The Traveltime Holographic Principle

huang, yunsong ; schuster, gerard t.;

Fermat’s interferometric principle isused to compute interior transmission travel times τpq from exterior transmission traveltimes τsp and τsq. Here, the exterior travel times are computed for sourcess 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 τpq. Therefore this interferometric approach can be more efficient than explicitly computing interior travel times τpq by ray tracing. Moreover, the memory requirement of the travel times 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 within terbed multiple (IM) elimination. Here, the IMs in the observed data a repredicted from the migration image and are subsequently removed by adaptive subtraction. This prediction is enabled by the knowledge of interior transmission traveltimes τpq 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.