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The rock surface temperature at the time of the generation of the AE amplitude and its frequency by temperature are shown in Figure 3; in Figure 3, data of an AE amplitude = 0 are excluded.

The maximum AE amplitude of the granite is at 20 °C and 60 °C, but the frequency is the highest at 70–80 °C. However, in the case of the marble and sandstone, the maximum AE is observed at approximately 20 °C, and its frequency is large. The appearance patterns for these rocks are different, as shown in Figure 2. The AE amplitude is observed when the temperature decreases in the marble and mainly when the temperature increases in the sandstone.

Figure 3: The AE amplitude versus the rock surface temperatures and its frequency by temperature. A: granite, B: marble, C: sandstone.

Thermal stress that causes AE is a result of the anisotropy in the thermal expansion properties of different minerals (Sirdesai et al. 2017) and the amount of certain minerals such as quartz. According to Kinoshita et al. (1995), in the case of granitic rock, even when heated at a slow heating rate that does not cause a temperature gradient inside the rock, due to the mismatch in the thermal expansion coefficient of the mineral particles, 183AE signals occur when the temperature reaches from approximately 60 °C to 70 °C, and its amplitude increases with heating. In other words, the reason why the frequency of the AE in the granite increased toward 70–80 °C is probably due to the difference in the thermal expansion coefficient of the constituent minerals. The sandstone is also composed of aggregates of various mineral grains. Although the porosity of the sandstone is high as previously described, the reason that the AE of the sandstone mainly occurred at the time of the temperature increase is thought to be due to the mismatch of the thermal expansion coefficients of the constituent minerals. The main constituent mineral of the sandstone and granite is quartz. Quartz thermally expands more than other minerals: quartz shows a thermal expansion of 0.14 % (⊥ c) and 0.08 % (||c); however, plagioclase shows an expansion of only 0.09 % (||a) and 0.03 % ( ⊥010), from 20 °C to 100 °C, respectively (Skinner 1966). Therefore, AE is generated at a relatively low temperature in rocks containing quartz. In addition, in such rocks, the increase in the AE with a subsequent temperature increase is remarkable.

Because marble is composed of only a single mineral, microcrack occurrence due to inconsistency in the thermal expansion coefficients of the minerals is difficult to recognize. However, calcite shows the thermal anisotropy of 0.189 % ( ⊥c) and −0.042 % (||c) from 20 °C to 100 °C, respectively (Skinner 1966).