")
assert_array_almost_equal(trav_srcs_ana, trav_srcs_eik, decimal=2)
assert_array_almost_equal(trav_recs_ana, trav_recs_ana, decimal=2)
assert_array_almost_equal(trav_ana, trav_eik, decimal=2)
# 3d
trav_ana, trav_srcs_ana, trav_recs_ana = _traveltime_table(
z, x, s3d, r3d, v0, y=y, mode="analytic")
trav_eik, trav_srcs_eik, trav_recs_eik = _traveltime_table(
z,
x,
s3d,
r3d,
v0 * np.ones((PAR["ny"], PAR["nx"], PAR["nz"])),
y=y,
mode="eikonal",
)
assert_array_almost_equal(trav_srcs_ana, trav_srcs_eik, decimal=2)
assert_array_almost_equal(trav_recs_ana, trav_recs_eik, decimal=2)
assert_array_almost_equal(trav_ana, trav_eik, decimal=2)
vel[:, 40:50] = 1800
vel[:, 50:80] = 2000
vel[:, 80:] = 2500
# Smooth velocity
nsmooth=20
velback = filtfilt(np.ones(nsmooth)/float(nsmooth), 1, vel, axis=0)
for _ in range(5):
velback = filtfilt(np.ones(nsmooth)/float(nsmooth), 1, velback, axis=1)
#%% Calculate the travel time using eikonal
nt = 401
dt = 0.004
t = np.arange(nt)*dt
trav, trav_srcs, trav_recs = _traveltime_table(z, x, sources, recs, velback, mode='eikonal')
itrav = (np.floor(trav/dt)).astype(np.int32)
travd = (trav/dt - itrav)
itrav = itrav.reshape(nx, nz, ns*nr)
travd = travd.reshape(nx, nz, ns*nr)
#%% Modelling
Sop = Spread(dims=(nx, nz), dimsd=(ns*nr, nt), table=itrav, dtable=travd, engine='numba')
dottest(Sop, ns*nr*nt, nx*nz, verb=True)
wav, wavt, wavc = ricker(t[:41], f0=20)
Cop = Convolve1D(ns*nr*nt, h=wav, offset=wavc, dims=(ns*nr, nt), dir=1)
Dop = FirstDerivative(nx*nz, dims=(nx, nz), dir=1)
LSMop = Cop*Sop*Dop
plt.title('Velocity')
plt.xlim(x[0], x[-1])
plt.figure(figsize=(10,5))
im = plt.imshow(refl.T, cmap='gray', extent = (x[0], x[-1], z[-1], z[0]))
plt.scatter(recs[0], recs[1], marker='v', s=150, c='b', edgecolors='k')
plt.scatter(sources[0], sources[1], marker='*', s=150, c='r', edgecolors='k')
plt.colorbar(im)
plt.axis('tight')
plt.xlabel('x [m]'),plt.ylabel('y [m]')
plt.title('Reflectivity')
plt.xlim(x[0], x[-1]);
#%% Computes travel times for homogenous medium
trav, trav_srcs, trav_recs = _traveltime_table(z, x, sources, recs, v0, mode='analytic')
fig, axs = plt.subplots(1, 3, figsize=(14, 3))
im = axs[0].imshow(trav_srcs[:, ns//2].reshape((nx, nz)).T, cmap='rainbow',
extent = (x[0], x[-1], z[-1], z[0]))
axs[0].scatter(sources[0, ns//2], sources[1, ns//2], marker='*', s=150, c='r', edgecolors='k')
axs[0].axis('tight')
axs[0].set_xlabel('x [m]')
axs[0].set_ylabel('y [m]')
axs[0].set_title('Source traveltime')
axs[0].set_ylim(z[-1], z[0])
plt.colorbar(im, ax=axs[0])
im = axs[1].imshow(trav_recs[:, nr//4].reshape((nx, nz)).T, cmap='rainbow',
extent = (x[0], x[-1], z[-1], z[0]))
axs[1].scatter(recs[0, nr//4], recs[1, nr//4], marker='v', s=150, c='b', edgecolors='k')
axs[1].axis('tight')
