# Assessment of the Influence of Astronomical Cyclicity on Sedimentation Processes in the Eastern Paratethys Based on Paleomagnetic Measurements Using Discrete Mathematical Analysis

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

- Time series analysis, including spectral analysis (Fourier, spectrogram, and wavelet analysis), autocorrelation, cross-correlation, smoothing, filtering, and extremum search.
- Multivariate data analysis, including multivariate distributions and cluster analysis.
- Statistical methods, such as statistical distributions, correlation, regression, and chi-square tests.
- Neural networks (including deep learning neural networks).

#### 2.1. Classical Spectral Methods

#### 2.2. DMA-Algorithm for the Identification of Periods in Data Arrays

_{m}{f, T, t}.

_{p}with a positive exponent p of the sequence |∆{f, T, t}|:

_{p}|∆{f, T, t}|.

_{p}, C indicates the proximity of the sequence |∆{f, T, t}| to zero.

_{|}

_{∆{f,}

_{T}

_{,}

_{t}

_{}|}:

_{|}

_{∆{f,}

_{T}

_{,}

_{t}

_{}|}.

_{p}:

_{p}(C(f, T, t), t ∈ [a, a + T)), p ≥ 0.

#### 2.3. Time Series for the Demonstration of the Efficiency of the Algorithm

#### 2.4. Magnetic Susceptibility Data of Zhelezny Rog Cape

## 3. Results

#### 3.1. Demonstration of the Efficiency of the Algorithms

#### 3.2. Identification of Periods in Magnetic Susceptibility Data

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Schwarzacher, W. Mathematical geology and the development of cyclostratigraphy. Geoinformatics
**1993**, 4, 353–356. [Google Scholar] [CrossRef] [Green Version] - Foucault, A. Sedimentary record of orbital cycles, methodology, results and perspectives. Bull. Soc. Geol. Fr.
**1992**, 163, 325–335. [Google Scholar] - Strasser, A.; Hilgen, F.J.; Heckel, P.H. Cyclostratigraphy—Concepts, definitions and applications. Newsl. Stratigr.
**2006**, 42, 75–114. [Google Scholar] [CrossRef] [Green Version] - Agayan, S.M.; Bogoutdinov, S.R.; Krasnoperov, R.I. Short introduction into DMA. Russ. J. Earth Sci.
**2018**, 18, ES2001. [Google Scholar] [CrossRef] [Green Version] - Gvishiani, A.D.; Agayan, S.M.; Bogoutdinov, S.R.; Soloviev, A.A. Discrete mathematical analysis and applications in geology and geophysics. Vestn. KRAUNTs Nauk. Zemle
**2010**, 2, 109–125. [Google Scholar] - Gvishiani, A.D.; Agayan, S.M.; Bogoutdinov, S.R. Discrete mathematical analysis and monitoring of volcanoes. Inzh. Ekol.
**2008**, 5, 26–31. [Google Scholar] - Widiwijayanti, C.; Mikhailov, V.; Diament, M.; Deplus, C.; Louat, R.; Tikhotsky, S.; Gvishiani, A. Structure and evolution of the Molucca Sea area: Constraints based on interpretation of a combined sea-surface and satellite gravity dataset. Earth Planet. Sci. Lett.
**2003**, 215, 135–150. [Google Scholar] [CrossRef] - Bogoutdinov, S.R.; Gvishiani, A.D.; Agayan, S.M.; Soloviev, A.A.; Kihn, E. Recognition of disturbances with specified morphology in time series. Part 1: Spikes on magnetograms of the worldwide INTERMAGNET network. Izv. Phys. Solid Earth
**2010**, 46, 1004–1016. [Google Scholar] [CrossRef] - Gvishiani, A.; Soloviev, A.; Krasnoperov, R.; Lukianova, R. Automated Hardware and Software System for Monitoring the Earth’s Magnetic Environment. Data Sci. J.
**2016**, 15, 18. [Google Scholar] [CrossRef] - Soloviev, A.A.; Bogoutdinov, S.R.; Agayan, S.M.; Gvishiani, A.D.; Kihn, E. Detection of hardware failures at INTERMAGNET observatories: Application of artificial intelligence techniques to geomagnetic records study. Russ. J. Earth Sci.
**2009**, 11, ES2006. [Google Scholar] [CrossRef] - Gvishiani, A.D.; Lukianova, R.Y. Geoinformatics and observations of the Earth’s magnetic field: The Russian segment. Izv. Phys. Solid Earth
**2015**, 51, 157–175. [Google Scholar] [CrossRef] - Gvishiani, A.D.; Mikhailov, V.O.; Agayan, S.M.; Bogoutdinov, S.R.; Graeva, E.M.; Diament, M.; Galdeano, A. Artificial intelligence algorithms for magnetic anomaly clustering. Izv. Phys. Solid Earth
**2002**, 38, 545–559. [Google Scholar] - Gvishiani, A.D.; Dzeboev, B.A.; Agayan, S.M. FCAZm intelligent recognition system for locating areas prone to strong earth-quakes in the Andean and Caucasian mountain belts. Izv. Phys. Solid Earth
**2016**, 52, 461–491. [Google Scholar] [CrossRef] - Gvishiani, A.D.; Agayan, S.M.; Bogoutdinov, S.R.; Zlotnicki, J.; Bonnin, J. Mathematical methods of geoinformatics. III. Fuzzy comparisons and recognition of anomalies in time series. Cybern. Syst. Anal.
**2008**, 44, 309–323. [Google Scholar] [CrossRef] - Lomb, N.R. Least-squares frequency analysis of unequally spaced data. Astrophys. Space Sci.
**1976**, 39, 447–462. [Google Scholar] [CrossRef] - Schulz, M.; Mudelsee, M. REDFIT: Estimating red-noise spectra directly from unevenly spaced paleoclimatic time series. Comput. Geosci.
**2002**, 28, 421–426. [Google Scholar] [CrossRef] - Lisiecki, L.E.; Raymo, M.E. A Pliocene-Pleistocene stack of 57 globally distributed benthic δ 18O records. Paleoceanography
**2005**, 20, 1–17. [Google Scholar] [CrossRef] [Green Version] - Rybkina, A.I.; Rostovtseva, Y.V. Astronomically-tuned cyclicity in Upper Maeotian deposits of the Eastern Paratethys (Zheleznyi Rog Section, Taman). Mosc. Univ. Geol. Bull.
**2014**, 69, 341–346. [Google Scholar] [CrossRef] - Rostovtseva, Y.V.; Rybkina, A.I. The Messinian event in the Paratethys: Astronomical tuning of the Black Sea Pontian. Mar. Pet. Geol.
**2017**, 80, 321–332. [Google Scholar] [CrossRef] - Hammer, Ø.; Harper, D.A.T. Paleontological Data Analysis; Blackwell Publishing: Hoboken, NJ, USA, 2005; Volume 351. [Google Scholar] [CrossRef]
- Carbonell, M.; Oliver, R.; Ballester, J.L. Power spectra of gapped time series: A comparison of several methods. Astron. Astrophys.
**1992**, 264, 350–360. [Google Scholar] - Zgurovsky, M.Z.; Pankratova, N.D. System Analysis: Theory and Applications (Data and Knowledge in a Changing World); Springer: Berlin/Heidelberg, Germany, 2007; Volume 447. [Google Scholar] [CrossRef]

