Skip to main content
SpringerLink
Log in

Regression Derivatives and Their Application to the Study of Geomagnetic Jerks

  • Published:
Geomagnetism and Aeronomy Aims and scope Submit manuscript

Abstract

New mathematical constructions are developed for the regression smoothing of discrete time series defined on an irregular grid. The new method is used to study secular trends for the period 1991–2015 and relies on observations of three components of the magnetic field at five geomagnetic observatories of the INTERMAGNET network. The detected changes in the trend coincided in time with the jerk properties calculated by conventional methods, which indicates the applicability of the method of regression derivatives to geophysical problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.

Similar content being viewed by others

REFERENCES

  1. Agayan, S.M., Bogoutdinov, Sh.R., Gvishiani, A.D., Graeva, E.M., Zlotniki, Zh., and Rodkin, M.V., Study of the signal morphology on the basis of fuzzy logic algorithms, Geofiz. Issled., Moscow: IFZ RAN, 2005, vol. 1, pp. 143–155.

    Google Scholar 

  2. Agayan, S., Bogoutdinov, S., Soloviev, A., and Sidorov, R., The study of time series using the DMA methods and geophysical applications, Data Sci. J., 2016, vol. 15, pp. 1–21. https://doi.org/10.5334/dsj-2016-016

    Article  Google Scholar 

  3. Agayan, S.M., Bogoutdinov, Sh.R., and Krasnoperov, R.I., Short introduction into DMA, Russ. J. Earth. Sci., 2018, vol. 18, ES2001. https://doi.org/10.2205/2018ES000618

    Article  Google Scholar 

  4. Bogoutdinov, S.R., Gvishiani, A.D., Agayan, S.M., Solovyev, A.A., and 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, vol. 46, pp. 1004–1016.

    Article  Google Scholar 

  5. Brown, W.J., Mound, J.E., and Livermore, P.W., Jerks abound: An analysis of geomagnetic observatory data from 1957 to 2008, Phys. Earth Planet. Inter., 2013, vol. 223, pp. 62–76.

    Article  Google Scholar 

  6. Chulliat, A. and Maus, S., Geomagnetic secular acceleration, jerks, and a localized standing wave at the core surface from 2000 to 2010, J. Geophys. Res.: Solid Earth, 2014, vol. 119, pp. 1531–1543. https://doi.org/10.1002/2013JB010604

    Article  Google Scholar 

  7. Chulliat, A., Thebault, E., and Hulot, G., Core field acceleration pulse as a common cause of the 2003 and 2007 geomagnetic jerks, Geophys. Res. Lett., 2010, vol. 37, L07301. https://doi.org/10.1029/2009GL042019

    Article  Google Scholar 

  8. Chulliat, A., Alken, P., and Maus, S., Fast equatorial waves propagating at the top of the Earth’s core, Geophys. Res. Lett., 2015, vol. 42, pp. 3321–3329. https://doi.org/10.1002/2015GL064067

    Article  Google Scholar 

  9. Chulliat, A., Matzka, J., Masson, A., and Milan, S.E., Key ground-based and space-based assets to disentangle magnetic field sources in the Earth’s environment, Space Sci. Rev., 2017, vol. 206, pp. 123–156. https://doi.org/10.1007/s11214-016-0291-y

    Article  Google Scholar 

  10. De Michelis, P. and Tozzi, R., A local intermittency measure (LIM) approach to the detection of geomagnetic jerks, Earth Planet. Sci. Lett., 2005, vol. 235, nos. 1–2, pp. 261–272.

    Article  Google Scholar 

  11. Fikhtengol’ts, G.M., Kurs differentsial’nogo i integral’nogo ischisleniya (Course of Differential and Integral Calculus), Moscow: Nauka, 1969, vol. 2.

  12. Finlay, C.C., Dumberry, M., Chulliat, A., and Pais, A., Short timescale core dynamics: Theory and observations, Space Sci. Rev., 2010, vol. 155, pp. 177–218.

    Article  Google Scholar 

  13. Finlay, C.C., Olsen, N., Kotsiaros, S., Gillet, N., and Toeffner-Clausen, L., Recent geomagnetic secular variation from swarm and ground observatories as estimated in the CHAOS-6 geomagnetic field model, Earth Planets Space, 2016, vol. 68, no. 112. https://doi.org/10.1186/s40623-016-0486-1

  14. Gumbel, E.J., Statistics of Extremes, New York: Columbia University Press, 1958; Moscow: Mir, 1965.

  15. Gvishiani, A.D., Agayan, S.M., and Bogoutdinov, Sh.R., Fuzzy recognition of anomalies in time series, Dokl. Earth Sci., 2008a, vol. 421, no. 1, pp. 838–842.

