Multiarrival wavefronts in phase space: Level Set and ray based methods

Abstract

First arrival raypaths tend to avoid the slow regions of a heterogeneous velocity medium. Later arrivals do not avoid slow regions and hence contain additional information about the velocity structure which can be exploited to improve seismic imaging. However current state of the art algorithms for the computation of traveltimes only provide first arrivals. In this study we compare an Eulerian and a Lagrangian approach for the computation of multiarrival traveltimes in two dimensions. The Lagrangian approach tracks the wavefront in phase space by evolving a set of points which discretely represents the wavefront, while the Eulerian approach uses the Level Set Method for the evolution of the wavefront in phase space. In theory, both methods can produce multiarrival traveltimes. The implicit definition of the wavefront within an Eulerian framework is an advantage when compared with a Lagrangian scheme where the adding and removing of points can introduce error. However, our results show that the Lagrangian scheme is clearly superior for the prediction of multiarrival traveltimes when computational speed, implementation and accuracy are taken into account.