The suggested method is aimed at studying the dynamics of the magnetospheric current systems during magnetic storms. The method is based on algorithmic solutions for processing of geomagnetic field variations, detection of local increases in geomagnetic disturbance intensity and estimation of their dynamic characteristics. Parameters of the algorithms allow us to evaluate the characteristics of small-scale local features emerging during geomagnetic activity slight increases and large-scale variations observed during magnetic storms. To evaluate the method, geomagnetic data from the stations located in the north-east of Russia and equatorial India were used. The method testing showed the possibility to apply it for the detection of pre-storm anomalous effects in geomagnetic data.
Image Processing, Geoinformation Technology and Information Security / O. Mandrikova et al.
terms of wavelets, the authors of this paper suggested a new model of geomagnetic field variations [
In the papers [
n jD n jD n where j j,n n is the wavelet-basis, j j,n n is the basis, obtained from a scaling function, coefficients c j,n (1) and d j,n are defined from the equations: c j,n f , j,n , d j,n f , j,n , D is a set of indices of the disturbed components, j is the scale, the inferior index «0» denotes that the initial discrete data belong to a domain of scale «0».
Component ftrend (t) c6,n 6,n (t) describes the undisturbed level of the horizontal component of the Earth magnetic n field during quiet geomagnetic field, and the component f dist (t ) g j (t ) where g j (t) d j,n j,n (t) describes jD n where m is the sample mean, v is the index of disturbed field variation, k is the index of calm field variation, and is a positive number.
Assuming that Aj and A kj
are normally distributed with mean , k , k and variances 2, , 2,k , it is possible to estimate j as j x1a / 2 ,
where kj is the variance of the greatest wavelet coefficients (for scale j ) for kj
n k quiet days (this variance is determined as a result of multiple measurements); x1a / 2 is the 1 a / 2 quintile of the standard normal distribution; nk is the number of analyzed quiet-field variations. If a 0.1 , the confidence probability is 1 a / 2 0.95 , the quintile is x1a / 2 1.96 , and j 1.96
The measure of geomagnetic disturbance of the component g j (t) on the scale j is [
.
Aj max d j,n .
n
Taking into account that the component f dist (t ) g j (t ) , where g j (t) d j,n j,n (t) describes the disturbances
jD n
(see relation (1)), and the equivalence of discrete and continuous wavelet decompositions, in order to obtain more detailed
information on the properties of the function f under analysis, continuous wavelet transform may be applied [
In this case, when a scale a vanishes, the wavelet coefficients
function f in the vicinity of the instant time t b [
W f b, a characterize the local properties of the
Following the relation (3) as a measure of geomagnetic disturbance intensity, it is logical to consider the wave coefficient amplitude the case of field negative disturbances (variation decrease relatively the characteristic level), I b value is negative.
To distinguish the periods of increased geomagnetic activity, the following threshold function is applied: W fb,a , если W fb,a Ta PTa (W fb,a ) 0, если W fb,a Ta , W fb,a , если W fb,a Ta where Ta U * St l a is the threshold function where St l a the time window length, W f b,a is the average value, U is the threshold coefficient.
It is obvious that the parameters of function (5), the window length l and the threshold coefficient U , are adjustable and determine the size of a time window within which geomagnetic disturbances are estimated and the level of determined geomagnetic disturbances (we applied the window length of l 1440 that corresponds to 24 hours and the threshold coefficient U 7 ).
To estimate the intensity of the detected disturbances at an instant time t b according to the paper [
d
and taking into account that a wavelet is a window function [
Based on the suggested method, we processed and analyzed the data from the sites in the north-eastern segment of Russia
(Table 1). To analyze the processes in the magnetosphere at the near equatorial latitudes, the data of the Indian HYB
“Hydarabad” and CPL “Choutuppal” sites were used. The considered events and the results of application of the developed
method for detection of anomalous increases of geomagnetic disturbance intensity before magnetic storms is shown in Table 2.
Analysis of the results of Table 2 indicates the possibility of occurrence of weak geomagnetic disturbances before magnetic
storms, which was first mentioned in the papers [
Note: site affiliation is indicated in brackets (1) – IKIR FEB RAS, (2) – CSIR-National Geophysical Research Institute.
