This study focuses on inverting the co-seismic slip characteristics on the rupture fault plane of the 2023 Jishishan earthquake, using the reconstructed ascending and descending InSAR co-seismic deformation fields as constraints. First, an optimal geometry for the seismic fault is obtained using a nonlinear inversion method. Next, a linear method is applied to determine the detailed slip distribution characteristics on the rupture fault plane. To minimize the influence of far-field noise on the inversion results and enhance efficiency, a non-uniform sampling method is employed, with a 500 m interval for near-field sampling and a 2 km interval for far-field sampling of the deformation area. After downsampling, the number of ascending track points is 2,847 and the number of descending track points is 2,962 (Lohman et al., 2005). Different research institutions have reported consistent earthquake source mechanisms based on far-field body wave inversion (Table 1). Results from the P-wave first motion polarities suggest that this earthquake may have occurred on either an eastward-dipping NNW-trending thrust fault or a westward-dipping SSE-trending thrust fault. Because the earthquake's source depth was shallow and it did not rupture to the surface, determining the fault dip using InSAR observations is challenging. Therefore, this study uses two sets of fault plane parameters released by GCMT as references for the eastward and westward dipping models. The fault inversion utilizes the SDM program (Wang et al., 2013) and performs inversion tests on the rupture model using a two-step approach, with the basic principles discussed by numerous scholars (Tu et al., 2016; Zhang et al., 2021; Yu et al., 2023), and will not be elaborated further here.
4.1 East-Dipping Seismic Fault Model
Using the first set of fault parameters provided by GCMT (strike 303°, dip 52°, and slip angle 62°) as a reference, the search ranges for the fault's strike, dip, and slip angle during inversion were set to [300°, 330°], [40°, 90°], and [0°, 180°], respectively. Based on the characteristics of the InSAR deformation field (Fig. 2), the search ranges for the fault’s length and width were defined as [0, 25] km and [0, 15] km during the inversion process. A nonlinear search for the geometric parameters of the seismic fault was conducted using an optimized multi-peak particle swarm algorithm (Feng et al., 2013). Under east-dipping conditions, the optimal uniform slip fault parameters obtained are shown in Table 1: fault strike of 306°, dip angle of 59°, and average slip angle of 107°. After determining the geometric reference of the seismic fault, distributed fault slip modeling inversion was performed using SDM software (Wang et al., 2013). To prevent boundary effects during the inversion, the dimensions of the rectangular fault plane (length along strike and width along dip) were adjusted to create a 30 km × 20 km rectangular dislocation model, discretizing the fault plane into 1 km × 1 km rectangular elements. The fault strike and position were fixed during the inversion, allowing the slip angle for each sub-fault to freely vary within the range of [0°, 180°]. Additionally, a smoothing factor was introduced to reduce the influence of instability, and the smoothing factor was searched within the range of [0, 0.1] (with a step size of 0.01). Ultimately, under the constraint of an optimal smoothing factor of 0.06, the fine slip distribution characteristics of the SE-dipping fault model were obtained. Figures 4 (a) and (b) demonstrate the coseismic slip distribution characteristics of the 2023 Jishi Mountain earthquake when the fault was east-dipping. Both figures indicate that the coseismic slip distribution is primarily concentrated at depths of 10 to 18 km, with a maximum slip of approximately 0.37 m and a moment magnitude of Mw 6.0. Figures 5 (a) to (f) present the observed coseismic deformation field, the forward modeling deformation field, and the residuals for the 2023 Jishi Mountain earthquake with the fault dipping eastward. Overall, the east-dipping fault model fits the surface deformation field observed by InSAR well, with fitting accuracies of 93.1% for ascending and 93.2% for descending tracks, corresponding to root mean square residuals of 0.62 cm and 0.64
4.2 Model of the Northwest-Dipping Source Fault
Using the second set of fault parameters provided by GCMT (strike 164°, dip 46°, slip angle 122°) as a reference, the search ranges for the fault strike, dip, and slip angle during the inversion process were set to [0°, 180°], [40°, 90°], and [0°, 180°], respectively. Based on the characteristics of the InSAR deformation field (Fig. 2), the search ranges for the length and width of the fault were set to [0, 25] km and [0, 15] km. A nonlinear search for the geometric parameters of the source fault was conducted using an optimized multi-peak particle swarm algorithm (Feng et al., 2013). The results indicated that under a NW dip, the optimal parameters for a uniformly slipping fault are listed in Table 1, with a fault strike of 149°, a dip of 33°, and an average slip angle of 111°. Similarly, to mitigate the effects of instability factors during inversion, a smoothing factor was introduced, with the search range for the smoothing factor set between [0, 0.1] (with a search step of 0.01). Ultimately, under the constraint of the optimal smoothing factor of 0.08, the detailed slip distribution characteristics for the NW-dipping fault model were obtained. Figures 6 (a) and (b) illustrate the coseismic slip distribution features of the 2023 Jishishan earthquake when the fault is southwest-dipping. Both figures show that the coseismic slip distribution is primarily concentrated at depths between 10 and 20 km, with a maximum slip of approximately 0.39 m and a moment magnitude of Mw 6.0. Figures 7 (a) to (f) display the coseismic observed deformation field, forward modeling deformation field, and residual maps for the 2023 Jishishan earthquake with an east-dipping fault. Overall, the east-dipping fault model fits the InSAR-observed surface deformation field well, with a fitting degree of 92.5% for ascending track observations and 91.7% for descending track observations, corresponding to root mean square residuals of 0.66 cm and 0.67 cm, respectively.