## 3 Result and Discussion
### Implication of Stress Accumulation and Earthquake Potential Stress  
The geodetic strain rate within the deforming zone reflects the stress accumulation that will be released in future earthquakes. Although the recorded seismicity based on modern instruments shows limited occurrences [35], evaluating the stress field is essential to provide earthquake mechanisms, which provide valuable insight into future seismic hazards. The extension of back-arc thrust across the Flores shows the north---south orientation of the stress field perpendicular to the trench and has dominant thrust faulting [35]. The north---south orientation of the stress field is consistent with our generally north---south compression for long wavelength features from regional scale strain rate (Figure 7). On the other hand, the limited stress data by the World Stress Map (WSM) based on the focal mechanism demonstrates a slightly northern trend in Central Java and a gradual shift to the NE in East Java [36]. This trend is pretty similar to a gradual shift of principal strain rate from the NW trend in Central Java to the NE trend in East Java (Figure 7). We evaluated the seismic moment accumulation rate for assessing earthquake potential based on the estimated strain rate, as has been demonstrated in previous studies [18; 37; 38]. The moment accumulation rate was calculated based on Ward [39], which originated from Kostrov [40] as follows:  
\[\dot{M}_{\bar{\mathrm{ij}}}=2\mu H\sum_{\mathrm{i=1}}^{n}\sum_{\mathrm{j=1}}^{n} A_{\bar{\mathrm{ij}}}Max(|\dot{e}_{1,\mathrm{ij}}|,\ |\dot{e}_{2,\mathrm{ij}}|) \tag{5}\]  
where \(\dot{M}_{\bar{\mathrm{ij}}}\) is the moment accumulation rate, \(\mu\) is the rigidity, \(H\) is the depth of the seismogenic layer at which most of the earthquakes occur, \(A_{\bar{\mathrm{ij}}}\) is the gridded surface area, and \(\dot{e}_{1}\) and \(\dot{e}_{2}\) are the absolute eigenvalues of the strain rate tensor of the grid cells within each seismogenic zone. We assumed the rigidity is set to 30 GPa, where the elastic thickness \(H\) is fixed at a maximum of 12.5 km, according to [PERSON] et al. [20]. We divided the seismogenic zone into three main segments, SG1, SG2, and SG3, as shown in Figure 8. In SG1, with a total area of approximately 2975 km\({}^{2}\), the seismic moment accumulation rate was estimated to be \(1.69\times 10^{17}\) N m/year. In SG2, with a total area of approximately 3450 km\({}^{2}\), the seismic accumulation rate was estimated to be \(1.44\times 10^{17}\) N m/year. Meanwhile, in SG3, with a total area of approximately 4100 km\({}^{2}\), the seismic accumulation rate was estimated to be \(3.01\times 10^{17}\) N m/year. According to previous studies, historical earthquakes based on the estimated magnitude and fault slip rate in East Java were about 181 \(\pm\) 16 years ago [20; 41]. We computed the seismic moment of SG1, SG2, and SG3, accumulating the moment rate to date, suggesting earthquake potentials of Mw 6.9, Mw 6.9, and Mw 7.1, respectively. As mentioned above, the dilatation rate and maximum shear strain were considered as oblique and strike-slip earthquake potential. We also evaluated the earthquake potential based on the earthquake mechanism shown by the strain rate signal (Figure 8) divided by the oblique zone as OB1 and OB2 and the strike-slip zone as SS0. We obtained the moment accumulation rates of OB1, OB2, and SS0 are \(7.88\times 10^{16}\) N m/year, \(1.20\times 10^{17}\) N m/year, and \(6.41\times 10^{16}\) N m/year, respectively. If those moment accumulation rates last for 181 \(\pm\) 16 years, they would be considered as Mw 6.7, Mw 6.8, and Mw 6.6 earthquake potential. The M6- to M7-class earthquake potential in the back-arc thrust along Eastern Java is aligned with previous studies [18; 20; 41] and historical earthquakes along the extension of the back-arc thrust from the Flores [12; 13], the Lombok [4; 5; 6; 7; 8], the Bali [14], and the Situbondo [15] earthquakes. The strain rate modeling in this study has certain limitations.