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

Forecast models in statistical seismology are commonly evaluated with log-likelihood (LL) scores of the full distribution P(n) of earthquake numbers, yet fat tails and out-of-range observations (realized counts exceeding all simulations) can bias model ranking. We develop a tail-aware evaluation framework that estimates cell-wise P(n) using adaptive Gaussian kernel density estimation and tests three strategies for handling out-of-range counts (power law extrapolation, fixed minimum probability, and exclusion). Using the AoyuX platform, we perform an ∼25-yr (2000–2023) month-by-month pseudoprospective forecast experiment in the China Seismic Experimental Site (CSES), comparing epidemic-type aftershock sequence (ETAS) model with a homogeneous background (ETASμ) with a spatially heterogeneous variant (ETASμ(x,y)) across six spatial resolutions and five magnitude thresholds; each forecast window is supported by 100,000 simulations. Empirical frequency distributions of counts per cell are well described by power laws P(n)∼n−(1+a) with exponents a ≈ 1.02 ± 0.23 across all settings. Using previous theoretical results, this provides a robust estimate of the productivity exponent, α=0.83±0.19 using a b value equal to 0.85 ± 0.002, providing a valuable quantification of this key parameter in aftershock modeling. Model ranking is sensitive to how the tail of the full distribution P(n) of earthquake counts is treated: power law extrapolation is both theoretically justified and empirically the most robust, whereas the apparent superiority of the fixed-probability approach in a few coarse low-magnitude cases can be attributed to noise. Cumulative information gain (CIG) shows that ETASμ(x,y) outperforms ETASμ in data-rich configurations (e.g., Mt=3.0 to 3.5 and whole-region tests), with positive mean information gain spatially concentrated in regions where M ≥ 5 earthquakes occurred during the study period, whereas in data-poor settings, stochastic fluctuations dominate. A coefficient-of-variation analysis of per-window LL differences distinguishes genuine upward trends in CIG from noise-dominated fluctuations. By aligning a fat tail–aware scoring methodology with an open testing platform, our work advances fair and statistically grounded assessment of earthquake forecasting models for the CSES and beyond.