def GradientOperator(model,
geometry,
space_order=4,
save=True,
kernel='OT2',
**kwargs):
"""
Construct a gradient operator in an acoustic media.
Parameters
----------
model : Model
Object containing the physical parameters.
geometry : AcquisitionGeometry
Geometry object that contains the source (SparseTimeFunction) and
receivers (SparseTimeFunction) and their position.
space_order : int, optional
Space discretization order.
save : int or Buffer, optional
Option to store the entire (unrolled) wavefield.
kernel : str, optional
Type of discretization, centered or shifted.
"""
m, damp = model.m, model.damp
# Gradient symbol and wavefield symbols
grad = Function(name='grad', grid=model.grid)
u = TimeFunction(name='u',
grid=model.grid,
save=geometry.nt if save else None,
time_order=2,
space_order=space_order)
v = TimeFunction(name='v',
grid=model.grid,
save=None,
time_order=2,
space_order=space_order)
rec = Receiver(name='rec',
grid=model.grid,
time_range=geometry.time_axis,
npoint=geometry.nrec)
s = model.grid.stepping_dim.spacing
eqn = iso_stencil(v, m, s, damp, kernel, forward=False)
if kernel == 'OT2':
gradient_update = Inc(grad, -u.dt2 * v)
elif kernel == 'OT4':
gradient_update = Inc(
grad, -(u.dt2 + s**2 / 12.0 * u.biharmonic(m**(-2))) * v)
# Add expression for receiver injection
receivers = rec.inject(field=v.backward, expr=rec * s**2 / m)
# Substitute spacing terms to reduce flops
return Operator(eqn + receivers + [gradient_update],
subs=model.spacing_map,
name='Gradient',
**kwargs)
def test_symbolic_constant_times_add(self):
grid = Grid(shape=(10, 10))
dt = grid.time_dim.spacing
u = TimeFunction(name="u", grid=grid, space_order=4, time_order=2)
f = Function(name='f', grid=grid)
eq = Eq(u.forward, u.laplace + dt**0.2 * u.biharmonic(1 / f))
leq = collect_derivatives.func([eq])[0]
assert len(eq.rhs.args) == 3
assert len(leq.rhs.args) == 2
assert all(isinstance(i, Derivative) for i in leq.rhs.args)
