THE RELATIONSHIP BETWEEN SCATTERING-THEORY AND THE PRIMARIES AND MULTIPLES OF REFLECTION SEISMIC DATA

The application of scattering theory represents a powerful wave theore tic approach to understanding and processing seismic data. Recently, i nverse scattering series have been used to successfully remove multipl es from seismic data. These methods depend on an understanding of how the forward scattering series generates primaries and multiples. This paper enhances this understanding by studying in detail the forward se ries to clarify the relationship between the point scatterer model and the generation of primaries and multiples. Analytic calculation of th e forward scattering Born series for simple one dimensional layered sc attering problems shows that the higher order terms in the series alte r the amplitude and adjust the propagation velocity of the scattered w avefield as well as describe inter-layer multiple reflections. Primary reflections are described by all of the terms in the series following the first term whereas a multiple which contains n reflections is des cribed by the n(th) and all higher order terms. For a layered model, t he Born series converges if the reference velocity is less than root 2 times the lowest velocity in the scattering region.