A fast sweeping method for calculating qP-wave traveltimes in 3-D vertical transversely isotropic media using a quadratic equation

Abstract

SUMMARY Traveltime computations are an important aspect of seismic data processing applications such as traveltime tomography, migration and seismic source localization. Seismic anisotropy is a widespread feature of the Earth. Solutions to the eikonal equation that account for such anisotropy are needed for high-resolution seismic imaging and inversion. The fast sweeping method (FSM) has been widely used in computing the first-arrival traveltimes for anisotropic media because it does not need to expand the wave front from the point of the smallest traveltime. To apply FSM on strong anisotropic media, one has to solve the slowness equation derived from the Christoffel equation. All the previous developed FSM methods transform the quartic coupled slowness surface equation of quasi-P (qP) and quasi-SV (qSV) waves to the quartic equation in terms of the unknown traveltime, then numerically solve this quartic equation to compute the first-arrival traveltimes of the qP waves. However, the computational cost is significantly increased due the numerically solving the quartic equation, especially for the 3-D problems. In this study, we find a way to transform the quartic slowness equation into a quadratic one if a specific triangular-pyramid stencil around a target point is used. As the quadratic equation has the analytical solution and does not need a numerical solver, the computational efficiency of the scheme is greatly improved. We apply this methodology to develop an efficient 3-D FSM to compute the first-arrival traveltimes for qP waves in 3-D vertical transversely isotropic (VTI) media. We use both layered VTI model and complex VTI model to demonstrate the efficiency of the proposed method to obtain accurate traveltimes in 3-D VTI media involving strong anisotropy.