A neural network algorithm for high-precision prediction of deep temperature using seismic data

№2 (2026)

Spichak V.V., Zakharova O.K.

УДК 550.361+550.34.01
https://doi.org/10.47148/1609-364X-2026-2-34-44

AbstractAbout the AuthorsReferences
The algorithm of high-accuracy temperature prediction at large depths from seismic sounding data is suggested. The accuracy of its prediction is validated using neural network modeling. To this end the seismic sounding data along the latitudinal profile of the Northern Tien Shan and 2-D temperature model built earlier up to the depth of 27 km are used. The assessment of the prediction accuracy indicated that it practically does not depend on the ratio between the depths of the target and borehole, the data from which are used for neural network training. Therewith the average relative accuracy of the temperature prediction from longitudinal and transverse wave velocity up to the depth of 20 km was 92–93 % and 95–96 %, accordingly. The algorithm suggested could be used for high-accuracy temperature prediction at depth many times exceeding the borehole depth. This enables to increase the effectiveness of the geothermal exploration (in particular, of unconventional resources) and search for the hydrocarbons of organic nature.

Viacheslav V. Spichak
Doctor of Physical and Mathematical Sciences
Head of the Lab methodology of the EM data interpretation
Geoelectromagnetic Research Centre
of the Institute of the Physics of the Earth RAS
POB 30, GEMRC, Troitsk, Moscow Region, 108840, Russia
e-mail: v.spichak@mail.ru
ORCID ID: 0000-0001-6121-190X
SPIN-code: 7363-0529
AuthorID: 61066

Olga K. Zakharova
Candidate of Physical and Mathematical Sciences
Leading Researcher of the Lab methodology
of the EM data interpretation IPE RAS
Geoelectromagnetic Research Centre
of the Institute of the Physics of the Earth RAS
POB 30, GEMRC, Troitsk, Moscow Region, 108840, Russia
e-mail: okzakharova@mail.ru
AuthorID: 61066

