LAUSR

The temperature of the Earth’s crust increases by approximately 25 °C per kilometre of depth (Wolfson 2012). The significant influences of temperature on the hydraulic, mechanical and wave characteristics of rock masses have been observed and analysed by previous studies (Sano et al. 1992; Zhao and Brown 1992; Zhao 1994; Wang 2001; Nara et al. 2011). Understanding the effect of temperature on the behaviour of waves through rock masses containing fluids is of great importance to academic developments and practical applications in the fields of geophysics, geomechanics, geothermics, and so on (Grab et al. 2017). Over the past several decades, the thermal effect on wave characteristics of subterranean fluids (e.g., groundwater and hydrocarbons) and the corresponding fluid-saturated rock masses have been extensively investigated (Timur 1977; Jones and Nur 1983; Wang et al. 1990; Wang and Nur 1990; Batzle and Wang 1992; Jaya et al. 2010; Dashti and Riazi 2014; Pimienta et al. 2014; Maraghechi et al. 2016). For instance, Wang et al. (1990) measured Pand S-wave velocities in porous rocks saturated with air, water, light oil and heavy oil over the temperature range from 22 to 92 °C using the ultrasonic pulse-transmission technique. It was found that the P-wave velocity decreases faster in the rock sample saturated with heavy oil than those with either air, water or light oil as the temperature increases, whereas the S-wave velocity is much less sensitive to the type of filling fluid. Wang and Nur (1991) reported that velocities of hydrocarbons approximately linearly decrease with increasing temperature, a finding based on wave velocities measured in pure hydrocarbons and their mixtures in the temperature range from − 10 to 120 °C. More recently, Xi et al. (2007, 2011) investigated temperature-dependent wave attenuation in fluid-saturated rocks and found that the attenuated peak shifts to a higher frequency as the temperature increases. Nakao et al. (2016) found that P-wave velocities in rock masses (including three kinds of sandstones and one granite) decrease with increasing humidity and environmental temperature. Numerous investigations have shown that sparsely distributed large-scale rock joints (including non-filled and filled joints) strongly affect wave propagation and attenuation (Pyrak et al. 1990; Li and Ma 2009; Li et al. 2010, 2015a; b; Fan et al. 2013; Wu et al. 2014; Xie et al. 2020). Despite considerable efforts devoted to the temperature-dependent wave attributes of subterranean fluids and rocks with fluidsaturated micro-cracks/pores, the thermal effect on wave behaviours across sparsely distributed large-scale fluidfilled rock joints is still poorly understood. Pyrak (1988) reported that heat appears to increase spectral amplitudes of transmitted waves across fractures based on ultrasonic tests on single water-saturated fractures at room temperature and * J. B. Zhu [email protected]