Statistical and Extreme-Value Modeling of Earthquake Magnitudes in Pakistan: A Declustered, Regionally Stratified Analysis
Statistical Modeling of Earthquake Magnitudes in Pakistan
Keywords:
Earthquake magnitude, Earthquake catalog, Magnitude–frequency distribution, Statistical seismology, Extreme value theory , DeclusteringAbstract
Earthquakes are among the most destructive natural disasters, causing significant harm to human lives and infrastructure. This study examines the Pakistan-Hindu Kush-Pamir-Makran (PHKPM) earthquake catalogue for the period 1973-2025, which is characterized by modern and comprehensive digital monitoring. The catalogue comprises 20,617 seismic events. An independent fuzzy-duplicate audit was conducted, resulting in the removal of 133 multi-agency repeat reports from the initial 20,750 raw records. The data have been standardized to moment magnitude. The magnitude of completeness is determined once for the pooled national catalogue, with the σ-versus-T test establishing the completeness threshold, and the Goodness-of-Fit Test confirming = 5.5. Using the nearest-neighbor-distance method for declustering, 318 out of 369 Mc-complete events are retained, resulting in a 13.8% reduction. This independent-event catalogue is subsequently divided into North (= 248) and South ( = 70) regions, thereby avoiding the boundary effects that a region-by-region analysis would introduce. The analysis of the 23-candidate distribution race demonstrates that the Skewed Generalized Error (SGE) distribution is suitable across all three catalogues. This distribution is consistently employed based on goodness-of-fit and Q-Q plot evaluations, rather than relying on the Akaike Information Criterion (AIC), whose ordering among the adequate candidates is sensitive to the tie-breaking jitter. Fitted strictly to the annual-maximum series Gumbel is preferred nationally in the North, but Generalized Extreme Value (GEV) in the South. A peaks-over-threshold Generalized Pareto distribution (GPD) is a statistically significant improvement over the classical Gutenberg-Richter law in the combined catalogue and the South, with the North just inside the 5% boundary. The three GPD shape parameters are positive and exhibit the greatest magnitude in the South, which aligns with the positive annual-maximum shape parameter observed in this region. Both extreme-value frameworks thus agree on the presence of a pronounced tail in the Southern domain. Return levels are reported with 95% bootstrap confidence intervals to a 100-year horizon, with explicit caution against reading them as physical ceilings.
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