The retrospective development of methods of analytical continuation of potential geophysical fields is considered. The possibilities of developing these methods in various directions are proposed. An example of the practical application of the method in complex geological and geophysical conditions is given.

Konstantin M. Ermokhin
Doctor of Engineering Sciences
Leading Researcher of Saint-Petersburg branch of Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation named after Nikolay Pushkov of the Russian Academy of Sciences (StPB of IZMIRAN),
5 liter Б, Universitetskaya naberezhnaya, Saint-Petersburg,
199034, Russia

1. Andreev B.A., Klushin I.G. Geologicheskoe istolkovanie gravitatsionnykh anomalii [Geological interpretation of gravity anomalies]. Leningrad: Gostoptekhizdat; 1962. 495 p.
2. Berezkin V.M., Kirichek M.A., Kunarev A.A. Primenenie geofizicheskikh metodov razvedki dlya pryamykh poiskov mestorozhdenii nefti i gaza [Application of geophysical methods of exploration for direct prospecting of oil and gas fields]. Moscow: Nedra; 1978. 223 p.
3. Gaysin R.M., Nabatov V.V. Detection of anomalous zones by the continuation method in underground electric exploration. Mining information and analytical bulletin. 2018;6:107–112. DOI: 10.25018/0236-1493-2018-6-0-107-112.
4. Gvishiani A.D., Kaftan V.I., Krasnoperov R.I., Tatarinov V.N., Vavilin E.V. Geoinformatics and systems analysis in geophysics and geodynamics. Izvestiya. Physics of the Solid Earth. 2019;55(1):33–49. DOI: 10.1134/S1069351319010038.
5. Jones W.B., Tron W.J. Continued Fractions: Analytic Theory and Applications. Reading: Addison-Wesley; 1980. 428 p.
6. Ermokhin K.M. Analytical continuation of gravitational and magnetic fields through masses. Doklady Earth Sciences. 2017;476(1):104–107. DOI: 10.1134/S1028334X17090021.
7. Ermohin K.M. Technology of cut construction by the geophysical fields analytical continuation method. Geoinformatika. 2010;2:51–60.
8. Ermokhin K.M., Soldatov V.A. On the determination of sources and internal structure of the Earth’s magnetic field based on analytical continetion by continued frations. Geoinformatika. 2020;3:20–28. DOI: 10.47148/1609-364X-2020-3-20-28.
9. Zhdanov M.S. Geophysical inverse theory and regularization problems. Amsterdam: Elsevier, 2002. 609 p.
10. Ladynin A.V. Dipole sources of the main geomagnetic field. Russian Geology and Geophysics. 2014;55(4):495–507. DOI: 10.1016/j.rgg.2014.03.007.
11. Logachev A.A., Zakharov V.P. Magnitorazvedka [Magnetic prospecting]. Leningrad: Nedra; 1979. 351 p.
12. Malovichko A.K., Kostitsyn V.I., Tarunina O.L. Detal’naya gravirazvedka na neft’ i gaz [Detailed gravity exploration for oil and gas]. Moscow: Nedra; 1989. – 224 p.
13. Strakhov V.N. Analiticheskoe prodolzhenie potentsial’nykh polei. Osobye tochki potentsial’nykh polei. Svyaz’ osobykh tochek s geometriei vozmushchayushchikh mass [Analytical continuation of potential fields. Singular points of potential fields. Relationship of singular points with the geometry of perturbing masses]. In: Gravirazvedka: spravochnik geofizika. E.A. Mudretsova, K.E. Veselov, eds. Moscow: Nedra; 1990. pp. 324–340.
14. Suetin P.K. Klassicheskie ortogonal’nye mnogochleny [Classical orthogonal polynomials]. Moscow: Nauka; 1979. 415 p.
15. Khovanskii A.N. Prilozhenie tsepnykh drobei i ikh obobshchenii k voprosam priblizhennogo analiza [Application of continued fractions and their generalizations to questions of approximate analysis]. Moscow: Gostekhizdat, 1956. 203 p.
16. Shalaev S.V. Primenenie v geofizike analiticheskogo prodolzheniya potentsial’noi funktsii v nizhnyuyu poluploskost’ [Application in geophysics of analytical continuation of a potential function into the lower half-plane]. Journal of Leningrad Mining Institute. 1959;36(2):15–26.
17. Yanovskii B.M. Zemnoi magnetizm [Terrestrial magnetism]. Ed. 4. Leningrad: Izd-vo Leningradskogo un-ta; 1978. 591 p.
18. Yanovskii B.M. Zemnoi magnetizm. T. 2. Teoreticheskie osnovy magnitometricheskogo metoda issledovaniya zemnoi kory i geomagnitnye izmereniya [Terrestrial magnetism. Vol. 2. Theoretical foundations of the magnetometric method for studying the earth’s crust and geomagnetic measurements]. Ed. 3. Leningrad: Izd-vo Leningradskogo un-ta; 1963. 463 p.
19. Binosi D. Schlessinger Point Method: Theory and Applications. In: Continuum Functional Methods for QCD at New Generation Facilities (ECT, Italy. May 7-10, 2019). Trento: ECT; 2019. 50 p. Available at: https://indico.ectstar.eu/event/46/contributions/991/attachments/678/899/DB-spectral.pdf (accessed 10.12.2021).
20. Fedi M, Florio G. Downward continuation within the quasi-harmonic region. In: EGM International Workshop. Adding new value to Electromagnetic, Gravity and Magnetic Methods for Exploration (Capri, Italy, April 11–14, 2010). 2010. 5 p. – Available at: https://www.eageseg.org/data/egm2010/Sessione%20C/Oral%20papers/C_OP_14.pdf (accessed: 10.12.2021).
21. Geosoft. Oasis Montaj v7.1. Руководство пользователя. 79p. 2013.
22. Litvinov G.L. Error Autocorrection in Rational Approximation and Interval Estimates. [A survey of results]. Open Mathematics. 2003;1:36–60. DOI: https://doi.org/10.2478/BF02475663.
23. Viskovatov B. De la méthode générale pour réduire toutes sortes des quantités en fractions continues. Mémoires de l’Académie impériale des sciences de St.-Pétersbourg. 1809;1:226–247.