Research On Computing Method Of Seismic Travel Time Based On Factorization Algorithm And High-order Weno Scheme

The calculation of seismic travel times is the foundation of seismic travel time tomography,and the fast scanning method for solving the eikonal equation has become the mainstream approach for travel time calculation.This paper conducts in-depth research on the fast scanning method based on the eikonal equation and proposes improvements and methods in two aspects:(1)For irregular boundary problems,the construction of an unstructured mesh model and travel time calculation are proposed.In seismology,underground velocity models are usually composed of several irregular interfaces,while traditional fast scanning methods are mostly based on rectangular grids.To adapt to the requirements of irregular interfaces,it is necessary to divide the computational domain into irregular triangular grids.The paper presents the principles of the triangular mesh method and the fast scanning algorithm on triangular grids,establishes a velocity model based on unstructured grids,and performs travel time calculations.(2)For the singularity problem in seismic wave travel time calculation algorithms,a fast scanning seismic wave travel time calculation based on factorization algorithms and high-order WENO formats is proposed.In a Cartesian coordinate system,the wavefront is a plane perpendicular to the ray direction.In travel time calculations with a point source as the initial condition,the source point is a prominent singularity.The singularity problem caused by the source singularity makes the calculated travel times inaccurate.Therefore,all solutions of the eikonal equation based on finite difference formats suffer from source singularity problems,and the travel time errors caused by the source singularity extend to the entire computational domain,resulting in inaccurate travel times.This paper provides an overview of several traditional methods for handling point source singularities,including factorization algorithms and fast scanning methods based on high-order WENO formats,and outlines their principles and computational procedures.By combining factorization algorithms and high-order WENO formats,this paper proposes a fast scanning seismic wave travel time calculation method based on factorization algorithms and high-order WENO formats,decomposing the travel time into two multiplicative factors.The decomposed equation is numerically solved using a third-order WENO-based Lax-Friedrichs scanning method.The advantage of decomposing the travel time into two multiplicative factors is that one known factor captures the source singularity point,while the other factor is smooth at the source point.Separating the two factors into a constant factor and a perturbation factor is more conducive to travel time calculation.Numerical simulation results demonstrate the improved computational accuracy and reliability in solving source singularity problems,providing a reference and assistance for future research.