def test_MDC_Nvirtualsources(par):
"""Dot-test and comparison with pylops for MDC operator of N virtual source
"""
if par['twosided']:
par['nt2'] = 2*par['nt'] - 1
else:
par['nt2'] = par['nt']
v = 1500
it0_m = 25
t0_m = it0_m * par['dt']
theta_m = 0
phi_m = 0
amp_m = 1.
it0_G = np.array([25, 50, 75])
t0_G = it0_G * par['dt']
theta_G = (0, 0, 0)
phi_G = (0, 0, 0)
amp_G = (1., 0.6, 2.)
# Create axis
t, _, x, y = makeaxis(par)
# Create wavelet
wav = ricker(t[:41], f0=par['f0'])[0]
# Generate model
_, mwav = linear3d(x, x, t, v, t0_m, theta_m, phi_m, amp_m, wav)
# Generate operator
_, Gwav = linear3d(x, y, t, v, t0_G, theta_G, phi_G, amp_G, wav)
# Add negative part to data and model
if par['twosided']:
mwav = np.concatenate((np.zeros((par['nx'], par['nx'], par['nt'] - 1)),
mwav), axis=-1)
Gwav = np.concatenate((np.zeros((par['ny'], par['nx'], par['nt'] - 1)),
Gwav), axis=-1)
# Define MDC linear operator
Gwav_fft = np.fft.fft(Gwav, par['nt2'], axis=-1)
Gwav_fft = Gwav_fft[..., :par['nfmax']]
dMDCop = dMDC(da.from_array(Gwav_fft.transpose(2, 0, 1)), nt=par['nt2'],
nv=par['nx'], dt=par['dt'], dr=par['dx'],
twosided=par['twosided'])
MDCop = MDC(Gwav_fft.transpose(2, 0, 1), nt=par['nt2'], nv=par['nx'],
dt=par['dt'], dr=par['dx'], twosided=par['twosided'],
transpose=False, dtype='float32')
dottest(dMDCop, par['nt2'] * par['ny'] * par['nx'],
par['nt2'] * par['nx'] * par['nx'],
chunks=((par['nt2'] * par['ny'] * par['nx'],
par['nt2'] * par['nx'] * par['nx'])))
mwav = mwav.T
dy = (dMDCop * da.from_array(mwav.flatten())).compute()
y = MDCop * mwav.flatten()
assert_array_almost_equal(dy, y, decimal=5)
def MakeSeismic_paper(samples,
img_size=128,
freq_low=5,
freq_high=30,
num_events=6):
"""Simple generation of noisy synthetic linear seismic events.
Input:
samples = Number of samples in your dataset you want
Output:
clean_signal, noise, noisy_signal"""
random.seed(101)
# empty list to be filled with numpy arrays
clean_signal = []
noise = []
noisy_signal = []
# Parameters for the seismic canvas
par = {
'ox': 0,
'dx': 12.5,
'nx': img_size, # offsets
'ot': 0,
'dt': 0.004,
'nt': img_size, # time
'f0': 20,
'nfmax': 50
}
# Make canvas
t, t2, x, y = makeaxis(par)
# Make wavelet
wav = ricker(np.arange(41) * par['dt'], f0=par['f0'])[0]
# Parameters for events
v = 1500
ang_range = 50
amp_range = 2
i = 0
amp_lim = 0.2
t0 = [0.2, 0.3, 0.5, 0.8]
amp = [-0.5, 1.2, -1.5, 0.8]
theta = [10, -10, 5, -30]
while i < samples:
# Making events
mlin, mlinwav = linear2d(x, t, v, t0, theta, amp, wav)
# Creating noise
n = np.random.normal(loc=0, scale=0.25, size=(
img_size, img_size)) * random.uniform(-2, 2)
# Adding noise
s = mlinwav
ns = s + n
clean_signal.append(s)
noise.append(n)
noisy_signal.append(ns)
i += 1
return np.array(clean_signal).reshape(
samples, img_size, img_size, 1), np.array(noise).reshape(
samples, img_size, img_size,
1), np.array(noisy_signal).reshape(samples, img_size, img_size, 1)
def test_ChirpRadon3D(par):
"""Dot-test, forward, analytical inverse and sparse inverse
for ChirpRadon3D operator
"""
parmod = {
"ot": 0,
"dt": 0.004,
"nt": par["nt"],
"ox": par["nhx"] * 10 / 2,
"dx": 10,
"nx": par["nhx"],
"oy": par["nhy"] * 10 / 2,
"dy": 10,
"ny": par["nhy"],
"f0": 40,
}
theta = [
20,
]
phi = [
0,
]
t0 = [
0.1,
]
amp = [
1.0,
]
# Create axis
t, t2, hx, hy = makeaxis(parmod)
# Create wavelet
wav, _, wav_c = ricker(t[:41], f0=parmod["f0"])
# Generate model
_, x = linear3d(hy, hx, t, 1500.0, t0, theta, phi, amp, wav)
Rop = ChirpRadon3D(
t,
hy,
hx,
(par["pymax"], par["pxmax"]),
engine=par["engine"],
dtype="float64",
**dict(flags=("FFTW_ESTIMATE",), threads=2)
)
assert dottest(
Rop, par["nhy"] * par["nhx"] * par["nt"], par["nhy"] * par["nhx"] * par["nt"]
)
y = Rop * x.ravel()
xinvana = Rop.inverse(y)
assert_array_almost_equal(x.ravel(), xinvana, decimal=3)
xinv, _, _ = FISTA(Rop, y, 30, eps=1e0, returninfo=True)
assert_array_almost_equal(x.ravel(), xinv, decimal=3)
def test_ricker(par):
"""Create ricker wavelet and check size and central value"""
t = np.arange(par["nt"]) * par["dt"]
wav, twav, wcenter = ricker(t, f0=20)
assert twav.size == (par["nt"] - 1 if par["nt"] %
2 == 0 else par["nt"]) * 2 - 1
assert wav.shape[0] == (par["nt"] - 1 if par["nt"] %
2 == 0 else par["nt"]) * 2 - 1
assert wav[wcenter] == 1
def test_MDC_1virtualsource(par):
"""Dot-test and inversion for MDC operator of 1 virtual source
"""
if par['twosided']:
par['nt2'] = 2*par['nt'] - 1
else:
par['nt2'] = par['nt']
v = 1500
t0_m = 0.2
theta_m = 0
amp_m = 1.
t0_G = (0.1, 0.2, 0.3)
theta_G = (0, 0, 0)
phi_G = (0, 0, 0)
amp_G = (1., 0.6, 2.)
