Linear and nonlinear poroelastic AVO
Steven M. Kim, Kristopher A. Innanen
The purpose of our research is to merge the results of two recent theoretical and practical studies. First, Russell, and his fellow co-authors, has argued for a parameterization of the linearized AVO problem which highlights jumps in poroelastic properties across a reflecting boundary. The parameterization brings the Biot fluid term to the foreground. Second, Innanen has recently introduced an approach to analyzing linear and nonlinear AVO which mirrors the more general problem of scattering, and which accounts for low order nonlinearity in an intuitive way. This paper summarizes a project in which the poroelastic AVO problem is cast in terms of this nonlinear formalism. We derive first, second, and third order terms in an expansion for Rpp. The expansion is in terms of changes in density, shear modulus, and the Biot fluid term. We confirm mathematically the role second and third order fluid terms play in determining Rpp amplitudes. We comment on future directions the work can take, including moving towards a general poroelastic scattering picture, and incorporating dynamic poroelastic models also.