Mesh-free radial-basis-function-generated finite differences and their application in reverse time migration

ABSTRACT Compared with one-way wave equation migration and ray-based migration, reverse time migration (RTM) using two-way wave propagation information can produce accurate imaging results for complex structures. Its computational accuracy and efficiency are mainly determined by numerical methods for wavefield simulation. When using traditional regular grids for seismic modeling, scattering artifacts may occur due to the stepped approximation of layer interfaces and rugged topography. On the other hand, irregular grids require a complex grid generation algorithm, despite having certain geometric flexibility. Mesh-free RTM can effectively reduce the scattered noise under regular grids and avoid the extra computation in the process of irregular grid generation. For implementation of the mesh-free RTM method, an algorithm with fast generation of node distributions is used to discretize the underground velocity model, and radial-basis-function-generated finite difference is used to realize the numerical simulation of wave propagation; the crosscorrelation imaging condition is adopted for imaging. The mesh-free RTM method, which has the flexibility of the simulation region and an abundance of wavefield information, reduces the storage required for RTM, shows the potential of high-accuracy migration in the case of an undulating surface, and provides more accurate migration imaging results for oil and gas exploration under complex geologic conditions.