def critical_dt(self):
"""Critical computational time step value from the CFL condition."""
# For a fixed time order this number goes down as the space order increases.
#
# The CFL condtion is then given by
# dt < h / (sqrt(2) * max(vp)))
return self.dtype(.5*mmin(self.spacing) / (np.sqrt(2)*mmax(self.vp)))
def _max_vp(self):
"""
Maximum velocity
"""
try:
return mmax(self.vp)
except ValueError:
return np.max(self.vp)
def critical_dt(self):
"""Critical computational time step value from the CFL condition."""
# For a fixed time order this number goes down as the space order increases.
#
# The CFL condtion is then given by
# dt <= coeff * h / (max(velocity))
coeff = 0.38 if len(self.shape) == 3 else 0.42
dt = self.dtype(coeff * mmin(self.spacing) / (self.scale*mmax(self.vp)))
return .001 * int(1000 * dt)
def critical_dt(self):
"""
Critical computational time step value from the CFL condition.
"""
# For a fixed time order this number goes down as the space order increases.
#
# The CFL condtion is then given by
# dt < h / (sqrt(2) * max(vp)))
return self.dtype(.5 * np.min(self.spacing) /
(np.sqrt(2) * mmax(self.vp)))
def critical_dt(self):
"""
Critical computational time step value from the CFL condition.
"""
# For a fixed time order this number decreases as the space order increases.
# See Blanch, J. O., 1995, "A study of viscous effects in seismic modelling,
# imaging, and inversion: methodology, computational aspects and sensitivity"
# for further details:
return self.dtype(6. * np.min(self.spacing) /
(7. * np.sqrt(self.grid.dim) * mmax(self.vp)))
def critical_dt(self):
"""
Critical computational time step value from the CFL condition.
"""
# For a fixed time order this number goes down as the space order increases.
#
# The CFL condtion is then given by
# dt <= coeff * h / (max(velocity))
coeff = 0.38 if len(self.shape) == 3 else 0.42
dt = self.dtype(coeff * mmin(self.spacing) /
(self.scale * mmax(self.vp)))
return .001 * int(1000 * dt)
def demo_model(preset, **kwargs):
"""
Utility function to create preset `Model` objects for
demonstration and testing purposes. The particular presets are ::
* `constant-isotropic` : Constant velocity (1.5 km/sec) isotropic model
* `constant-tti` : Constant anisotropic model. Velocity is 1.5 km/sec and
Thomsen parameters are epsilon=.3, delta=.2, theta = .7rad
and phi=.35rad for 3D. 2d/3d is defined from the input shape
* 'layers-isotropic': Simple two-layer model with velocities 1.5 km/s
and 2.5 km/s in the top and bottom layer respectively.
2d/3d is defined from the input shape
* 'layers-tti': Simple two-layer TTI model with velocities 1.5 km/s
and 2.5 km/s in the top and bottom layer respectively.
Thomsen parameters in the top layer are 0 and in the lower layer
are epsilon=.3, delta=.2, theta = .5rad and phi=.1 rad for 3D.
2d/3d is defined from the input shape
* 'circle-isotropic': Simple camembert model with velocities 1.5 km/s
and 2.5 km/s in a circle at the center. 2D only.
* 'marmousi2d-isotropic': Loads the 2D Marmousi data set from the given
filepath. Requires the ``opesci/data`` repository
to be available on your machine.
* 'marmousi2d-tti': Loads the 2D Marmousi data set from the given
filepath. Requires the ``opesci/data`` repository
to be available on your machine.
* 'marmousi3d-tti': Loads the 2D Marmousi data set from the given
filepath. Requires the ``opesci/data`` repository
to be available on your machine.
"""
space_order = kwargs.pop('space_order', 2)
if preset.lower() in ['constant-elastic']:
# A constant single-layer model in a 2D or 3D domain
# with velocity 1.5 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbl = kwargs.pop('nbl', 10)
dtype = kwargs.pop('dtype', np.float32)
vp = kwargs.pop('vp', 1.5)
vs = 0.5 * vp
rho = 1.0
return ModelElastic(space_order=space_order,
vp=vp,
vs=vs,
rho=rho,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
**kwargs)
if preset.lower() in ['constant-viscoelastic']:
# A constant single-layer model in a 2D or 3D domain
# with velocity 2.2 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbl = kwargs.pop('nbl', 10)
dtype = kwargs.pop('dtype', np.float32)
vp = kwargs.pop('vp', 2.2)
qp = kwargs.pop('qp', 100.)
vs = kwargs.pop('vs', 1.2)
qs = kwargs.pop('qs', 70.)
rho = 2.
