Estimating Magnitude Completeness in Earthquake Catalogs: A Comparative Study of Catalog-Based Methods

Abstract

Without careful attention to the earthquake catalog completeness, claims of novel discoveries or forecasting skills lack credibility. Estimating the completeness magnitude (M_c) is therefore a critical step in seismological analysis. Among the available techniques, catalog-based methods are the most accessible and widely adopted, and they also often form the basis for more sophisticated techniques. However, current frameworks for evaluating methods do not provide a standardized strategy for generating synthetic catalogs that are independent of any specific M_c estimation technique. An effective evaluation framework should also allow for the simulation of data sets with spatially and temporally varying M_c values. In this study, we introduce a robust evaluation framework specifically designed to benchmark catalog-based M_c estimation methods, including six established and three newly proposed methods, under realistic and controlled simulation conditions. The proposed methods are evaluated on both simulated data sets, with homogeneous and heterogeneous M_c distributions, and on real-world earthquake catalogs from China, California, and New Zealand. In the synthetic tests, The traditional method MBS-WW and two new methods, BSReLU and especially AEReLU, consistently deliver reliable M_c estimates, provided the data are sufficiently dense and well-resolved. Among them, AEReLU demonstrates superior accuracy and adaptability, particularly under challenging conditions. When applied to six empirical catalogs, AEReLU produces the most robust and physically meaningful M_c estimates. Its predicted M_c values closely align with known regional completeness thresholds (e.g., M_c ≈ 1.8) and remain stable across diverse tectonic environments. Moreover, AEReLU yields consistent b-values and reveals spatial variations in the asymmetry parameter β, which captures differences in how detection completeness converges below and above M_c, reflecting region-specific patterns of seismicity and catalog incompleteness. Unlike traditional methods that impose a sharp M_c cut-off, BSReLU and AEReLU adopt a probabilistic framework that models the smooth transition in detection likelihood from zero to one as magnitude increases. This formulation better reflects the gradual shift from incomplete to complete reporting, effectively overcoming the limitations of step-function-based models. By rigorously comparing these methods, the present study not only identifies the contexts in which each is most suitable but also enhances our understanding of seismicity, earthquake forecasting, and hazard assessment, underscoring the critical role of data completeness in all such analyses.