Uncertainties in Intensity-Based Earthquake Magnitude Estimates

Estimating the magnitude of historical earthquakes is crucial for assessing seismic hazard. Magnitudes of early-instrumental earthquakes can be inferred using a combination of instrumental records, field observations, and the observed distribution of shaking intensity determined from macroseismic observations. For earthquakes before 1900, shaking intensity distributions often provide the only information to constrain earthquake magnitude. Considerable effort has been made to develop methods to estimate the magnitude of moderate-to-large historical earthquakes using shaking intensities derived from macroseismic data. In this study, we consider earthquakes in California with known instrumental magnitudes to explore uncertainties in estimating the magnitude of historical earthquakes from intensity information alone. We use three California-specific intensity prediction equations (IPEs) and an IPE based on a global ground-motion model (GMM) to determine optimum intensity-based magnitudes for 33 moderate-to-large California earthquakes between 1979 and 2021. Intensity-based magnitudes are close to instrumental magnitudes on average. However, intensity-based magnitudes for individual events differ by as much as 2.2 magnitude units from instrumental magnitudes. This result reflects the weak dependence of ground motions and shaking intensities on moment magnitude and their strong dependence on stress drop. Considering the intensity distributions of the 1906 San Francisco and 1989 Loma Prieta earthquakes, we show that information that could constrain rupture length is discarded when considering only the 2D decay of intensity with distance. We also show that ground-motion intensity conversion equations used in a GMM-based approach may cause a systematic overestimation of large historical earthquake magnitudes. This study underscores both the reducible and potentially irreducible uncertainties associated with using intensity data to estimate magnitudes of historical earthquakes using IPEs and highlights the value of using additional information to constrain rupture dimensions. Using intensity observations alone, moment magnitude uncertainties are typically on the order of a full unit.