return ModelViscoelastic(space_order=space_order,
vp=vp,
qp=qp,
vs=vs,
qs=qs,
rho=rho,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
**kwargs)
if preset.lower() in ['constant-isotropic']:
# A constant single-layer model in a 2D or 3D domain
# with velocity 1.5 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbl = kwargs.pop('nbl', 10)
dtype = kwargs.pop('dtype', np.float32)
vp = kwargs.pop('vp', 1.5)
return Model(space_order=space_order,
vp=vp,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
**kwargs)
elif preset.lower() in ['constant-tti']:
# A constant single-layer model in a 2D or 3D domain
# with velocity 1.5 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbl = kwargs.pop('nbl', 10)
dtype = kwargs.pop('dtype', np.float32)
v = np.empty(shape, dtype=dtype)
v[:] = 1.5
epsilon = .3 * np.ones(shape, dtype=dtype)
delta = .2 * np.ones(shape, dtype=dtype)
theta = .7 * np.ones(shape, dtype=dtype)
phi = None
if len(shape) > 2:
phi = .35 * np.ones(shape, dtype=dtype)
return Model(space_order=space_order,
vp=v,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
epsilon=epsilon,
delta=delta,
theta=theta,
phi=phi,
**kwargs)
elif preset.lower() in [
'layers-isotropic', 'twolayer-isotropic', '2layer-isotropic'
]:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.5 km/s,
# and the bottom part of the domain has 2.5 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbl = kwargs.pop('nbl', 10)
ratio = kwargs.pop('ratio', 3)
vp_top = kwargs.pop('vp_top', 1.5)
vp_bottom = kwargs.pop('vp_bottom', 2.5)
# Define a velocity profile in km/s
v = np.empty(shape, dtype=dtype)
v[:] = vp_top # Top velocity (background)
v[..., int(shape[-1] / ratio):] = vp_bottom # Bottom velocity
return Model(space_order=space_order,
vp=v,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
**kwargs)
elif preset.lower() in [
'layers-elastic', 'twolayer-elastic', '2layer-elastic'
]:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.5 km/s,
# and the bottom part of the domain has 2.5 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbl = kwargs.pop('nbl', 10)
ratio = kwargs.pop('ratio', 2)
vp_top = kwargs.pop('vp_top', 1.5)
vp_bottom = kwargs.pop('vp_bottom', 2.5)
# Define a velocity profile in km/s
v = np.empty(shape, dtype=dtype)
v[:] = vp_top # Top velocity (background)
v[..., int(shape[-1] / ratio):] = vp_bottom # Bottom velocity
vs = 0.5 * v[:]
rho = v[:] / vp_top
return ModelElastic(space_order=space_order,
vp=v,
vs=vs,
rho=rho,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
**kwargs)
elif preset.lower() in [
'layers-viscoelastic', 'twolayer-viscoelastic',
'2layer-viscoelastic'
]:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.6 km/s,
# and the bottom part of the domain has 2.2 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbl = kwargs.pop('nbl', 10)
ratio = kwargs.pop('ratio', 3)
vp_top = kwargs.pop('vp_top', 1.6)
qp_top = kwargs.pop('qp_top', 40.)
vs_top = kwargs.pop('vs_top', 0.4)
qs_top = kwargs.pop('qs_top', 30.)
rho_top = kwargs.pop('rho_top', 1.3)
vp_bottom = kwargs.pop('vp_bottom', 2.2)
qp_bottom = kwargs.pop('qp_bottom', 100.)
vs_bottom = kwargs.pop('vs_bottom', 1.2)
qs_bottom = kwargs.pop('qs_bottom', 70.)
rho_bottom = kwargs.pop('qs_bottom', 2.)
