Wave Propagation in Dispersive Marine Sediments: A Memorial to David G. Crighton

摘要

Marine sediments support compressional and shear waves, both of which show weak dispersion and an attenuation that scales essentially as the first power of frequency. Such behavior emerges naturally from a new, linear theory of wave propagation in saturated unconsolidated granular media. The theory is based on the physics of inter-granular shearing, taking account of the microscopically rough surfaces of the mineral grains and the molecularly thin film of pore fluid that separates grains. A stochastic treatment of stress-relaxation occurring at points of contact between asperities, combined with a strain-hardening argument for the behavior of the thin fluid film as shearing progresses, leads to two wave equations, one for compressional and the other for shear waves. From these equations, expressions emerge for the dispersion and attenuation of both types of wave. These theoretical expressions for the phase speeds and attenuations are well behaved at all frequencies and are in agreement with the available experimental evidence.