Estimation of Uncertainty in the Average Rate of Earthquakes Exceeding a Magnitude Threshold

We propose a method to estimate the uncertainty of the average rate of earthquakes exceeding a magnitude threshold in a future period of given length based on observed variability of the earthquake process in an existing catalog. We estimate the ratio R of the variability to that of a stationary Poisson process. R is estimated from subsets of the catalog over a wide range of timescales. The method combines the epistemic uncertainty in estimating the rate from the catalog and the aleatory variability of the rate in future time periods. If R is stable over many timescales, there is a solid basis for estimating the uncertainty of earthquake rate estimates. In the 2022 revision of the New Zealand National Seismic Hazard Model (NZ NSHM), estimation of the total shallow earthquake rate over the next 100 yr and its uncertainty is an important element. Using a 70 yr New Zealand catalog with hypocentral depths ≤40 km and standardized magnitudes M ≥ 4.95, we find stable estimates of R for timescales from 3 days to 2.4 yr. This gives a standard error of 0.95 on the estimated annual rate of M ≥ 4.95, in the next 100 yr. R becomes unstable and has poor precision for longer subperiods. We investigate potential causes using synthetic catalogs with known inhomogeneities. Analysis of International Seismological Centre-Global Earthquake Model (ISC-GEM) catalog, to investigate the effect of higher magnitude thresholds, shows that R is lower for M ≥ 6.95 than for M ≥ 5.45. The ISC-GEM catalog restricted to New Zealand gives comparable stable estimates of R to the NZ NSHM 2022 catalog for M ≥ 5.45 and lower estimates than the NZ NSHM 2022 catalog for M ≥ 4.95. We also verify that magnitude standardization of the New Zealand GeoNet catalog has reduced the uncertainty of rate estimates by decreasing R throughout the entire range of timescales.