Empirical evaluation of the magnitude-independence assumption

Abstract

The most common earthquake forecasting models assume that the magnitude of the next earthquake is independent from the past. This feature severely limits the capability to forecast large earthquakes with high probabilities. Here we investigate empirically on the magnitude-independence assumption, exploring if: (i) background and triggered earthquakes have the same frequency–magnitude distribution, (ii) variations of seismicity in the space–time–magnitude domain encode some information on the future earthquakes size. For this purpose, and to verify the stability of the findings, we consider seismic catalogues covering different space–time–magnitude windows, such as the Alto Tiberina Near Fault Observatory (TABOO), the California and Japanese seismic catalogues. Our approach is inspired by the nearest-neighbour method proposed by Baiesi & Paczuski and elaborated by Zaliapin et al. to distinguish between triggered and background earthquakes. Here we implement the same metric-based correlation to identify the precursory seismicity of any triggered earthquake; this allows us to analyse, for each triggered earthquake, the space–time–magnitude distribution of the seismicity that likely contributed to its occurrence. Our results show that the magnitude-independence assumption holds reasonably well in all catalogues, with a remarkable exception that is consistent with a previous independent study; this departure from the magnitude-independence assumption shows that larger events tend to nucleate at a higher distance from the ongoing sequence. We also notice that the reliability of this assumption may depend on the spatial scale considered; it holds for seismic catalogues of large areas, but we identify possible departures in small areas, reflecting different ways to release locally seismic energy. Finally, we come across an important issue that may lead to misleading results in similar studies, that is, if a seismic catalogue appears overall complete above a fixed magnitude threshold, it may still yield spurious signals into the analysis. Specifically, we show that some significant departures from the magnitude-independence assumption do not survive when considering spatiotemporal variations of the magnitude of completeness.