Multistage Grid-Characteristic Method of Increased Order of Accuracy for Acoustic Problems

Introduction. Seismic exploration is a widely used technology for locating hydrocarbon deposits. An important stage of this process is the simulation of seismic wave propagation in a geological model of the medium with specified physical characteristics. Due to the high computational cost of this problem, the acoustic approximation is widely used in practice, allowing for the correct description of longitudinal wave propagation. The most common approach to seismic modeling is the use of finite-difference schemes on staggered Cartesian computational grids. Despite their simplicity of implementation and high computational efficiency, such methods exhibit insufficient accuracy when modelling complex geological structures, including curvilinear interfaces between geological layers. A promising direction is the development of new high-order computational methods on curvilinear computational grids. This paper presents a stable fifth-order grid-characteristic method successfully applied to solving the problem of acoustic wave propagation in the two-dimensional case.

Materials and Methods. The study employs a grid-characteristic method with a fifth-degree interpolation polynomial constructed on an extended spatial stencil. A class of curvilinear grids is identified that makes it possible to retain the accuracy achieved when solving a one-dimensional problem. Furthermore, the use of a multistage splitting method allows the preservation of the scheme’s order in both time and space for multidimensional formulations.

Results. The formulas of the computational algorithm are presented, the achievement of the declared convergence order is empirically confirmed, and wavefield patterns of the dynamic process are calculated.

Discussion. The results demonstrate lower numerical dissipation of the proposed computational algorithm. The trade-off for this improvement is a significant increase in computation time.

Conclusion. The developed computational algorithm ensures high accuracy in calculating seismic fronts, which is critically important for seismic exploration tasks in layered geological massifs.

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