## 3 Results and Discussion
### Interpretation of SIP Signatures
[PERSON] and [PERSON] proposed the  
Figure 5: Principal component analysis of the Cole-Cole parameters, in terms of relaxation time (T), volume (vol), chargeability (M), normalized chargeability (Mn), maximum phase value (max \(\varphi\)), grain size, and salinity of the (**a**) graphite plugs, (**b**) disseminated sediments and (**c**) commercial graphite. normalized chargeability as the parameter quantifying the polarization magnitude in SIP measurements [52]. They argue that normalizing the chargeability by the electrical conductivity, helps to reduce inferences in the data due to the fluid conductivity. However, plots in Figure 4i,j and Figure 5c shows a dependency between our samples and the fluid conductivity thus, the normalized chargeability offers a more robust approach for the prediction of graphite content from SIP measurements as M\({}_{\text{n}}\) accounts for the changes in fluid conductivity. This apparent inconsistency is due to the presence of the electrical conductors which is not considered in the study by [PERSON] and [PERSON] [52]. The studies by [PERSON] et al. also revealed a change in the SIP response accompanying variations in the fluid conductivity from a numerical point of view, while [PERSON] and [PERSON] also observed such variations in SIP measurements by changing fluid conductivity in laboratory measurements [15; 28]. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Fitted Parameters** & **Grain ID** & **Fitted Equation** & **Quality of Fit** \\ \hline \multirow{2}{*}{Graphite content and M} & d1 and d2 & \(\varnothing=2.2+18.4\)-M\({}^{6.5}\) & \(R^{2}=0.84\) \\  & d3 and d4 & \(\varnothing=2.5+36.6\)-M\({}^{4.7}\) & \(R^{2}=0.85\) \\ \hline \multirow{2}{*}{Graphite content and M\({}_{\text{n}}\)} & d1 and d2 & \(\varnothing=45.1\)-M\({}_{\text{n}}^{0.5}\) & \(R^{2}=0.94\) \\  & d3 and d4 & \(\varnothing=175\)-M\({}_{\text{n}}^{0.8}\) & \(R^{2}=0.76\) \\ \hline \multirow{2}{*}{Grain size and \(\tau\)} & all & \(\tau=0.03\)-\(d^{0.8}\) & \(R^{2}=0.88\) \\ \hline \multirow{2}{*}{Graphite content and M} & Plugs and d4 & \(\varnothing=25\)-M\({}^{1.8}\) & \(R^{2}=0.72\) \\ \hline \multirow{2}{*}{Graphite content and M\({}_{\text{n}}\)} & Plugs and d4 & \(\varnothing=108.7\)-M\({}_{\text{n}}^{0.5}\) & \(R^{2}=0.55\) \\ \hline \multirow{2}{*}{Salinity and M} & commercial & M = \(0.4\sigma_{fl}^{-0.08}\) & \(R^{2}=0.97\) \\  & d1 & M = \(0.4\sigma_{fl}^{-0.03}\) & \(R^{2}=0.75\) \\  & d3 & M = \(0.3\sigma_{fl}^{-0.03}\) & \(R^{2}=0.50\) \\ \hline \multirow{2}{*}{Salinity and Mn} & commercial & M\({}_{\text{n}}=0.001+\sigma_{fl}\)-0.09 & \(R^{2}=0.99\) \\  & d1 & M\({}_{\text{n}}=0.002+\sigma_{fl}\)-0.09 & \(R^{2}=0.82\) \\  & d3 & M\({}_{\text{n}}=0.003+\sigma_{fl}\)-0.06 & \(R^{2}=0.99\) \\ \hline \multirow{2}{*}{Salinity and \(\tau\)} & commercial & \(\tau=0.002\sigma_{fl}^{-1.65}\) & \(R^{2}=0.99\) \\  & d1 & \(\tau=0.015\sigma_{fl}^{-1.09}\) & \(R^{2}=0.99\) \\  & d3 & \(\tau=10.82\sigma_{fl}^{-0.8}\) & \(R^{2}=0.99\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Cole-Cole parameter of the collected sediments in terms of chargeability (M), normalized chargeability (Mn) and relaxation time (\(\tau\)), the volumetric graphite content in the sand-graphite mixture and the mean grain size of the graphite sediments. Figure 6: Cole-Cole parameters versus volumetric graphite content. (**a**) Chargeability M versus the volumetric graphite content of the sand-graphite sediment samples. (**b**) Normalized chargeability, Mn versus the volumetric graphite content. (**c**) Mean grain size versus the characteristic relaxation time \(\tau\) of the sand-graphite sediment samples (all samples with the grain ID d1 to d4). The dashed and solid lines show the fitted power-law relationships. Consistent with previous studies [25], we also observed an increase in relaxation time with increasing grain size (Figure 6c).