Detector-Area Requirements for Imaging the Summit Conduit of Mount Vesuvius by Cosmic-Ray Muons

This paper computes the muon attenuation, exposure and resolution budget for imaging Mount Vesuvius with cosmic-ray muons. Sight lines through 700 metres of volcanic rock at a density of 2.6 grams per cubic centimetre present an opacity of 1.82e+05 grams per square centimetre (1820 metres of water equivalent), which sets a minimum muon energy of 509 GeV and a transmitted vertical intensity of 0.002906 per square metre per second per steradian. For a detector of 1 square metres with the stated acceptance and efficiency, divided among 400 image elements, the stated feature produces a flux contrast of 0.8556 and reaches five standard deviations in 194.3 days of counting, while the target precision of 0.05 per image element requires 2276 days. A deployment of 365 days delivers a per-element precision of 0.1249, corresponding to a thickness sensitivity of 87.4 metres. The combined angular resolution is 4.092 milliradians, of which tracking contributes 2.828 milliradians and multiple scattering at the threshold momentum 2.957 milliradians. The budget is compared with published muography of the same class of target, for which muography campaigns at Vesuvius with the MURAVES detector have reported density structure in the upper cone after exposures of many months with detectors of order one square metre. Every number is computed by the accompanying script from the stated inputs. Computed, not measured.