Exact, linear and nonlinear AVO modeling in poroelastic media
Steven M. Kim
An exact, analytical solution for PP reflection amplitudes is derived for poroelastic media as a result of incorporating the poroelastic parameters of fluid (ƒ), shear modulus (μ), and density (ρ) into the elastic Zoeppritz equations. This solution contains many terms which may be neglected to produce first (linear), second (nonlinear) and third (nonlinear) order approximations. These approximations are derived in terms of perturbations (aƒ, aμ, aρ) and reflectivities (Δƒ/ƒ, Δμ/μ, Δρ/ρ). These results are expected to extend to dynamic poroelastic models of wave propagation and initial groundwork for this extension is reported. When modeling reflection amplitudes of media with small poroelastic contrasts (10%), the first order approximation yields 5% error for the zero offset reflection amplitude and much less than 1% error for the third order approximation. By changing the media properties to replicate large poroelastic contrasts (50%), the first order approximation produces 20% error for the zero offset reflection amplitude and less than 1% error for the third order approximation. Nonlinear corrective terms of order 2 and 3 are, therefore, relevant for poroelastic AVO analysis in geophysically realistic scenarios.