## 3 Methods
### Inversion of Slip Rate and Locking Depth along the Weihe Fault  
The cumulative seismic moment was directly related to the fault slip rate, locking depth, and fault length [33]. The accumulated seismic energy will increase with the locking depth and slip rate of the fault when the accumulation time and fault length are fixed.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Order, \(q\)**} & \multirow{2}{*}{**Faces, \(F_{q}\)**} & \multirow{2}{*}{**Vertices, \(V_{q}\)**} & \multicolumn{2}{c}{**Average Side**} & \multirow{2}{*}{**Max Respentiable Bandwidth, \(\overline{l}_{q}\)**} \\  & & & & **Arc-Length, \({}^{\text{a}}\)\(\tilde{L}_{q}\)** & \\ \hline
0 & 20 & 12 & 63.435\({}^{\circ}\) & 7053.64 km & 3 \\
1 & 80 & 42 & 31.718\({}^{\circ}\) & 3526.82 km & 6 \\
2 & 320 & 162 & 15.859\({}^{\circ}\) & 1763.41 km & 11 \\
3 & 1280 & 642 & 7.929\({}^{\circ}\) & 881.71 km & 23 \\
4 & 5120 & 2562 & 3.965\({}^{\circ}\) & 440.85 km & 45 \\
5 & 20,480 & 10,242 & 1.982\({}^{\circ}\) & 220.43 km & 91 \\
6 & 81,920 & 40,962 & 0.991\({}^{\circ}\) & 110.21 km & 182 \\
7 & 327,680 & 163,842 & 0.496\({}^{\circ}\) & 55.11 km & 363 \\
8 & 1,310,720 & 655,362 & 0.248\({}^{\circ}\) & 27.55 km & 726 \\
9 & 5,242,880 & 2,621,442 & 0.124\({}^{\circ}\) & 13.78 km & 1453 \\
10 & 20,917,520 & 10485,762 & 0.062\({}^{\circ}\) & 6.89 km & 2906 \\
11 & 83,886,080 & 141,943,042 & 0.031\({}^{\circ}\) & 3.44 km & 5811 \\
12 & 335,544,320 & 167,772,162 & 0.016\({}^{\circ}\) & 1.72 km & 11,623 \\ \(q\) & \(F_{q}=20\times 4^{q}\) & \(V_{q}=10\times 4^{q}+2\) & \(\overline{l}_{q}=2^{-q}\overline{l}_{0}\) & \(\overline{l}_{q}=int(\pi/\overline{L}_{q})\) \\ \hline \hline \end{tabular}  
* \(\bar{L}_{0}=cos^{-1}\{\cos(72^{\circ})/[1-\cos(72^{\circ})]\}\approx 1.1071 \approx 63.43^{\circ}\).  
\end{table}
Table 2: Geometric properties of the spherical–triangular grids [32].  
Therefore, the slip rate and locking depth are two important parameters for assessing the seismic hazard and tectonic activity of an active fault [34]. Velocity profiles can provide direct observations to determine the slip rate and locking depth. In this study, a series of fault-perpendicular profiles (6 km wide and 20 km long) from the secular vertical velocity field after wavelet decomposition was extracted to invert the slip rate and locking depth. Taking into account the minimal horizontal movement in the study area, an improved dip-slip model was used to investigate the current slip rate and locking depth of the Weihe Fault [35]. The mathematical expression of the improved dip-slip model is shown as follows:  
\[u_{z}=-\frac{s}{\pi}\left\{\text{sin}\delta\text{tan}^{-1}\left[\frac{\left(x -\frac{d}{\text{tan}}\right)}{d}\right]+\frac{\text{cos}\delta+\frac{\left(x- \frac{d}{\text{tan}}\right)}{d}\text{sin}\delta}{1+\left[\frac{\left(x-\frac{d} {\text{tan}}\right)}{d}\right]^{2}}\right\} \tag{2}\]  
where \(s\) is the relative slip rate between the hangingwall and footwall, \(u_{z}\) is the vertical slip rate, \(x\) is the distance from the observation point to the fault, \(d\) is the locking depth, and \(\delta\) is the dip. Figure 3 shows the geometry of the dip-slip fault.