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Forbush effects caused by powerful X-class solar flares are studied using URAGAN muon hodoscope data for the period 2007–2019. The URAGAN muon hodoscope registers the cosmic ray muon flux on the Earth’s surface from different directions simultaneously. This allows study of the energy, angular, and space–time characteristics of variations in the cosmic ray muon flux during Forbush effects. The dependence of the measured Forbush effects on the parameters of heliospheric and geomagnetic disturbances is analyzed.

Variations of secondary cosmic rays on the Earth’s surface depend on the solar activity. To study these variations, neutron monitors and muon detectors are used. Observations of muons and hadrons complement each other in terms of the energies of the primary cosmic rays and their angular distribution. Muons save the direction of the motion of primary particles and make it possible to obtain the angular distribution of cosmic ray modulations using a single setup—as a muon hodoscope. This paper presents a comparison of variations of muon and neutron components of cosmic rays at the Earth surface at different phases of the solar activity in the period from 2008 to 2018. For the comparison, data of two neutron monitors (Moscow and Apatity stations) and the muon hodoscope URAGAN were used.

Cross-correlation between observation matrixes of the URAGAN muon hodoscope and the Dst index was studied. Functions of total intensity and anomaly were introduced. The results of calculations of cross-correlations on 2D diagrams were considered. It was shown that time periods with increased geomagnetic activity were almost always preceded by time periods with increased values of the modulus of the Pearson correlation coefficient.

A method for elimination of periodical diurnal, annual, and 27-day and 11-year solar variations in the matrix observations of the URAGAN muon hodoscope was developed. The analysis of the parameters of these variations in the time and frequency domains was performed. Two-dimensional bandpass filtering of sequences of muon hodoscope matrix observations was implemented. The structure of a two-dimensional filter is developed, based on the operation of elementwise matrix multiplications and additions. Examples of eliminating variations in the URAGAN muon hodoscope matrix observations are discussed.

This paper presents a method for identifying heliospheric anomalies using the introduced function of characteristic deviations for the muon hodoscope matrices. The estimation of the averaged hardware function is considered. Spatial filtering is proposed to eliminate fluctuations in the functions of the characteristic deviations. An example of the implementation of the developed method using the example of the storm July 13, 2017. It is shown that for this event, the identified anomaly precedes by several hours a sharp increase in the Kp index.

Results of investigation of the high-energy cosmic-ray flux anisotropy using data on muon bundles are presented. The events were recorded in the period of 2013–2017 with the DECOR coordinate-tracking detector, which is a part of the unique scientific setup of the Experimental complex NEVOD. Methods for experimental data processing and taking atmospheric effects into account are described. Results of the analysis of two types of muon bundle events, which correspond to different ranges of primary particle energies (E > 1015 eV and E > 1016 eV) are discussed. Upper limits of the anisotropy amplitude for the two types of events are obtained.

The method of flicker-noise spectroscopy is used for remote identification of geoeffective disturbances of the solar wind. The method is based on the study of short-term variations in the cosmic-ray flux that arise when it crosses the perturbed regions in the inner heliosphere. The magnitude of the effect is usually small and it is hidden in statistical noise. The analysis uses data from a continuous flux of secondary atmospheric muons. Bumps of the “nonstationarity” parameter of time series of muons indicate the emergence of advanced signals (predictors) 1–3 days before the disturbances enter the Earth’s magnetosphere. Geoeffective events with a low threshold (Ap > 30 nT) for various types of solar wind are analyzed. The results are obtained using a ground-based muon hodoscope URAGAN (Moscow). The technique can be used for continuous monitoring of space weather.

Problems of digital processing of Poisson-distributed data time series from various counters of radiation particles, photons, slow neutrons etc. are relevant for experimental physics and measuring technology. A low-pass filtering method for normalized Poisson-distributed data time series is proposed. A digital quasi-Gaussian filter is designed, with a finite impulse response and non-negative weights. The quasi-Gaussian filter synthesis is implemented using the technology of stochastic global minimization and modification of the annealing simulation algorithm. The results of testing the filtering method and the quasi-Gaussian filter on model and experimental normalized Poisson data from the URAGAN muon hodoscope, that have confirmed their effectiveness, are presented.

Muon flux intensity modulation (MFIM) recognition is a relevant solar-terrestrial physics problem. The MFIM discussed are due to geoeffective solar coronal mass ejections.The necessary observations are carried out using a computerized muon hodoscope (MH) URAGAN developed by NRNU MEPhI, registering muon fluxes intensity. In the MH, the number of muons falling on its aperture per unit time is counted. MH matrix data time series are formed, in which angular and temporal modulations take place due to MH design features, athmospheric disturbances and noises, the values of which significantly exceed the MFIM values.The MFIM recognition method based on the mathematical apparatus of indicator matrices (IM) and spatial-temporal filtering is proposed.The time series of MH matrix data, consisting of a set of Poisson processes corresponding to azimuthal and zenithal elements of MH matrices, are considered.A reference time span is assigned where MFIM are known to be missing. For it, matrices of estimates of mathematical expectations are calculated and, taking into account the Poisson property, the matrices of reference confidence intervals are calculated. Next, the current time sections are formed, on which the matrices of the current confidence intervals are calculated. Based on the comparison of the matrices of the reference and current confidence intervals, the current matrices of anomalies are formed, which are compared with the specified threshold matrix. Thresholds exceedings correspond to anomalous events. Binary IM are formed: ones correspond to anomalous events, zeros correspond to the absence of anomalies. Recognition is to analyze IM sequence and identify areas of non-zero elements condensation that lead to the conclusion that there are significant MFIM. To reduce the recognition errors, the space-time IM filtering has been developed.MFIM recognition technique, based on the use of IM time series with spatial-temporal filtering has been tested on model and experimental MH data.Testing on the generated time series of model Poisson MH matrix data with model MFIM confirmed the conclusion about the possibility of MFIM recognition by the proposed method with a decrease level of 3-4%. Application of spatial-temporal filtering made it possible to recognize MFIM with decreases with a level half as much.Testing on the formed experimental matrix MH data time series with model MFIM led to a conclusion that it is possible to recognize MFIM with the magnitudes of decreases almost commensurate with the decreases for the case of model MH data.The proposed MFIM recognition method based on indicator matrices for MH observation data allows optimization of parameters and can be successfully applied to solve problems of MFIM recognition and early diagnostics of geomagnetic storms.

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.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.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.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.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.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.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.