# Create axis
t, _, x, y = makeaxis(par)
# Create wavelet
wav = ricker(t[:41], f0=par['f0'])[0]
# Generate model
_, mwav = linear2d(x, t, v, t0_m, theta_m, amp_m, wav)
# Generate operator
_, Gwav = linear3d(x, y, t, v, t0_G, theta_G, phi_G, amp_G, wav)
# Add negative part to data and model
if par['twosided']:
mwav = np.concatenate((np.zeros((par['nx'], par['nt'] - 1)), mwav), axis=-1)
Gwav = np.concatenate((np.zeros((par['ny'], par['nx'], par['nt'] - 1)), Gwav), axis=-1)
# Define MDC linear operator
Gwav_fft = np.fft.fft(Gwav, par['nt2'], axis=-1)
Gwav_fft = Gwav_fft[..., :par['nfmax']]
MDCop = MDC(Gwav_fft, nt=par['nt2'], nv=1,
dt=par['dt'], dr=par['dx'],
twosided=par['twosided'], dtype='float32')
dottest(MDCop, par['nt2']*par['ny'], par['nt2']*par['nx'])
# Create data
d = MDCop * mwav.flatten()
d = d.reshape(par['ny'], par['nt2'])
# Apply mdd function
minv = MDD(Gwav[:, :, par['nt']-1:] if par['twosided'] else Gwav,
d[:, par['nt']-1:] if par['twosided'] else d,
dt=par['dt'], dr=par['dx'], nfmax=par['nfmax'],
twosided=par['twosided'], adjoint=False, psf=False, dtype='complex64',
dottest=False,
**dict(damp=1e-10, iter_lim=50, show=1))
assert_array_almost_equal(mwav, minv, decimal=2)
def test_ChirpRadon3D(par):
"""Dot-test, forward, analytical inverse and sparse inverse
for ChirpRadon3D operator
"""
parmod = {
'ot': 0,
'dt': 0.004,
'nt': par['nt'],
'ox': par['nhx'] * 10 / 2,
'dx': 10,
'nx': par['nhx'],
'oy': par['nhy'] * 10 / 2,
'dy': 10,
'ny': par['nhy'],
'f0': 40
}
theta = [
20,
]
phi = [
0,
]
t0 = [
0.1,
]
amp = [
1.,
]
# Create axis
t, t2, hx, hy = makeaxis(parmod)
# Create wavelet
wav, _, wav_c = ricker(t[:41], f0=parmod['f0'])
# Generate model
_, x = linear3d(hy, hx, t, 1500., t0, theta, phi, amp, wav)
Rop = ChirpRadon3D(t,
hy,
hx, (par['pymax'], par['pxmax']),
engine=par['engine'],
dtype='float64',
**dict(flags=('FFTW_ESTIMATE', ), threads=2))
assert dottest(Rop, par['nhy'] * par['nhx'] * par['nt'],
par['nhy'] * par['nhx'] * par['nt'])
y = Rop * x.ravel()
xinvana = Rop.inverse(y)
assert_array_almost_equal(x.ravel(), xinvana, decimal=3)
xinv, _, _ = FISTA(Rop, y, 30, eps=1e0, returninfo=True)
assert_array_almost_equal(x.ravel(), xinv, decimal=3)
def test_MDC_compute(par):
"""Ensure that forward and adjoint of MDC return numpy array when
compute=True
"""
par['nt2'] = par['nt']
v = 1500
it0_m = 25
t0_m = it0_m * par['dt']
theta_m = 0
amp_m = 1.
it0_G = np.array([25, 50, 75])
t0_G = it0_G * par['dt']
theta_G = (0, 0, 0)
phi_G = (0, 0, 0)
amp_G = (1., 0.6, 2.)
