# A New Look at the Stress State Across the Bohai Strait, China
## 3 Materials and Methods
### HF Measurements in Xiangli and Changdao
\(P_{\text{s}}\) is acknowledged as the most critical parameter because it directly equals \(S_{\text{h}}\) and is then used to estimate the value of \(S_{\text{H}}\). Many methods that derive \(P_{\text{s}}\) from the HF pressure-time curve have been proposed and studied [49; 50]. Of these methods, the inflection point method draws a straight line tangent to the pressure-time curve from the point where the pump is closed and defines such a point at which the line leaves the curve as the shut-in pressure [57]. This procedure is based on the closure theory of the fracture and has been widely completed by computer, effectively reducing subject uncertainty. The \(\text{d}t/\text{d}P\) vs. \(P\) method [58] and the \(\text{d}P/\text{d}t\) vs. \(P\) method [59] are based on rigorous mechanical theory, that is, the pressure decay in the test interval during the fracture closure stage exhibits an exponential of time. According to this theory, the closure procedure can be divided into three (\(\text{d}t/\text{d}P\) vs. \(P\)) or two (\(\text{d}P/\text{d}t\) vs. \(P\)), and the shut-in pressure is defined as the inflection point of the curves analyzed using the functions. Previous studies indicate that the three methods provide slightly different shut-in points relative to the entire closure procedure, and the applicability is different for different types of rock. The ISRM recommends using at least two methods to calculate the \(P_{\text{s}}\) to ensure the reliability of the determination of shut-in pressure and improve accuracy [50]. In this study, the inflection point method [57], the \(\mathrm{d}t/\mathrm{d}P\) vs. \(P\) method [58], and the \(\mathrm{d}P/\mathrm{d}t\) vs. \(P\) method [59] were adopted to calculate the \(P_{\mathrm{s}}\) magnitude. The mathematical mean of the three methods is taken as the final value of the shut-in pressure. Figure 4 elucidates the determination of \(P_{\mathrm{s}}\) values using the three methods, with a case at the 208.5 m depth in the XL borehole as an example. The magnitude of \(P_{\mathrm{s}}\) for the 208.5 m interval is 10.57 \(\pm\) 0.28 MPa; therefore, the uncertainty of \(S_{\mathrm{H}}\), which is three times that of \(S_{\mathrm{h}}\), does not exceed \(\pm\) 0.84 MPa under the assumption that \(P_{\mathrm{r}}\) is reliably derived from the pressure-time curve, consistent with the allowable accuracy range of the HF method [51]. We also calculated the uncertainties of all \(S_{\mathrm{h}}\) for the XL borehole and found that the maximum uncertainty of \(S_{\mathrm{h}}\) is less than \(\pm\)0.30 MPa, under a \(S_{\mathrm{h}}\) in the range of 5.31-17.84 MPa [56]. For the determination of \(P_{\mathrm{r}}\), the tangent method was utilized [59], which is achieved by using automatic software to reduce the subjectivity uncertainty. The results of the HF measurements in the XL and CD boreholes are summarized in Table 1.  
Figure 3: The interpreted azimuths and the traces of the induced fractures following the hydraulic fracturing tests in the Xiangli and Changdao boreholes. Figure 2: Typical hydraulic fracturing pressure–time curves obtained from the Xiangli borehole. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Borehole** & \begin{tabular}{c} **Depth** \\ **(m)** \\ \end{tabular}  & \begin{tabular}{c} **P\({}_{\text{b}}\)** \\ **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **P\({}_{\text{r}}\)** \\ **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **P\({}_{\text{s}}\)** \\ **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **P\({}_{\text{0}}\)** \\ **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **S\({}_{\text{h}}\)** \\ **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **S\({}_{\text{h}}\)** \\ **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **S\({}_{\text{v}}\)** \\ **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **K\({}_{\text{av}}\)** \\ **(MPa)** \\ \end{tabular}  & \begin{tabular}{c} **K\({}_{\text{av}}\)** \\ **(MPa)** \\ \end{tabular}  & \ \begin{tabular}{c} **K\({}_{\text{hv}}\)** \\ **(MPa)** \\ \end{tabular}