A Restricted Maximum Likelihood Framework for Earthquake Magnitude Conversion in Data-limited Regions of the East African Rift

The East African Rift System (EARS) is an active continental rift that experiences frequent earthquakes, yet seismic hazard assessment across the region remains difficult. Challenges stem from sparse monitoring networks, the absence of standardized guidelines, and numerous active faults that remain unmapped or poorly characterized. In addition, regional earthquake catalogs are incomplete and often depend on limited data, introducing considerable uncertainty into seismic hazard estimates. Despite these issues, conventional least-squares regression methods are still commonly used for magnitude conversion, even though they are sensitive to outliers, rely on assumptions that are made but rarely validated, and possess several limitations. These limitations constrain the generation of reliable homogenized earthquake catalogs essential for seismicity, seismotectonic, and hazard assessments.

This study proposes a robust statistical framework for deriving regional magnitude conversion relationships using the Restricted Maximum Likelihood (REML) estimation method. REML is particularly advantageous for data-scarce regions such as EARS, as it explicitly accounts for measurement uncertainties, non-constant variance, and the prevalence of outliers common in mixed-magnitude earthquake catalogs. The methodology incorporates rigorous statistical tests, including Box–Cox transformations for date normality, residual diagnostics, and variance stability evaluations.

To demonstrate its usefulness, the proposed framework is applied to catalogs from three regions along the EARS: (1) the Main Ethiopian Rift (Eastern Branch), (2) Sudan (a tectonically stable region), and (3) Malawi (Western Branch). The resulting magnitude conversion relationships exhibit significantly reduced uncertainty and provide confidence bounds, thereby enhancing the reliability of homogenized earthquake catalogs. The proposed approach strengthens the consistency of earthquake datasets across East Africa and offers a valuable tool for improving seismic hazard and risk assessments in similar data- limited regions worldwide.