Dimensionless Delay Angle and Double-Bounded Resonance: Intermittent Retreat Mechanism and Impedance Matching in the Earth-Moon System

By restoring long-period micro-seismic waveforms previously filtered out as background noise in seismic time-series data, this study uncovers the non-linear coupling structure within the Earth-Moon system. We establish the integer-ratio coupling mechanism of micro-multi-resonant cycles (Ts ≈25.01 s, Tw ≈150.04 s, Tr ≈299.86 s) propagating along the crustal waveguide and derive the physical significance of the Dimensionless Delay Angle (δ*), defined as the phase lag between tidal potential and actual crustal displacement.

Mathematical derivation and RMS residual analysis (RMS = 0.012 rad) demonstrate that the delay angle functions as an indispensable Impedance Adjustment Value, preventing resonance destruction and locking the system into a 6×6×50 double-bounded resonance framework. Furthermore, field validation at Himalayan glacial lakes confirms that closed mountain basins operate as resonant cavities, triggering explosive Q-factor build-ups interlocked with lunar tidal phases.

This theoretical paper provides the physical foundation for the GLOF case studies reported in 10.5281/zenodo.23193435.

Key findings:
- Ts = 25.01 s (Surface Resonant Period)
- Tw = 150.04 s = 6×Ts
- Tr = 299.86 s ≈ 300 s (Delay Angle Correction)
- Ttotal = 6×Tw×50 = 1800×Ts = 45,018 s
- RMS delay angle residual = 0.012 rad

Empirical validation: South Lhonak (2023), Thame/Thyanbo (2024), Rasuwa (2026) - all show identical 25s/150s resonance.

Keywords: Effective Resonator, Dimensionless Delay Angle, GLOF, Tidal Resonance, Impedance Matching