The traveltime holographic principle

Abstract

Fermat's interferometric principle is used to compute interior transmission traveltimes τ pq from exterior transmission traveltimes τ sp and τ sq. Here, the exterior traveltimes are computed for sources s on a boundary B that encloses a volume V of interior points p and q. Once the exterior traveltimes are computed, no further ray tracing is needed to calculate the interior times τ pq. Therefore this interferometric approach can be more efficient than explicitly computing interior traveltimes τ pq by ray tracing. Moreover, the memory requirement of the traveltimes is reduced by one dimension, because the boundary B is of one fewer dimension than the volume V. An application of this approach is demonstrated with interbed multiple (IM) elimination. Here, the IMs in the observed data are predicted from themigration image and are subsequently removed by adaptive subtraction. This prediction is enabled by the knowledge of interior transmission traveltimes τ pq computed according to Fermat's interferometric principle. We denote this principle as the 'traveltime holographic principle', by analogy with the holographic principle in cosmology where information in a volume is encoded on the region's boundary.