TRANSVERSELY ISOTROPIC MEDIA EQUIVALENT TO THIN ISOTROPIC LAYERS

Any set of isotropic layers is equivalent, in the long wavelength limi t, to a unique transversely isotropic (TI) layer; to find the elastic moduli of that layer is a solved problem. The converse problem is to f ind a set of isotropic layers equivalent to a given TI media. Here, ex plicit necessary and sufficient conditions on the TI stiffness moduli for the existence of an equivalent set of isotropic layers are found b y construction of a minimal decomposition consisting of either two or three isotropic constituent layers. When only two constituents are req uired, their elastic properties are uniquely determined. When three co nstituents are required, two have the same Poisson's ratio and the sam e thickness fraction, and even then there is a one-parameter family of satisfactory minimal decompositions. The linear slip model for fractu red rock (aligned fractures in an isotropic background) yields a restr icted range of transverse isotropy dependent on only four independent parameters. If the ratio of the normal to tangential fracture complian ce is small enough, the medium is equivalent to thin isotropic layerin g and in general its minimal decomposition consists of three constitue nts.