## 3 Results and Discussion
### Interpretation of SIP Signatures
In the case of our measurements, we obtained a power-law relationship, written as:  
\[\tau=0.03\cdot d^{0.8} \tag{6}\]  
As observed in Figure 6c, the Equation (6) fits our data (correlation coefficient of \(R^{2}=0.88\)), as in general, we observe a large variability in the relaxation time for the different grain sizes. This may also reflect a larger heterogeneity in the actual grain size of the particles in d4. We present the exact Cole-Cole parameters in terms of chargeability, normalized chargeability and relaxation time and the graphite volume for each grain size in Table 4. In contrast, Table 6 shows the fitted parameters for the models describing the link between Cole-Cole parameters and the graphite content and grain size (i.e., associated with Equations (4) and (5)). Similar to [PERSON] et al. [20], we found that the chargeability increases--and the relaxation time decreases--with increasing graphite content, whereas the chargeability decreases--and the relaxation time increases--with increasing the grain size. Although we have resolved a relationship between graphite content and the SIP response for laboratory measurements, evaluating the observed relationship for field measurements is still necessary. To this end, we present in Figure 7 spectra extracted from the complex conductivity imaging results of the profile P2b at a distance of 50 m and 125 m close to the surface (z \(>\) 450 m). Moreover, in Figure 7 we present the spectra measured on the site with the PSIP unit (at positions Z1 and Z5, referred to as in-situ PSIP from now on). For the sake of comparison, we present in Figure 7 also the spectra in ground samples with the largest grain size (d4). Figure 7 reveals similar spectra for those extracted from the imaging plane (at a profile distance of 125m), those collected in-situ PSIP, and in the ground samples. The in-situ PSIP and imaging measurements (carried out with the DAS1 instrument) were conducted on different days, which can explain some spectral differences. The field spectra (both DAS1 and PSIP measurements) do not reveal a clear frequency peak, i.e., the spectra are almost flat, clearly different from the measurements in samples with well-defined grain size samples. Hence, our measurements suggest that materials in Zettlitz quarry are well sorted (i.e., even distribution of different grain sizes), at least within the range of frequencies captured with our measurements. Nonetheless, Figure 7 indicates a slight increase with increasing frequency, suggesting that the frequency peak may be found at frequencies above 100 Hz, which, according to the mechanistic models, is indicative of the dominating fine grains, as predicted by the mechanistic models [25; 27; 28]. However, field data measured at higher frequencies is needed to thoroughly investigate the possible frequency peak. Figure 7: Complex conductivity spectra in terms of (**a**) in-phase and (**b**) quadrature conductivity, exported from the imaging results of Profile P2b (circle and square), the in situ PSIP measurements (Z1, Z5—star) and the laboratory measurements of the collected sediments (d4—pentagon). The z coordinate represents the height of the imaging results, and the x coordinates the position at the profile length. In Figure 8, we present plots of the graphite volumetric content as a function of chargeability and normalized chargeability. Here we present only the parameters obtained for spectra measured in plugs 2 and 4 as well as those obtained for the ground samples with the largest grain (d4). SIP data for plugs 2 to 4 indicate that these correspond to similar composition, although the exact graphite content is only known for plug 4. We account for the size of the samples (plugs and ground material) to compute the graphite volumetric content. We found a power-law correlation between the chargeability and graphite volume (Figure 8a) and normalized chargeability and graphite volume (Figure 8b) and applied the Equations (7) and (8) (respectively) to determine the graphite content of both the rock and the ground samples.