# Create axis
t, _, x, y = makeaxis(par)
# Create wavelet
wav = ricker(t[:41], f0=par['f0'])[0]
# Generate model
_, mwav = linear2d(x, t, v, t0_m, theta_m, amp_m, wav)
# Generate operator
_, Gwav = linear3d(x, y, t, v, t0_G, theta_G, phi_G, amp_G, wav)
# Define MDC linear operator
Gwav_fft = np.fft.fft(Gwav, par['nt2'], axis=-1)
Gwav_fft = Gwav_fft[..., :par['nfmax']]
dMDCop = dMDC(da.from_array(Gwav_fft.transpose(2, 0, 1)),
nt=par['nt2'],
nv=1,
dt=par['dt'],
dr=par['dx'],
twosided=par['twosided'],
todask=(True, True),
compute=(True, True))
assert isinstance(dMDCop.matvec(np.ones(dMDCop.shape[1])), np.ndarray)
assert isinstance(dMDCop.rmatvec(np.ones(dMDCop.shape[0])), np.ndarray)
def test_ChirpRadon2D(par):
"""Dot-test, forward, analytical inverse and sparse inverse
for ChirpRadon2D operator
"""
parmod = {
'ot': 0,
'dt': 0.004,
'nt': par['nt'],
'ox': par['nhx'] * 10 / 2,
'dx': 10,
'nx': par['nhx'],
'f0': 40
}
theta = [
20,
]
t0 = [
0.1,
]
amp = [
1.,
]
# Create axis
t, t2, hx, _ = makeaxis(parmod)
# Create wavelet
wav, _, wav_c = ricker(t[:41], f0=parmod['f0'])
# Generate model
_, x = linear2d(hx, t, 1500., t0, theta, amp, wav)
Rop = ChirpRadon2D(t, hx, par['pxmax'], dtype='float64')
assert dottest(Rop, par['nhx'] * par['nt'], par['nhx'] * par['nt'])
y = Rop * x.ravel()
xinvana = Rop.inverse(y)
assert_array_almost_equal(x.ravel(), xinvana, decimal=3)
xinv, _, _ = FISTA(Rop, y, 30, eps=1e0, returninfo=True)
assert_array_almost_equal(x.ravel(), xinv, decimal=3)
def test_ChirpRadon2D(par):
"""Dot-test, forward, analytical inverse and sparse inverse
for ChirpRadon2D operator
"""
parmod = {
"ot": 0,
"dt": 0.004,
"nt": par["nt"],
"ox": par["nhx"] * 10 / 2,
"dx": 10,
"nx": par["nhx"],
"f0": 40,
}
theta = [
20,
]
t0 = [
0.1,
]
amp = [
1.0,
]
# Create axis
t, t2, hx, _ = makeaxis(parmod)
# Create wavelet
wav, _, wav_c = ricker(t[:41], f0=parmod["f0"])
# Generate model
_, x = linear2d(hx, t, 1500.0, t0, theta, amp, wav)
Rop = ChirpRadon2D(t, hx, par["pxmax"], dtype="float64")
assert dottest(Rop, par["nhx"] * par["nt"], par["nhx"] * par["nt"])
y = Rop * x.ravel()
xinvana = Rop.inverse(y)
assert_array_almost_equal(x.ravel(), xinvana, decimal=3)
xinv, _, _ = FISTA(Rop, y, 30, eps=1e0, returninfo=True)
assert_array_almost_equal(x.ravel(), xinv, decimal=3)
def test_MDC_1virtualsource(par):
"""Dot-test and inversion for MDC operator of 1 virtual source"""
if par["twosided"]:
par["nt2"] = 2 * par["nt"] - 1
else:
par["nt2"] = par["nt"]
v = 1500
it0_m = 25
t0_m = it0_m * par["dt"]
theta_m = 0
amp_m = 1.0
it0_G = np.array([25, 50, 75])
t0_G = it0_G * par["dt"]
theta_G = (0, 0, 0)
phi_G = (0, 0, 0)
amp_G = (1.0, 0.6, 2.0)
# Create axis
t, _, x, y = makeaxis(par)
# Create wavelet
wav = ricker(t[:41], f0=par["f0"])[0]
# Generate model
_, mwav = linear2d(x, t, v, t0_m, theta_m, amp_m, wav)
# Generate operator
_, Gwav = linear3d(x, y, t, v, t0_G, theta_G, phi_G, amp_G, wav)
# Add negative part to data and model
if par["twosided"]:
mwav = np.concatenate((np.zeros((par["nx"], par["nt"] - 1)), mwav),
axis=-1)
Gwav = np.concatenate((np.zeros(
(par["ny"], par["nx"], par["nt"] - 1)), Gwav),
axis=-1)
# Define MDC linear operator
Gwav_fft = np.fft.fft(Gwav, par["nt2"], axis=-1)
Gwav_fft = Gwav_fft[..., :par["nfmax"]]
MDCop = MDC(
Gwav_fft,
nt=par["nt2"],
nv=1,
dt=par["dt"],
dr=par["dx"],
fftengine="fftw",
twosided=par["twosided"],
dtype="float32",
)
dottest(MDCop, par["nt2"] * par["ny"], par["nt2"] * par["nx"])
# Create data
d = MDCop * mwav.ravel()
d = d.reshape(par["ny"], par["nt2"])
# Check that events are at correct time and correct amplitude
for it, amp in zip(it0_G, amp_G):
ittot = it0_m + it
if par["twosided"]:
ittot += par["nt"] - 1
assert (np.abs(d[par["ny"] // 2, ittot] -
np.abs(wav**2).sum() * amp_m * amp * par["nx"] *
par["dx"] * par["dt"] * np.sqrt(par["nt2"])) < 1e-2)
# Check that MDC with prescaled=True gives same result
MDCpreop = MDC(
np.sqrt(par["nt2"]) * par["dt"] * par["dx"] * Gwav_fft,
nt=par["nt2"],
nv=1,
dt=par["dt"],
dr=par["dx"],
fftengine="fftw",
twosided=par["twosided"],
prescaled=True,
dtype="float32",
)
