  Analytical formulas are derived to compute the first-order effects produced
by plane inhomogeneities on the point source seismic response of a fluid-filled
stratified porous medium. The derivation is achieved by a perturbation analysis
of the poro-elastic wave equations in the plane-wave domain using the Born
approximation. This approach yields the Fr\'echet derivatives of the P -- SV -
and SH-wave responses in terms of the Green's functions of the unperturbed
medium. The accuracy and stability of the derived operators are checked by
comparing, in the time-distance domain, differential seismograms computed from
these analytical expressions with complete solutions obtained by introducing
discrete perturbations into the model properties. For vertical and horizontal
point forces, it is found that the Fr\'echet derivative approach is remarkably
accurate for small and localized perturbations of the medium properties which
are consistent with the Born approximation requirements. Furthermore, the
first-order formulation appears to be stable at all source-receiver offsets.
The porosity, consolidation parameter, solid density and mineral shear modulus
emerge as the most sensitive parameters in forward and inverse modeling
problems. Finally, the Amplitude-Versus-Angle response of a thin layer shows
strong coupling effects between several model parameters.
