Finite-Difference Time Domain (FDTD) methods with Summation By Parts (SBP) operators and Simultaneous Approximation Terms (SAT) are used to model wave propagation in an ocean with an irregular anelastic seafloor. SBP–SAT combines the ease and flexibility of FDTD methods for modelling wave propagation with a weak formulation of modelling boundary conditions (e.g., a fluid/solid boundary condition) to an arbitrary order of accuracy. We then use a coordinate transform to model an irregular seafloor by mapping the physical model to a Cartesian computational domain which in effect results in a modification (anisotropic) of the model material properties to obtain a computational Cartesian model with an equivalent effect on the propagating waves. An adjoint formulation of our 3-D acoustic/viscoelastic anisotropic modelling methodology can be used to invert ocean acoustic and marine seismic data for seafloor bathymetry and its anelastic properties. The acoustic properties of the water layer are well-known and sound speed profiles are fairly straight-forward to measure. Instead, the parameters related to the coordinate transform to our Cartesian computational model that describes the seafloor topography can be inverted for. Synthetic data examples will be discussed.
Robertsson et al. (Wed,) studied this question.