dottest(MDCpreop, par["nt2"] * par["ny"], par["nt2"] * par["nx"])
dpre = MDCpreop * mwav.ravel()
dpre = dpre.reshape(par["ny"], par["nt2"])
assert_array_equal(d, dpre)
# Apply mdd function
minv = MDD(Gwav[:, :, par["nt"] - 1:] if par["twosided"] else Gwav,
d[:, par["nt"] - 1:] if par["twosided"] else d,
dt=par["dt"],
dr=par["dx"],
nfmax=par["nfmax"],
twosided=par["twosided"],
adjoint=False,
psf=False,
dtype="complex64",
dottest=False,
**dict(damp=1e-10, iter_lim=50, show=0))
assert_array_almost_equal(mwav, minv, decimal=2)
# Same tests for future behaviour (remove tests above in v2.0.0)
MDCop = MDC(
Gwav_fft.transpose(2, 0, 1),
nt=par["nt2"],
nv=1,
dt=par["dt"],
dr=par["dx"],
twosided=par["twosided"],
transpose=False,
dtype="float32",
)
dottest(MDCop, par["nt2"] * par["ny"], par["nt2"] * par["nx"])
mwav = mwav.T
d = MDCop * mwav.ravel()
d = d.reshape(par["nt2"], par["ny"])
for it, amp in zip(it0_G, amp_G):
ittot = it0_m + it
if par["twosided"]:
ittot += par["nt"] - 1
assert (np.abs(d[ittot, par["ny"] // 2] -
np.abs(wav**2).sum() * amp_m * amp * par["nx"] *
par["dx"] * par["dt"] * np.sqrt(par["nt2"])) < 1e-2)
minv = MDD(Gwav[:, :, par["nt"] - 1:] if par["twosided"] else Gwav,
d[par["nt"] - 1:].T if par["twosided"] else d.T,
dt=par["dt"],
dr=par["dx"],
nfmax=par["nfmax"],
twosided=par["twosided"],
add_negative=True,
adjoint=False,
psf=False,
dtype="complex64",
dottest=False,
**dict(damp=1e-10, iter_lim=50, show=0))
assert_array_almost_equal(mwav, minv.T, decimal=2)
m = np.log(vp * rho)
mback = filtfilt(np.ones(nsmooth) / float(nsmooth), 1, m)
# 2d model
inputfile = 'testdata/avo/poststack_model.npz'
model = np.load(inputfile)
x, z, m2d = model['x'][::3], model['z'][::3], \
np.log(model['model'][::3, ::3])
nx, nz = len(x), len(z)
mback2d = filtfilt(np.ones(nsmooth) / float(nsmooth), 1, m2d, axis=0)
mback2d = filtfilt(np.ones(nsmooth) / float(nsmooth), 1, mback2d, axis=1)
# wavelet
wav = ricker(t0[:ntwav // 2 + 1], 20)[0]
par1 = {
'epsR': None,
'epsRL1': None,
'epsI': None,
'simultaneous': False
} # unregularized
par2 = {
'epsR': 1e-4,
'epsRL1': None,
'epsI': 1e-6,
'simultaneous': False
} # regularized
par3 = {
'epsR': None,
par1 = PAR.copy() # analytical
par1['kind'] = 'analytical'
par2 = PAR.copy() # inverse
par2['kind'] = 'inverse'
# separation params
vel_sep = 1000.0 # velocity at separation level
rho_sep = 1000.0 # density at separation level
critical = 0.9
ntaper = 41
nfftf = 2**8
nfftk = 2**7
# axes and wavelet
t, t2, x, y = makeaxis(PAR)
wav = ricker(t[:41], f0=PAR['f0'])[0]
@pytest.fixture(scope="module")
def create_data2D():
"""Create 2d dataset
"""
t0_plus = np.array([0.05, 0.12])
t0_minus = t0_plus + 0.04
vrms = np.array([1400., 1800.])
amp = np.array([1., -0.6])
_, p2d_minus = hyperbolic2d(x, t, t0_minus, vrms, amp, wav)
_, p2d_plus = hyperbolic2d(x, t, t0_plus, vrms, amp, wav)
UPop = \
sy = np.linspace(y.min(), y.max(), PAR['nsy'])
sx = np.linspace(x.min(), x.max(), PAR['nsx'])
syy, sxx = np.meshgrid(sy, sx, indexing='ij')
s2d = np.vstack((sx, 2 * np.ones(PAR['nsx'])))
s3d = np.vstack(
(syy.ravel(), sxx.ravel(), 2 * np.ones(PAR['nsx'] * PAR['nsy'])))
ry = np.linspace(y.min(), y.max(), PAR['nry'])
rx = np.linspace(x.min(), x.max(), PAR['nrx'])
ryy, rxx = np.meshgrid(ry, rx, indexing='ij')
r2d = np.vstack((rx, 2 * np.ones(PAR['nrx'])))
r3d = np.vstack(
(ryy.ravel(), rxx.ravel(), 2 * np.ones(PAR['nrx'] * PAR['nry'])))
wav, _, wavc = ricker(t[:41], f0=40)
par1 = {'mode': 'analytic'}
par2 = {'mode': 'eikonal'}
par3 = {'mode': 'byot'}
def test_identify_geometry():
"""Identify geometry, check expected outputs
"""
# 2d
ndims, shiftdim, dims, ny, nx, nz, ns, nr, dy, dx, dz, dsamp, origin = \
_identify_geometry(z, x, s2d, r2d)
assert ndims == 2
assert shiftdim == 0
assert [1, 2] == [1, 2]
def test_MDC_Nvirtualsources(par):
"""Dot-test and inversion for MDC operator of N virtual source
"""
if par['twosided']:
par['nt2'] = 2 * par['nt'] - 1
else:
par['nt2'] = par['nt']
v = 1500
it0_m = 25
t0_m = it0_m * par['dt']
theta_m = 0
phi_m = 0
amp_m = 1.
it0_G = np.array([25, 50, 75])
t0_G = it0_G * par['dt']
theta_G = (0, 0, 0)
phi_G = (0, 0, 0)
amp_G = (1., 0.6, 2.)
