Muon Sensitivity Budgets for Internal Erosion in Flood-Defence Embankments

This paper computes the muon attenuation, exposure and resolution budget for imaging a flood-defence embankment with cosmic-ray muons. Sight lines through 12 metres of compacted earth and clay at a density of 1.9 grams per cubic centimetre present an opacity of 2280 grams per square centimetre (22.8 metres of water equivalent), which sets a minimum muon energy of 4.578 GeV and a transmitted vertical intensity of 6.907 per square metre per second per steradian. For a detector of 0.5 square metres with the stated acceptance and efficiency, divided among 120 image elements, the stated feature produces a flux contrast of 0.6101 and reaches five standard deviations in 0.04539 days of counting, while the target precision of 0.05 per image element requires 0.2704 days. A deployment of 45 days delivers a per-element precision of 0.003876, corresponding to a thickness sensitivity of 0.04651 metres. The combined angular resolution is 32.3 milliradians, of which tracking contributes 2.357 milliradians and multiple scattering at the threshold momentum 32.22 milliradians. The budget is compared with published muography of the same class of target, for which muon imaging trials on embankments and levees have reported sensitivity to internal density structure and moisture-driven density change. Every number is computed by the accompanying script from the stated inputs. Computed, not measured.