Estimator dependence of hydrological Newtonian noise in torsion-balance measurements of the gravitational constant

Abstract

Nearby water perturbs a torsion balance through gravity, but its effect on a measurement of the gravitational constant depends on both water transport and signal estimation. We connect groundwater and shallow storage, partly filled conduits, pump cycles, and localized events to finite-duration estimators. No measured hydrological time series are used; all numerical values are conditional scenarios. For a specified fixed shear channel and approximately 3-day cosine lock-in, alternative unresolved high-frequency spectra give a shallow-storage contribution of 0.14–3.5 ppm. These spectra share a low-frequency anchor, not a common total variance. Additional spatial-covariance and vertical-redistribution tests change the amplitudes but preserve the distinction between the tested mean and lock-in estimators. The conduit result at 6.37 mHz is only a sensitivity estimate outside the reduced hydraulic model’s nominal range. The framework separates stochastic uncertainty from deterministic contamination and makes explicit the roles of transport, detector response, and estimator phase and window.