# A Method for Recognition of Sudden Commencements of Geomagnetic Storms Using Digital Differentiating Filters

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Formulation of the SC Recognition Problem—Maximum Amplitude Derivatives and a Decision-Making Rule

_{0}is also the sub-interval size, and ${n}_{f}$ is the total number of sub-intervals with ${n}_{f}\mathsf{\Delta}{i}_{0}={N}_{f}$. For each sub-interval $n$, we calculate the absolute values of the derivatives $\left|{H}_{Nd,rp}^{\circ}\left(T\left(i\right),n\right)\right|$, ${i}_{1n}\text{}\le \text{}i\le {i}_{2n}$, $r=0,1\dots ,3$, and $p=1,\dots ,{P}_{0}$. Next, we find the maximum amplitude derivative,

#### 2.2. The Procedure for Selecting the Optimal Digital Differentiating Filters

#### 2.3. Computation of Estimates of Probabilities of Correct and False SC Recognition

## 3. Results

#### 3.1. An Example of Optimal Differentiating FIR Filter Selection

- ${k}_{0}$ = 1, ${i}_{d}$ = 2, for m = 1;
- ${k}_{0}$ = 1, ${i}_{d}$ = 3, for m = 2;
- ${k}_{0}$ = 2, ${i}_{d}$ = 4, for m = 3;
- ${k}_{0}$ = 3, ${i}_{d}$ = 5, for m = 4.

#### 3.2. An Example of Estimates of Probabilities of True and False SC Recognitions

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Plots of one-minute-averaged data of the components ${H}_{x}$, ${H}_{y},$ ${H}_{z}$ and the total intensity ${H}_{0}$ of the geomagnetic field strength vector with SC during 22 June 2015.

**Figure 2.**Results of calculating the derivatives of the components and the modulus of the geomagnetic field (nT/min), ASP observatory.

**Figure 3.**Estimated probability of correct (blue line with circles) and false (black line without circles) SC recognition. The red dashed line shows the optimal threshold value.

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**MDPI and ACS Style**

Getmanov, V.; Sidorov, R.; Gvishiani, A.
A Method for Recognition of Sudden Commencements of Geomagnetic Storms Using Digital Differentiating Filters. *Appl. Sci.* **2022**, *12*, 413.
https://doi.org/10.3390/app12010413

**AMA Style**

Getmanov V, Sidorov R, Gvishiani A.
A Method for Recognition of Sudden Commencements of Geomagnetic Storms Using Digital Differentiating Filters. *Applied Sciences*. 2022; 12(1):413.
https://doi.org/10.3390/app12010413

**Chicago/Turabian Style**

Getmanov, Victor, Roman Sidorov, and Alexei Gvishiani.
2022. "A Method for Recognition of Sudden Commencements of Geomagnetic Storms Using Digital Differentiating Filters" *Applied Sciences* 12, no. 1: 413.
https://doi.org/10.3390/app12010413