The effect of the extent of freezing on seismic velocities in unconsolidated permafrost

Abstract We develop a model to relate velocities of seismic waves in unconsolidated permafrost to porosity and the extent of freezing. The permafrost is idealized as an assemblage of spherical quartz grains imbedded in a matrix composed of spherical water inclusions in ice. The theory of Kuster and Toksoz, based on wave-scattering considerations, is used to determine the effective elastic moduli, and hence the wave speeds. The Hashin-Shtrikman theoretical bounds on the elastic moduli of heterogeneous materials and other considerations establish the plausibility of the model. The model predicts V p and V s to be decreasing functions of both the porosity and the water-to-ice ratio, and the ratio V p /V s to be an increasing function of these two parameters. In laboratory measurements of shear- and compressional-wave velocities in 23 permafrost samples from different sites in the Beaufort Sea, Mackenzie River valley, and Canadian Arctic islands, no direct measurements were made of the extents of freezing in these samples, but the data are consistent with the predictions of the model. The theory can be used to predict the extent of freezing of the water in the pore spaces, based on the porosity and either of the two wave speeds.--Modified journal abstract.