Duration Magnitude Uncertainty due to Seismic Noise: Inferences on the Temporal Pattern of GR b-value at Mt. Vesuvius, Italy

We analyze the statistical properties of seismic noise amplitude at seismic station OVO in the Mt. Vesuvius Volcano (southern Italy) monitoring network. The root mean square of seismic noise amplitude has a lognormal distribution. Using the mean and standard deviation of this distribution, we evaluate the uncertainties in the estimate of duration magnitude (MD) for the volcano-tectonic seismic events at Mt. Vesuvius. We develop a method based on knowledge of the coda-envelope pattern of local events and find an empirical formula for determining the standard deviation of MD. We then recalculate the b-value time pattern for Mt. Vesuvius from 1972 to the present using a weighted least-squares approach, where the inversion weights are given by the magnitude errors and the number of events included in each magnitude bin. Results are compared to a suite of synthetic catalogs with the same number of events, the same magnitude errors, and the same completeness threshold as the true Mt. Vesuvius catalog. Our results indicate that the method presented in this note has a lower bias than the maximum likelihood approach previously used for calculating b-values at Vesuvius. Propagation of uncertainties in MD measurements into the estimate of b-value indicates that previously determined time changes in b-values at Mt. Vesuvius are not statistically significant.