The Gutenberg-Richter exponent b is a measure of the relative proportion of large and small earthquakes. It is commonly used to infer material properties such as heterogeneity, or mechanical properties such as the state of stress from earthquake populations. It is 'well known' that the b-value tends to be high or very high for volcanic earthquake populations relative to b=1 for those of tectonic earthquakes, and that b varies significantly with time during periods of unrest. We first review the supporting evidence from of 34 case studies, and identify weaknesses in this argument due predominantly to small sample size, the narrow bandwidth of magnitude scales available, variability in the methods used to assess the minimum or cutoff magnitude Mc, and to infer b. Informed by this, we use synthetic realisations to quantify the effect of choice of the cutoff magnitude on maximum likelihood estimates of b, and suggest a new work flow for this choice. We present the first quantitative estimate of the error in b introduced by uncertainties in estimating Mc, as a function of the number of events and the b-value itself. This error can significantly exceed the commonly-quoted statistical error in the estimated b-value, especially for the case that the underlying b-value is high. We apply the new methods to data sets from recent periods of unrest in El Hierro and Mount Etna. For El Hierro we confirm significantly high b-values of 1.5-2.5 prior to the 10 October 2011 eruption. For Mount Etna the b-values are indistinguishable from b=1 within error, except during the flank eruptions at Mount Etna in 2001-2003, when 1.5
The Gutenberg‐Richter b value is commonly used in volcanic eruption forecasting to infer material or mechanical properties from earthquake distributions. Such studies typically analyze discrete time windows or phases, but the choice of such windows is subjective and can introduce significant bias. Here we minimize this sample bias by iteratively sampling catalogs with randomly chosen windows and then stack the resulting probability density functions for the estimated
trueb˜ value to determine a net probability density function. We examine data from the El Hierro seismic catalog during a period of unrest in 2011–2013 and demonstrate clear multimodal behavior. Individual modes are relatively stable in time, but the most probable
trueb˜ value intermittently switches between modes, one of which is similar to that of tectonic seismicity. Multimodality is primarily associated with intermittent activation and cessation of activity in different parts of the volcanic system rather than with respect to any systematic inferred underlying process.
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