Detecting Abandoned Mine Workings by Muon Imaging: Column-Deficit and Exposure Budgets

This paper computes the muon attenuation, exposure and resolution budget for imaging abandoned mine workings with cosmic-ray muons. Sight lines through 60 metres of coal-measure strata at a density of 2.45 grams per cubic centimetre present an opacity of 1.47e+04 grams per square centimetre (147 metres of water equivalent), which sets a minimum muon energy of 30.17 GeV and a transmitted vertical intensity of 0.3077 per square metre per second per steradian. For a detector of 0.5 square metres with the stated acceptance and efficiency, divided among 160 image elements, the stated feature produces a flux contrast of 2.206 and reaches five standard deviations in 0.1323 days of counting, while the target precision of 0.05 per image element requires 10.3 days. A deployment of 90 days delivers a per-element precision of 0.01691, corresponding to a thickness sensitivity of 1.015 metres. The combined angular resolution is 13.39 milliradians, of which tracking contributes 2.424 milliradians and multiple scattering at the threshold momentum 13.17 milliradians. The budget is compared with published muography of the same class of target, for which muon surveys for void detection above and below ground have reported sensitivity to mine workings and shafts at depths of tens of metres. Every number is computed by the accompanying script from the stated inputs. Computed, not measured.