Proper boundary conditions in reflection seismograms

Abstract

During the last few years it became feasible to record in the marine environment the reflection seismograms of the acoustic pressure field along two horizontal streamers emersed one below the other. This enables a more exact treatment of the wave equation as a second-order partial differential equation requiring two boundary conditions such as the pressure field and its gradient. According to Green's representation theorem, if the actual source is located above the two streamers, the wave field can be reconstructed for any point below them provided the medium parameters are known. Alternatively, if the dual acoustic field, namely, the pressure and particle velocity, is measured along a single horizontal streamer placed below the source, both dual fields may be reconstructed. As a first step to demonstrate the power of processing simultaneously the dual fields, we show how the source signature estimation, deghosting and deconvolution can be deterministically derived. As far as we know these processes cannot be done with a single set of boundary conditions.