*Article* **Space-Time Trade-Off of Precursory Seismicity in New Zealand and California Revealed by a Medium-Term Earthquake Forecasting Model**

**Sepideh J. Rastin \*, David A. Rhoades and Annemarie Christophersen**

> GNS Science, Lower Hutt 5010, New Zealand; d.rhoades@gns.cri.nz (D.A.R.); a.christophersen@gns.cri.nz (A.C.) **\*** Correspondence: s.rastin@gns.cri.nz

> **Abstract:** The 'Every Earthquake a Precursor According to Scale' (EEPAS) medium-term earthquake forecasting model is based on the precursory scale increase (Ψ) phenomenon and associated scaling relations, in which the precursor magnitude *MP* is predictive of the mainshock magnitude *Mm*, precursor time *TP* and precursory area *AP*. In early studies of Ψ, a relatively low correlation between *TP* and *AP* suggested the possibility of a trade-off between time and area as a second-order effect. Here, we investigate the trade-off by means of the EEPAS model. Existing versions of EEPAS in New Zealand and California forecast target earthquakes of magnitudes *M* > 4.95 from input catalogues with *M* > 2.95. We systematically vary one parameter each from the EEPAS distributions for time and location, thereby varying the temporal and spatial scales of these distributions by two orders of magnitude. As one of these parameters is varied, the other is refitted to a 20-year period of each catalogue. The resulting curves of the temporal scaling factor against the spatial scaling factor are consistent with an even trade-off between time and area, given the limited temporal and spatial extent of the input catalogue. Hybrid models are formed by mixing several EEPAS models, with parameter sets chosen from points on the trade-off line. These are tested against the original fitted EEPAS models on a subsequent period of the New Zealand catalogue. The resulting information gains sugges<sup>t</sup> that the space–time trade-off can be exploited to improve forecasting.

> **Keywords:** earthquake forecasting; precursors; statistical seismology; earthquake likelihood models; seismicity patterns; New Zealand; California
