Influence of ice properties on wave propagation characteristics in partially frozen soils and rocks: a temperature-dependent rock-physics model

A better understanding of the temperature effects on the propagation characteristics of elastic waves in frozen soils and rocks is imperative for accurately quantifying their freezing degrees. While existing rock-physics models based on the three-phase Biot (TPB) theory adeptly interpret observed velocity versus temperature (VVT) curves, they often lack a comprehensive understanding of the mechanisms underlying attenuation versus temperature (AVT) curves. In this study, we first extend the TPB theory to incorporate the temperature-dependent properties of ice, including changes in volumetric fraction, morphology, and viscoelasticity, by integrating relevant thermodynamic laws. Model parameters related to ice properties and interactions, such as rigidity, shear moduli, density, and friction, are redefined. Then, using a numerical rock-physics modeling approach, we examine influential factors and modes of wave VVT and AVT responses. Our results show that both P- and S-wave velocities increase with source frequency, consolidation degree, and frame-supporting ice content, while decreasing with temperature and pore-floating ice content. Both P- and S-wave attenuation factors increase with frame-supporting ice content and decrease with consolidation degree. Rising temperatures tend to amplify the peak magnitude of P-wave attenuation factors and shift the central frequency of S-wave attenuation factors. Finally, within a temperature-controlled laboratory environment, we conduct ultrasonic wave transmission testing on brine-saturated sediment and rock specimens. Results demonstrate that as the temperature increases from –15 to –3 °C, both the P- and S-wave velocities decrease, while the P-wave attenuation factors decrease and the S-wave attenuation factors initially rise before declining. Our viscoelastic TPB theory outperforms existing ones in interpreting S-wave AVT observations. This temperature-dependent rock-physics model holds promise for interpreting sonic logging data in time-lapse monitoring of permafrost, glaciers, and Antarctica.