# Define a velocity profile in km/s
vp = np.empty(shape, dtype=dtype)
qp = np.empty(shape, dtype=dtype)
vs = np.empty(shape, dtype=dtype)
qs = np.empty(shape, dtype=dtype)
rho = np.empty(shape, dtype=dtype)
# Top and bottom P-wave velocity
vp[:] = vp_top
vp[..., int(shape[-1] / ratio):] = vp_bottom
# Top and bottom P-wave quality factor
qp[:] = qp_top
qp[..., int(shape[-1] / ratio):] = qp_bottom
# Top and bottom S-wave velocity
vs[:] = vs_top
vs[..., int(shape[-1] / ratio):] = vs_bottom
# Top and bottom S-wave quality factor
qs[:] = qs_top
qs[..., int(shape[-1] / ratio):] = qs_bottom
# Top and bottom density
rho[:] = rho_top
rho[..., int(shape[-1] / ratio):] = rho_bottom
return ModelViscoelastic(space_order=space_order,
vp=vp,
qp=qp,
vs=vs,
qs=qs,
rho=rho,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
**kwargs)
elif preset.lower() in ['layers-tti', 'twolayer-tti', '2layer-tti']:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.5 km/s,
# and the bottom part of the domain has 2.5 km/s.\
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbl = kwargs.pop('nbl', 10)
ratio = kwargs.pop('ratio', 2)
vp_top = kwargs.pop('vp_top', 1.5)
vp_bottom = kwargs.pop('vp_bottom', 2.5)
# Define a velocity profile in km/s
v = np.empty(shape, dtype=dtype)
v[:] = vp_top # Top velocity (background)
v[..., int(shape[-1] / ratio):] = vp_bottom # Bottom velocity
epsilon = .3 * (v - 1.5)
delta = .2 * (v - 1.5)
theta = .5 * (v - 1.5)
phi = None
if len(shape) > 2:
phi = .25 * (v - 1.5)
model = Model(space_order=space_order,
vp=v,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
epsilon=epsilon,
delta=delta,
theta=theta,
phi=phi,
**kwargs)
if len(shape) > 2:
model.smooth(('epsilon', 'delta', 'theta', 'phi'))
else:
model.smooth(('epsilon', 'delta', 'theta'))
return model
elif preset.lower() in [
'layers-tti-noazimuth', 'twolayer-tti-noazimuth',
'2layer-tti-noazimuth'
]:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.5 km/s,
# and the bottom part of the domain has 2.5 km/s.\
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbl = kwargs.pop('nbl', 10)
ratio = kwargs.pop('ratio', 2)
vp_top = kwargs.pop('vp_top', 1.5)
vp_bottom = kwargs.pop('vp_bottom', 2.5)
# Define a velocity profile in km/s
v = np.empty(shape, dtype=dtype)
v[:] = vp_top # Top velocity (background)
v[..., int(shape[-1] / ratio):] = vp_bottom # Bottom velocity
epsilon = .3 * (v - 1.5)
delta = .2 * (v - 1.5)
theta = .5 * (v - 1.5)
return Model(space_order=space_order,
vp=v,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
epsilon=epsilon,
delta=delta,
theta=theta,
**kwargs)
elif preset.lower() in ['circle-isotropic']:
# A simple circle in a 2D domain with a background velocity.
# By default, the circle velocity is 2.5 km/s,
# and the background veloity is 3.0 km/s.
dtype = kwargs.pop('dtype', np.float32)
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbl = kwargs.pop('nbl', 10)
vp = kwargs.pop('vp', 3.0)
vp_background = kwargs.pop('vp_background', 2.5)
r = kwargs.pop('r', 15)
# Only a 2D preset is available currently
assert (len(shape) == 2)
v = np.empty(shape, dtype=dtype)
v[:] = vp_background
a, b = shape[0] / 2, shape[1] / 2
y, x = np.ogrid[-a:shape[0] - a, -b:shape[1] - b]
v[x * x + y * y <= r * r] = vp
return Model(space_order=space_order,
vp=v,
origin=origin,
shape=shape,
dtype=dtype,
spacing=spacing,
nbl=nbl,
**kwargs)
elif preset.lower() in ['marmousi-isotropic', 'marmousi2d-isotropic']:
shape = (1601, 401)
spacing = (7.5, 7.5)
origin = (0., 0.)
nbl = kwargs.pop('nbl', 20)
# Read 2D Marmousi model from opesc/data repo
data_path = kwargs.get('data_path', None)
if data_path is None:
raise ValueError(
"Path to opesci/data not found! Please specify with "
"'data_path=<path/to/opesci/data>'")
path = os.path.join(data_path, 'Simple2D/vp_marmousi_bi')
v = np.fromfile(path, dtype='float32', sep="")
v = v.reshape(shape)
# Cut the model to make it slightly cheaper
v = v[301:-300, :]
return Model(space_order=space_order,
vp=v,
origin=origin,
shape=v.shape,
dtype=np.float32,
spacing=spacing,
nbl=nbl,
**kwargs)
elif preset.lower() in ['marmousi-elastic', 'marmousi2d-elastic']:
shape = (1601, 401)
spacing = (7.5, 7.5)
origin = (0., 0.)
# Read 2D Marmousi model from opesc/data repo
data_path = kwargs.get('data_path', None)
if data_path is None:
raise ValueError(
"Path to opesci/data not found! Please specify with "
"'data_path=<path/to/opesci/data>'")
path = os.path.join(data_path, 'Simple2D/vp_marmousi_bi')
v = np.fromfile(path, dtype='float32', sep="")
v = v.reshape(shape)
# Cut the model to make it slightly cheaper
v = v[301:-300, :]
vs = .5 * v[:]
rho = v[:] / mmax(v[:])
return ModelElastic(space_order=space_order,
vp=v,
vs=vs,
rho=rho,
origin=origin,
shape=v.shape,
dtype=np.float32,
spacing=spacing,
nbl=20)
elif preset.lower() in ['marmousi-tti2d', 'marmousi2d-tti']:
shape_full = (201, 201, 70)
shape = (201, 70)
spacing = (10., 10.)
origin = (0., 0.)
