## 4 Results and Discussion
### Nonlinear Optimization  
Based on the assumption of homogeneous elastic half-space, the geodetic data can be associated with a shear dislocation model that contains a set of fault source parameters. The Okada model is widely applied into the inversion of the main fault source parameters [36; 37; 38; 39; 40; 41; 42; 43]. The fault source parameters can be derived by minimizing the discrepancies between the observed and simulated surface displacements. We set different objective functions to search optimum fault source parameters, including fault length, width, strike, dip, rake, slip, and depth.  
When LOS deformation data sets were applied to inversion, the objective function can be expressed by Equation (3)  
\[\text{costfunction}=\sum\limits_{i=1}^{k}\left(\frac{1}{N_{i}}\sum\limits_{j=1 }^{N_{i}}\left(\frac{\mathbf{u}_{i}-f_{i}(\mathbf{t})}{\sigma_{i}}\right)^{2}\frac{a_{ i}}{\sum\limits_{i=1}^{k}a_{i}}\right) \tag{3}\]  
where \(k\) is the number of data sets; \(i\) is the index, \(j\) is the number \(i\) data sets' index; \(\alpha_{i}\) is the weight factor of number \(I\) data sets; \(N_{i}\) is the counts of observation of number \(i\) data sets; \(u_{i}\),\(f_{i}(\mathbf{t})\) and \(\sigma_{i}\) are observed deformation; simulated deformation and corresponding RMS the of number \(i\) data sets.  
When the 3D deformation data sets were applied to inversion, the objective function can be defined as Equation (4) [20],  
\[H=\left[\mathbf{u}_{3d}-G_{3d}(\mathbf{t})\cdot\mathbf{s}\right]^{T}\times\Sigma_{uu}^{-1} \times\left[\mathbf{u}_{3d}-G_{3d}(\mathbf{t})\cdot\mathbf{s}\right] \tag{4}\]  
where \(\mathbf{u}_{3d}=[D_{u},D_{n},D_{e}]\) denotes the 3D motion vector; \(G_{3d}(\mathbf{t})=[G_{u},G_{n},G_{e}]^{\text{T}}\) denotes the Green's functions that describe how slip across rectangular dislocation causes displacement at the ground surface [36; 37]; \(\mathbf{t}\) represents a set of the fault geometric parameters; \(\mathbf{s}\) represents a set of the slips of all the fault patches; \(G_{3d}(\mathbf{t})\cdot\mathbf{s}\) denotes the simulated deformation at a ground point; \(\Sigma_{uu}\) is the variance-covariance matrix describing the quality of the highly spatially correlated observation data, which can be determined by using an exponential covariance function [20].  
Based on the objective functions, we searched the optimum fault source parameters in intervals provided by the GCMT (Global Centroid Moment Tensor), using the Levenberg-Marquardt algorithm which added damping factor [30]. We set the initial damping factor as 0.06. Table 2 shows the fault geometric parameters of our experiments and other studies [1; 2]  
It can be seen that our two results are quite similar with each other and closing to the published fault geometric parameters [1; 2]. The strike is approximately 353\({}^{\circ}\), close to NNW. The dip is approximately 15\({}^{\circ}\), thus the fault slip has thrust property. The rake is approximately 138\({}^{\circ}\), thus the fault slip has dextral property.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Institution/Individual** & **Longitude (\(\mathbf{t}\))** & **Latitude (\(\mathbf{t}\))** &
\begin{tabular}{c} **Moment** \\ **Magnitude Mw** \\ \end{tabular} & **Stike (\(\mathbf{t}\))** & **Dip (\(\mathbf{t}\))** & **Rake (\(\mathbf{t}\))** & **Depth (km)** \\ \hline GCMT & 45.84 & 34.83 & 7.4 & 351 & 11 & 140 & 17.86 \\ USGS [2] & 45.96 & 34.91 & 7.3 & 351 & 16 & 137 & 19 \\ CSI & 45.79 & 34.93 & 7.8 & 343 & 10 & 128 & 25 \\ Taymaz [1] & – & – & 7.4 & 358 & 16 & 149 & 19\(\pm\)2 \\ Experiment A & 45.86 & 34.74 & 7.3 & 352.65 & 14.44 & 139.29 & 18.52 \\ Experiment B & 45.86 & 34.73 & 7.3 & 352.63 & 14.76 & 137.1 & 14.17 \\ \hline \hline \end{tabular}  
* Denotes the “Experiment A” and “Experiment B” represents the results based on the LOS and 3D deformation data sets, respectively.  
\end{table}
Table 2: Fault geometric parameters from nonlinear optimizations assuming uniform slip (this study and earlier publications).