Maximum-likelihood estimation of seismic magnitude

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Abstract
Seismic networks often tend to overestimate the magnitude of earthquakes, because those stations within the network that do not detect a particular event are ignored in the conventional magnitude-averaging procedure. By assuming a normal distribution of worldwide magnitudes for any given event, it is possible to establish a simple statistical model that includes the additional information that event magnitudes at nondetecting stations must be below a certain threshold value. In this paper, maximum likelihood estimation is applied to determine event magnitude based on this model. The advantages and limitations of the technique are discussed using both simulated and real data. It is found that the maximum likelihood method, when applied properly, has the potential to yield a significant improvement in network magnitude estimates compared to the conventional averaging technique.

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