Unfolding Density

In this note we outline a procedure for determining the mass density of material surrounding the muon detector by comparing measured muon fluxes with reference or background data-sets and adjusting a set of parameters which describe the density to achieve a best overall agreement between signal and background fluxes. Information on muon fluxes is stored in “data-cubes” which are histograms giving the numbers of detected or simulated muon tracks nt accumulated over a given period of time in bins of the measured track parameters t = {φt, cot θt, zt, bt} [1, 2]. The distribution and density of material surrounding the detector will affect the measured values of nt . Using techniques of computed tomography (CT), measured fluxes can be used to unfold material density ρv in suitably chosen 3D voxels (indexed by v) located in the vicinity of the detector. To do so, one compares the numbers of tracks nt found in data-cube cells with fluxes (described by bt) determined from reference or background sets where the voxel material densities are described by reference values ρ0v . The unfolding procedure outlined here seeks to determine differences in densities ∆ρv = ρv − ρ0v. Various approaches are suggested for determining background fluxes needed to infer densities: