Design and Implementation of a 25-Yr Pseudoprospective Earthquake Forecasting Experiment in China (AoyuX)

Abstract

Forecast models in statistical seismology are commonly evaluated using log-likelihood (LL) scores for the full distribution $P(n)$ of earthquake counts. However, fat tails and out-of-range observations (realized counts exceed all simulations) can bias model rankings. We develop a tail-aware framework that estimates cell-wise $P(n)$ using adaptive Gaussian kernel density estimation and compares three treatments of out-of-range counts: power-law extrapolation, a fixed minimum probability, and exclusion. Using the AoyuX platform, we conduct a 25-year (2000--2023) month-by-month pseudoprospective experiment in the China Seismic Experimental Site. We compare an epidemic-type aftershock sequence model with a homogeneous background, ETAS$\mu$, with a spatially heterogeneous variant, ETAS$\mu (x,y)$, across six spatial resolutions and five magnitude thresholds, using 100,000 simulations per forecast window. Count distributions follow power laws, $P(n)\sim n^{-(1+a)}$, with $a\approx 1.02\pm 0.23$, yielding a productivity exponent $\alpha =0.83\pm 0.19$ for $b=0.85\pm 0.002$. Model rankings depend on tail treatment: power-law extrapolation is theoretically justified and empirically most robust, whereas occasional advantages of the fixed-probability approach in coarse, low-magnitude settings are attributable to noise. Cumulative information gain shows that ETAS$\mu (x,y)$ outperforms ETAS$\mu$ in data-rich configurations, especially for $M_t=3.0$--$3.5$ and whole-region tests. Positive mean information gain is concentrated where earthquakes with $M\ge 5$ occurred, whereas stochastic fluctuations dominate data-poor settings. A coefficient-of-variation analysis distinguishes genuine upward trends from noise. The framework supports statistically grounded evaluation of earthquake forecasting models.

30 pages, 7 figures, 1 table