A Reduced Madelung-Type Model for Seismic Activation: Localization Dynamics and Baseline-Aware Validation

We developed a one-dimensional Madelung-type model to test whether seismic activation dynamics improve agreement with future earthquake distributions beyond empirical baselines. The model couples activation density, activation-flow velocity, effective loading, structural heterogeneity, and a curvature-sensitive potential. Synthetic simulations examined localization, while temporally separated United States Geological Survey (USGS) Japan–western Pacific catalog tests compared the model with persistence and historical relative intensity. Principal component analysis (PCA) preprocessing excluded holdout data, and weak-evolution parameters were calibrated independently on 2022 data. On the July–December 2023 complete-catalog holdout, weak evolution underperformed persistence on most metrics, including Pearson correlation (0.4156 versus 0.4837); paired moving-block bootstrap intervals for correlation and cosine differences included zero. In January–June 2023, several continuous metrics improved over persistence, but operating-point results remained mixed. Declustering favored weak evolution over persistence on most metrics, while relative intensity retained higher Pearson and Spearman correlations. Removing the curvature term produced stronger concentration, indicating a regularizing rather than uniquely focusing role. Grid refinement revealed resolution sensitivity in strong evolution. These results support a mechanistic and numerical proof of concept whose empirical performance depends on catalog treatment, forecast window, and metric; they do not establish robust earthquake forecast superiority.