# Create axis
t, _, x, y = makeaxis(par)
# Create wavelet
wav = ricker(t[:41], f0=par['f0'])[0]
# Generate model
_, mwav = linear3d(x, x, t, v, t0_m, theta_m, phi_m, amp_m, wav)
# Generate operator
_, Gwav = linear3d(x, y, t, v, t0_G, theta_G, phi_G, amp_G, wav)
# Add negative part to data and model
if par['twosided']:
mwav = np.concatenate((np.zeros(
(par['nx'], par['nx'], par['nt'] - 1)), mwav),
axis=-1)
Gwav = np.concatenate((np.zeros(
(par['ny'], par['nx'], par['nt'] - 1)), Gwav),
axis=-1)
# Define MDC linear operator
Gwav_fft = np.fft.fft(Gwav, par['nt2'], axis=-1)
Gwav_fft = Gwav_fft[..., :par['nfmax']]
MDCop = MDC(Gwav_fft,
nt=par['nt2'],
nv=par['nx'],
dt=par['dt'],
dr=par['dx'],
twosided=par['twosided'],
dtype='float32')
dottest(MDCop, par['nt2'] * par['ny'] * par['nx'],
par['nt2'] * par['nx'] * par['nx'])
# Create data
d = MDCop * mwav.flatten()
d = d.reshape(par['ny'], par['nx'], par['nt2'])
# Check that events are at correct time
for it, amp in zip(it0_G, amp_G):
ittot = it0_m + it
if par['twosided']:
ittot += par['nt'] - 1
assert d[par['ny'] // 2, par['nx'] // 2, ittot] > \
d[par['ny'] // 2, par['nx'] // 2, ittot - 1]
assert d[par['ny'] // 2, par['nx'] // 2, ittot] > \
d[par['ny'] // 2, par['nx'] // 2, ittot + 1]
# Apply mdd function
minv = MDD(Gwav[:, :, par['nt'] - 1:] if par['twosided'] else Gwav,
d[:, :, par['nt'] - 1:] if par['twosided'] else d,
dt=par['dt'],
dr=par['dx'],
nfmax=par['nfmax'],
twosided=par['twosided'],
adjoint=False,
psf=False,
dtype='complex64',
dottest=False,
**dict(damp=1e-10, iter_lim=50, show=1))
assert_array_almost_equal(mwav, minv, decimal=2)
# Same tests for future behaviour (remove tests above in v2.0.0)
MDCop = MDC(Gwav_fft.transpose(2, 0, 1),
nt=par['nt2'],
nv=par['nx'],
dt=par['dt'],
dr=par['dx'],
twosided=par['twosided'],
transpose=False,
dtype='float32')
dottest(MDCop, par['nt2'] * par['ny'] * par['nx'],
par['nt2'] * par['nx'] * par['nx'])
mwav = mwav.transpose(2, 0, 1)
d = MDCop * mwav.flatten()
d = d.reshape(par['nt2'], par['ny'], par['nx'])
for it, amp in zip(it0_G, amp_G):
ittot = it0_m + it
if par['twosided']:
ittot += par['nt'] - 1
assert d[ittot, par['ny'] // 2, par['nx'] // 2] > \
d[ittot - 1, par['ny'] // 2, par['nx'] // 2]
assert d[ittot, par['ny'] // 2, par['nx'] // 2] > \
d[ittot + 1, par['ny'] // 2, par['nx'] // 2]
minv = MDD(
Gwav[:, :, par['nt'] - 1:] if par['twosided'] else Gwav,
d[par['nt'] -
1:].transpose(1, 2, 0) if par['twosided'] else d.transpose(1, 2, 0),
dt=par['dt'],
dr=par['dx'],
nfmax=par['nfmax'],
twosided=par['twosided'],
add_negative=True,
adjoint=False,
psf=False,
dtype='complex64',
dottest=False,
**dict(damp=1e-10, iter_lim=50, show=1))
assert_array_almost_equal(mwav, minv.transpose(2, 0, 1), decimal=2)
m = np.log(vp * rho)
mback = filtfilt(np.ones(nsmooth) / float(nsmooth), 1, m)
# 2d model
inputfile = 'testdata/avo/poststack_model.npz'
model = np.load(inputfile)
x, z, m2d = model['x'][::3], model['z'][::3], \
np.log(model['model'][::3, ::3])
nx, nz = len(x), len(z)
mback2d = filtfilt(np.ones(nsmooth) / float(nsmooth), 1, m2d, axis=0)
mback2d = filtfilt(np.ones(nsmooth) / float(nsmooth), 1, mback2d, axis=1)
# stationary wavelet
wav = ricker(t0[:ntwav // 2 + 1], 20)[0]
# non-stationary wavelet
f0s = np.flip(np.arange(nt0) * 0.05 + 3)
wavs = np.array([ricker(t0[:ntwav], f0)[0] for f0 in f0s])
wavc = np.argmax(wavs[0])
par1 = {
'epsR': None,
'epsRL1': None,
'epsI': None,
'simultaneous': False
} # unregularized
par2 = {
'epsR': 1e-4,
'epsRL1': None,
# steps, such as angle muting.
#
# To get started, let us create a 2D seismic dataset containing some hyperbolic
# events representing reflections from flat reflectors.
# Events are created with a true RMS velocity, which we will be using as if we
# picked them from, for example, a semblance panel.
par = dict(ox=0, dx=40, nx=80, ot=0, dt=0.004, nt=520)
t, _, x, _ = makeaxis(par)
t0s_true = np.array([0.5, 1.22, 1.65])
vrms_true = np.array([2000.0, 2400.0, 2500.0])
amps = np.array([1, 0.2, 0.5])
freq = 10 # Hz
wav, *_ = ricker(t[:41], f0=freq)
_, data = hyperbolic2d(x, t, t0s_true, vrms_true, amp=amps, wav=wav)
###############################################################################
# NMO correction plot
pclip = 0.5
dmax = np.max(np.abs(data))
opts = dict(
cmap="gray_r",
extent=[x[0], x[-1], t[-1], t[0]],
aspect="auto",
vmin=-pclip * dmax,
vmax=pclip * dmax,
###############################################################################
# Let's start by creating a very simple 2d data composed of 3 linear events
# input parameters
par = {'ox': 0, 'dx': 2, 'nx': 70, 'ot': 0, 'dt': 0.004, 'nt': 80, 'f0': 20}
v = 1500
t0_m = [0.1, 0.2, 0.28]
theta_m = [0, 30, -80]
phi_m = [0]
amp_m = [1., -2, 0.5]
# axis
taxis, t2, xaxis, y = makeaxis(par)
# wavelet
wav = ricker(taxis[:41], f0=par['f0'])[0]
# model
_, x = linear2d(xaxis, taxis, v, t0_m, theta_m, amp_m, wav)