nbl = kwargs.pop('nbl', 20)
# Read 2D Marmousi model from opesc/data repo
data_path = kwargs.pop('data_path', None)
if data_path is None:
raise ValueError(
"Path to opesci/data not found! Please specify with "
"'data_path=<path/to/opesci/data>'")
path = os.path.join(data_path, 'marmousi3D/vp_marmousi_bi')
# velocity
vp = 1e-3 * np.fromfile(os.path.join(data_path,
'marmousi3D/MarmousiVP.raw'),
dtype='float32',
sep="")
vp = vp.reshape(shape_full)
vp = vp[101, :, :]
# Epsilon, in % in file, resale between 0 and 1
epsilon = np.fromfile(os.path.join(data_path,
'marmousi3D/MarmousiEps.raw'),
dtype='float32',
sep="") * 1e-2
epsilon = epsilon.reshape(shape_full)
epsilon = epsilon[101, :, :]
# Delta, in % in file, resale between 0 and 1
delta = np.fromfile(os.path.join(data_path,
'marmousi3D/MarmousiDelta.raw'),
dtype='float32',
sep="") * 1e-2
delta = delta.reshape(shape_full)
delta = delta[101, :, :]
# Theta, in degrees in file, resale in radian
theta = np.fromfile(os.path.join(data_path,
'marmousi3D/MarmousiTilt.raw'),
dtype='float32',
sep="")
theta = np.float32(np.pi / 180 * theta.reshape(shape_full))
theta = theta[101, :, :]
return Model(space_order=space_order,
vp=vp,
origin=origin,
shape=shape,
dtype=np.float32,
spacing=spacing,
nbl=nbl,
epsilon=epsilon,
delta=delta,
theta=theta,
**kwargs)
elif preset.lower() in ['marmousi-tti3d', 'marmousi3d-tti']:
shape = (201, 201, 70)
spacing = (10., 10., 10.)
origin = (0., 0., 0.)
nbl = kwargs.pop('nbl', 20)
# Read 2D Marmousi model from opesc/data repo
data_path = kwargs.pop('data_path', None)
if data_path is None:
raise ValueError(
"Path to opesci/data not found! Please specify with "
"'data_path=<path/to/opesci/data>'")
path = os.path.join(data_path, 'marmousi3D/vp_marmousi_bi')
# Velcoity
vp = 1e-3 * np.fromfile(os.path.join(data_path,
'marmousi3D/MarmousiVP.raw'),
dtype='float32',
sep="")
vp = vp.reshape(shape)
# Epsilon, in % in file, resale between 0 and 1
epsilon = np.fromfile(os.path.join(data_path,
'marmousi3D/MarmousiEps.raw'),
dtype='float32',
sep="") * 1e-2
epsilon = epsilon.reshape(shape)
# Delta, in % in file, resale between 0 and 1
delta = np.fromfile(os.path.join(data_path,
'marmousi3D/MarmousiDelta.raw'),
dtype='float32',
sep="") * 1e-2
delta = delta.reshape(shape)
# Theta, in degrees in file, resale in radian
theta = np.fromfile(os.path.join(data_path,
'marmousi3D/MarmousiTilt.raw'),
dtype='float32',
sep="")
theta = np.float32(np.pi / 180 * theta.reshape(shape))
# Phi, in degrees in file, resale in radian
phi = np.fromfile(os.path.join(data_path, 'marmousi3D/Azimuth.raw'),
dtype='float32',
sep="")
phi = np.float32(np.pi / 180 * phi.reshape(shape))
return Model(space_order=space_order,
vp=vp,
origin=origin,
shape=shape,
dtype=np.float32,
spacing=spacing,
nbl=nbl,
epsilon=epsilon,
delta=delta,
theta=theta,
phi=phi,
**kwargs)
else:
raise ValueError("Unknown model preset name")
def _max_vp(self):
"""
Maximum velocity
"""
return mmax(self.vp)
def __init__(self,
origin,
spacing,
shape,
space_order,
vp,
nbpml=20,
dtype=np.float32,
epsilon=None,
delta=None,
theta=None,
phi=None,
subdomains=(),
**kwargs):
super(Model, self).__init__(origin, spacing, shape, space_order, nbpml,
dtype, subdomains)
# Create square slowness of the wave as symbol `m`
if isinstance(vp, np.ndarray):
self.m = Function(name="m",
grid=self.grid,
space_order=space_order)
else:
self.m = Constant(name="m", value=1 / vp**2)
self._physical_parameters = ('m', )
# Set model velocity, which will also set `m`
self.vp = vp
# Create dampening field as symbol `damp`
self.damp = Function(name="damp", grid=self.grid)
initialize_damp(self.damp, self.nbpml, self.spacing)
# Additional parameter fields for TTI operators
self.scale = 1.
