Determination of stress in the geological medium on the basis of well data using acoustoelastic correlations


  • H. H. Guliyev Institute of Geology and Geophysics of Azerbaijan National Academy of Sciences, Azerbaijan
  • K. B. Aghayev Institute of Geology and Geophysics of Azerbaijan National Academy of Sciences, Azerbaijan
  • G. A. Sultanova Institute of Geology and Geophysics of Azerbaijan National Academy of Sciences, Azerbaijan



A method has been developed to determine normal components of the stress tensor in deformed geological media on the basis of geophysical well logging. The theoretical basis of the method is the acoustic correlations of the non-classical linearized approach of nonlinear elastodynamics. Analytical formulae are obtained to calculate the stress in the geological medium in cases of small and large deformations. Geophysical well logging data located in the South Caspian basin have been used. Thin-layered one-dimensional models of the medium have been compiled on velocities of pressure and shear waves, density and lithology of rocks. The thickness of each layer of the model is several centimeters, which is equal to the observations in the well. The data of each model related to the same rock lithology is divided into clusters using artificial neural networks to consider the influence of changes of thermobaric conditions of the geological medium on acoustic properties of rocks. Values of elasticity moduli of the second and third orders and components of normal stress tensor have been calculated according to models for each lithology of rocks and a cluster of data. It has been revealed that elasticity moduli of the third order are much more sensitive to the variability of elastic properties of the medium than moduli of the second order. The obtained numerical results on all clusters of each lithology of rocks are averaged. At the same time, the number of medium layers on each data cluster has been used as weights. The number of medium layers in each rock has been used as weights while averaging the results for all the rocks. The correlations between numerical values of normal components of stress tensor caused by geostatic pressure and similar values caused by geodynamic changes of stress tensor have been studied. It has been revealed that values of stress bulk caused by geostatic pressure are significantly lower than stress caused by geodynamic changes. The obtained acoustic formulae allow determining values of stress in the geological medium of any region considering the influence of modern geodynamic processes.


Abasov, M. T., Guliyev, H. H., & Dzhevanshir, R. D. (2000). The model of lithosphere development. Vestnik RAN, 70(2), 129—135 (in Russian).

Aghayeva, S. T., & Babayev, G. R. (2008). Analysis of earthquake foci of large and small Caucasus according to the method of constructing a world stress map. In Catalogue of seismoforecasting research carried out in Azerbaijan territory (pp. 51—55). Baku (in Russian).

Akbarov, S. D. (2015). Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized Three-Dimensional Approach. Springer-Heildelberg, Newswork, 1003 p.

Alexandrov, K. S., Prodaivoda, G. T., & Maslov, B. P. (2001). Method of determination of nonlinear elastic properties of rocks. Doklady RAN, 380(1), 109—112 (in Russian).

Anderson, D. (2007). New Theory of the Earth. Cambridge University Press, New York, USA. 385 p.

Babaev, D. Kh., & Gadzhiev, A. N. (2006). Deep structure and oil and gas potential of the Caspian Sea basin. Baku: Nafta-Press, 305 p. (in Russian).

Bakulin, V. N., & Protoseniya, A. G. (1982). The presence of nonlinear effects during the propagation of elastic waves in rocks. Doklady AN SSSR, 263 (2), 314—316 (in Russian).

Balakina, L. M., Vvedenskaya, A. V., Golubeva, N. V., Misharina, L. A., & Shirokova, E. I. (1972). Field of the Earth’s elastic stresses and the mechanism of earthquake sources. Moscow: Nauka, 191 p. (in Russian).

Bayuk, E. I., Tomashevskaya, I. S., & Dobrynin, V. M. (1988). Physical properties of minerals and rocks within high thermodynamic parameters: Handbook. Moscow: Nedra, 255 p. (in Russian).

Biot, M. A. (1965). Mechanics of incremental deformations. Ph.D. Dissertation. New York: Wiley, 560 p.

Garotta, R. (2000). Transverse waves: from registration to interpretation. Short course of lectures for higher educational institutions. The publication of the American Society of Exploration Geophysicists (SEG), 221 p. (in Russian)

Chashkov, A. V., & Valery, V. M. (2011). Use of the cluster analysis and artificial neural network technology for log data interpretation. Zhurnal Sibirskogo federalnogo universiteta. Tekhnika i tekhnologiya, 4(4), 453— 462 (in Russian).

