Breaking the Nyquist Limit in Seismic Wavefield Modeling Using Implicit DRPSM Scheme

Accurate and efficient seismic wavefield modeling near or beyond the Nyquist limit remains a critical challenge in computational geophysics. In our previous work, we introduced an Implicit Finite Difference (IFD) method for solving the acoustic wave equation, which achieves high numerical accuracy with compact stencils. In this study, we further extend the method by integrating ideas from the Dispersion-Relation Preserving Stereo-Modeling (DRPSM) scheme proposed by Jing et al. (2017), which demonstrated that forward modeling is feasible using fewer than two grid points per wavelength. We propose a new hybrid approach, the Implicit DRPSM (IDRPSM) scheme, which combines the compactness and stability of IFD with the dispersion control of DRPSM to enable sub-Nyquist modeling. Through rigorous dispersion-relation analysis, we demonstrate that the IDRPSM method can significantly relax spatial sampling requirements while maintaining wavefield fidelity. Although numerical simulations in complex models such as BP 2D and homogeneous domains are ongoing, the theoretical results provide strong evidence for the feasibility of high-accuracy modeling with reduced grid density. The proposed IDRPSM scheme opens a promising pathway for efficient large-scale seismic modeling and imaging in high-frequency regimes.