ATTENUATION OF FREE-SURFACE MULTIPLES IN MULTI-OFFSET VSP DATA

In this paper, we present a new method for attenuating free-surface mu ltiples for marine multi-offset walkaway VSP data. The method is an ad aptation to marine walkaway VSP geometries of the inverse scattering s eries approach used for attenuating free-surface multiples in surface seismic reflection data. This method is multi-dimensional and does not require knowledge of the subsurface. All related free-surface multipl es, including higher order multiples, are modelled. We have proposed t wo alternative constructions of the inverse scattering series for atte nuating free-surface multiples in walkaway VSP data: (i) a constructio n that is exclusively based on well log data and (ii) a construction t hat uses the surface seismic data. In the first construction, density and velocity logs are used to build a depth-dependent reference medium . Using the WKBJ Green's function of this reference medium, we back-pr opagate the upgoing wavefield to create some of the geometrical paths needed for multiple attenuation. In this construction of the inverse s cattering series, the reference medium does not have to describe exact ly the medium away from the borehole. However, the method requires an up-down separation of the wavefield at the receiver location. It also requires that the length of the source and receiver arrays be sufficie nt to allow accurate spatial Fourier transforms of the wavefield. In t he second construction of the inverse scattering series for attenuatin g free-surface multiples in walkaway VSP data, we assume that the surf ace seismic data are also available. The up-down separation of the VSP wavefield is not required in this case, and no assumption is made abo ut the length of the source or receiver arrays. A nonlinear synthetic data example is presented to illustrate the procedure.