Hierarchical Bayesian Modeling for Improved High-Resolution Mapping of the Completeness Magnitude of Earthquake Catalogs

Abstract

Abstract Assessing the completeness magnitude Mc is essential for most seismicity studies. However, when studying the spatial variation of Mc in a region, the conventional methods that compute Mc based on the frequency–magnitude distribution (FMD) tend to give gaps and large uncertainties of Mc in subregions of low seismicity, thus rendering high-resolution Mc mapping infeasible. To address the limitations of the FMD-based methods, the Bayesian magnitude of completeness (BMC) method was proposed a decade ago to incorporate a priori information about Mc derived from its empirical relationship to the seismic network spatial configuration Mc=f(d), with d being the distance to the kth (typically k = 4 or 5) nearest seismic station at each node in space. Although widely used, the BMC method has several critical shortcomings that have long been neglected. In this study, we propose a hierarchical Bayesian model that inherently overcomes these shortcomings of the BMC method for high-resolution Mc mapping coined hierarchical Bayesian magnitude of completeness (H-BMC), which provides a unified and more appropriate approach to the integration of a priori information and local observations concerning Mc. We use an earthquake catalog from the Taiwan region to demonstrate that, compared with the FMD-based methods based solely on observed magnitudes, the proposed H-BMC method effectively utilizes a priori information via prior distributions and thereby gives complete and more reliable high-resolution Mc mapping in terms of gap filling and uncertainty reduction. We also highlight that the H-BMC method for Mc mapping serves as a generic and flexible modeling framework for logically combining imprecise information about Mc from different sources.