Accurate estimation of the magnitude of seismic events is essential to effective monitoring of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). The standard estimator of body-wave magnitude in the International Data Center (IDC) bulletins is the average mb reading at the detecting stations in a prescribed distance window. Two sources of bias may affect these magnitudes. First, some stations may tend to give high readings and others low readings, so the average may be biased by the particular set of detecting stations. Second, the averaging method ignores eligible stations that could have, but failed to, detect an event. The first source of bias can be reduced by estimating station correction terms. The second source of bias can be handled by applying maximum likelihood methods that take into account both detecting and nondetecting stations.
We compare several different methods that have been proposed to estimate station correction terms and show that a joint maximum likelihood method is clearly superior to other alternatives. A least-squares method that was used by Murphy and Barker (2003) to estimate correction terms leads to biased estimates of correction terms because it fails to take into account nondetecting stations. The joint method provides accurate estimates of station correction terms and is also superior to applying maximum likelihood to single events without estimating station corrections or with the least-squares corrections. We illustrate our ideas by analyzing data from about 15,000 seismic events recorded by the prototype IDC. We caution that our correction terms are for primary stations only and are not meant to be final estimates; to obtain final correction terms would require applying our methods to a complete data set including both primary and auxiliary stations.