A method for recognizing the muon flux intensity modulations using the normalized variation functions for the URAGAN hodoscope matrix data

<p>Muon flux intensity modulation (MFIM) recognition is a relevant solar-terrestrial physics problem. The considered MFIM, recorded on the Earth's surface, are caused by extreme heliospheric events – the geoeffective solar coronal mass ejections.</p><p>The URAGAN muon hodoscope (MH), developed by NRNU MEPhI, a computerized device that measures the intensities of muon fluxes, is used. In the MH, the number of muons falling per unit time on the MH aperture is calculated for the selected system of zenith and azimuthal angles. MH matrix data time series are formed. In the MH data, there are angular modulations due to the action of the hardware function HF, temporal modulations due to atmospheric disturbances and noise: the values of these modulations significantly exceed the values of MFIM of cosmic origin. This circumstance prevents effective MFIM recognition.</p><p>A method for MFIM recognition is proposed, based on the mathematical apparatus of the introduced normalized variation functions for MH matrix data, and focused on overcoming the noted circumstance.</p><p>A two-dimensional normalized HF is defined for MH. A quite realistic hypothesis is accepted about the initialiy uniform muon flux intensity distributions on a small reference time interval, where there are no extreme heliospheric events and the corresponding reference MH data do not contain significant MFIMs. The estimation of the two-dimensional normalized HF is carried out on the basis of a multiparameter model and its optimization fit to the reference MH data. In order to reduce noise errors, the estimate of the two-dimensional normalized HF is subjected to two-dimensional filtering and subsequent threshold filtering.</p><p>Two-dimensional functions of variations of matrix MH datas with respect to two-dimensional normalized AF are calculated. The normalized variation functions are calculated by dividing the two-dimensional functions of variations of matrix MH data by the two-dimensional normalized HF. MFIM recognition method was tested on model and experimental MH data.</p><p>A time series of model matrix MH data containing model MFIM was generated. Testing led to a conclusion that it is possible to recognize MFIM with decreases of about 2-3%. A time series of experimental matrix MH data was generated, in which the model MFIM-containing areas were made. Testing led to a conclusion that it is possible to recognize MFIM with the magnitudes of the decreases almost commensurate with the decreases for the case of model MH data.</p><p>The proposed MFIM recognition method based on the normalized variation functions for matrix MH data has a favorable perspective for its application in solving problems of geomagnetic storm early diagnostics.</p>