Study of Small Variations in the Cosmic-Ray Muon Flux in the Atmosphere

This paper presents a method for analyzing data from cosmic-ray muon detectors, enabling the detection of subtle flux variations that are indistinguishable in the integral muon count rate. The complete mathematical framework of the method is provided. It requires detectors capable of distinguishing muons by their azimuthal arrival angles and, for optimal performance, multiple independent detectors with similar characteristics. A key feature of the proposed approach is that it considers not only the amplitude of the signal (reflecting muon flux variations) but also its direction, which can be correlated with the spatial characteristics of sources of variation, such as atmospheric phenomena. Each step of the method is illustrated using the example of a warm front approaching Moscow, as well as an atmospheric event accompanied by a cloud line. Additionally, the paper presents a visualization of data for the new method that allows a large amount of data to be reduced to a single diagram that can be plotted on satellite images and the observed muon variations to be compared with atmospheric phenomena in situ.