Fast Marching method for the computation of first-arrival travel time of seismic waves in anisotropic media


Speciality : Mathématiques Appliquées

14/10/2022 - 13:00 François Desquilbet (Université Grenoble-Alpes) ISTerre, amphi Kilian

The first arrival traveltime for the propagation of a wave, in the high frequency approximation, is described by the eikonal equation. We present numerical schemes for the computation of the solution to such eikonal equations. These numerical schemes are based on the Fast Marching method (FMM), generalized to complex and non-Riemannian anisotropy settings in 3D media. The FMM is a single pass method, in which the propagation front is discretized and followed throughout the medium, leading to fast computation time. We also explore an opposite paradigm for high performance computation, based on a massively parallel GPU solver. 

In particular, we consider the case of seismic waves propagating inside a geophysical medium, with a propagation speed defined by an anisotropic Hooke tensor. In this context of geophysics, we propose two numerical schemes, generalizing ideas from previous schemes and referred to as ``semi-Lagrangian'' scheme and ``Eulerian'' scheme.  The semi-Lagrangian scheme can handle fullly general anisotropy, but with a limitation based on the strength of the anisotropy, defined as the ratio between the fastest and slowest speed achievable depending on the orientation. A review of the known and tabulated anisotropy properties of geological materials suggests that the method is applicable in most scenarios of interest.

On the other hand, the Eulerian scheme is limited to Tilted Transversely Isotropic (TTI) medium and cannot handle more complex anisotropy type, but it does not have any limitation on the strength of the anisotropy. It works by expressing the TTI eikonal equation as a maximum or minimum of a family of Riemannian eikonal equations, for which efficient discretizations are known. We consider an implementation of the Eulerian scheme on to massively parallel GPU architectures, leading to a computation fifty times faster than the sequential FMM implementation, using a single GPU node.


Emmanuel Maître (Université Grenoble-Alpes)


  • Ludovic Métivier (Université Grenoble-Alpes )
  • Jean-Marie Mirebeau (ENS Paris-Saclay )


  • Jean-David Benamou (INRIA Paris )
  • Sergey Fomel (Jackson School of Geosciences )


  • Jean Virieux (Université Grenoble-Alpes )