Born series forward modelling of seismic primary and multiple reflections: An inverse scattering shortcut

Abstract

Forward modelling of any data event in a reflection seismic experiment with the Born series requires the calculation of a large number of terms, if the perturbation is large and spatially extended. Various partial series summations, the De Wolf approximation for instance, can be devised to separately model primary reflections. One such scheme has recently been used to derive direct inverse techniques for reflection seismic data. In this paper we extend this scheme to accommodate media with arbitrary 3-D heterogeneity, and point out that once any partial summation for primary reflections has been completed-however it is done-further arduous calculation for the similarly non-linear forward modelling of multiples can be avoided by using the de-multiple algorithms of inverse scattering. One by-product of these developments is a forward modelling expression for direct transmitted wave data, which may be of use for cross-well geophysical applications. Extension to absorptive media is straightforward. © 2009 The Authors Journal compilation © 2009 RAS.