def born(model, src_coords, rcv_coords, wavelet, space_order=8,
save=False, q=None, free_surface=False, isic=False, ws=None):
"""
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 wavefield
u = wavefield(model, space_order, save=save, nt=wavelet.shape[0])
ul = wavefield(model, space_order, name="l")
# 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, fsu = wave_kernel(model, u, fs=free_surface, q=q)
pdel, fsul = wave_kernel(model, ul, q=lin_src(model, u, isic=isic), fs=free_surface)
# Setup source and receiver
geom_expr, _, _ = src_rec(model, u, src_coords=src_coords, wavelet=wavelet)
geom_exprl, _, rcvl = src_rec(model, ul, rec_coords=rcv_coords, nt=wavelet.shape[0])
# Create operator and run
subs = model.spacing_map
op = Operator(pde + geom_expr + pdel + geom_exprl + fsu + fsul,
subs=subs, name="born"+name(model))
op(**op_kwargs(model, fs=free_surface))
# Output
return rcvl.data, u
def forward(model,
src_coords,
rcv_coords,
wavelet,
space_order=8,
save=False,
q=None,
return_op=False,
freq_list=None,
dft_sub=None,
ws=None,
t_sub=1,
**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=save, nt=nt, t_sub=t_sub)
# Expression for saving wavefield if time subsampling is used
u_save, eq_save = wavefield_subsampled(model, u, nt, t_sub)
# 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)
# On-the-fly Fourier
dft, dft_modes = otf_dft(u, freq_list, model.critical_dt, factor=dft_sub)
# Create operator and run
subs = model.spacing_map
op = Operator(pde + dft + geom_expr + eq_save,
subs=subs,
name="forward" + name(model),
opt=opt_op(model))
op.cfunction
if return_op:
return op, u, rcv
summary = op()
# Output
return rcv, dft_modes or (u_save if t_sub > 1 else u), 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
def born(model,
src_coords,
rcv_coords,
wavelet,
space_order=8,
save=False,
q=None,
isic=False,
ws=None,
t_sub=1):
"""
Low level propagator, to be used through `interface.py`
Compute adjoint wavefield v = adjoint(F(m))*y
and related quantities (||v||_w, v(xsrc))
"""
nt = wavelet.shape[0]
# Setting wavefield
u = wavefield(model, space_order, save=save, nt=nt, t_sub=t_sub)
ul = wavefield(model, space_order, name="l")
# Expression for saving wavefield if time subsampling is used
u_save, eq_save = wavefield_subsampled(model, u, nt, t_sub)
# 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, tmpu = wave_kernel(model, u, q=q)
pdel, tmpul = wave_kernel(model, ul, q=lin_src(model, u, isic=isic))
# Setup source and receiver
geom_expr, _, _ = src_rec(model, u, src_coords=src_coords, wavelet=wavelet)
geom_exprl, _, rcvl = src_rec(model,
ul,
rec_coords=rcv_coords,
nt=wavelet.shape[0])
# Create operator and run
subs = model.spacing_map
op = Operator(tmpu + tmpul + pde + geom_expr + geom_exprl + pdel + eq_save,
subs=subs,
name="born" + name(model),
opt=opt_op(model, no_ms=ws is not None))
summary = op()
# Output
return rcvl, (u_save if t_sub > 1 else u), summary
def born(model,
src_coords,
rcv_coords,
wavelet,
space_order=8,
save=False,
q=None,
return_op=False,
isic=False,
freq_list=None,
dft_sub=None,
ws=None,
t_sub=1,
nlind=False):
"""
Low level propagator, to be used through `interface.py`
Compute linearized wavefield U = J(m)* δ m
and related quantities.
"""
nt = wavelet.shape[0]
# Setting wavefield
u = wavefield(model, space_order, save=save, nt=nt, t_sub=t_sub)
ul = wavefield(model, space_order, name="l")
# Expression for saving wavefield if time subsampling is used
u_save, eq_save = wavefield_subsampled(model, u, nt, t_sub)
# 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)
if model.dm == 0:
pdel = []
else:
pdel = wave_kernel(model, ul, q=lin_src(model, u, isic=isic))
# Setup source and receiver
geom_expr, _, rcvnl = src_rec(model,
u,
rec_coords=rcv_coords if nlind else None,
src_coords=src_coords,
wavelet=wavelet)
geom_exprl, _, rcvl = src_rec(model, ul, rec_coords=rcv_coords, nt=nt)
# On-the-fly Fourier
dft, dft_modes = otf_dft(u, freq_list, model.critical_dt, factor=dft_sub)
# Create operator and run
subs = model.spacing_map
op = Operator(pde + geom_expr + geom_exprl + pdel + dft + eq_save,
subs=subs,
name="born" + name(model),
opt=opt_op(model))
op.cfunction
outrec = (rcvl, rcvnl) if nlind else rcvl
if return_op:
return op, u, outrec
summary = op()
# Output
return outrec, dft_modes or (u_save if t_sub > 1 else u), summary
