A comparative analysis of two-dimensional multi-valued ray tracing techniques

Seismic wavefront self-intersection (or multi-valued seismic rays) is a natural phenomenon when a seismic wave propagates through a complex medium, which is commonly ignored in most previous studies. The later arrivals not only contain useful information regarding low velocity anomalous zones and/or irregular reflecting interfaces, but also have the potential to improve the ray coverage in subsequent seismic imaging. Due to the relative immaturity of this field of research, it is instructive to compare different algorithms and therefore develop more advanced, efficient, and practical schemes for tracing multi-valued arrivals between the source and the receivers when the medium is heterogeneous and incorporates irregular or curved interfaces. For these reasons, we first modify the so-called reduced phase space method, in which a continuous wavefront mapping method is implemented for efficient and accurate consideration, and then compare it with two newly developed grid-based algorithms for tracing multi-valued direct arrivals in heterogeneous media and multi-valued reflected arrivals when undulating interfaces are present. The results show that the modified reduced phase space method is a potent and useful algorithm for tracking both multi-valued direct and reflected arrivals. The first-order “raylet” method is simple in principle but is unable to trace all possible later arrivals. Under such circumstances, the extremal solution method is a good choice to trace the multi-valued reflected arrivals; it is comparable to the modified reduced phase space method in practical application.