A Unified Quadratic Scaling Relation Between Potency and Local Earthquake Magnitudes for −1.8 ≤ M L ≤ 7.5

Abstract

Abstract Quantifying earthquake size across scales requires linking physical source parameters to empirical magnitude measures, especially for microearthquakes where attenuation, scattering, and instrumental limitations complicate source characterization. We combine regional results with near‐source observations from the Tony Creek dual Microseismic Experiment, dense nodal data from Ridgecrest, and regional broadband data from San Jacinto to extend potency–magnitude scaling to local‐magnitude . Bayesian spectral inference yields robust potency estimates across seven potency magnitude units and nine units. The combined data sets follow a continuous quadratic relation . Synthetic modeling shows that source scaling, attenuation, and the finite Wood–Anderson passband can produce similar nonlinearity, although rupture‐scaling differences may also contribute. Despite sensitivity to observational and regional factors, the independent data sets are broadly consistent with the established quadratic relation, supporting it as a general empirical scaling over the investigated size range.