REFLECTIVITY TRANSMISSIVITY FOR ONE-DIMENSIONAL INHOMOGENEOUS RANDOM ELASTIC MEDIA - DYNAMIC-EQUIVALENT-MEDIUM APPROACH/

We study the influence of 1-D randomly stratified media on both the tr ansmissivity and reflectivity of obliquely incident elastic plane wave s. For this, a combination of the invariant embedding method with the small-perturbation expansion is used. The resulting analytic expressio ns for the plane time-harmonic and transient P- and SV-wave transmissi vities and reflectivities can be used for both deterministically and s tatistically specified stratifications. They do not have any essential restrictions concerning the frequency range of validity. However, it is assumed that the fluctuations of the density and compressional and shear velocities are small in comparison with the average values of th ese parameters. The analytic expressions for the attenuation coefficie nts and phase velocities of the P and SV transmissivities predict thei r smoothed behaviour well in one single realization of a 1-D random me dium. Both expressions can be considered as fundamental wave attribute s for a 'dynamic-equivalent medium'. They can also be looked upon as a generalization of the well-known O'Doherty-Anstey formula, which can now account for oblique incidence and mode-conversion effects in an in homogeneous 1-D medium with depth-dependent statistics. Likewise, the resulting frequency-dependent phase velocities can be considered as a broad-frequency-range generalization of their static approximations, o btained by what is known as Backus averaging. They postulate a frequen cy-dependent elastic transverse isotropy of the dynamic-equivalent med ium, which replaces the random 1-D medium. We use the dynamic-equivale nt-medium description to formulate some simple approximations of the P - and SV-wave reflectivities.