Borehole Seismic Source Radiation In Layered Isotropic And Anisotropic Media: Boundary Element Modeling

Abstract

An algorithm based on the boundary element method is established for modeling seismic source radiation from open or cased boreholes in layered transversely isotropic (TI) media. The axis of symmetry of TI layers is assumed to be parallel to the borehole axis. Under this assumption, the problem is significantly simplified because the element discretization of the borehole remains one dimensional. For fluid-filled open boreholes, three equivalent sources on each element are required to represent the boundary effects on the inner fluid and the outer solid. The three boundary conditions for a f1uidsolid interface set up a system of equations for the equivalent sources on all elements. Once the sources are known, displacements in the solid and pressure in the fluid are obtained. For fluid-filled and cased boreholes, the method treats borehole fluid, casing, and cement as a cylindricaliy layered isotropic medium. In this case, the boundary conditions to be satisfied at the borehole wall are four (continuity of the normal and tangential displacements and stresses). The implementation of the method is illustrated through a few examples.