What Gravity Cannot See: The Depth Limit and Mass-Depth Degeneracy of a Buried Sphere

The vertical gravity anomaly of a buried sphere depends only on its total anomalous mass and centre depth. Setting the peak anomaly equal to noise floors of 10 and 50 microgal gives detection limits: a 1 metre air-filled void (density contrast -1600 kg/m3) is undetectable below a centre depth of 2.11 m at 10 microgal and undetectable at any depth at 50 microgal, while a 10 metre void reaches 66.88 m at 10 microgal and 29.91 m at 50 microgal; a 10 metre ore body (+1000 kg/m3) reaches 52.87 m and 23.65 m respectively. Radius and density contrast are exactly degenerate at fixed mass and depth. Depth is degenerate within noise: for a 5 metre void centred at 12 m with a 38.83 microgal peak, matched-peak models centred from 7.48 m to 19.24 m, a factor of 2.57, agree with the reference curve within 10 microgal everywhere on a 120 m profile. Station spacing of about half the target centre depth or less is required, costing about 1,681 stations per hectare for targets centred at 5 m. The total anomalous mass is firmly measured by the surface flux integral; size and depth from anomaly data alone are a family, not a point. All numbers are computed by the accompanying script. AI use is disclosed: this paper was produced with the assistance of Dave, an AI system, which carried out the computation and drafting under the direction of the named author. William Alexander Aldred is sole author of record.