The fast marching method: An effective tool for tomographic imaging and tracking multiple phases in complex layered media

The accurate prediction of seismic traveltimes is required in many areas of seismology, including the processing of seismic reflection profiles, earthquake location, and seismic tomography at a variety of scales. In this paper, we present two seismic applications of a recently developed grid-based numerical scheme for tracking the evolution of monotonically advancing interfaces, via finite-difference solution of the eikonal equation, known as the fast marching method (FMM). Like most other practical grid-based techniques, FMM is only capable of locating the first-arrival phase in continuous media; however, its combination of unconditional stability and rapid computation make it a truly practical scheme for velocity fields of arbitrary complexity. The first application of FMM that we present focuses on the prediction of multiple reflection and refraction phases in complex 2D layered media. By treating each layer that the wavefront enters as a separate computational domain, we show that sequential application of FMM can be used to track phases comprising any number of reflection and transmission branches in media of arbitrary complexity. We also show that the use of local grid refinement in the source neighbourhood, where wavefront curvature is high, significantly improves the accuracy of the scheme with little extra computational expense. The second application of FMM that we consider is in the context of 3D teleseismic tomography, which uses relative traveltime residuals from distant earthquakes to image wavespeed variations in the Earth?s crust and upper mantle beneath a seismic array. Using teleseismic data collected in Tasmania, we show that FMM can rapidly and robustly calculate two-point traveltimes from an impinging teleseismic wavefront to a receiver array located on the surface, despite the presence of significant lateral variations in wavespeed in the intervening crust and upper mantle. Combined with a rapid subspace inversion method, the new FMM based tomographic scheme is shown to be extremely efficient and robust.