if epsilon is not None:
if isinstance(epsilon, np.ndarray):
self._physical_parameters += ('epsilon', )
self.epsilon = Function(name="epsilon", grid=self.grid)
initialize_function(self.epsilon, 1 + 2 * epsilon, self.nbpml)
# Maximum velocity is scale*max(vp) if epsilon > 0
if mmax(self.epsilon) > 0:
self.scale = np.sqrt(mmax(self.epsilon))
else:
self.epsilon = 1 + 2 * epsilon
self.scale = epsilon
else:
self.epsilon = 1
if delta is not None:
if isinstance(delta, np.ndarray):
self._physical_parameters += ('delta', )
self.delta = Function(name="delta", grid=self.grid)
initialize_function(self.delta, np.sqrt(1 + 2 * delta),
self.nbpml)
else:
self.delta = delta
else:
self.delta = 1
if theta is not None:
if isinstance(theta, np.ndarray):
self._physical_parameters += ('theta', )
self.theta = Function(name="theta",
grid=self.grid,
space_order=space_order)
initialize_function(self.theta, theta, self.nbpml)
else:
self.theta = theta
else:
self.theta = 0
if phi is not None:
if self.grid.dim < 3:
warning(
"2D TTI does not use an azimuth angle Phi, ignoring input")
self.phi = 0
elif isinstance(phi, np.ndarray):
self._physical_parameters += ('phi', )
self.phi = Function(name="phi",
grid=self.grid,
space_order=space_order)
initialize_function(self.phi, phi, self.nbpml)
else:
self.phi = phi
else:
self.phi = 0
# Compute smooth data and full forward wavefield u0
_, u0, _ = solver.forward(vp=vp_in, save=True, rec=d_syn)
# Compute gradient from data residual and update objective function
residual = compute_residual(residual, d_obs, d_syn)
objective += .5 * norm(residual)**2
solver.gradient(rec=residual, u=u0, vp=vp_in, grad=grad)
return objective, grad
# Compute gradient of initial model
ff, update = fwi_gradient(model0.vp)
print(ff, mmin(update), mmax(update))
assert np.isclose(ff, 57010, atol=1e1, rtol=0)
assert np.isclose(mmin(update), -1198, atol=1e1, rtol=0)
assert np.isclose(mmax(update), 3558, atol=1e1, rtol=0)
# Run FWI with gradient descent
history = np.zeros((fwi_iterations, 1))
for i in range(0, fwi_iterations):
# Compute the functional value and gradient for the current
# model estimate
phi, direction = fwi_gradient(model0.vp)
# Store the history of the functional values
history[i] = phi
# Artificial Step length for gradient descent
def __init__(self, origin, spacing, shape, space_order, vp, nbpml=20,
dtype=np.float32, epsilon=None, delta=None, theta=None, phi=None,
subdomains=(), **kwargs):
super(Model, self).__init__(origin, spacing, shape, space_order, nbpml, dtype,
subdomains)
# Create square slowness of the wave as symbol `m`
if isinstance(vp, np.ndarray):
self.m = Function(name="m", grid=self.grid, space_order=space_order)
else:
self.m = Constant(name="m", value=1/vp**2)
self._physical_parameters = ('m',)
# Set model velocity, which will also set `m`
self.vp = vp
# Create dampening field as symbol `damp`
self.damp = Function(name="damp", grid=self.grid)
initialize_damp(self.damp, self.nbpml, self.spacing)
# Additional parameter fields for TTI operators
self.scale = 1.
if epsilon is not None:
if isinstance(epsilon, np.ndarray):
self._physical_parameters += ('epsilon',)
self.epsilon = Function(name="epsilon", grid=self.grid)
initialize_function(self.epsilon, 1 + 2 * epsilon, self.nbpml)
# Maximum velocity is scale*max(vp) if epsilon > 0
if mmax(self.epsilon) > 0:
self.scale = np.sqrt(mmax(self.epsilon))
else:
self.epsilon = 1 + 2 * epsilon
self.scale = epsilon
else:
self.epsilon = 1
if delta is not None:
if isinstance(delta, np.ndarray):
self._physical_parameters += ('delta',)
self.delta = Function(name="delta", grid=self.grid)
initialize_function(self.delta, np.sqrt(1 + 2 * delta), self.nbpml)
else:
self.delta = delta
else:
self.delta = 1
if theta is not None:
if isinstance(theta, np.ndarray):
self._physical_parameters += ('theta',)
self.theta = Function(name="theta", grid=self.grid,
space_order=space_order)
initialize_function(self.theta, theta, self.nbpml)
else:
self.theta = theta
else:
self.theta = 0
if phi is not None:
if self.grid.dim < 3:
warning("2D TTI does not use an azimuth angle Phi, ignoring input")
self.phi = 0
elif isinstance(phi, np.ndarray):
self._physical_parameters += ('phi',)
self.phi = Function(name="phi", grid=self.grid, space_order=space_order)
initialize_function(self.phi, phi, self.nbpml)
else:
self.phi = phi
else:
self.phi = 0
def demo_model(preset, **kwargs):
"""
Utility function to create preset :class:`Model` objects for
demonstration and testing purposes. The particular presets are ::
* `constant-isotropic` : Constant velocity (1.5km/sec) isotropic model
* `constant-tti` : Constant anisotropic model. Velocity is 1.5 km/sec and
Thomsen parameters are epsilon=.3, delta=.2, theta = .7rad
and phi=.35rad for 3D. 2d/3d is defined from the input shape
* 'layers-isotropic': Simple two-layer model with velocities 1.5 km/s
and 2.5 km/s in the top and bottom layer respectively.