    Article  Google Scholar 

  16. Gvishiani, A.D., Agayan, S.M., Bogoutdinov, Sh.R., Zlotnicki, J., and Bonnin, J., Mathematical methods of geoinformatics: III. Fuzzy comparisons and recognition of anomalies in time series, Cybern. Syst. Anal., 2008b, vol. 44, no. 3, pp. 309–323.

    Article  Google Scholar 

  17. Gvishiani, A.D., Agayan, S.M., Bogoutdinov, Sh.R., and Solov’ev, A.A., Discrete mathematical analysis and geological–geophysical applications, Vestn. Kamchatskoi Reg. Assots. Uchebno-Nauchnyi Tsentr, Nauki Zemle, 2010, no. 16, pp. 109–25.

  18. Gvishiani, A., Lukianova, R., Soloviev, A., and Khokhlov, A., Survey of geomagnetic observations made in the northern sector of Russia and new methods for analysing them, Surv. Geophys., 2014, vol. 35, no. 5, pp. 1123–1154. https://doi.org/10.1007/s10712-014-9297-8

    Article  Google Scholar 

  19. Gvishiani, A.D., Sidorov, R.V., Lukianova, R.Yu., and Soloviev, A.A., Geomagnetic activity during St. Patrick’s Day storm inferred from global and local indicators, Russ. J. Earth Sci., 2016a, vol. 16, ES6007. https://doi.org/10.2205/2016ES000593

    Article  Google Scholar 

  20. Gvishiani, A., Soloviev, A., Krasnoperov, R., and Lukianova, R., Automated hardware and software system for monitoring the Earth’s magnetic environment, Data Sci. J., 2016b, vol. 15, p. 18. https://doi.org/10.5334/dsj-2016-018

    Article  Google Scholar 

  21. Kagan, A.I., Agayan, S.M., and Bogoutdinov, Sh.R., Determination of stochastic continuity by fuzzy logic methods and geophysical applications, in Mezhdunarodnaya konferentsiya “Itogi Elektronnogo Geofizicheskogo Goda”. 3–6 iyunya 2009 g., Tezisy dokladov (International Conference “Results of the Electron Geophysical Year”, 3–6 June 2009, Abstracts of Presentations), Pereslavl’-Zalesskii, 2009, p. 99.

  22. Kerridge, D., INTERMAGNET: Worldwide near-real-time geomagnetic observatory data, Proc. of the Workshop on Space Weather, Noordwijk, The Netherlands: ESTEC, 2001.

  23. Kolmogorov, A.N. and Fomin, S.V., Elementy teorii funktsii i funktsional’nogo analiza (Elements of the Theory of Functions and Functional Analysis), Moscow: Nauka, 1976.

  24. Kulchinsky, R.G., Kharin, E.P., Shestopalov, I.P., Gvishiani, A.D., Agayan, S.M., and Bogoutdinov, Sh.R., Fuzzy logic methods for geomagnetic events detections and analysis, Russ. J. Earth Sci., 2010, vol. 11, RE4003. https://doi.org/10.2205/2009ES000371

    Article  Google Scholar 

  25. Leadbetter, M.R., Lindgren, G., and Rootzén, H., Extremes and Related Properties of Random Sequences and Processes, New York: Springer, 1983; Moscow: Mir, 1989.

  26. Love, J.J. and Chulliat, A., An international network of magnetic observatories, EOS: Trans. Am. Geophys. Union, 2013, vol. 94, no. 42, pp. 373–374. https://doi.org/10.1002/2013EO420001

    Article  Google Scholar 

  27. Lyubushin, A.A., Analiz dannykh sistem geofizicheskogo i ekologicheskogo monitoringa (Analysis of Geophysical and Ecological Systems Data), Moscow: Nauka, 2007.

  28. Mallat, S., A Wavelet Tour of Signal Processing, Amsterdam: Elsevier, 1999; Moscow: Mir, 2005.

  29. Mandea, M. and Bellanger, E., Le Mouël, J.L., A geomagnetic jerk for the end of the 20th century?, Earth Planet. Sci. Lett., 2000, vol. 183, nos. 3–4, pp. 369–373. https://doi.org/10.1016/S0012-821X(00)00284-3

    Article  Google Scholar 

  30. Mandea, M., Holme, R., Pais, A., Pinheiro, K., Jackson, A., and Verbanac, G., Geomagnetic jerks: Rapid core field variations and core dynamics, Space Sci. Rev., 2010, vol. 155, pp. 147–175.

    Article  Google Scholar 

  31. Olsen, N. and Mandea, M., Investigation of a secular variation impulse using satellite data: The 2003 geomagnetic jerk, Earth Planet. Sci. Lett., 2007, vol. 255, pp. 94–105.

