!! SIGMA Consortium - bigray

MBTT formulation

Multivalued Finite-Difference Solutions
of the Eikonal Equation

Eikonal Finite-difference methods such as those of Vidale, Van-Trier/Symes or more recently Sethian are limited to the computation of first arrival traveltimes. This limitation is a consequence of the ``upwind'' strategy which confers nice numerical properties (stability, accuracy...) to these schemes.

We overcome this difficulty by automatically sorting the different branches of multivalued traveltimes occurring in triplications. The sort uses information obtained by finite-difference computations of the geometrical spreading and the a priori knowledge on the generic structure of triplications.

Our algorithm therefore computes the multivalued ``phase-space'' solution only using gridded finite-differences and is completely free from ray tracing. We present numerical results in two dimensions. The extension of the method to three dimensions is theoretically possible but the sorting process is more complicated.

A technical report is available at: http://www.inria.fr/RRRT/RR-3414.html


	velocity model	point source ray tracing reference solution
	isochrons	geometrical spreading
1st triplication
2nd triplication
multivalued traveltimes
	our method	two point ray tracing