## 3 Results and Discussion
### Temperature Effect  
Aside from investigating the effect of both \(\sigma_{1}\) and \(\sigma_{2}\) on the seismic velocity, the effect of temperature was studied as well (Table 6 and Figure 3). Experimental conditions include a \(\sigma_{1}\) of 0.069 \(\pm\) 0.002 MPa and a \(\sigma_{2}\) equal to atmospheric pressure. Figure 12 presents the P-wave velocity as a function of increasing temperature for the limestone, marble, and calcschist samples studied. The temperature-P-wave velocity relationships for the other rock types are shown in Figure S7 (see Supplementary Materials). Figures S8 and S9, shown in the Supplementary Materials, present the temperature-dependence of the S-wave velocity.  
Most of the rock samples studied (Table 6) reveal reducing P-wave velocities as a function of increasing temperature, with the exception of the mud- and siltstone samples. The latter two porous media disclose a roughly constant velocity with increasing temperature. The reducing velocities, with increasing temperature, were expected and are related to the thermal expansion of the constituting minerals, leading to loosening of the rock's internal structure [28; 29; 41; 42]. Consequently, the mineral-to-mineral contact area reduces, lowering the bulk density, and finally resulting in lower P-wave velocities.  
Of the investigated samples, the marble and calcschist cores show the largest decrease in P-wave velocity as a function of increasing temperature (40-240 \({}^{\circ}\)C): 42% (marble) and 36% (calcschist). In order to explain this observation, one has to think in terms of thermal expansion coefficients of the comprising minerals. Table 7 shows that the calcschist and marble contain 98% and 99% fully recrystallized calcite and dolomite minerals, respectively. From the literature it is known that calcite minerals possess relatively high thermal expansion coefficients, parallel to the crystallographic c-axis, of 24-29 \(\times\) 10\({}^{-6}\) K\({}^{-1}\)[42; 43; 44]. A study aiming at calcitic and dolomite marbles from Andalusia (Spain) reported averaged linear thermal expansion coefficients, measured between 20-90 \({}^{\circ}\)C, of 11 \(\times\) 10\({}^{-6}\) K\({}^{-1}\) for both types of marbles [43]. On average, these are somewhat higher than reported mean expansion coefficients, assessed in a range of 20-100 \({}^{\circ}\)C, for sandstones and limestones of 10 and 8 \(\times\) 10\({}^{-6}\) K\({}^{-1}\), respectively [45]. It is most likely that the thermal expansion coefficients, related to calcite and dolomite minerals, resulted in the overall large drop in velocity, with increasing temperature, observed for the marble and calcschist samples in this study.  
Figure 12: P-wave velocity as a function of temperature (\({}^{\circ}\)C), and thus depth below the surface, for the limestone (purple), marble (black), and calcschist (blue) samples assessed. For all three experiments, a linear regression has been applied to the data. A total of three to five measurements were taken every 20 \({}^{\circ}\)C. The error bars shown represent the standard deviation, whereas the actual data points denote the averaged seismic velocity. Non-linear temperature–depth relationship is taken from [36].