# A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures
## 1 Introduction
Let us name the most important of them today: energy \(E\) (dispersion and continuity), spread \(O\) (Cauchy fundamentality), jaggedness \(L\) (frequency and length), and increase rate \(G\) (modulus of the derivative). Their set is open for replenishment. This is determined by practice and gives great flexibility to the analysis of data records using DMA. The second stage of the DMA-based studies of data records is focused mainly on geomagnetism (in particular, search for the patterns of known waveform in INTERMAGNET observatory data [12]). A meaningful analysis of the geomagnetic data records presupposes taking into account a whole complex of parameters and cannot be reduced to a quantitative approach using a single straightening. It requires a set of straightenings and their integration into a single point of view. This cannot be done mechanically due to the fact that the straightenings of different natures are initially incomparable. The solution found was to proceed from a record straightening to its activity measure. The activity measure shows the level of the expert's interest in the data record behavior in one or another point, based on the selected straightening [13] within a fuzzy scale ([0, 1] or [-1,1]). This two-step transition \"data record \(\rightarrow\) straightening \(\rightarrow\) activity measure\" completely translates the DMA-based studies of data records into the language of fuzzy sets, which immediately opens up new opportunities for these studies. Let us discuss two of them. The first one: it becomes possible to formalize the expert's complex point of view on the record. The \"straightening \(\rightarrow\) activity measure\" transition translates the data analysis into the fuzzy mathematics language: the measures of activity for different straightenings take values in a single fuzzy scale ([0, 1] or [-1, 1]) and can be combined in any compositions and any quantities with the help of numerous operations of fuzzy logic and all kinds of averaging, and, therefore, are able to model the activity measure for a complicated view of an expert at the record. All of this led to the new geomagnetic activity indicators [13; 14]. The second one: measures of activity of various records and, moreover, of a completely different nature, express the same essence, namely, the expert's interest in them. Therefore, if the records cannot be directly compared, then their activity measures can be. This circumstance served as the basis for DMA-based monitoring of geophysical processes, which is understood as a system of geophysical data records [15; 16]. Thus, at the second stage, the focus on DMA-based data records studies shifted to the analysis of their activity measures, which, together with parallel achievements in DMA clustering (DPS algorithm), made it possible to largely solve the problem of recognizing anomalies [13]. Summarizing the results of the second stage of the DMA-based studies of records, we should note that DMA was the one of the origins of the functions of the MAGNUS system designed for geomagnetic information acquisition, processing, storage and analysis [17; 18]. The third stage: DMA-based studies of data records in the first two stages represent a sequential improvement in the formalization of the expert's logic. The main thing here is the expert with his/her view of the record, including both the property of his/her interest and the scale of its consideration on the record. Therefore, the modeling taking into account this circumstance and its results is necessarily limited. At the third stage, we remove this restriction by studying the relationship between a property and a record in different scales. The idea of different scales, which came from wavelets and fractals, makes the property, and not the expert, the main thing in the analysis of the recording. This makes it possible to understand the connection between them more fully and objectively. The first step in this direction is the construction of a multiscale activity measure for a given property of an analyzed record.