k G as a Passive Lithological Compliance Index Derivation from Independent Spectral Residuals and Validation across Seven Lithologies

We present k G = π × f₀ / (Q × V s ) as a passive lithological compliance index measurable from ambient seismic noise without drilling or active sources. The fundamental frequency f₀ is extracted from spectral residuals after subtraction of the common seismic mode (oceanic microseism), while V s and Q are drawn from published borehole measurements. Using this three-source independent framework across nine broadband seismic stations spanning seven lithological classes — granite, ophiolite, basalt, limestone, marl, alluvium, and soft sediment — we find a near-perfect Spearman correlation between k G and Q × V s (ρ = −0.941, p = 0.0002, N = 9). The lithological ordering granite < ophiolite < basalt < limestone < marl < alluvium < sediment is recovered consistently across six spectral window lengths (5 min to 2 h), with coefficient of variation below 3% at five of nine stations. A formal independence test confirms that f₀ carries no information about Q × V s (ρ = −0.008, p = 0.98), ruling out algebraic circularity. In Theban limestone, the empirically calibrated value k G = 23.1 /km (Gasque, 2026; ρ = 0.786, p = 0.021, N = 8 tombs) exceeds the borehole-derived compliance value of 0.055 /km by a factor of 420, encoding cavity resonance amplification. We propose k G as a single-station, equipment-agnostic site-characterization parameter complementary to V s30 , requiring no instrument deployment beyond existing network infrastructure. All data, methods, and results are fully reproducible from public seismic archives.