DECOMPOSITION AND INVERSION OF ELASTIC REFLECTION DATA - FIRST-ORDER ANGULAR-DEPENDENCE AND APPLICATIONS

The elastic wave displacement equation is transformed into pressure-st ress coordinates, where the Born approximation of the Lippman-Schwinge r equation in the Fourier-transform domain is employed to decompose th e observed fields into their scattered components: P-P, P-S, S-P, and S-S. Triple Fourier transforms of the scattered elastic wave data are linear combinations of the double Fourier transforms of the relative c hanges in the medium properties. Angular-dependent reflection coeffici ents for each of the scattering modes are constructed, and an inversio n algorithm is outlined. Inversion of the observed elastic wave fields is accomplished in a manner similar to the acoustic problem. Density, bulk modulus, and shear modulus variations in an elastic earth can be recovered by utilizing the angular-dependent information present in t he observed wave fields. Examples illustrate these points. Transformin g the elastic wave data back to displacement coordinates and assuming a compressional source, an analysis of recorded amplitudes yields some practical answers about converted-wave data. Significant amounts of P --> S data should typically be generated by compressional sources, wi th significant contributions at smaller angles. However, signal-to-noi se calculations suggest that more sweeps and more geophone channels at longer offsets will typically be necessary to get P-S sections of com parable quality to P-P sections. (C) 1995 Academic Press. Inc.