# A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures
## 1 Introduction  
One of the directions of the development of discrete methods for data analysis and discrete mathematics in general is associated with modeling the expert's ability to deal with data. An expert is able to highlight the anomalies in physical data of small dimension, switch from the local level of anomalies to the global one for a holistic interpretation, find the signals of the desired morphology on the data records of a small length, and do so much more efficiently than any formal apparatus, but an expert is powerless in cases of large dimensions and volumes. Our attempts to overcome this contradiction, i.e., to solve the problem of \"algorithmization of an Expert\", began 20 years ago. Solution concept: the advantage of an expert over mathematics is that he/she understands the natural manifestations of fundamental properties of proximity, limit, continuity, connectivity, and trend (forming the basis of data analysis) in a more natural and stable way of perception. Solution technique: the fact that an expert thinks and operates not with numbers, but with fuzzy concepts was immediately taken into account. Therefore, the basis of our approach was formed by fuzzy sets, some of which were models of discrete analogs of the mathematical properties mentioned above as well as fuzzy logic that allows you to combine fuzzy models into data analysis algorithms, in particular, according to the scenarios of classical mathematics. Solution result: the \"discrete mathematical analysis\" (DMA)--a new approach to data analysis--is expert-oriented and an intermediate between \"hard\" mathematical methods and \"soft\" combinatorial ones [1; 2]. The solution to the problem within the DMA framework consists of two parts. The first part is informal. In it, the logic of the expert is analyzed, the necessary concepts are introduced, and the scheme and principles of the solution are explained. The second part has a formal character: with the help of the DMA apparatus, all concepts receive strict definitions in the framework of fuzzy mathematics and fuzzy logic, and the scheme and principles become algorithms. This is how the DMA-based studies of data records began, the informal basis of which was the logic of an expert looking for anomalies on data records [3]. Let us remind the reader: the expert scans the record, evaluating the activity of small (in his/her opinion) fragments of it, similar to each other, with positive numbers. Thus, from the initial data, the expert proceeds to a non-negative function, which is called the straightening of the record since the more active points of the initial data record correspond to the larger values of this function. Further, the expert's search for an anomaly in the data is reduced to the search for extreme values on its straightening. Thus, the expert operates at two levels: local (straightening of a data record), and global (search for extreme values on straightening). The formalization of this logic became the main one in the DMA-based data studies at the first stage. The algorithms DRAS, FLARS, and FCARS [4; 5; 6; 7; 8] created at that time competed quite adequately with the classical spectral analysis algorithms in searching for anomalies, and a number of effective geophysical applications, implementing the new algorithms, was discovered [1; 3; 9; 10; 11]. At the local stage of constructing straightenings, they acted similarly to each other, and at the global stage of searching for maximums on straightening, they acted in different ways. The algorithms allowed the experts to freely understand and select a straightening as a quantitative expression of the property of interest. Nevertheless, reality has shown the stability of the following choice: a set of basic straightenings is formed that most experts would like to deal with. There is a fundamental mathematical concept behind each of them, which confirmed the correctness of our guidelines when creating the DMA.