First-order perturbations of the seismic response of fluid-filled stratified poro-elastic media
Résumé
We derive analytical formulas for the first-order effects produced by plane inhomogeneities on the seismic response of a stratified porous medium. The approach used for the derivation is similar to the one employed in the elastic case; it is based on a perturbation analysis of the poro-elastic wave propagation equations. The final forms of the sensitivity operators, which are often referred to as the Fréchet derivatives, are expressed in terms of the Green's functions of the solid and fluid displacements in the frequency--ray parameter domain. We compute here the Fréchet derivatives with respect to eight parameters, namely, the fluid and mineral density and bulk moduli, porosity, permeability, consolidation parameter and shear modulus. The accuracy and stability of the derived expressions are checked by comparing differential seismograms computed from the analytical expressions of the Fréchet derivatives with solutions obtained by introducing discrete perturbations into the model properties. We find that the Fréchet derivative approach is generally accurate for perturbations of the medium properties of up to 10%, and for layer thicknesses less than one fifth of the dominant wavelength.
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