  The emergence of long-offset sparse stationary-recording surveys carried out
with ocean bottom nodes (OBN) makes frequency-domain full waveform inversion
(FWI) attractive to manage compact volume of data and perform attenuation
imaging. One challenge of frequency-domain FWI is the forward problem, which
requires the solution of large and sparse linear systems with multiple
right-hand sides. While direct methods are suitable for dense acquisitions and
problems involving less than 100 million unknowns, iterative solver are more
suitable for large computational domains covered by sparse OBN surveys. Here,
we solve these linear systems with a Krylov subspace method preconditioned with
the two-level Optimized Restricted Additive Schwarz (ORAS) domain decomposition
preconditioner, the prefix optimized referring to the use of absorbing
conditions at the subdomain interfaces. We implement this method with finite
differences on uniform grid and finite elements on unstructured tetrahedral
meshes. A simulation in a model where the velocity linearly increases with
depth allows us to validate the accuracy of the two schemes against an
analytical solution while highlighting how their relative cost varies with the
band of propagated wavelengths. A simulation in the overthrust model involving
up to 2 billions of parameters allows us to tune the method and highlights its
scalability.