2d/3d is defined from the input shape
* 'layers-tti': Simple two-layer TTI model with velocities 1.5 km/s
and 2.5 km/s in the top and bottom layer respectively.
Thomsen parameters in the top layer are 0 and in the lower layer
are epsilon=.3, delta=.2, theta = .5rad and phi=.1 rad for 3D.
2d/3d is defined from the input shape
* 'circle-isotropic': Simple camembert model with velocities 1.5 km/s
and 2.5 km/s in a circle at the center. 2D only.
* 'marmousi2d-isotropic': Loads the 2D Marmousi data set from the given
filepath. Requires the ``opesci/data`` repository
to be available on your machine.
* 'marmousi2d-tti': Loads the 2D Marmousi data set from the given
filepath. Requires the ``opesci/data`` repository
to be available on your machine.
* 'marmousi3d-tti': Loads the 2D Marmousi data set from the given
filepath. Requires the ``opesci/data`` repository
to be available on your machine.
"""
space_order = kwargs.pop('space_order', 2)
if preset.lower() in ['constant-elastic']:
# A constant single-layer model in a 2D or 3D domain
# with velocity 1.5km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbpml = kwargs.pop('nbpml', 10)
dtype = kwargs.pop('dtype', np.float32)
vp = kwargs.pop('vp', 1.5)
vs = 0.5 * vp
rho = 1.0
return ModelElastic(space_order=space_order, vp=vp, vs=vs, rho=rho, origin=origin,
shape=shape, dtype=dtype, spacing=spacing, nbpml=nbpml,
**kwargs)
if preset.lower() in ['constant-isotropic']:
# A constant single-layer model in a 2D or 3D domain
# with velocity 1.5km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbpml = kwargs.pop('nbpml', 10)
dtype = kwargs.pop('dtype', np.float32)
vp = kwargs.pop('vp', 1.5)
return Model(space_order=space_order, vp=vp, origin=origin, shape=shape,
dtype=dtype, spacing=spacing, nbpml=nbpml, **kwargs)
elif preset.lower() in ['constant-tti']:
# A constant single-layer model in a 2D or 3D domain
# with velocity 1.5km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbpml = kwargs.pop('nbpml', 10)
dtype = kwargs.pop('dtype', np.float32)
v = np.empty(shape, dtype=dtype)
v[:] = 1.5
epsilon = .3*np.ones(shape, dtype=dtype)
delta = .2*np.ones(shape, dtype=dtype)
theta = .7*np.ones(shape, dtype=dtype)
phi = None
if len(shape) > 2:
phi = .35*np.ones(shape, dtype=dtype)
return Model(space_order=space_order, vp=v, origin=origin, shape=shape,
dtype=dtype, spacing=spacing, nbpml=nbpml, epsilon=epsilon,
delta=delta, theta=theta, phi=phi, **kwargs)
elif preset.lower() in ['layers-isotropic', 'twolayer-isotropic',
'2layer-isotropic']:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.5 km/s,
# and the bottom part of the domain has 2.5 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbpml = kwargs.pop('nbpml', 10)
ratio = kwargs.pop('ratio', 3)
vp_top = kwargs.pop('vp_top', 1.5)
vp_bottom = kwargs.pop('vp_bottom', 2.5)
# Define a velocity profile in km/s
v = np.empty(shape, dtype=dtype)
v[:] = vp_top # Top velocity (background)
v[..., int(shape[-1] / ratio):] = vp_bottom # Bottom velocity
return Model(space_order=space_order, vp=v, origin=origin, shape=shape,
dtype=dtype, spacing=spacing, nbpml=nbpml, **kwargs)
