ROYAL NORWEGIAN COUNCIL FOR SCIENTIFIC AND INDUSTRIAL RESEARCH KJELLER
In this paper some statistical models in connection with seismic magnitude are presented. Two main situations are treated. The first deals with the estimation of magnitude for an event using a fixed network of stations and taking into account the detection and bias properties of the individual stations. The second treats the problem of estimating seismicity and detection and bias properties of individual stations. The models are applied to analyze the magnitude bias effects for an earthquake aftershock sequence from Japan, as recorded by a hypothetical network of 15 stations. It is found that network magnitudes computed by the conventional averaging technique are considerably biased, and that a maximum likelihood approach using instantaneous noise level estimates for non-detecting stations gives the most consistent magnitude estimates. Finally, the models are applied to evaluate the detection characteristics and associated seismicity as recorded by three VELA arrays UBO, TFO, WMO.