Gintov, O. B. (2005). Field tectonophysics and its application in the study of deformation of the Earth’s crust. Kiev: Feniks, 572 p. (in Russian).

Guliyev, H. H. (2000). Determination of Poisson’s ratio in the strained medi. Doklady AN, 370(4), 534—537 (in Russian).

Guliyev, H. H. (2018a). Geomechanical analysis of elastic parameters of the solid core of the Earth. Geomechanics and Engineering, 14(1), 19—27.

Guliyev, H. H. (2018b). On the elastic parameters of the strained media. Structural Engineering and Mechanics, 67(1), 53—67.

Guliyev, H. H., & Aghayev, Kh. B. (2011). Determination of physicomechanical properties of sedimentary cover rocks on the basis of seismic, borehole data and the theory of elastic waves of stressed media. Geofizicheskiy zhurnal, 33(6), 126—135. (in Russian).

Guliyev, H. H., Aghayev, Kh. B., & Hasanova, G. H. (2016). Determining the Elastic Moduli of the Third Order for Sedimentary Rocks Based on Well-Logging Data. Izvestiya, Physics of the Solid Earth, 52(6), 836—843. doi: 10.1134/S1069351316050062.

Guliyev, H. H., & Dzhabbarov, M. D. (1998). The propagation of elastic waves in the strained anisotropic media. Doklady Akademii nauk Azerbaydzhanskoy SSR, (2), 103—112 (in Russian).

Guliyev, H. H., Javanshir, R. J., & Hasanova, G. H. (2018). Determination of elastic parameters of the deformable solid bodies with respect to the Earth model. Geomechanics and Engineering, 15(5), 1071—1080.

Guz, A. N. (2004). Elastic Waves in Bodies with Initial (Residual) Stresses. Kiev: A.S.K., 672 p. (in Russian).

Guz, A. N., Makhort, F. G., Gushcha, O. I., &

Lebedev, V. K. (1974). Fundamentals of the ultrasonic non-destructive method for the

determination of stress in solids. Kiev: Naukova Dumka, 106 p. (in Russian).

Gzovsky, M. V. (1975). Fundamentals of Tectonophysics. Moscow: Nauka, 536 p. (in Russian).

Heidbach, O., Barth, A., Connolly, P., Fuchs, K., Müller, B., Tingay, M., Reinecker, J., Sperner, B., & Wenzel, F. (2004). Stress maps in a minute: the 2004 World Stress Map release. EOS Trans, 85(49), 521―529.

Li, X. & Tao, M. (2015). The influence of initial stress on wave propagation and dynamic elastic coefficients. Geomechanics and Engineering, 8(3), 377—390.

Müller, B., Barth, A., Heidbach, O., Reinecker, J., Sperner, B., Tingay, M., & Wenzel, F. (2005). The World Stress Map-an essential and easy accessible tool for geohazard assessment. International Workshop Recent Geodynamics, Georisk and Sustainable Development in the Black Sea to Caspian Region, Baku, AIP, 825, 19—31.

Poulton, M. M. (2002). Neural networks as an intelligence amplification tool: A review of applications. Geophysics, 67(3), 979—993.

Reinecker, J., Heidbach, O., & Müller, B. (2005). The 2005 release of the World Stress Map. Retrieved from

Teachavorasinskun, S., & VSPongvithayapanu, P. (2016). Shear wave velocity of sands subject to large strain triaxial loading. Geomechanics and Engineering, 11(5), 713—723.

Tromp, J., Marcondes, M. L., Wentzcovitch, R., & Trampert, J. (2019). Effects of Induced Stress on Seismic Waves: Validation Based on Ab Initio Calculations. Journal of Geophysical Research: Solid Earth, 124(1), 729—741.

Vyzhva, S. A., Maslov, B. P., & Prodaivoda, G. T. (2005). Effective elastic properties of nonlinear multicomponent geological media. Geofizicheskiy zhurnal, 27(6), 1012—1022 (in Russian).

Yin, H., & Rasolofosaon, P. (1994). Nonlinear and linear elastic behavior of anisotropic rocks: Ultrasonic experiments versus Theoretical predictions. Abstract, 64 SEG meeting, Los Angeles, Expanded Abstract, paper SL3.4, 1129—1132.




How to Cite

Guliyev, H. H., Aghayev, K. B., & Sultanova, G. A. (2019). Determination of stress in the geological medium on the basis of well data using acoustoelastic correlations. Geofizicheskiy Zhurnal, 41(6), 173–182.