Recent studies suggest that the secular variation dynamics of geomagnetic field exhibits periodic patterns indicate underlying wave processes in Earth’s core. However, as long analytical core models are based on geographically sparse and noisy observatory data, they have apparent limitations for studying fine structure its spatiotemporal variations. The advent satellite measurements full vector 1999 removed this limitation made it possible to produce reliable highly accurate...

Results of Euler deconvolution strongly depend on the selection viable solutions. Synthetic calculations using multiple causative sources show that solutions cluster in vicinity bodies even when they do not group densely about perimeter bodies. We have developed a clustering technique to serve as tool for selecting appropriate The uses methodology based artificial intelligence, and it was originally designed classify large data sets. It is geometrical approach study object concentration...

In this paper, a new approach to the detection of anomalies in geophysical records is connected with fuzzy mathematics application. The theory discrete mathematical analysis and collection algorithms for time series processing constructed on its basis represents results research direction. These are consequence modeling logic an interpreter who visually recognizes records. They allow analyzing large data sets that not subjected manual processing. efficiency these demonstrated several...

<p class="p1"><span class="s1">The discrete mathematical analysis (DMA) is a series of algorithms aimed at the solution basic problems data analysis: clustering and tracing in multidimensional arrays, morphological reliefs, search for anomalies trends records etc. All DMA are universal nature, joined by same formal foundation, based, its turn, on fuzzy logic (FL) mathematics (FM).</span> class="p2"><span current study finalizes one-dimensional time within scope DMA: here initial concept an...

In the present paper we apply a recently developed pattern recognition algorithm SPs to problem of automated detection artificial disturbances in one-second magnetic observatory data. The relies on theory discrete mathematical analysis, which has been by some authors for more than 10 years. It continues authors’ research morphological analysis time series using fuzzy logic techniques. We show that, after learning phase, this is able recognize spikes uniformly with low probabilities target...

Herein, we present a newly developed indicator for estimating geomagnetic activity. It is based on the magnitude of measure anomalousness (MA) magnetometer recordings at given time or interval. intended automated estimation activity level in area specific magnetic station region using data set stations. reflects different observatories single scale [-1, 1], regardless their latitudinal location and consequently typical disturbance amplitudes. To certain extent MA an analog traditional K...

The method of analyzing data known as Discrete Mathematical Analysis (DMA) incorporates fuzzy mathematics and logic. This paper focuses on applying DMA to study the morphology time series by utilizing language mathematics. morphological characteristics series, such background, slopes, vertices, are considered sets within domain its definition. allows for use logic in examining ultimately leading detection anomalies.

The authors develop the theory of discrete differentiation and, on its basis, solve problem detecting trends in records, using idea connection between and derivatives classical analysis but implementing it fuzzy logic methods. solution to this is carried out by constructing measures trend extremum for a recording. theoretical justification regression approach continuous case given work provides an answer question what is, which used extremum. detection more stable higher quality than...

The article addresses the issue of clustering multidimensional data arrays with a noise using methods discrete mathematical analysis (DMA clustering). theory DMA through logical densities calculus is detailed, and new algorithm Linear Discrete Perfect Sets (LDPS) described. main objective LDPS to identify linearly stretched anomalies in array geo-spatial (geophysical fields, geochemistry, satellite images, local topography, maps recent crustal movements, seismic monitoring data, etc.). These...

The results presented in this paper are obtained as part of the continued development and research clustering algorithms based on discrete mathematical analysis. article briefly describes theory Discrete Perfect Sets (DPS-sets) that is basis for construction DPS-clustering algorithms. main task previously constructed DPS-algorithms to search clusters multidimensional arrays with noise. have two stages: first stage recognition maximum perfect set a given density level from initial array,...

The present paper continues the series of publications by authors devoted to solving problem recognition regions with potential high seismicity. It is aimed at development mathematical apparatus and algorithmic base FCAZ method, designed for effective earthquake-prone areas. A detailed description both algorithms included in its original form those developed this given. Using California as an example, it shown that a significantly makes possible increase reliability accuracy recognition. In...

The article is focused on the approach based discrete mathematical analysis conception and continues a series of studies related to application previously developed methodology geophysical data analysis. main idea study modification earlier conceptions regarding interpreter’s logic that allows introducing multiscale performing time using activity measure plots, implying vertical scale. This was used morphology several intense geomagnetic storms at final stages 23rd 24th solar cycles....

Discrete Mathematical Analysis (DMA) is a data analysis method that uses fuzzy mathematics and logic. DMA involves the active participation of researcher in study records, offering technologies algorithms for analyzing records through properties interest to researcher. In present work, such are related regression derivatives, results obtained applied magnetic records. The possibilities morphological geomagnetic storms demonstrated on example three strongest have occurred since beginning...

The Topological Filtering Algorithm, Discrete Perfect Set (DPS) by Agayan et al. (2018), was developed within the framework of discrete mathematical analysis, which involves fuzzy models analogs fundamental concepts classical analysis. It is designed to select clusters observations according a given criterion (classification belonging one clusters) (Gordon, 1981). In this study, we applied iterative S-DPS modification DPS algorithm (Agayan al., 2022) for sequential extraction linear...

Integration interpretation of geophysical anomalies is a procedure for extracting geological and information about the object under study from observed physical fields. Interpretations are closely related to solutions systems linear algebraic equations (SLAE), therefore possibility most complete constructive description all SLAE particular importance. It will allow you take into account additional obtain highest quality interpretation. The paper presents authors’ results on its application...

Структура дискретного временного ряда тесно связана со свойствами процесса, который он описывает. В рамках математического анализа имеется несколько подходов к анализу структуры дискретных рядов: геометрические меры, динамические коридоры и концепция тренда. Для ряда, заданного в общем случае на нерегулярной сетке, с характером тренда тесным образом регрессионная производная: области ее положительного (отрицательного) значения соответствуют возрастающим (убывающим) трендам, а границы между...

В настоящее время существует ряд способов определения трендов и экстремумов на стохастических временных рядах, что неудивительно, поскольку тренды временного ряда являются фундаментальной характеристикой динамики процесса, стоящего за ним. Реальные стохастические совсем не похожи идеальные математические, посколько в них случаются сбои. Это смущает исследователя, изначально обладающего адаптивным восприятием фундаментальных свойств предельности, непрерывности, связности, тренда т. д. Он...

Регрессионное дифференцирование и регрессионное интегрирование конечных рядов 1 С.М. Агаян, Ш. Р. Богоутдинов, М. Н. Добровольский, О. В

Despite the impressive list of examples integration pattern recognition theory into various activities in development oil and gas fields, authors propose a fundamentally new approach to use artificial intelligence. The paper considers detail algorithm for searching extremity zones, based on discrete mathematical analysis (DMA), as applied problem identifying geological hazards. application method is shown models physical properties rocks reconstructed from seismic data. Potentially, it can...

In this paper, we describe the TeslaSwarm online system [http://aleph.gcras.ru/teslaswarm] for visualizing field-aligned currents in upper ionosphere, using data from Swarm low-orbit satellites. The provides researchers with a simple and convenient tool event selection detailed analysis of electromagnetic fields ionosphere. user can select satellite passages over given region, visualize geomagnetic field structure currents, compare pattern auroral particle precipitation map, OVATION-Prime...