Reflectivity method for geomechanical equilibria

Abstract

It is shown that the block LU decomposition of the transfer and scattering matrix convert these matrices into each other. This allows to introduce a generalization of the Kennett reflectivity method, which is applicable to arbitrary systems of linear differential equations. The introduced method is convenient to analyse equilibria, where the governing matrix is degenerate. The resulting algorithm is compact and numerically stable. To illustrate the concept, we consider elastic equilibrium of a layered medium. We also derive closed-form expressions for a quasi-stationary poroelastic case taking into account solid-fluid and electrokinetic coupling. © 2007 Shell International Exploration and Production B.V. Journal compilation © 2007 RAS.