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From Reflection Data to Transmission Coda

Using 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 calculate the transmission coda 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 it is possible to solve the implicit relation for the coda operator, using an eigenvalue decomposition on the correlation of the reflection response. 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.