Foreshock counts may be underestimated: reversing declustering finds 30-40% more small foreshocks in Southern California

The inferred number of foreshocks changes with the temporal direction built into the declustering metric, and the standard choice systematically misses small foreshocks. The conventional nearest-neighbor declustering looks only forward, letting the magnitude of the earlier event set the correlation range, which suits aftershock identification. On synthetic catalogs with known true genealogies, the reverse nearest-neighbor residual distributions sit closer to zero, while standard nearest neighbor is shifted negative, that is, underestimating, in the bins with small foreshocks and small mainshocks.

Reverse nearest neighbor hands the correlation range to the later event, which is equivalent to applying standard nearest neighbor to a time-reversed catalog. Standard nearest neighbor asks which past earthquake is large and close enough to explain the present event; reverse nearest neighbor asks which future earthquake is large and close enough to organize preceding events as its foreshocks. The two metrics differ only in which event's magnitude enters the Gutenberg-Richter factor, so they diverge when the magnitude contrast between candidate foreshock and mainshock is large and converge when the magnitudes are comparable.

On a real catalog, reverse nearest neighbor identifies systematically more foreshocks than standard nearest neighbor. The synthetic experiments give the direction of bias against a known truth; a real catalog has no known genealogy, so only the difference between the two metrics can be compared. In the Southern California catalog, reverse nearest neighbor finds almost 30-40% more foreshocks in the bins with small to intermediate foreshocks and intermediate mainshocks, and a higher fraction of mainshocks carry at least one foreshock in every mainshock magnitude class.

The work addresses researchers in statistical seismology and catalog analysis: the synthetic catalogs cover two limiting cases, purely bottom-up triggering and mixed preparatory triggering, and the real-data part uses Southern California events above the completeness magnitude threshold. The authors propose extending the comparison to additional tectonic regions, exploring adaptive combinations of the two metrics, and testing whether the discrepancy between forward and reverse declustering can serve as an empirical diagnostic of preparatory organization.

The authors state that the true genealogy of earthquakes is unknown in real catalogs, so the comparison between the two metrics cannot by itself determine the physical origin of foreshocks; the advantage of reverse nearest neighbor is concentrated in the low-magnitude regime, while at moderate and large magnitudes the two methods give similar results and standard nearest neighbor is marginally favored in some high-magnitude bins. The authors also stress that ETAS and ETAFS are controlled limiting cases, and that natural earthquake preparation may involve several interacting mechanisms at once.