Anisotropic parameters of layered media in terms of composite elastic properties

Abstract

In elastic earth models, at a wide variety of scales, the subsurface is a layered sequence of different constituent media. It is therefore important to understand the elastic properties of such a sequence, in particular to determine the response of the layering to an investigating seismic wave. It can be shown that if the individual layer thicknesses are much less than the wavelength of a seismic wave passing through the stack, the wave will propagate as though it were traversing a homogenous, anisotropic medium (Postma, 1955). This property has been subjected to rigorous testing both experimentally (Melia and Carlson, 1984) and numerically (Carcione et al., 1991). The elastic properties of this “equivalent medium” can be derived algebraically from the elastic properties of the materials that compose the layers (Backus, 1962). The homogenous equivalent medium will be transversely isotropic (hereafter referred to as TI), the axis of symmetry lying perpendicular to the layering.