Model parameter estimation bias induced by earthquake magnitude cut-off

Abstract

We evaluate the bias in parameter estimates of the ETAS model.We showthatwhen a simulated catalogue is magnitude-truncated there is considerable bias, whereas when it is not truncated there is no discernible bias. We also discuss two further implied assumptions in the ETAS and other self-exciting models. First, that the triggering boundary magnitude is equivalent to the catalogue completeness magnitude. Secondly, the assumption in the Gutenberg-Richter relationship that numbers of events increase exponentially as magnitude decreases. These two assumptions are confounded with the magnitude truncation effect. We discuss the effect of these problems on analyses of real earthquake catalogues.