1. Podgornykh L.V., Gramberg I.S., Khutorskoi M.D., Leonov Yu.G. A geothermal 3D-model of the Kara sea shelf and forecast for its petroleum potential. Doklady Earth Sciences. 2001;380:782–786.
2. Ollinger D., Baujard C., Kohl T., Moeck I. Distribution of thermal conductivities in the Groß Schönebeck (Germany) test site based on 3D inversion of deep borehole data. Geothermics. 2010;39(1):46–58. DOI: 10.1016/j.geothermics.2009.11.004.
3. Spichak V.V., Zakharova O.K., Rybin A.K. Possibility of realization of contact-free electromagnetic geothermometer. Doklady Earth Sciences. 2007;417(2):1370–1374. DOI: 10.1134/S1028334X07090176.
4. Spichak V.V., Zakharova O.K. Ehlektromagnitnyi geotermometr [Electromgnetic geothermometer]. Moscow : Nauchnii Mir: 2013. 170 p.
5. Spichak V.V., Zakharova O.K. Application of the electromagnetic geothermometer in geothermics and geothermal exploration. Russian Geology and Geophysics. 2022;63(9):1078–1092. DOI: 10.2113/rgg20214284.
6. Spichak V.V., Zakharova O.K. Feasibility study of application of electromagnetic geothermometer for hydrocarbon prospecting. Journal of Geophysics. 2020;(1):56–59.
7. Goes S., Govers R., Vacher P. Shallow mantle temperatures under Europe from P and S wave tomography. Journal of Geophysical Research: Solid Earth. 2000;105(B5):11153–11169. DOI: 10.1029/1999JB900300.
8. Jaya M.S., Shapiro S., Kristindóttir L., Bruhn D., Milsch H. and Spangenberg E. Temperature-Dependence of Seismic Properties in Geothermal Core Samples at In-Situ Reservoir Conditions. In: Proceedings of World Geothermal Congress (Bali, Indonesia, 25–29 April 2010). 2010. 8 p. Available at: http://www.geothermal-energy.org/pdf/IGAstandard/WGC/2010/1358.pdf (accessed 07.04.2010).
9. Perry H.K.C., Jaupart C., Mareschal J.-C., Shapiro N.M. Upper mantle velocity-temperature conversion and composition determined from seismic refraction and heat flow. Journal of Geophysical Research: Solid Earth. 2006;11(B7):B07301. DOI: 10.1029/2005JB003921.
10. Poletto F., Farina B., Carcione J.M. Sensitivity of seismic properties to temperature variations in a geothermal reservoir. Geothermics. 2018;76:149–163. DOI: 10.1016/j.geothermics.2018.07.001.
11. Kuskov O.L., Kronrod V.A. Determining the temperature of the Earth’s continental upper mantle from geochemical and seismic data. Geochemistry International. 2006;44(3):232–248. DOI: 10.1134/S0016702906030025.
12. Cammarano F., Goes S., Vacher P., Giardini D. Inferring upper-mantle temperatures from seismic velocities. Physics of the Earth and Planetary Interiors. 2003;138(3-4):197–222. DOI: 10.1016/S0031-9201(03)00156-0.
13. Furlong K.P., Spakman W., Wortel R. Thermal structure of the continental lithosphere: Constraints from seismic tomography. Tectonophysics. 1995;224(1–3):107–117. DOI: 10.1016/0040-1951(94)00220-4.
14. Ryan G.A., Shalev E. Seismic Velocity / Temperature Correlations and a Possible New Geothermometer: Insights from Exploration of a High-Temperature Geothermal System on Montserrat, West Indies. Energies. 2014;7(10):6689–6720. DOI: 10.3390/en7106689.
15. Sobolev S.V., Zeyen H., Stoll G., Werling F., Altherr R., Fuchs K. Upper mantle temperatures from teleseismic tomography of French Massif Central including effects of composition, mineral reactions, anharmonicity, anelasticity, and partial melt. Earth and Planetary Science Letters. 1996;139(1-2):147–163. DOI: 10.1016/0012-821X(95)00238-8.
16. Zakharova O.K., Spichak V.V. Earth’s interior temperature assessment from seismotomography data. Journal of geophysics. 2025;(1):35–42. DOI: 10.34926/geo.2025.13.28.006.
17. Zakharova O.K., Spichak V.V. Neural network modeling of the temperature prediction at depth according to the seismic sounding data. Geophysical research. 2025;26(1); 67–78. DOI: 10.21455/gr2025.1-4.
18. Spichak V.V., Goidina A.G., Zakharova O.K. Estimating thermophysical rock properties from electromagnetic sounding data and laboratory measurements. Geologiya i geofizika. 2023;64(3):431–446. DOI: 10.15372/GiG2022126.
19. Spichak V.V., Zakharova O.K. Electromagnetic permeability forecast beyond boreholes. Geophysical research. 2022;23(2):18–38. DOI: 10.21455/gr2022.2-2.
20. Spichak V.V., Zakharova O.K. The electromagnetic prediction of the open porosity beyond boreholes. Russian Geology and Geophysics. 2023;64(1):116–122. DOI: 10.2113/rgg20214363.
21. Spichak V.V., Zakharova O.K. Neural network modeling of electromagnetic prediction of geothermal reservoir properties. Izvestiya, Physics of the Solid Earth. 2023;59(1):67–80. DOI: 10.1134/s1069351323010068.
22. Ghose S., Hamburger M.W., Virieux J. Three-dimensional velocity structure and earthquake locations beneath the northern Tien Shan of Kyrgyzstan, central Asia. Journal of Geophysical Research: Solid Earth. 1998;103(B2):2725–2748. DOI: 10.1029/97JB01798.
23. Spichak V.V., Khutorskoi M.D. Construction of temperature model along a sublatitudinal profile in the Chu depression, Northern Tien Shan, based on seismic tomography data. Izvestiya, Physics of the Solid Earth. 2025;61(5):891–896. DOI: 10.1134/S1069351325700703.
24. Yudakhin F.N. Geofizicheskie polya, glubinnoe stroenie i seismichnost’ Tyan’-Shanya [Geophysical fields, deep structure and seismicity of Tien Shan]. Frunze: Ilim; 1983. 248 p.
25. Shvartsman Yu.G. Teplovoe pole, seismichnost’ i geodinamika Tyan’-Shanya [Thermal field, seismicity and geodynamics of Tien Shan]: diss. abstract for the degree of Doctor of geological and mineralogical sciences. Bishkek, 1992. 38 p.
26. Duchkov A.D., Shvartsman Yu.G., Sokolova L.S. Deep heat flow in the Tien Shan: advances and drawbacks. Geologiya i Geofizika. 2001;42(10):1516–1531.
27. Haykin S. Neural Networks: A Comprehensive Foundation / 2-nd ed. Upper Saddle River: Prentice Hall, 1999. 842 p.
28. Spichak V.V., Nenyukova A.I. Cluster analysis of section properties with the aim of searching areas for drilling exploration geothermal wells. Geoinfomatika. 2023;(2):56–65. DOI: 10.47148/1609-364X-2023-2-57-66.

Key words: temperature, seismic wave velocity, prediction, geothermometer, artificial neural network

Section: Modeling geo objects and geo-processes