From Reflection to Transmission Data

From the reciprocity theorem of the correlation type an implicit relation between seismic reflection and transmission data has previously been derived. In this paper this relation is used to estimate the transmission coda, at a certain depth, from reflection data measured at the surface. The transmission response is represented by a generalized propagator, consisting of a primary propagator and a coda operator. Using this representation, 1D approximations, and an eigenvalue decomposition on the correlation of the reflection response, it is possible, to solve the implicit relation for the coda operator. The calculated coda response may be used in seismic reflection imaging to obtain an image in which the internal multiple scattering effects are suppressed. A simple example for the estimation of the transmission coda illustrates the discussed procedure.