Acceptance and Counting Budgets for Borehole Muon Density Logging in Mineral Exploration

This paper computes the muon attenuation, exposure and resolution budget for imaging a borehole muon detector with cosmic-ray muons. Sight lines through 90 metres of host rock around a borehole at a density of 2.7 grams per cubic centimetre present an opacity of 2.43e+04 grams per square centimetre (243 metres of water equivalent), which sets a minimum muon energy of 50.73 GeV and a transmitted vertical intensity of 0.1306 per square metre per second per steradian. For a detector of 0.05 square metres with the stated acceptance and efficiency, divided among 30 image elements, the stated feature produces a flux contrast of 0.2144 and reaches five standard deviations in 30.14 days of counting, while the target precision of 0.06 per image element requires 15.39 days. A deployment of 30 days delivers a per-element precision of 0.04298, corresponding to a thickness sensitivity of 3.868 metres. The combined angular resolution is 10.9 milliradians, of which tracking contributes 3.771 milliradians and multiple scattering at the threshold momentum 10.22 milliradians. The budget is compared with published muography of the same class of target, for which borehole muon detector development for mineral exploration has demonstrated detectors fitting standard borehole diameters, with density-logging concepts based on the flux from the rock surrounding the hole. Every number is computed by the accompanying script from the stated inputs. Computed, not measured.