Multi Valued Travel Times for Crustal Scale Applications

Multi valued travel times have traditionally not been used in seismic imaging, with only a handful of notable exceptions in the field of exploration geophysics. For studies on local and regional scales (e.g. local earthquake/teleseismic tomography), the focus has largely been on first arrivals, and numerous ray and grid based schemes have been developed for predicting this class of data. However, later arrivals often contribute to the length and shape of a recorded wavetrain, particularly in regions of complex geology. These arrivals are likely to contain additional information about seismic structure, as their two point path differs from that of the first arrival; in particular, they are more amenable to sampling regions of lower velocity. Recently, several grid based schemes have been proposed for solving the multi valued travel time problem. Although promising, they currently require significant computational resources for crustal scale problems, and further development is required before practical application becomes feasible. An alternative approach, sometimes referred to as wavefront construction, is to represent the wavefront as a set of points, and use local ray tracing and interpolation to advance the wavefront in a series of time steps. In this paper, we use the wavefront construction principle as the basis of a new scheme for computing multi- valued traveltimes that arise from smooth variations in both velocity structure and interface geometry. The wavefront tracking is performed in reduced phase space, which significantly enhances the method's ability to correctly resolve complex features such as triplications. Tests with a variety of models show that the scheme is robust in the presence of strong velocity heterogeneity and interface curvature, with phases comprising multiple reflections, refractions and triplications successfully tracked. A Gaussian beam method is applied using the computed ray paths, and allows rapid estimation of synthetic seismograms, which can be used to help discriminate between later arrivals in observed data. Using our new method, we show that exploiting later arrivals in travel time tomography can result in superior images. Another potential application of the scheme is in the generation of synthetic receiver functions in laterally varying media; current methods for predicting receiver functions assume that seismic structure varies with depth only.