Applications of a Multivalued Travel Time Solver in two and three Dimensions

In complex media, seismic energy can travel along more than one path between two points. This means that at a given receiver, one might observe a wavetrain containing several different arrivals. Later arrivals provide additional structural information when compared with first arrivals, as they have taken different paths through the medium. The wavefront construction principle is used as the basis of a new scheme for the computation of multivalued travel times that arise from smooth variations in both velocity structure and interface geometry. In two dimensions, the idea 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. Performing the wavefront tracking in reduced phase space significantly enhances the methods capability to resolve complex features such as swallowtails. Later arrivals can be used to improve the quality of images obtained by seismic tomography, as they sample different parts of the model compared to the first arrivals traditionally used in tomography. The wavefront tracking scheme proposed here is not limited to local or regional scale problems; it can be used to compute global phases and associated later arrivals generated by lateral velocity or interface anomalies. Another application is to combine the scheme with the Gaussian beam method and calculate the response of a structure beneath a receiver to an incoming plane wave. This could potentially be used in receiver function analysis and would have the advantage that later arrivals arising from lateral heterogeneity could also be modelled. In three dimensions, the wavefront becomes a surface and can be described using a mosaic of triangles. Evolving a complex surface with a given accuracy is a well known problem in the field of computer graphics. Schemes developed in this field for surface refinement and simplification are applied here to a propagating wavefront in order to maintain a fixed density of nodes. This forms the basis of the method, proposed in this work, for tracking wavefronts in the presence of complex three dimensional velocity models. Application of the new scheme to structures containing strong velocity contrasts, including the SEG/EAGE salt dome model, demonstrate it to be robust and efficient for practical application.