Estimation of elastic specular reflectivity by Kirchhoff prestack depth migration:
WKBJ least-squares theory

David E. Lumley

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ABSTRACT

Estimation of elastic specular reflectivity from seismic reflection data is important in that it may provide crucial information about subsurface physical properties related to lithology, rock physics, pore-fluid content, and physical states. I derive a generalized least-squares solution for elastic reflectivity in terms of local seismic wavefield displacement vectors. Solutions for the local wavefields are derived as representation integrals over surface source and receiver displacement fields, weighted by a WKBJ approximate Green's tensor. The resulting integral solution is a vector analogy of the Kirchhoff-Rayleigh-Sommerfeld integrals for scalar waves. In particular, I give explicit formulas for the least-squares evaluation of the $\grave{P}\!\acute{P}$ and $\grave{P}\!\acute{S_1}$ elastic specular reflection coefficients.