# Study on Microseismic Monitoring of Landslide Induced by Blasting Caving
## 4 Microseismic Monitoring Analysis of Landslide
### Principal Component Analysis of the Orientation of the Slip Surface
\]  
The angle between vector \(\overrightarrow{t}\) and the x axis corresponds to the dip direction of the plane formed by \(\overrightarrow{v}_{1}\) and \(\overrightarrow{v}_{2}\), the value is:  
\[\alpha=\arccos(-0.8153)+180^{\circ}=324.6^{\circ}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Event** & **Coordinate** & \multicolumn{2}{c}{**Event**} & \multicolumn{2}{c}{**Coordinate**} & \\
**Number** & **North/m** & **East/m** & **Depth/m** & **Number** & **North/m** & **East/m** & **Depth/m** \\ \hline
1 & 0.44020 & 0.33790 & 1.16045 & 28 & \(-1.20832\) & \(-1.77069\) & \(-0.70801\) \\
2 & 0.04045 & \(-0.11441\) & 0.02512 & 29 & 0.22202 & 0.21480 & 0.47272 \\
3 & 0.76398 & 0.71001 & \(-0.56928\) & 30 & 0.70557 & 0.80840 & \(-0.25787\) \\
4 & 0.15790 & 0.12527 & 0.04379 & 31 & 0.69013 & 0.77016 & \(-0.32363\) \\
5 & \(-1.18928\) & \(-0.78634\) & 0.59490 & 32 & \(-1.52596\) & \(-1.50724\) & 1.60423 \\
6 & \(-1.85080\) & \(-2.30367\) & 1.94788 & 33 & \(-1.46692\) & \(-0.87307\) & 1.84860 \\
7 & \(-1.55495\) & \(-0.33590\) & \(-0.40169\) & 34 & \(-1.48046\) & \(-1.65319\) & 0.86813 \\
8 & 1.52433 & 0.38640 & \(-1.73091\) & 35 & 0.20488 & 0.18682 & \(-0.04786\) \\
9 & \(-1.19859\) & \(-1.04420\) & 1.24870 & 36 & 0.76229 & 0.63960 & \(-1.08518\) \\
10 & 0.78112 & 0.90818 & \(-0.32575\) & 37 & 0.94746 & 0.64286 & \(-1.78013\) \\
11 & 0.83445 & 1.21594 & \(-0.23835\) & 38 & \(-1.52194\) & \(-0.24684\) & 1.54059 \\
12 & 0.71785 & 0.80000 & \(-0.32490\) & 39 & 0.44697 & \(-0.01788\) & 0.04039 \\
13 & 0.65542 & 0.71560 & \(-0.52727\) & 40 & 0.63235 & 0.74265 & \(-0.36224\) \\
14 & 0.68039 & 0.78135 & \(-0.22605\) & 41 & 0.66515 & 0.74218 & \(-0.28756\) \\
15 & 0.20213 & \(-0.10135\) & 0.07985 & 42 & \(-1.28641\) & \(-1.29927\) & 0.17234 \\
16 & 0.26667 & 0.05206 & 0.26949 & 43 & 0.80546 & 0.82285 & \(-0.70122\) \\
17 & 0.31238 & \(-0.17642\) & 0.66618 & 44 & 0.37947 & \(-0.50097\) & \(-0.52855\) \\
18 & \(-1.86286\) & \(-2.06726\) & 2.15492 & 45 & \(-1.43264\) & \(-2.05094\) & 0.60721 \\
19 & \(-0.85703\) & \(-1.39439\) & 1.57920 & 46 & \(-1.53337\) & \(-1.333098\) & 2.21432 \\
20 & \(-1.04537\) & \(-0.53920\) & \(-0.13271\) & 47 & 0.15409 & 0.000077 & 0.09767 \\
21 & 0.62981 & 0.61069 & \(-0.70207\) & 48 & \(-1.36196\) & \(-2.05607\) & \(-0.24259\) \\
22 & 0.62431 & 0.51370 & \(-0.94517\) & 49 & 0.70790 & 0.91005 & \(-0.28247\) \\
23 & 0.81138 & 0.77342 & \(-0.57267\) & 50 & 0.71446 & 0.91797 & \(-0.39193\) \\
24 & 0.81308 & 0.87974 & \(-0.50564\) & 51 & 1.65427 & 0.41997 & \(-1.72455\) \\
25 & 0.79361 & 0.85456 & \(-0.53576\) & 52 & 1.05284 & 0.99491 & \(-1.33974\) \\
26 & 0.81900 & 1.42624 & \(-0.73431\) & 53 & 0.67785 & 0.77669 & \(-0.49800\) \\
27 & 0.26752 & 0.52349 & \(-1.74449\) & 54 & \(-1.18229\) & 0.96507 & 1.54186 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Standardized spatial coordinates of microseismic events. Thus, the dip direction of the plane is \(324.6^{\circ}\). Similarly, the cosine of the angle between the normal vector \(\overrightarrow{n}\) and its projection vector \(\overrightarrow{t}\) onto the horizontal plane can be calculated:  
\[\cos\beta=\frac{\overrightarrow{t}\cdot\overrightarrow{n}}{\left| \overrightarrow{t}\right|\left|\overrightarrow{n}\right|}=\frac{-0.7807\times (-0.7807)+0.5545\times 0.5545+0\times\left(-0.2882\right)}{\sqrt{\left(-0.7807^{2} \right)+0.5545^{2}+0^{2}}+\sqrt{\left(-0.7807^{2}\right)+0.5545^{2}+\left(-0.2 882\right)^{2}}}=\ 0.9576\]  
Thus, the dip angle of the plane is \(\gamma=90^{\circ}-\beta=90^{\circ}-16.8^{\circ}=73.2^{\circ}\). Based on the aforementioned microseismic principal component analysis method, by analyzing the first and second principal components of the spatial locations of the 54 events, the attitude of the slip surface is determined as follows: the dip direction of the collapse slip surface is \(324.6^{\circ}\), and the dip angle is \(73.2^{\circ}\).