On the phase speed and attenuation of an interface wave in an unconsolidated marine sediment

The phase speed and attenuation of the interface wave at the seawater-sedim ent boundary are obtained by solving the characteristic equation for one of its complex roots. The characteristic equation itself is derived on the ba sis of a recently developed theory of wave propagation in porous media. Cen tral to the theory is the stress relaxation that occurs when mineral grains slide against one another during the passage of a seismic wave. This type of stress relaxation is characterized by material response functions for co mpressional and shear waves of the form h(t)(proportional to)t(-n), where t is time since the sliding began and Ir is a small positive number. The pha se speed of the interface wave relative to that of the shear wave depends w eakly on the grain size, increasing from about 85% for fine-grained sills a nd clays to 90% for coarse sands. The loss tangent of the interface wave, b eta(i). is found to be independent of the mechanical properties (grain size , porosity, and density) of the sediment, and is the same as that for the s hear wave: beta(i)approximate to 0.04. Since the loss tangent and phase spe ed are, in effect, independent of frequency, the attenuation coefficient of the interface wave scales as the first power of frequency. It turns out th at the characteristic equation for the interface wave, as derived from the intergranular stress-relaxation mechanism, is exactly the same as if the se diment had been treated as an elastic solid, However, the elastic descripti on fails to account for the grain-size dependencies exhibited by the compre ssional and shear waves. These dependencies emerge naturally from the stres s-relaxation model. (C) 1999 Acoustical Society of America. [S0001-4966(99) 00710-9].