Ak. Benson, DECOMPOSITION AND INVERSION OF ELASTIC REFLECTION DATA - FIRST-ORDER ANGULAR-DEPENDENCE AND APPLICATIONS, Journal of computational physics, 121(1), 1995, pp. 102-114
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.