Theoretical basis and analyses of temperature responses of water-saturated rocks to rapid changes in confining pressure

Abstract

The temperature response of water-saturated rocks to stress changes is critical for understanding thermal anomalies in the crust, because most porous rocks in the shallow crust are saturated with water. Based on the adiabatic effective stress law and porothermoelasticity theory, we derived the adiabatic pressure derivative of temperature (β = (∂T/∂P)_s) of water-saturated rock (β_wet) in terms of that of dry rock (β_dry) and water (β_dry), and other measurable physical parameters. Then, we calculated the ranges of β_wet for 15 representative water-saturated rocks at background temperature (T₀) between 23 and 50°C. The results showed that β_wet (1.58–10.79 mK/MPa) was greater than β_dry (1.52–6.15 mK/MPa) for all rocks. The ratio of β_wet to β_dry is more significant for rocks with higher compressibility. For instance, for rocks with drained bulk modulus no more than 10 GPa, β_wet at 50°C (10.71 mK/MPa for Berea sandstone) can be as much as twice of β_dry at 23°C (5.86 mK/MPa). Also, β_wet was observed to linearly increase with the increase of T₀. The theory allows us to gain understanding on the coseismic temperature responses, such as the temperature anomalies documented in boreholes drilled through seismically ruptured active faults after the Chi-Chi, Wenchuan, and Tohoku earthquakes.