###############################################################################
# We can now define the spatial locations along which the data has been
# sampled. In this specific example we will assume that we have access only to
# 40% of the 'original' locations.
perc_subsampling = 0.6
nxsub = int(np.round(par['nx'] * perc_subsampling))
iava = np.sort(np.random.permutation(np.arange(par['nx']))[:nxsub])
# restriction operator
Rop = pylops.Restriction(par['nx'] * par['nt'],
dt0 = 0.004
t0 = np.arange(nt0) * dt0
vp = 1200 + np.arange(nt0) + filtfilt(
np.ones(5) / 5., 1, np.random.normal(0, 80, nt0))
rho = 1000 + vp + filtfilt(np.ones(5) / 5., 1, np.random.normal(0, 30, nt0))
vp[201:] += 500
rho[201:] += 100
m = np.log(vp * rho)
# smooth model
nsmooth = 100
mback = filtfilt(np.ones(nsmooth) / float(nsmooth), 1, m)
# wavelet
ntwav = 41
wav, twav, wavc = ricker(t0[:ntwav // 2 + 1], 20)
# dense operator
PPop_dense = pylops.avo.poststack.PoststackLinearModelling(wav,
nt0=nt0,
explicit=True)
# lop operator
PPop = pylops.avo.poststack.PoststackLinearModelling(wav, nt0=nt0)
# data
d_dense = PPop_dense * m.flatten()
d = PPop * m
# add noise
dn_dense = d_dense + np.random.normal(0, 2e-2, d_dense.shape)
v = 1500
t0 = [0.1, 0.2, 0.3]
theta = [0, 0, 0]
amp = [1.0, -2, 0.5]
# parabolic event
tp0 = [0.13]
px = [0]
pxx = [5e-7]
ampp = [0.7]
# create axis
taxis, taxis2, xaxis, yaxis = pylops.utils.seismicevents.makeaxis(par)
# create wavelet
wav = ricker(taxis[:41], f0=par["f0"])[0]
# generate model
y = (pylops.utils.seismicevents.linear2d(xaxis, taxis, v, t0, theta, amp,
wav)[1] +
pylops.utils.seismicevents.parabolic2d(xaxis, taxis, tp0, px, pxx, ampp,
wav)[1])
###############################################################################
# We can now create the :py:class:`pylops.signalprocessing.Radon2D` operator.
# We also apply its adjoint to the data to obtain a representation of those
# 3 linear events overlapping to a parabolic event in the Radon domain.
# Similarly, we feed the operator to a sparse solver like
# :py:class:`pylops.optimization.sparsity.FISTA` to obtain a sparse
# represention of the data in the Radon domain. At this point we try to filter
# out the unwanted event. We can see how this is much easier for the sparse
import pytest
import numpy as np
from numpy.testing import assert_array_equal
from pylops.utils.wavelets import ricker
from pylops.utils.seismicevents import makeaxis, linear2d, linear3d
from pylops.utils.seismicevents import parabolic2d, hyperbolic2d, hyperbolic3d
# Wavelet
wav = ricker(np.arange(41) * 0.004, f0=10)[0]
par1 = {
'ot': 0,
'dt': 1,
'nt': 300,
'ox': 0,
'dx': 2,
'nx': 200,
'oy': 0,
'dy': 2,
'ny': 100
} # even axis
par2 = {
'ot': 0,
'dt': 1,
'nt': 301,
'ox': -200,
'dx': 2,
'nx': 201,
rho[131:] += 100
vsvp = 0.5
m = np.stack((np.log(vp), np.log(vs), np.log(rho)), axis=1)
# background model
nsmooth = 50
mback = filtfilt(np.ones(nsmooth) / float(nsmooth), 1, m, axis=0)
# angles
ntheta = 21
thetamin, thetamax = 0, 40
theta = np.linspace(thetamin, thetamax, ntheta)
# wavelet
ntwav = 41
wav = ricker(t0[: ntwav // 2 + 1], 15)[0]
# lop
PPop = pylops.avo.prestack.PrestackLinearModelling(
wav, theta, vsvp=vsvp, nt0=nt0, linearization="akirich"
)
# dense
PPop_dense = pylops.avo.prestack.PrestackLinearModelling(
wav, theta, vsvp=vsvp, nt0=nt0, linearization="akirich", explicit=True
)
# data lop
dPP = PPop * m.ravel()
dPP = dPP.reshape(nt0, ntheta)
def test_MDC_1virtualsource(par):
"""Dot-test and comparison with pylops for MDC operator of 1 virtual source
"""
if par['twosided']:
par['nt2'] = 2 * par['nt'] - 1
else:
par['nt2'] = par['nt']
v = 1500
it0_m = 25
t0_m = it0_m * par['dt']
theta_m = 0
amp_m = 1.
it0_G = np.array([25, 50, 75])
t0_G = it0_G * par['dt']
theta_G = (0, 0, 0)
phi_G = (0, 0, 0)
amp_G = (1., 0.6, 2.)
