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 np.sqrt(1. / mmin(self.m))
except ValueError:
return np.sqrt(1. / np.min(self.m))
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 * mmin(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:
# FIXME: Fix 'Constant' so that that mmax(self.vp) returns the data value
return self.dtype(6. * mmin(self.spacing) /
(7. * np.sqrt(self.grid.dim) * mmax(self.vp.data)))
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)
# 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