Seismic Velocities in Unconsolidated Permafrost

A model has been developed to relate the velocities of seismic waves in unconsolidated permafrost to the porosity and the extent of freezing. The permafrost is idealized as an assemblage of spherical quartz grains imbedded in a matrix which itself is composed of spherical water inclusions in ice. The theory of Kuster and Toksöaz, based on wave-scattering considerations, is used to determine the effective elastic moduli, and hence the wave speeds. The model predicts Vp and Vs to be decreasing functions of both the porosity and the water/ice ratio, and Vp/Vs to be an increasing function of these two parameters. The theory has been applied to laboratory measurements of shear and compressional wave velocities in thirty-three permafrost samples from different sites in the North American Arctic. Although no direct measurements were made of the extents of freezing in these samples, the data are consistent with the predictions of the model. The theory can be used to infer the extent of freezing of the water in the pore spaces, based on knowledge of the porosity and either of the two wave speeds.