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

benjamin gasque gasque 

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.