def gradient(model, residual, rcv_coords, u, return_op=False, space_order=8, t_sub=1,
w=None, free_surface=False, freq=None, dft_sub=None, isic=True):
"""
Low level propagator, to be used through `interface.py`
Compute adjoint wavefield v = adjoint(F(m))*y
and related quantities (||v||_w, v(xsrc))
"""
# Setting adjoint wavefieldgradient
v = wavefield(model, space_order, fw=False)
# Set up PDE expression and rearrange
pde, fs = wave_kernel(model, v, fw=False, fs=free_surface)
# Setup source and receiver
geom_expr, _, _ = src_rec(model, v, src_coords=rcv_coords,
wavelet=residual, fw=False)
# Setup gradient wrt m
gradm = Function(name="gradm", grid=model.grid)
g_expr = grad_expr(gradm, u, v, model, w=w, freq=freq, dft_sub=dft_sub, isic=isic)
# Create operator and run
subs = model.spacing_map
op = Operator(pde + geom_expr + g_expr + fs,
subs=subs, name="gradient"+name(model))
if return_op:
return op, gradm, v
op(**op_kwargs(model, fs=free_surface))
# Output
return gradm.data
def gradient(model,
residual,
rcv_coords,
u,
return_op=False,
space_order=8,
w=None,
freq=None,
dft_sub=None,
isic=False):
"""
Low level propagator, to be used through `interface.py`
Compute the action of the adjoint Jacobian onto a residual J'* δ d.
"""
# Setting adjoint wavefieldgradient
v = wavefield(model, space_order, fw=False)
# Set up PDE expression and rearrange
pde = wave_kernel(model, v, fw=False)
# Setup source and receiver
geom_expr, _, _ = src_rec(model,
v,
src_coords=rcv_coords,
wavelet=residual,
fw=False)
# Setup gradient wrt m
gradm = Function(name="gradm", grid=model.grid)
g_expr = grad_expr(gradm,
u,
v,
model,
w=w,
freq=freq,
dft_sub=dft_sub,
isic=isic)
# Create operator and run
subs = model.spacing_map
op = Operator(pde + geom_expr + g_expr,
subs=subs,
name="gradient" + name(model),
opt=opt_op(model))
try:
op.cfunction
except:
op = Operator(pde + geom_expr + g_expr,
subs=subs,
name="gradient" + name(model),
opt='advanced')
op.cfunction
if return_op:
return op, gradm, v
summary = op()
# Output
return gradm, summary
def forward_grad(model,
src_coords,
rcv_coords,
wavelet,
v,
space_order=8,
q=None,
ws=None,
isic=False,
w=None,
freq=None,
**kwargs):
"""
Low level propagator, to be used through `interface.py`
Compute forward wavefield u = A(m)^{-1}*f and related quantities (u(xrcv))
"""
# Number of time steps
nt = as_tuple(q)[0].shape[0] if wavelet is None else wavelet.shape[0]
# Setting forward wavefield
u = wavefield(model, space_order, save=False)
# Add extended source
q = q or wf_as_src(u, w=0)
q = extented_src(model, ws, wavelet, q=q)
# Set up PDE expression and rearrange
pde = wave_kernel(model, u, q=q)
# Setup source and receiver
geom_expr, _, rcv = src_rec(model,
u,
src_coords=src_coords,
nt=nt,
rec_coords=rcv_coords,
wavelet=wavelet)
# Setup gradient wrt m
gradm = Function(name="gradm", grid=model.grid)
g_expr = grad_expr(gradm, v, u, model, w=w, isic=isic, freq=freq)
# Create operator and run
subs = model.spacing_map
op = Operator(pde + geom_expr + g_expr,
subs=subs,
name="forward_grad" + name(model),
opt=opt_op(model))
summary = op()
# Output
return rcv, gradm, summary