Copula-Based Dependence Modeling for Seismic Gap Analysis in Tehran Province

Traditional approaches to testing the seismic gap hypothesis often rely on rigid assumptions about the joint distribution between earthquake magnitude and the time elapsed since the previous event. In this study, we introduce a flexible, copula-based statistical framework to model this dependence structure without enforcing a specific parametric form. Uniquely, our analysis also incorporates spatial dimensions by exploring the potential dependence between magnitude and geographic location (latitude and longitude). To address uncertainty in model selection, we adopt a model averaging technique that combines several candidate copulas, chosen based on their performance in minimizing Mahalanobis distance. This strategy enhances robustness and reduces the risk of bias from selecting a single dependence model. We apply this methodology to a real earthquake catalog from Tehran province—a densely populated and highly active seismic zone. Our findings reveal no significant dependence between magnitude and recurrence intervals, casting doubt on the validity of the seismic gap hypothesis in this region. These results provide new insights into seismic recurrence behavior and demonstrate the potential of copula-based models to support more data-driven seismic hazard assessments.