Biases in Estimating B-Values in Small Catalogues of Induced and Volcanic Earthquakes

The Gutenberg-Richter (GR) b-value describes the relative weighting of small and large earthquakes in a scale-free population. At low magnitudes, the scale-free behaviour breaks down due to censoring of the data, when the instrumentation used is incapable of completely recording all earthquakes in the study region. The threshold above which all events are assumed to be recorded is termed the completeness magnitude, M_c. At high magnitudes, the scale-free behaviour must also break down because natural tectonic and volcano-tectonic processes are incapable of an infinite release of energy, which is difficult to estimate accurately.

We use the modified GR distribution (MGR) to describe the breakdown of scale-free behaviour at large magnitudes, introducing an exponential roll-off to the incremental distribution and hence an extra parameter. This requires more data to justify the additional model complexity. In tectonic regions, the b-value is close to unity, with reports of much higher b-values in induced and volcanic areas. However, many studies resulting in high b-value estimates also have used relatively small datasets - both in sample size and bandwidth (magnitude range) above M_c, easily introducing biases.

Using synthetic data, we show that when we have little data and low bandwidth, it is statistically challenging to test whether the sample is representative of the scale-free GR behaviour or whether it is controlled primarily by the finite size roll-off seen in MGR. Here, I will present new analyses of induced and volcanic seismicity and the potential biases that arise when the data does not permit for the distinction between competing models to be made. I will also discuss the implications for the interpretation of studies with estimated high b-values.