elif preset.lower() in ['layers-elastic', 'twolayer-elastic',
'2layer-elastic']:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.5 km/s,
# and the bottom part of the domain has 2.5 km/s.
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbpml = kwargs.pop('nbpml', 10)
ratio = kwargs.pop('ratio', 2)
vp_top = kwargs.pop('vp_top', 1.5)
vp_bottom = kwargs.pop('vp_bottom', 2.5)
# Define a velocity profile in km/s
v = np.empty(shape, dtype=dtype)
v[:] = vp_top # Top velocity (background)
v[..., int(shape[-1] / ratio):] = vp_bottom # Bottom velocity
vs = 0.5 * v[:]
rho = v[:]/vp_top
return ModelElastic(space_order=space_order, vp=v, vs=vs, rho=rho,
origin=origin, shape=shape,
dtype=dtype, spacing=spacing, nbpml=nbpml, **kwargs)
elif preset.lower() in ['layers-tti', 'twolayer-tti', '2layer-tti']:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.5 km/s,
# and the bottom part of the domain has 2.5 km/s.\
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbpml = kwargs.pop('nbpml', 10)
ratio = kwargs.pop('ratio', 2)
vp_top = kwargs.pop('vp_top', 1.5)
vp_bottom = kwargs.pop('vp_bottom', 2.5)
# Define a velocity profile in km/s
v = np.empty(shape, dtype=dtype)
v[:] = vp_top # Top velocity (background)
v[..., int(shape[-1] / ratio):] = vp_bottom # Bottom velocity
epsilon = scipy_smooth(.3*(v - 1.5))
delta = scipy_smooth(.2*(v - 1.5))
theta = scipy_smooth(.5*(v - 1.5))
phi = None
if len(shape) > 2:
phi = scipy_smooth(.25*(v - 1.5), shape)
return Model(space_order=space_order, vp=v, origin=origin, shape=shape,
dtype=dtype, spacing=spacing, nbpml=nbpml, epsilon=epsilon,
delta=delta, theta=theta, phi=phi, **kwargs)
elif preset.lower() in ['layers-tti-noazimuth', 'twolayer-tti-noazimuth',
'2layer-tti-noazimuth']:
# A two-layer model in a 2D or 3D domain with two different
# velocities split across the height dimension:
# By default, the top part of the domain has 1.5 km/s,
# and the bottom part of the domain has 2.5 km/s.\
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
dtype = kwargs.pop('dtype', np.float32)
nbpml = kwargs.pop('nbpml', 10)
ratio = kwargs.pop('ratio', 2)
vp_top = kwargs.pop('vp_top', 1.5)
vp_bottom = kwargs.pop('vp_bottom', 2.5)
# Define a velocity profile in km/s
v = np.empty(shape, dtype=dtype)
v[:] = vp_top # Top velocity (background)
v[..., int(shape[-1] / ratio):] = vp_bottom # Bottom velocity
epsilon = .3*(v - 1.5)
delta = .2*(v - 1.5)
theta = .5*(v - 1.5)
return Model(space_order=space_order, vp=v, origin=origin, shape=shape,
dtype=dtype, spacing=spacing, nbpml=nbpml, epsilon=epsilon,
delta=delta, theta=theta, **kwargs)
elif preset.lower() in ['circle-isotropic']:
# A simple circle in a 2D domain with a background velocity.
# By default, the circle velocity is 2.5 km/s,
# and the background veloity is 3.0 km/s.
dtype = kwargs.pop('dtype', np.float32)
shape = kwargs.pop('shape', (101, 101))
spacing = kwargs.pop('spacing', tuple([10. for _ in shape]))
origin = kwargs.pop('origin', tuple([0. for _ in shape]))
nbpml = kwargs.pop('nbpml', 10)
vp = kwargs.pop('vp', 3.0)
vp_background = kwargs.pop('vp_background', 2.5)
r = kwargs.pop('r', 15)
# Only a 2D preset is available currently
assert(len(shape) == 2)
v = np.empty(shape, dtype=dtype)
v[:] = vp_background
a, b = shape[0] / 2, shape[1] / 2
y, x = np.ogrid[-a:shape[0]-a, -b:shape[1]-b]
v[x*x + y*y <= r*r] = vp
return Model(space_order=space_order, vp=v, origin=origin, shape=shape,
dtype=dtype, spacing=spacing, nbpml=nbpml, **kwargs)
elif preset.lower() in ['marmousi-isotropic', 'marmousi2d-isotropic']:
shape = (1601, 401)
spacing = (7.5, 7.5)
origin = (0., 0.)
# Read 2D Marmousi model from opesc/data repo
data_path = kwargs.get('data_path', None)
if data_path is None:
raise ValueError("Path to opesci/data not found! Please specify with "
"'data_path=<path/to/opesci/data>'")
path = os.path.join(data_path, 'Simple2D/vp_marmousi_bi')
v = np.fromfile(path, dtype='float32', sep="")
v = v.reshape(shape)
# Cut the model to make it slightly cheaper
v = v[301:-300, :]
return Model(space_order=space_order, vp=v, origin=origin, shape=v.shape,
dtype=np.float32, spacing=spacing, nbpml=nbpml, **kwargs)
elif preset.lower() in ['marmousi-elastic', 'marmousi2d-elastic']:
shape = (1601, 401)
spacing = (7.5, 7.5)
origin = (0., 0.)
