Abstract
Assessing the completeness magnitude is essential for most seismicity studies. However, when studying the spatial variation of in a region, the conventional methods that compute based on the frequency–magnitude distribution (FMD) tend to give gaps and large uncertainties of in subregions of low seismicity, thus rendering high‐resolution 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 derived from its empirical relationship to the seismic network spatial configuration , 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 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 . 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 mapping in terms of gap filling and uncertainty reduction. We also highlight that the H‐BMC method for mapping serves as a generic and flexible modeling framework for logically combining imprecise information about from different sources.