    Article  Google Scholar 

  32. Sidorov, R.V., Soloviev, A.A., and Bogoutdinov, Sh.R., Application of the SP algorithm to the INTERMAGNET magnetograms of the disturbed geomagnetic field, Izv., Phys. Solid Earth, 2012, vol. 48, no. 5, pp. 410–414.

    Article  Google Scholar 

  33. Soloviev, A.A., Agayan, S.M., Gvishiani, A.D., Bogoutdinov, Sh.R., and Chulliat, A., Recognition of disturbances with specified morphology in time series: Part 2. Spikes on 1-s magnetograms, Izv., Phys. Solid Earth, 2012a, vol. 48, no. 5, pp. 395–409.

    Article  Google Scholar 

  34. Soloviev, A., Chulliat, A., Bogoutdinov, S., Gvishiani, A., Agayan, S., Peltier, A., and Heumez, B., Automated recognition of spikes in 1 Hz data recorded at the Easter Island magnetic observatory, Earth Planets Space, 2012b, vol. 64, no. 9, pp. 743–752. https://doi.org/10.5047/eps.2012.03.004

    Article  Google Scholar 

  35. Soloviev, A., Bogoutdinov, S., Gvishiani, A., Kulchinskiy, R., and Zlotnicki, J., Mathematical tools for geomagnetic data monitoring and the INTERMAGNET Russian segment, Data Sci. J., 2013, vol. 12, pp. 114–119. https://doi.org/10.2481/dsj.WDS-019

    Article  Google Scholar 

  36. Soloviev, A., Agayan, S., and Bogoutdinov, S., Estimation of geomagnetic activity using measure of anomalousness, Ann. Geophys., 2016, vol. 59, no. 6, G0653. https://doi.org/10.4401/ag-7116

    Google Scholar 

  37. Soloviev, A., Chulliat, A., and Bogoutdinov, S., Detection of secular acceleration pulses from observatory data, Phys. Earth Planet. Inter., 2017, vol. 270, pp. 128–142. https://doi.org/10.1016/j.pepi.2017.07.005

    Article  Google Scholar 

  38. Torta, J.M., Pavón-Carrasco, F.J., Marsal, S., and Finlay, C.C., Evidence for a new geomagnetic jerk in 2014, Geophys. Rev. Lett., 2015, vol. 42, pp. 7933–7940. https://doi.org/10.1002/2015GL065501

    Article  Google Scholar 

  39. Zelinskiy, N.R., Kleimenova, N.G., Kozyreva, O.V., Agayan, S.M., Bogoutdinov, Sh.R., and Soloviev, A.A., Algorithm for recognizing Pc3 geomagnetic pulsations in 1-s data from INTERMAGNET equatorial observatories, Izv., Phys. Solid Earth, 2014, vol. 50, no. 2, pp. 240–248.

    Article  Google Scholar 

  40. Zlotnicki, J., Le Mouël, J.-L., Gvishiani, A., Agayan, S., Mikhailov, V., Bogoutdinov, Sh., Kanwar, R., and Yvetot, P., Automatic fuzzy-logic recognition of anomalous activity on long geophysical records: Application to electric signals associated with the volcanic activity of La Fournaise volcano (Reunion Island), Earth Planet. Sci. Lett., 2005, vol. 234, nos. 1–2, pp. 261–278.

    Article  Google Scholar 

Download references

ACKNOWLEDGMENTS

The results presented in this paper rely on data collected at magnetic observatories. We thank the national institutes that support them and INTERMAGNET for promoting high standards of magnetic observatory practice (www.intermagnet.org). We used services of the Collective Use Center “Geomagnetic Analytical Center” of the GC RAS.

Funding

The work was performed within the framework of the state assignment of the GC RAS and approved by the Ministry of Science and Higher Education of Russia.

Author information

Authors and Affiliations

  1. Geophysical Center, Russian Academy of Sciences, Moscow, Russia

    S. M. Agayan, A. A. Soloviev, Sh. R. Bogoutdinov & Yu. I. Nikolova

  2. Institute of Physics of the Earth, Russian Academy of Sciences, Moscow, Russia

    A. A. Soloviev & Sh. R. Bogoutdinov

Authors
  1. S. M. Agayan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Soloviev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sh. R. Bogoutdinov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu. I. Nikolova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. I. Nikolova.

Additional information

Translated by M. Hannibal

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Agayan, S.M., Soloviev, A.A., Bogoutdinov, S.R. et al. Regression Derivatives and Their Application to the Study of Geomagnetic Jerks. Geomagn. Aeron. 59, 359–367 (2019). https://doi.org/10.1134/S0016793219030022

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0016793219030022

Search

Navigation