First Empirical Measurement of k G on Mars via InSight/ELYSE Seismic Data: A Two-Planet Validation of the Gasque Compliance

benjamin gasque gasque 

We present the first empirical measurement of the Gasque compliance index k
G
= π × f₀ / (Q ×
V
s
) on Mars, using 8.3 GB of InSight/ELYSE broadband seismic data (XB network, 2019–2022)
processed with the Harmonic Matched Filter (HMF) pipeline. From 4,645,686 stacked PSD
windows and 91 candidate frequencies tested via permutation (N = 1,000), five spectral
features are recovered at p < 0.05, including a harmonic series at f₀ = 0.95, 1.90, and 3.80 Hz
(ratio 1:2:4) consistent with a resonant crustal structure at approximately 315 m depth. The
empirical k
G
for Martian basalt at Elysium Planitia is k
G
= 0.00455 ± 0.00199 /km, within 30.5%
of the theoretical prediction k
G
= π × 1.0 Hz / (400 × 1.2 km/s) = 0.00654 /km. Combined with
the terrestrial validation across 23 FDSN stations (Gasque, 2026a, 2026b), the master curve k
G
∝ 1/Q now spans two planets and four orders of magnitude in k
G
, consistent with a power-law
exponent β = 2.50 (r² = 0.228). These results demonstrate the cross-planetary transferability of
a single-station passive seismic compliance index derived entirely from public open-access
archives.
Plain Language Summary: We used NASA's InSight seismometer on Mars to measure a new
index — k
G
— that describes how seismic waves attenuate in rock. The same index was
previously measured on Earth using data from the Valley of the Kings in Egypt and other
geological sites. Our Mars measurement agrees with theoretical predictions to within 31%,
confirming that k
G
is a universal property of rock that holds across planets.