We calculate the compressional- and shear-wave velocities of permafros
t as a function of unfrozen water content and temperature. Unlike prev
ious theories based on simple slowness and/or moduli averaging or two-
phase models, we use a Biot-type three-phase theory that considers the
existence of two solids (solid and ice matrices) and a liquid (unfroz
en water). The compressional velocity for unconsolidated sediments obt
ained with this theory is close to the velocity computed with Wood's m
odel, since Blot's theory involves a Wood averaging of the moduli of t
he single constituents. Moreover, the model gives lower velocities tha
n the well-known slowness averaging theory (Wyllie's equation). For co
nsolidated Berea sandstone, the theory underestimates the value of the
compressional velocity below 0 degrees C. Computing the average built
moduli by slowness averaging the ice and solid phases and Wood averag
ing the intermediate moduli with the liquid phase yields a fairly good
fit of the experimental data. The proportion of unfrozen water and te
mperature are closely related. Fitting the wave velocity at a given te
mperature allows the prediction of the velocity at the whole range of
temperatures, provided that the average pore radius and its standard d
eviation are known.