# Create axis
t, _, x, y = makeaxis(par)
# Create wavelet
wav = ricker(t[:41], f0=par['f0'])[0]
# Generate model
_, mwav = linear2d(x, t, v, t0_m, theta_m, amp_m, wav)
# Generate operator
_, Gwav = linear3d(x, y, t, v, t0_G, theta_G, phi_G, amp_G, wav)
# Add negative part to data and model
if par['twosided']:
mwav = np.concatenate((np.zeros((par['nx'], par['nt'] - 1)), mwav),
axis=-1)
Gwav = np.concatenate((np.zeros(
(par['ny'], par['nx'], par['nt'] - 1)), Gwav),
axis=-1)
# Define MDC linear operator
Gwav_fft = np.fft.fft(Gwav, par['nt2'], axis=-1)
Gwav_fft = Gwav_fft[..., :par['nfmax']]
dGwav_fft = da.from_array(Gwav_fft.transpose(2, 0, 1))
dMDCop = dMDC(dGwav_fft,
nt=par['nt2'],
nv=1,
dt=par['dt'],
dr=par['dx'],
twosided=par['twosided'])
MDCop = MDC(Gwav_fft.transpose(2, 0, 1),
nt=par['nt2'],
nv=1,
dt=par['dt'],
dr=par['dx'],
twosided=par['twosided'],
transpose=False,
dtype='float32')
dottest(dMDCop,
par['nt2'] * par['ny'],
par['nt2'] * par['nx'],
chunks=((par['nt2'] * par['ny'], par['nt2'] * par['nx'])))
# Compare results with pylops implementation
mwav = mwav.T
dy = dMDCop * da.from_array(mwav.flatten())
y = MDCop * mwav.flatten()
assert_array_almost_equal(dy.compute(), y, decimal=5)
# Apply mdd function
dy = dy.reshape(par['nt2'], par['ny'])
print(dy)
minv = MDD(dGwav_fft,
dy[par['nt'] - 1:] if par['twosided'] else dy,
dt=par['dt'],
dr=par['dx'],
nfmax=par['nfmax'],
twosided=par['twosided'],
adjoint=False,
dottest=False,
**dict(niter=50))
print('minv', minv)
assert_array_almost_equal(mwav, minv.compute(), decimal=2)
t0_m = [0.2]
vrms_m = [700.0]
amp_m = [1.0]
t0_G = [0.2, 0.5, 0.7]
vrms_G = [800.0, 1200.0, 1500.0]
amp_G = [1.0, 0.6, 0.5]
# Taper
tap = taper3d(par["nt"], [par["ny"], par["nx"]], (5, 5), tapertype="hanning")
# Create axis
t, t2, x, y = makeaxis(par)
# Create wavelet
wav = ricker(t[:41], f0=par["f0"])[0]
# Generate model
m, mwav = hyperbolic2d(x, t, t0_m, vrms_m, amp_m, wav)
# Generate operator
G, Gwav = np.zeros((par["ny"], par["nx"], par["nt"])), np.zeros(
(par["ny"], par["nx"], par["nt"]))
for iy, y0 in enumerate(y):
G[iy], Gwav[iy] = hyperbolic2d(x - y0, t, t0_G, vrms_G, amp_G, wav)
G, Gwav = G * tap, Gwav * tap
# Add negative part to data and model
m = np.concatenate((np.zeros((par["nx"], par["nt"] - 1)), m), axis=-1)
mwav = np.concatenate((np.zeros((par["nx"], par["nt"] - 1)), mwav), axis=-1)
Gwav2 = np.concatenate((np.zeros((par["ny"], par["nx"], par["nt"] - 1)), Gwav),
par1 = PAR.copy() # analytical
par1["kind"] = "analytical"
par2 = PAR.copy() # inverse
par2["kind"] = "inverse"
# separation params
vel_sep = 1000.0 # velocity at separation level
rho_sep = 1000.0 # density at separation level
critical = 0.99
ntaper = 5
nfftf = 2**6
nfftk = 2**6
# axes and wavelet
t, t2, x, y = makeaxis(PAR)
wav = ricker(t[:41], f0=PAR["f0"])[0]
@pytest.fixture(scope="module")
def create_data2D():
"""Create 2d dataset"""
t0_plus = np.array([0.05, 0.12])
t0_minus = t0_plus + 0.04
vrms = np.array([1400.0, 1800.0])
amp = np.array([1.0, -0.6])
_, p2d_minus = hyperbolic2d(x, t, t0_minus, vrms, amp, wav)
_, p2d_plus = hyperbolic2d(x, t, t0_plus, vrms, amp, wav)
UPop = UpDownComposition2D(
PAR["nt"],
'nt': 200,
'f0': 40
}
t0_plus = np.array([0.2, 0.5, 0.7])
t0_minus = t0_plus + 0.04
vrms = np.array([1400., 1500., 2000.])
amp = np.array([1., -0.6, 0.5])
vel_sep = 1000.0 # velocity at separation level
rho_sep = 1000.0 # density at separation level
# Create axis
t, t2, x, y = makeaxis(par)
# Create wavelet
wav = ricker(t[:41], f0=par['f0'])[0]
# Create data
_, p_minus = hyperbolic2d(x, t, t0_minus, vrms, amp, wav)
_, p_plus = hyperbolic2d(x, t, t0_plus, vrms, amp, wav)
###############################################################################
# We can now combine them to create pressure and particle velocity data
critical = 1.1
ntaper = 51
nfft = 2**10
# 2d fft operator
FFTop = pylops.signalprocessing.FFT2D(dims=[par['nx'], par['nt']],
nffts=[nfft, nfft],
sampling=[par['dx'], par['dt']])
def MakeSeismic(samples, img_size=128, freq_low=5, freq_high=30, num_events=6):
"""Simple generation of noisy synthetic linear seismic events.
