An improved 27-point frequency-domain elastic-wave average-derivative method with applications to a moving point source

Abstract

Exploration seismology based on moving sources such as high-speed trains has attracted increasingly great attention. It is an important task to perform near-surface seismic imaging and inversion using moving sources. In this context, an accurate and efficient forward-modeling engine for moving sources is crucial. We initially consider a single moving point source. To implement the numerical simulation in terms of a moving point source, two aspects need to be considered: (1) the numerical discretization strategy of the seismic-wave equation and (2) the discrete representation of the moving point source. For the 3D heterogeneous elastic-wave equation, we develop an improved frequency-domain average-derivative numerical method (ADM) by introducing the weighted average of four sets of grid points for the mass-acceleration term. Due to the numerical discretization template, the continuously moving point source is discretized as a series of fixed sources located at different grid points and excited at different times. The corresponding discrete representation of spatio-temporal variation is given by modifying the right-hand side of the resulting linear system of equations. A numerical experiment in a 3D homogeneous half-space model validates the higher computational accuracy of the improved ADM and the feasibility of the numerical simulation scheme for a moving point source. Furthermore, we test the performance of the moving-point-source numerical simulation scheme in the 3D heterogeneous overthrust model. The successful implementation of the 3D frequency-domain numerical simulation for a moving point source establishes a foundation for subsequent practical applications of moving sources in seismic imaging to be performed in the future.