Geodetic Recurrence and Seismic Anisotropy in Global Seismicity: Evidence for Non-Random Spatio-Temporal Structure and Possible Deep-Earth Anisotropy

This study presents an original statistical analysis of the geodetic structure of global seismicity, based on the USGS catalog of 4710 events M≥5.5 over the period 2015–2026. The Geodetic Recurrence Index (GRI) and its seismic-energy-weighted version (WGRI) are introduced as measures of non-random geometric structure in seismic geodetic planes. The analysis is extended for the first time to the deep mantle (300–660 km). Main results, validated by a Synthetic Earth Control preserving the real geometry of subduction zones: (1) crustal WGRI Z=3.91 (p<0.001); (2) asymmetric tectonic→volcanic coupling (Z=3.30, p=0.004); (3) mean-reverting structure in the temporal angular sequence of earthquakes; (4) 26.2° alignment between the seismic signal and the LLSVP axis; (5) the deep mantle signal (300–660 km) survives the Synthetic Earth Control with WGRI=0.579, Z=5.20, p=0.012, while shallower layers collapse under the same test. The directional convergence of all three layers (crustal 185.3°, subcrustal 196.7°, deep mantle 175.1°, total dispersion <22°) suggests an anisotropic structure traversing more than 600 km of the planet vertically. A speculative appendix discusses the possible connection with primordial LLSVPs and the Theia impact (4.5 Ga). Computational analysis and statistical correlations performed with the support of Claude — Anthropic AI (claude.ai).