**Figure 1.**Temporal fluctuations of the isotopic composition of precipitation [17].

**Figure 2.**Magnetic susceptibility of deposits of the Zhelezny Rog Cape section: (

**a**) Lower-Upper Pontian; (

**b**) Lower Maeotian.

**Figure 3.**(

**a**) Fourier and Lomb periodograms; (

**b**) REDFIT spectrum. Constructed for the time series in Figure 1.

**Figure 5.**The results of applying spectral methods to the magnetic susceptibility data from the Lower-Upper Pontian deposits of the Zhelezny Rog Cape section (Figure 2a): (

**a**) Fourier and Lomb periodograms (the black bold solid line indicates the 95% confidence interval for the Lomb periodogram); (

**b**) the spectrum constructed by the REDFIT algorithm (the black bold solid line indicates the 95% confidence interval).

**Figure 6.**The results of applying spectral methods to the magnetic susceptibility data of the Lower Maeotian deposits of the Zhelezny Rog Cape section (Figure 2b): (

**a**) Fourier and Lomb periodograms (the black bold solid line indicates the 95% confidence interval for the Lomb periodogram); (

**b**) the spectrum constructed by the REDFIT algorithm (the black bold dotted line indicates the 95% confidence interval).

**Figure 7.**The results of applying the developed DMA-algorithm to identify the periods in the magnetic susceptibility data for rocks of Zhelezny Rog Cape: (

**a**) Lower-Upper Pontian deposits; (

**b**) Lower Maeotian deposits. The calculated constancy exponent of the series is shown in blue (construction—dispersion, see above). The ‘strongly’ smoothed version is shown in red.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Dzeboev, B.A.; Odintsova, A.A.; Rybkina, A.I.; Dzeranov, B.V.
Assessment of the Influence of Astronomical Cyclicity on Sedimentation Processes in the Eastern Paratethys Based on Paleomagnetic Measurements Using Discrete Mathematical Analysis. *Appl. Sci.* **2022**, *12*, 580.
https://doi.org/10.3390/app12020580

**AMA Style**

Dzeboev BA, Odintsova AA, Rybkina AI, Dzeranov BV.
Assessment of the Influence of Astronomical Cyclicity on Sedimentation Processes in the Eastern Paratethys Based on Paleomagnetic Measurements Using Discrete Mathematical Analysis. *Applied Sciences*. 2022; 12(2):580.
https://doi.org/10.3390/app12020580

**Chicago/Turabian Style**

Dzeboev, Boris A., Anastasia A. Odintsova, Alena I. Rybkina, and Boris V. Dzeranov.
2022. "Assessment of the Influence of Astronomical Cyclicity on Sedimentation Processes in the Eastern Paratethys Based on Paleomagnetic Measurements Using Discrete Mathematical Analysis" *Applied Sciences* 12, no. 2: 580.
https://doi.org/10.3390/app12020580