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

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.