# A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Initial Data and Assumptions

#### 2.2. Straightening

**Definition**

**1.**

- 1.
- A straightening construction D is a non-negative functional on T, parameterized by T:$$D:\mathfrak{F}\left(T\right)\times T\to {\mathbb{R}}^{+}$$
- 2.
- A straightening of a record f based on the construction D is non-negative function ${D}_{f}$: $t\to D(f,t)$.

#### 2.3. Simple Activity Measure

**Definition**

**2.**

#### 2.4. Complex Activity Measures

#### 2.5. Multiscale Activity Measures and Their Analysis

## 3. Results and Discussion

#### 3.1. Initial Geomagnetic and Interplanetary Data

#### 3.2. General Information on the Analyzed Geomagnetic Storms

#### 3.3. Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

DMA | Discrete Mathematical Analysis |

DPS | Discrete Perfect Sets |

SSC | Storm Sudden Commencement |

IMF | Interplanetary Magnetic Field |

## References

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**Figure 2.**The geomagnetic data and solar wind parameters during a geomagnetic storm of May 2005: HON observatory X component (

**a**), IMF ${B}_{y}$ (

**b**) and ${B}_{z}$ (

**c**) components, solar wind flux speed (

**d**) and proton density (

**e**).

**Figure 3.**The geomagnetic data and solar wind parameters during a geomagnetic storm of December 2006: HON observatory X component (

**a**), IMF ${B}_{y}$ (

**b**) and ${B}_{z}$ (

**c**) components, solar wind flux speed (

**d**) and proton density (

**e**).

**Figure 4.**The geomagnetic data and solar wind parameters during a geomagnetic storm of June 2015: HON observatory X component (

**a**), IMF ${B}_{y}$ (

**b**) and ${B}_{z}$ (

**c**) components, solar wind flux speed (

**d**) and proton density (

**e**).

**Figure 5.**The geomagnetic data and solar wind parameters during a geomagnetic storm of August 2018: HON observatory X component (

**a**), IMF ${B}_{y}$ (

**b**) and ${B}_{z}$ (

**c**) components, solar wind flux speed (

**d**) and proton density (

**e**).

**Figure 6.**The ${B}_{z}$ IMF component (

**a**) and the X magnetic field component from the HON observatory (

**c**) during a geomagnetic storm of May 2005. Below each component is the plot of its activity measure (

**b**,

**d**) based on the “Energy” indicator.

**Figure 7.**The ${B}_{z}$ IMF component (

**a**) and the X magnetic field component from the HON observatory (

**c**) during a geomagnetic storm of December 2006. Below each component is the plot of its activity measure (

**b**,

**d**) based on the “Energy” indicator.

**Figure 8.**The flux speed time series during a storm on 22–29 June 2015 (

**a**) and the activity measure plots for this time series based on indicators: “Energy” (

**b**), and “Length” (

**c**).

**Figure 9.**The X geomagnetic field component data registered during a storm on 26–28 August 2018 (

**a**) and the activity measure plots for these data, based on the “Length” indicator (

**b**).

**Figure 10.**Histograms of the activity measure levels for “Energy” (

**a**) and “Length” (

**b**) indicators built for the X component of geomagnetic observatory data during the storm on 22–29 June 2015.

Storm | Solar | Start Date and Time | End Date and Time | min Dst | SSC Time |
---|---|---|---|---|---|

Number | Cycle | (UTC) | (UTC) | (nT) | (UTC) |

1 | 23 | 2005-05-15 06:00 | 2005-05-19 06:00 | −263 | 02:38 |

2 | 23 | 2006-12-14 23:00 | 2006-12-16 17:00 | −146 | 14:14 |

3 | 24 | 2015-06-22 19:00 | 2015-06-29 01:00 | −204 | 18:33 |

4 | 24 | 2018-08-25 19:00 | 2018-08-28 21:00 | −174 | No SSC |

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**MDPI and ACS Style**

Agayan, S.; Bogoutdinov, S.; Krasnoperov, R.; Sidorov, R.
A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures. *Appl. Sci.* **2021**, *11*, 12120.
https://doi.org/10.3390/app112412120

**AMA Style**

Agayan S, Bogoutdinov S, Krasnoperov R, Sidorov R.
A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures. *Applied Sciences*. 2021; 11(24):12120.
https://doi.org/10.3390/app112412120

**Chicago/Turabian Style**

Agayan, Sergey, Shamil Bogoutdinov, Roman Krasnoperov, and Roman Sidorov.
2021. "A Multiscale Approach to Geomagnetic Storm Morphology Analysis Based on DMA Activity Measures" *Applied Sciences* 11, no. 24: 12120.
https://doi.org/10.3390/app112412120