Input:
samples = Number of samples in your dataset you want
Output:
clean_signal, noise, noisy_signal"""
random.seed(101)
# empty list to be filled with numpy arrays
clean_signal = []
noise = []
noisy_signal = []
# Parameters for the seismic canvas
par = {
'ox': 0,
'dx': 12.5,
'nx': img_size, # offsets
'ot': 0,
'dt': 0.004,
'nt': img_size, # time
'f0': random.randint(5, 70),
'nfmax': 50
}
# initial tests, max freq was 30
# Make canvas
t, t2, x, y = makeaxis(par)
# Make wavelet
wav = ricker(np.arange(41) * par['dt'], f0=par['f0'])[0]
# Parameters for events
v = 1500
ang_range = 50
amp_range = 2
i = 0
amp_lim = 0.2
while i < samples:
iEv = 0
t0 = []
theta = []
amp = []
while iEv <= num_events:
# Time of events
t0.append(random.uniform(t.min(), t.max()) * 0.7)
# Angle of events
theta.append(random.uniform(-ang_range, ang_range))
# Amplitude of events
amp.append(random.uniform(-amp_range, amp_range))
# clipping events to be above -0.2 and 0.2
if amp[iEv] < 0:
amp[iEv] = np.min([-amp_lim, amp[iEv]])
else:
amp[iEv] = np.max([amp_lim, amp[iEv]])
iEv += 1
# Making events
mlin, mlinwav = linear2d(x, t, v, t0, theta, amp, wav)
# Creating noise
n = np.random.normal(loc=0, scale=0.25, size=(img_size, img_size))
# Adding noise
s = mlinwav
ns = s + n
clean_signal.append(s)
noise.append(n)
noisy_signal.append(ns)
i += 1
return np.array(clean_signal).reshape(
samples, img_size, img_size, 1), np.array(noise).reshape(
samples, img_size, img_size,
1), np.array(noisy_signal).reshape(samples, img_size, img_size, 1)
print('PyLops-gpu working on %s...' % dev)
plt.close('all')
###############################################################################
# We will start by creating a zero signal of length :math:`nt` and we will
# place a unitary spike at its center. We also create our filter to be
# applied by means of :py:class:`pylops_gpu.signalprocessing.Convolve1D`
# operator.
nt = 1001
dt = 0.004
t = np.arange(nt)*dt
x = torch.zeros(nt, dtype=torch.float32)
x[int(nt/2)] = 1
h, th, hcenter = ricker(t[:101], f0=30)
h = torch.from_numpy(h.astype(np.float32))
Cop = pylops_gpu.signalprocessing.Convolve1D(nt, h=h, offset=hcenter,
dtype=torch.float32)
y = Cop*x
xinv = Cop / y
fig, ax = plt.subplots(1, 1, figsize=(10, 3))
ax.plot(t, x.cpu().numpy(), 'k', lw=2, label=r'$x$')
ax.plot(t, y.cpu().numpy(), 'r', lw=2, label=r'$y=Ax$')
ax.plot(t, xinv.cpu().numpy(), '--g', lw=2, label=r'$x_{ext}$')
ax.set_title('Convolve in 1st direction', fontsize=14, fontweight='bold')
ax.legend()
ax.set_xlim(1.9, 2.1)
def MakeSeismic_VN(samples, img_size=256, num_events=10):
"""Simple generation of noisy synthetic linear seismic events.
Input:
samples = Number of samples in your dataset you want
Output:
clean_signal, noise, noisy_signal"""
random.seed(101)
# empty list to be filled with numpy arrays
clean_signal = []
noise = []
noisy_signal = []
# Parameters for the seismic canvas
par = {
'ox': 0,
'dx': 12.5,
'nx': img_size, # offsets
'ot': 0,
'dt': 0.004,
'nt': img_size, # time
'f0': random.randint(5, 70),
'nfmax': 50
}
# initial tests, max freq was 50
# Make canvas
t, t2, x, y = makeaxis(par)
# Make wavelet
wav = ricker(np.arange(41) * par['dt'], f0=par['f0'])[0]
# Parameters for events
v = 1500
# orig amp range was 50
ang_range = 80
amp_range = 2
i = 0
amp_lim = 0.8
lv = 1500
hv = 5000
while i < samples:
iEv_l = 0
iEv_h = 0
t0_l = []
t0_h = []
theta_l = []
amp_l = []
amp_h = []
vel_h = []
num_lin = random.randint(2, num_events)
num_hyp = num_events - num_lin
while iEv_l <= num_lin:
# Time of events
t0_l.append(random.uniform(t.min(), t.max()) * 0.7)
# Angle of events
theta_l.append(random.uniform(-ang_range, ang_range))
# Amplitude of events
amp_l.append(random.uniform(-amp_range, amp_range))
# clipping events to be above -0.2 and 0.2
if amp_l[iEv_l] < 0:
amp_l[iEv_l] = np.min([-amp_lim, amp_l[iEv_l]])
else:
amp_l[iEv_l] = np.max([amp_lim, amp_l[iEv_l]])
iEv_l += 1
while iEv_h <= num_hyp:
# Time of events
t0_h.append(random.uniform(t.min(), t.max()) * 0.7)
# Amplitude of events
amp_h.append(random.uniform(-amp_range, amp_range))
# velocity of hyperbolic events
vel_h.append(random.uniform(lv, hv))
# clipping events to be above -0.2 and 0.2
if amp_h[iEv_h] < 0:
amp_h[iEv_h] = np.min([-amp_lim, amp_h[iEv_h]])
else:
amp_h[iEv_h] = np.max([amp_lim, amp_h[iEv_h]])
iEv_h += 1
# Making events
mlin, mlinwav = linear2d(x, t, v, t0_l, theta_l, amp_l, wav)
# print (t0_h, vel_h, amp_h)
# Generate model
m, mwav = hyperbolic2d(x, t, t0_h, vel_h, amp_h, wav)
s = mwav + mlinwav
# Creating and adding noise
ns1 = random_noise(s,
'speckle',
clip=False,
var=random.uniform(0.2, 2))
ns2 = random_noise(s,
'gaussian',
clip=False,
var=random.uniform(0.05, 0.5))
ns3 = random_noise(s,
's&p',
clip=False,
amount=random.uniform(0.05, 0.2))
# Noise
n1 = ns1 - s
n2 = ns2 - s
n3 = ns3 - s
clean_signal.append(s)
clean_signal.append(s)
clean_signal.append(s)
noise.append(n1)
noise.append(n2)
noise.append(n3)
noisy_signal.append(ns1)
noisy_signal.append(ns2)
noisy_signal.append(ns3)
i += 1
return np.array(clean_signal).reshape(
samples * 3, img_size, img_size, 1), np.array(noise).reshape(
samples * 3, img_size, img_size,
1), np.array(noisy_signal).reshape(samples * 3, img_size, img_size,
1)
