Abstract
The article is focused on the approach based on the discrete mathematical analysis conception and continues a series of studies related to the application of the previously developed methodology to geophysical data analysis. The main idea of the study is the modification of earlier conceptions regarding the interpreter’s logic that allows introducing a multiscale approach and performing the time series analysis using the activity measure plots, implying the vertical scale. This approach was used to study the morphology of several intense geomagnetic storms at the final stages of the 23rd and 24th solar activity cycles. Geomagnetic observatory data and interplanetary magnetic field parameters as well as the solar wind flux speed and proton density were analyzed for each of the studied storms using the activity measures. The developed methods, applied to geomagnetic storm morphological analysis, displayed good results in revealing the decreases and increases in various durations and intensities during storms, detecting low-amplitude disturbances, and storm sudden commencement recognition. The results provide an opportunity to analyze any physical data using a unified scale and, in particular, to implement this approach to geomagnetic activity studies.
Highlights
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
The practical part is focused on the geomagnetic storm analysis using the activity measure (10) for the “energy” and “length” properties
Summary
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. 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. 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
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