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 Toksöz, 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.
Geophysical techniques are of necessity playing an increasingly important role in the mapping of permafrost conditions in the Arctic. Knowledge of the physical properties of permanently frozen ground is required in the exploration for, and exploitation of, hydrocarbons and other mineral resources located in or below zones of permafrost. Construction of pipelines, and the erection of large permanent structures in permafrost, require estimates of the amount of ground ice present at depth, the thickness and area1 extent of permafrost, and the depth to the top of the permafrost. The drilling and completion of oil and gas wells in zones of permafrost require a detailed knowledge of the depth of permafrost, its ice content, and its strength. Interpretation of seismic reflection and vertical seismic profiling surveys, both of which are important techniques in exploration geophysics, depend upon seismic velocity control, particularly in near- surface sediments. It is these unconsolidated sediments that are often in the permanently frozen state in arctic regions. A number of studies have demonstrated that the presence of ice in the pore spaces of sediments can result in large increases in seismic velocity over that for the case when the interstitial water is unfrozen. Factors influencing the fraction of ice formed in the pore spaces of sediments are the temperature, the moisture content, the pore sizes and shapes, the pore-water chemistry, and the states of stress in both the solid frame and the pore fluid. Theoretical aspects of these points have been discussed in great detail by Anderson and Morgenstern (1973). Experimental studies of these factors have been described by Timur (1968), Nakano et al. (1972), Kurfurst (1976), Pandit and King (1979), King (1977), and King et al. (1982).
Timur (1968) concluded from studies of acoustic wave propagation in sedimentary rocks at permafrost temperatures that, as the temperature is decreased below 0°C, ice forms first in the larger pore spaces, and then in progressively smaller ones as the temperature is reduced still further.