Attenuation of Seismic Waves Due to Wave‐Induced Flow and Scattering in Randomly Heterogeneous Poroelastic Continua

Abstract

Attenuation and dispersion of compressional seismic waves in inhomogeneous, fluid‐saturated porous media are modeled in the framework of wave propagation in continuous random media. Two dominant attenuation mechanisms are analyzed in detail. First, attenuation due to wave‐induced flow, an intrinsic attenuation mechanism where a passing seismic wave introduces localized movements of the viscous fluid which are accompanied by internal friction. Second, attenuation due to scattering, the so‐called apparent attenuation where ordinary elastic scattering is responsible for a redistribution of wavefield energy in space and time. Despite the fact that both attenuation mechanisms have a quite different physical nature, the theory of wave propagation in random media provides a unified framework to model these effects in a consistent manner. In particular, it is shown that the method of statistical smoothing can be applied not only to energy conserving systems (elastic scattering) but also to energy absorbing systems (conversion scattering into diffusion waves). Explicit expressions for attenuation and dispersion for relevant correlation models are presented, and the asymptotic frequency scaling at low‐ and high frequencies of both attenuation mechanisms are compared and contrasted.