Characterizing subsurface lithology with elastic parameter contrasts from the decomposition and inversion of the elastic wave equation

Abstract

The ultimate objective of seismic exploration is to obtain reasonable estimates of the subsurface properties of rocks and fluids. A space-time algorithm is formulated that estimates the relative changes in subsurface density, bulk modulus, and shear modulus from the amplitude changes in the reflected compressional wave data as a function of offset. This is accomplished by transforming the elastic wave displacement equation into pressure-stress coordinates, where the Born approximation of the Lippman-Schwinger equation in the Fourier-transform domain is employed to decompose the observed fields into their compressional- and shear-wave scattered components. An inversion algorithm to generate physical properties is developed from the resulting angular-dependent reflection coefficients for each of the scattering modes. The relative change in bulk modulus indicates the presence of reservoir rocks containing hydrocarbons, the relative change in shear modulus indicates the rigidity of the reservoir rock, and the relative change in density delineates regions of high hydrocarbon concentration. Inverted data from the Gulf Coast are in good agreement with borehole data.