Shallow Karst Cavity Detection Above a Transport Tunnel: Muon Exposure and Sensitivity Budgets

This paper computes the muon attenuation, exposure and resolution budget for imaging karst cavities above a transport tunnel with cosmic-ray muons. Sight lines through 35 metres of limestone at a density of 2.4 grams per cubic centimetre present an opacity of 8400 grams per square centimetre (84 metres of water equivalent), which sets a minimum muon energy of 17.05 GeV and a transmitted vertical intensity of 0.789 per square metre per second per steradian. For a detector of 0.25 square metres with the stated acceptance and efficiency, divided among 160 image elements, the stated feature produces a flux contrast of 1.711 and reaches five standard deviations in 0.1347 days of counting, while the target precision of 0.05 per image element requires 6.311 days. A deployment of 60 days delivers a per-element precision of 0.01622, corresponding to a thickness sensitivity of 0.5676 metres. The combined angular resolution is 17.54 milliradians, of which tracking contributes 2.828 milliradians and multiple scattering at the threshold momentum 17.31 milliradians. The budget is compared with published muography of the same class of target, for which muon surveys from tunnels and underground galleries have reported detection of cavities and low-density zones in the overlying rock at depths of tens of metres. Every number is computed by the accompanying script from the stated inputs. Computed, not measured.