Application of the grid characteristic method for modeling the propagation of elastic waves in geological media with cracks using overset grids approach

The study of geological fault zones is crucial for determining oil and gas reserves in deposits. For modeling wave scattering in fracture zones, numerical methods are used on structured computational grids to optimize computing resources. However, these methods allow us to calculate the scattering of waves on cracks only in the direction of the coordinate axes. For modeling more realistic fractured fields, numerical methods are used on unstructured computational grids or structured curved computational grids that require large computing power and are important for solving inverse problems. In this paper, we propose a numerical method using overset grids approach, where calculations are carried out on structured regular computational grids with overset grids rotated along cracks. The main factor is the analytical assignment of the Jacobian of rotation of the objects describing the crack, and the small local size of the overset computational grids to save computational resources.