Phase space methods for multi-arrival wavefronts

Abstract

Most body wave seismic imaging schemes only exploit information contained in the first arrival of a seismic record. Later arrivals in the wavetrain, however, contain additional structural information, as the corresponding rays tend to sample slower regions of a medium that are often avoided by first-arrival raypaths. Here we investigate a Lagrangian (ray-based) and an Eulerian (grid-based) approach for the calculation of later arrivals. The Eulerian approach is based on the level set method, which implicitly evolves a wavefront by solving a pair of PDEs over a gridded velocity field in phase space. Our Lagrangian solver also uses phase space and represents the wavefront by a set of points, which are progressively moved through the velocity field using local ray tracing, with linear interpolation used to maintain a constant density of points. We compare the two methods using a velocity model of the subduction zone in the Tonga region. In theory both approaches can provide traveltimes for later arrivals. Our results clearly show that the Lagrangian approach is currently superior to the Eulerian scheme for the prediction of multi-arrival traveltimes when computation speed, ease of implementation, and accuracy are considered. In our experiments the Lagrangian solver is up to 6000 times faster, and successfully predicts later arrivals for our source receiver configuration in the subduction zone example. We then demonstrate the robustness and efficiency of the Lagrangian solver by tracking later arrivals in a smoothed version of the Marmousi model. By placing source points in certain parts of this model, we are able to find more than 60 secondary arrivals at surface receivers.