1] Multivalued traveltimes have traditionally not been used in seismic imaging, with only a handful of notable exceptions in the field of exploration geophysics. For studies at local and regional scales (e.g., local earthquake/teleseismic tomography), the focus has largely been on first arrivals, with numerous ray-and grid-based schemes developed for their calculation. However, later arrivals often contribute to the length and shape of a recorded wave train, particularly in regions of complex

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... ology. 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. In this work the wavefront construction principle is used as the basis of a new scheme for computing multivalued traveltimes that arise from smooth variations in both velocity structure and interface geometry. The idea is to represent the wavefront as a set of points in reduced phase space and use local ray tracing and interpolation to advance the wavefront in a series of time steps. The scheme is robust in the presence of strong velocity heterogeneity and interface curvature, with phases comprising multiple reflections, refractions, and triplications successfully tracked. Outside the field of exploration seismology wavefront construction techniques are rarely used, yet they hold great potential for addressing problems in other areas of seismology. This paper demonstrates the viability of the new wavefront construction scheme by applying it to a range of scenarios, including multiarrival body and surface wave tomography, teleseismic receiver function prediction using Gaussian beams, and the tracking of global phases such as PcP.