Velocity inversion using a stratified reference

Abstract

We present an inversion algorithm for backscattered (“stacked”) seismic data which will reconstruct the velocity profile in realistic earth conditions. The basic approach follows that of the original (constant reference speed) Cohen and Bleistein paper (1979a) in that hig‐hfrequency asymptotics and perturbation methods are used. However, we use a reference speed which may vary with depth, and this greatly enhances the validity of the perturbation assumption and hence the inversion results. The new algorithm enjoys the same economies and stability properties of the original algorithm, making it very competitive with current migration schemes. Four major assumptions are made: (1) the acoustic wave equation is an adequate model; (2) stacked data have amplitude information worth preserving fairly accurately; (3) the actual reflectivity coefficients can be adequately modeled as perturbations from a continuous reference velocity which depends only on the depth variable; and (4) the subsurface can be adequately modeled as a series of layers with jump discontinuities in the velocity (or impedance) at the interfaces. While the algorithm is particularly suited for data generated by a number of reflecting surfaces, its validity for a single reflector is demonstrated by applying the algorithm to Kirchhoff data for a quite general surface. A key feature of the approach used is the repeated application of high‐frequency asymptotic methods. A noteworthy point is that the underlying integral equation is in the form of a generalized Fourier integral equation; the method for its (approximate) inversion may prove to be applicable to a wide range of such problems.