Fig 1. Processing results of the data for January 7, 2015; a) Bz component of the Interplanetary Magnetic Field; b) AE-index (yellow line), AU-index (blue line) and AL-index (red line); c) Dst-index; d) H-component of the magnetic field; e) geomagnetic disturbance intensity (relation (5)); f) dynamic spectrum of geomagnetic disturbance intensity.
Fig. 1 shows the results of processing of geomagnetic data during the magnetic storm on January 7, 2015. This event was caused by coronal ejection of solar material (CME on January 4, http://ipg.geospace.ru/space-weather-review-07-01-2015.html). Its dynamics was of classical character with clearly defined major phases of a storm in Dst-variation (Fig. 1c). The results of estimation the geomagnetic disturbance intensity shows that during the initial stage of the storm, from about 07:00 UT, geomagnetic activity gradually increased and the Dst-index had positive values. Maxima of disturbance intensity (Fig. 1e) are observed during Dst-index decrease and AE-index increase characterizing the occurrence of an intensive substorm in the auroral zone. The dynamic spectrum of geomagnetic disturbance intensity (relation (5)) illustrated in Fig. 1f shows the regions of disturbance concentration and propagation in the areas under analysis. During the event, a general picture of the dynamics of magnetospheric current systems is observed. The beginning of the storm from 6:00 to 08:00 UT was the most clearly defined at the near equatorial site (India). During the main phase of the storm, activation areas are observed in the dynamic spectra of all the sites (Fig. 1f; red color is the intensity increase; blue color is the intensity decrease). They are likely to characterize largescale processes in the magnetosphere probably associated with energy accumulation and release during the event. At the most northern site Magadan, local regions (from 10:00 to 11:00 UT) are distinguished. They are likely to be associated with aurora l processes.
Fig. 2 shows the data processing for the magnetic storm on August 15, 2015 which was caused by a solar medium coronal mass ejection (CME on August 12) and high-velocity flows from a coronal hole (CIR). The magnetic storm began at 08:30 UT during a sharp increase of solar wind velocity and increase of the magnetic field horizontal component at all the sites under analysis. Short-period anomalous increases of geomagnetic activity began about 12 hours before the magnetic storm (Fig. 2e). The highest values of geomagnetic disturbance intensity are observed at the sites during the main phase of the storm (the period of significant decrease of Dst-indes). The wavelet spectrum of geomagnetic disturbance intensity shows that geomagnetic field
Image Processing, Geoinformation Technology and Information Security / O. Mandrikova et al. disturbances at all the sites increased in the vicinity of special points (points of local extreme periods, function inflection) of Dst-variation (08:00-10:00; 11:00-13:00 UT). It indicates active processes in the magnetosphere at these time periods. The disturbances at the near equatorial site CPL had the most clearly defined character.
The results of application of the developed method for detection of pre-storm anomalies of geomagnetic disturbance intensity increases are illustrated on the example of the event on August 15, 2015 in Fig. 3. Analysis of Fig. 3e shows synchronous anomalous increases of geomagnetic activity 18 hours before the magnetic storm. Several minutes before registration of the event at the sites, short-time geomagnetic disturbance intensity significantly increased and reached the maximum values during the initial phase.
A detailed analysis of geomagnetic data during strong magnetic storms in 2015 was carried out by the suggested method.
The dynamic spectrum of geomagnetic disturbance intensity showed spatial pattern of the events and allowed us to analyze
geomagnetic disturbance propagation along the observation meridian and at the near equatorial sites. During the main phases of
the storms, activation areas were detected. They have large spatial scales and are likely to be associated with the processes of
energy accumulation and release in the magnetosphere. Before the events, synchronous local increases of geomagnetic activity
were observed at the sites under analysis. They are likely to be associated with nonstationary effect of solar wind plasma on the
Earth magnetosphere in the course of an interplanetary disturbance approaching. Such anomalous pre-storm effects are
mentioned in the papers [
The development of the method for geomagnetic data analysis was supported by RSF Grant № 14-11-00194. The data primary analysis was supported by RFBR Grant № 16-55-45007. The authors are grateful to the Institutes supporting the magnetic observatories which data were used in the investigation.