# Earthquake Risk Probability Evaluation for Najin Lhasa in Southern Tibet
## 2 Methods  
We adopted the probabilistic seismic hazard analysis (PSHA model improved by the Chinese State Seismological Bureau [21]) method to evaluate the earthquake risk in this study area, which is mainly characterized by the spatial and temporal inhomogeneity of the seismic activity distribution (e.g., [22; 23; 24; 25]). The method and processes are as follows. First, the earthquake statistical unit (seismic zone) is determined. The seismic activity inside the seismic zone is inhomogeneous in both space and time, and the time course of the earthquake in the seismic zone follows a piecewise Poisson process. Suppose that the upper limit magnitude of the seismic statistical zone is \(m_{uz}\) (Table 1); the lower limit of the magnitude is \(m_{0}\); the time is \(t\) (year) and the average annual frequency of earthquakes with a magnitude of \(m_{0}\)-\(m_{uz}\) in t years is \(v_{0}\), which is determined by the future trend of seismic activity. Then, the probability of \(n\) earthquakes occurring in the seismic zone within \(t\) years is:  
\[P(n)=\frac{(v_{0}t)^{n}}{n!}exp[-v_{0}t] \tag{1}\]  
At the same time, the earthquake magnitude distribution satisfies the Gutenberg-Richter (G-R) relationship: \(Log\ N(m)=a-bm\)[26]. The \(a\) value indicates the overall rate of earthquakes in a region, and the \(b\) value indicates the relative ratio of small to large magnitudes [27; 28]. The PSHA seismicity model divides the magnitude domain into N magnitude intervals, and the corresponding magnitude probability density function is (e.g., [29; 30]):  
\[f(m)=\frac{\beta\ exp[-\beta(m-m_{0})]}{1-exp[-\beta(m_{uz}-m_{0})]} \tag{2}\]  
where \(\beta=bln10\), b is the parameter in the G-R relationship, and the value of b in this study can be found in Table 2. In practical work, the magnitude \(m\) is divided into \(N_{m}\) bins, and \(m_{i}\) represents the magnitude bins whose magnitude range is \((m_{j}\pm\frac{1}{2}\Delta m)\). Then, the probability of occurrence of \(m_{j}\) level earthquakes in the seismic zone is: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Earthquake Statistical Region** & **No.** & **Potential Source Regions** & **Area (km\({}^{2}\))** & \(m_{uz}\)\({}^{1}\) \\ \hline \multirow{8}{*}{Central Tibet earthquake statistical region} & 1 & Gangsang Duodi & 18,280 & 8.0 \\  & 2 & Nima North & 6256 & 7.0 \\  & 3 & Qinglong & 2644 & 7.0 \\  & 4 & Jiangcuo & 3556 & 8.5 \\  & 5 & Namucuo & 4292 & 7.0 \\  & 6 & Sangxiong & 2138 & 8.0 \\  & 7 & Dangxiong & 5045 & 8.5 \\  & 8 & Kangma & 9401 & 7.5 \\  & 9 & Rikaze & 6532 & 7.0 \\  & 10 & Naqu & 4367 & 7.0 \\  & 11 & Jiali & 4213 & 7.5 \\  & 12 & Jinda & 1493 & 7.0 \\  & 13 & Qushui & 4061 & 7.5 \\  & 14 & Qusong & 6180 & 7.5 \\  & 15 & Jiacha & 3650 & 7.5 \\ \hline \multirow{3}{*}{Himalayan earthquake statistical region} & 16 & Yadong & 8364 & 7.5 \\  & 17 & Luozha & 8128 & 7.5 \\ \cline{1-1}  & 18 & Jiayu & 7932 & 8.0 \\ \hline \hline \end{tabular} \({}^{1}\)\(m_{uz}\) is the upper limit of the earthquake magnitude.  
\end{table} 
Table 1: Parameters of 18 potential source areas. \[P\big{(}m_{j}\big{)}=\frac{2}{\beta}\cdot f\big{(}m_{j}\big{)}\cdot Sh\ \bigg{(}\frac{1}{2}\beta\Delta m\bigg{)} \tag{3}\]  
where \(sl\) denotes a sine hyperbolic function. Next, the potential source area is divided into the seismic zone, and the spatial distribution function of the potential source area is \(f_{i,m_{j}}\), which is used to reveal the spatial inhomogeneity of earthquakes of each magnitude in each potential source area. The seismic spatial distribution function of potential source areas \(f_{i,m_{j}}\) is a magnitude-related constant whose physical meaning is the probability that an earthquake with a magnitude of \(m_{i}\pm\frac{1}{2}\Delta m\) plots will occur within the \(i\)th potential source area.