Abstract Finite-difference (FD) techniques are widely used to model wave propagation through complex structures. Two main sources of error can be identified: (1) from numerical dispersion and numerical anisotropy and (2) by modeling the response of internal grid boundaries. Conventional discretization criteria to reduce the effects of numerical dispersion and numerical anisotropy have long been established (5-8 gridpoints per wavelength for a fourth-order accurate FD scheme). We analyze the second source of errors, comparing different staggered-grid FD solutions to the Cagniard-de Hoop solution in models with fluid– solid contacts. Our results confirm that it is sufficient to rely on conventional discretization criteria if the fluid–solid interface is aligned with the grid. If accurate modeling of the Scholte wave is required, then a new imaging method we propose should be used to allow for conventional sampling of the wavefield to minimize numerical dispersion. However, for an interface not aligned with the grid (irregular interfaces), a spatial sampling of at least 15 gridpoints per minimum wavelength is required to obtain acceptable results, particularly in seismic seabed applications where Scholte waves may need to be modeled more accurately.