A high-efficiency parallel fast marching method for large-scale seismic tomography in three-dimensional spherical coordinates

Abstract

The fast marching method is an essential step in the level set method, widely applied in seismic tomography. However, there are two key challenges in large-scale seismic tomography: significant time consumption and storage issues related to large-scale matrices. Therefore, it is crucial to develop a high-efficiency and high-accuracy parallel fast marching method. Although previous scholars have developed parallel fast marching algorithms based on various parallel strategies in Cartesian coordinates, these algorithms ignore the influence of the Earth’s curvature and generally achieve only first-order accuracy. To address these problems, this study introduces a distributed-memory parallel fast marching method based on domain decomposition to solve the eikonal equation in 3D spherical coordinates. By introducing spherical coordinates, the method naturally accounts for the Earth’s curvature. Additionally, this study designs a parallel strategy based on a second-order scheme and uses the multiplicative factorization technique to handle point source singularities. The parallel strategy ensures the global causality condition of the traveltime field and maintains global second-order accuracy. Numerical experiments show that the parallel algorithm can solve the factor eikonal equation for 8.5 billion grid points or greater. It distributes the over 200 GB memory requirement per node in sequential FMM across multiple nodes, significantly reducing computation time and memory needs while maintaining second-order accuracy. Furthermore, the algorithm proves to be suitable for earthquake location applications. This highly efficient and accurate parallel algorithm is applicable for large-scale seismic tomography and other related research.