We extend a random matrix theory (RMT) program, previously applied to geological boundaries, faults, mantle plumes, and ore deposits, to hydrogeological systems, testing whether the timing of fluid-release events carries a level-repulsion signature across six orders of magnitude in timescale. The motivation is a pressure-shadow hypothesis: a fluid-release event depletes local fluid pressure and thermal energy, which must re-accumulate before the next event, imposing a minimum recurrence interval analogous to eigenvalue repulsion. We examine three configurations. (A) Old Faithful Geyser (single source, n=271 eruption intervals): the spacing ratio r-bar = 0.738 far exceeds GUE (0.603), with CV = 0.20 and Brody beta = 3.0, the strongest repulsion observed in any geological system, reflecting the near-deterministic two-state charge-release cycle of a single hydrothermal conduit. (B) Yellowstone Basin (multi-source forward model, 15 independent geysers): collapses precisely to Poisson (r-bar = 0.383), confirming the spectral superposition theorem. (C) North Atlantic IRD events (single source, n=34 inter-peak spacings from DSDP Site 609 HSG peaks): r-bar = 0.550, with KS test preferring GOE, consistent with glacial charge-release dynamics at kiloyear timescales. Together with five previously studied deep-Earth systems, eight physically unrelated Earth systems now show the same pattern: single long-memory charge-release sources repel; superposed sources randomize. Fifth in a unified RMT program spanning Earth from geysers to the core-mantle boundary.
Ruqing Chen (Sun,) studied this question.