DYNAMIC GREEN'S FUNCTION FOR HOMOGENEOUS AND ISOTROPIC POROUS MEDIA

Abstract

The source terms that are meaningful in dynamic poroelasticity are those exciting the centre-of-mass field and the internal field. These fields are the sum of the mass weighted motion and the difference motion of the solid and fluid constituents, respectively. The corresponding homogeneous and isotropic Green's function valid for a uniform whole-space is obtained using Kupradze's method after the vector differential equations for these two fields are combined and expressed as a 6×6 matrix differential operator. The solution is quite amenable to numerical calculations and the results for a saturated Berea sandstone show that the fast P and S waves correspond to those usually detected by geophones at large distances from the source. The slow P wave, which is associated with fluid flow, is rapidly attenuated with distance from the source while the slow S wave, which is part of the solution, dies off rapidly in the near-neighbourhood of the source.