A Statistical Approach to Estimate Seismic Monitoring Stations’ Biases and Error Levels

Magnitudes are common and important measures for the size of seismic events. The International Data Centre (IDC) of the Comprehensive Nuclear-Test Ban Treaty Organization estimates an event magnitude by averaging the magnitudes calculated by individual stations that detected the event, excluding outliers. This approach assumes that all station magnitudes have the same error level and are unbiased, namely, they have no systematic errors. We show that the body-wave and surface-wave magnitudes published in the Reviewed Event Bulletin (REB) of the IDC are inconsistent with these assumptions. We thus consider a model where each station has an unknown bias and error level. Given a large collection of reported event magnitudes by a network of monitoring stations, we propose a novel approach to estimate each individual station’s bias and error level. From a statistical perspective, this is a challenging problem involving a huge number of variables, because in addition to the stations’ biases and error levels, the event magnitudes are also unknown. Our approach is based on analyzing differences between reported magnitude values at pairs of stations, which cancels out the unknown event magnitudes and allows us to derive a simple and computationally efficient algorithm. We use the estimated station biases as station correction terms and the estimated error levels to compute weights for event magnitude estimation. Using a large data set from the REB with millions of reported station magnitudes, we show that our approach yields more consistent station and event magnitudes.