# Read 2D Marmousi model from opesc/data repo
data_path = kwargs.get('data_path', None)
if data_path is None:
raise ValueError("Path to opesci/data not found! Please specify with "
"'data_path=<path/to/opesci/data>'")
path = os.path.join(data_path, 'Simple2D/vp_marmousi_bi')
v = np.fromfile(path, dtype='float32', sep="")
v = v.reshape(shape)
# Cut the model to make it slightly cheaper
v = v[301:-300, :]
vs = .5 * v[:]
rho = v[:]/mmax(v[:])
return ModelElastic(space_order=space_order, vp=v, vs=vs, rho=rho,
origin=origin, shape=v.shape,
dtype=np.float32, spacing=spacing, nbpml=20)
elif preset.lower() in ['marmousi-tti2d', 'marmousi2d-tti']:
shape_full = (201, 201, 70)
shape = (201, 70)
spacing = (10., 10.)
origin = (0., 0.)
nbpml = kwargs.pop('nbpml', 20)
# Read 2D Marmousi model from opesc/data repo
data_path = kwargs.pop('data_path', None)
if data_path is None:
raise ValueError("Path to opesci/data not found! Please specify with "
"'data_path=<path/to/opesci/data>'")
path = os.path.join(data_path, 'marmousi3D/vp_marmousi_bi')
# velocity
vp = 1e-3 * np.fromfile(os.path.join(data_path, 'marmousi3D/MarmousiVP.raw'),
dtype='float32', sep="")
vp = vp.reshape(shape_full)
vp = vp[101, :, :]
# Epsilon, in % in file, resale between 0 and 1
epsilon = np.fromfile(os.path.join(data_path, 'marmousi3D/MarmousiEps.raw'),
dtype='float32', sep="") * 1e-2
epsilon = epsilon.reshape(shape_full)
epsilon = epsilon[101, :, :]
# Delta, in % in file, resale between 0 and 1
delta = np.fromfile(os.path.join(data_path, 'marmousi3D/MarmousiDelta.raw'),
dtype='float32', sep="") * 1e-2
delta = delta.reshape(shape_full)
delta = delta[101, :, :]
# Theta, in degrees in file, resale in radian
theta = np.fromfile(os.path.join(data_path, 'marmousi3D/MarmousiTilt.raw'),
dtype='float32', sep="")
theta = np.float32(np.pi / 180 * theta.reshape(shape_full))
theta = theta[101, :, :]
return Model(space_order=space_order, vp=vp, origin=origin, shape=shape,
dtype=np.float32, spacing=spacing, nbpml=nbpml, epsilon=epsilon,
delta=delta, theta=theta, **kwargs)
elif preset.lower() in ['marmousi-tti3d', 'marmousi3d-tti']:
shape = (201, 201, 70)
spacing = (10., 10., 10.)
origin = (0., 0., 0.)
nbpml = kwargs.pop('nbpml', 20)
# Read 2D Marmousi model from opesc/data repo
data_path = kwargs.pop('data_path', None)
if data_path is None:
raise ValueError("Path to opesci/data not found! Please specify with "
"'data_path=<path/to/opesci/data>'")
path = os.path.join(data_path, 'marmousi3D/vp_marmousi_bi')
# Velcoity
vp = 1e-3 * np.fromfile(os.path.join(data_path, 'marmousi3D/MarmousiVP.raw'),
dtype='float32', sep="")
vp = vp.reshape(shape)
# Epsilon, in % in file, resale between 0 and 1
epsilon = np.fromfile(os.path.join(data_path, 'marmousi3D/MarmousiEps.raw'),
dtype='float32', sep="") * 1e-2
epsilon = epsilon.reshape(shape)
# Delta, in % in file, resale between 0 and 1
delta = np.fromfile(os.path.join(data_path, 'marmousi3D/MarmousiDelta.raw'),
dtype='float32', sep="") * 1e-2
delta = delta.reshape(shape)
# Theta, in degrees in file, resale in radian
theta = np.fromfile(os.path.join(data_path, 'marmousi3D/MarmousiTilt.raw'),
dtype='float32', sep="")
theta = np.float32(np.pi / 180 * theta.reshape(shape))
# Phi, in degrees in file, resale in radian
phi = np.fromfile(os.path.join(data_path, 'marmousi3D/Azimuth.raw'),
dtype='float32', sep="")
phi = np.float32(np.pi / 180 * phi.reshape(shape))
return Model(space_order=space_order, vp=vp, origin=origin, shape=shape,
dtype=np.float32, spacing=spacing, nbpml=nbpml, epsilon=epsilon,
delta=delta, theta=theta, phi=phi, **kwargs)
else:
raise ValueError("Unknown model preset name")
