Scaling seismicity with depth: b-value, correlation dimension, and return periods analysis in far Western Nepal

This study investigates the depth-dependent variations of b-value and fractal dimension using earthquake data from Far Western Nepal, employing three estimation methods: Maximum Likelihood Estimation (ML), Bayesian Method (BM), and Gumbel Method (GM). The results reveal a characteristic fractal scale of ~7.5 to 35 km, corresponding to the brittle-ductile transition zone in the crust. The correlation dimension increases from 0.4 (0–10 km depth) to ~1.2 (12–24 km), indicating a transition from clustered seismicity to more homogeneous stress distribution. The b-values exhibit a decreasing trend with depth, with higher values (0.57–0.74) in shallow crustal layers (0–10 km) and lower values (0.23–0.34) at greater depths (>20 km), suggesting a shift from heterogeneous fracture-dominated deformation to more uniform stress release in ductile regimes. A strong negative correlation (R² > 0.7) between b-value and correlation dimension is observed for ML and BM, while the GM shows weaker dependence (R² = 0.17). Return period analysis indicates frequent small-magnitude earthquakes (M ~5 to 5.5) with decadal recurrence, whereas larger events (M ≥5) have centennial return periods. The probability of exceedance analysis further confirms that minor earthquakes (M = 4 to 5) are likely within short timeframes, while larger events (M ≥ 5.5) become increasingly probable over longer periods. The notable difference in the seismic indicators with depth suggest future major earthquakes in Far Western Nepal will likely occur below 20 km depth. We recommend integrating these depth-varying seismic indicators into hazard models to enhance earthquake preparedness and risk reduction strategies.