Multi-phase seismic traveltime computation in 2D/3D undulated surface model using factored eikonal equation
ZHANG Yun1, LI Xihai1, BAI Chaoying2,3, NIU Chao1, WANG Yiting1, ZENG Xiaoniu1
1. Rocket Force University of Engineering, Xi'an, Shaanxi 710025, China; 2. Department of Geophysics, College of Geological Engineering and Geomatics, Chang'an University, Xi'an, Shaanxi 710054, China; 3. Institute of Computational Geophysics, Chang'an University, Xi'an, Shaanxi 710054, China
Abstract：The seismic traveltime computation scheme in undulating surface conditions is a basic tool to study the underground structures of such surface areas. The fast marching method (FMM) and the fast sweeping method (FSM) are both developed based on solving the eikonal equation with finite difference. They have the problem of source singularity due to the high curvature of the wavefront around the source. Previous studies show that the com-putational efficiency of FMM is higher than FSM for complex models. Thus, this paper employs the FMM to solve the factorization equation and avoid source singularity. Specifically, the original eikonal equation can be transformed into the factored eikonal equation, in which the seismic traveltime can be regarded as the product of a distance function T 0 and a correction factor T1 of traveltime. The correction factor T1 of traveltime can be solved by the FMM algorithm and then the distance function T0 is multiplied to obtain the traveltime(T). To address the problem that the upwind finite difference formula with even grid spacing is not applicable to surface/interface undulation, this paper constructs an upwind finite difference formula with uneven grid spacing. Finally, the multistage computational technique is adopted to propose a computation method for global multi-phase seismic traveltime. The simulation tests indicate that the new algorithm solves the source singularity of FMM, significantly improves the computational accuracy and efficiency of the original algorithm, and can accurately calculate the multi-phase seismic traveltime.
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