Seismic lithologic modelling of amplitude-versus-offset data

Abstract

For small angles of incidence, q, the reflection amplitude of plane p-waves from a planar interface between two elastic media is nearly linear with sin2q. For an NMO-corrected common-midpoint (CMP) gather, the linear fit of amplitude versus sin2q at each time sample yields two new kinds of seismic trace. The trace constructed from the zero-offset intercept, the so-called 'p-wave stack', represents the response to changes in acoustic impedance at reflecting boundaries. The trace constructed from the slope, the 'gradient stack', represents the response to changes in s-wave velocity as well as p-wave velocity and bulk density. Under certain assumptions, the difference between the p-wave trace and the gradient trace reflects changes in s-wave velocity alone, and the sum reflects changes solely in Poisson's ratio. Here, we demonstrate how the method of seismic lithologic modelling, a parameter-estimation technique that refines thin-layer models of p-wave velocity and density by iterative matching of synthetic data to CMP stack sections, can be extended to include s-wave velocity in the model. In this extended approach, a new form of synthetic data trace is matched to the gradient stack (or to either the 's-wave stack' or 'Poisson's ratio stack') as well. As with any other approach that attempts to obtain s-wave velocity structure from the offset-dependence of amplitude, success in application to field data depends heavily on the extent to which data can be conditioned so that they satisfy the assumptions upon which amplitude-versus-offset analysis is based.