Wavenumber Limitation of Medium in the Finite-Difference Modeling of Seismic-Wave Propagation: A Proof of Concept

Abstract When developing a finite-difference (FD) scheme, one of the key aspects that must be addressed is the spatial discretization of material parameters and the implementation of material interfaces. Mittet (2017) and Moczo et al. (2022) recently suggested a novel approach based on the wavenumber limitation of the medium. They demonstrated that, due to spatial discretization, a model of the medium must be wavenumber-limited by a wavenumber km smaller than the Nyquist wavenumber. Mittet (2021a) and Valovcan et al. (2024) proved that the wavefield (numerically simulated or exact) in a km-limited medium can only be accurate up to km/2. Here, we numerically demonstrate a perfect subcell resolution (capability to sense the position of interface within a grid cell) of FD modeling based on the wavenumber-limited medium using a finite spatial low-pass filter. The finding that it is possible to use a finite-length filter for wavenumber limitation of the medium is of key importance for the next development of the concept in terms of computational efficiency. We demonstrate an unprecedented accuracy for a canonical model—a material interface between two homogeneous half-spaces. The time–frequency envelope and phase misfits between the FD solution and the exact analytical solution are surprisingly small and are the same for any position of the interface within a grid spacing. We show that the misfits for the reflected and transmitted waves are solely due to grid dispersion. We compare the accuracy of the FD solution for the wavenumber-limited medium with that for the harmonically averaged modulus (Moczo et al., 2002). The FD modeling based on the wavenumber-limited medium is considerably more accurate. The proof of concept of the wavenumber limitation of the medium should be followed by development of a practical way of wavenumber limitation using finite spatial filters in 2D and 3D elastic problems.