Volume 11, no. 2Pages 5 - 13 # Mathematical Modelling of Effective Elastic Parameters

P.N. Aleksandrov, V.N. KrizskyThe article is devoted to the study of the laws of elastic field propagation in inhomogeneous anisotropic media. At the same time, anisotropy is introduced as effective (averaged) parameters of a thin-layered medium, which determines the macroanisotropic elastic parameters of the rock. It is shown that the effective elastic parameters obtained from the theory of elasticity (Lame equations) do not coincide with the effective parameters

obtained using the kinematic approach. On the basis of reduction of equations of the theory of elasticity to the systems of the ordinary differential equations of the first order the solution of a direct problem of seismic exploration (as a boundary value problem) for horizontally layered and anisotropic model of the geological environment is received. The given result of calculation of the seismic field registered on the daily surface in the case of an anisotropic object leads to the complex picture of the wave field. This means that it is necessary to improve the methods of seismic exploration in the course of the studying of anisotropic properties of the geological environment.

Full text- Keywords
- seismic anisotropy; effective parameters; systems of differential equations; eikonal equation.
- References
- 1. Bayuk I.O. Mezhdisciplinarny podkhod k prognozirovaniyu makroskopicheskikh i filtracionno emkostnykh svoystv kollektorov uglevodorodov [Interdisciplinary Approach to Prediction of Macroscopic and Filtration-Capacitive Properties of Hydrocarbon Reservoirs. Thesis of Doctor of Physical and Mathematical Sciences], Moscow, 2013. 228 p. (in Russian)

2. Wait J.E. Underground Sound - Application of Seismic Waves, Elsevier Science Publishers, Amsterdam, 1983.

3. Backus G.E. Long-Wave Anisotropy Produced by Horizontal Layering. Journal of Geophysical Research, 1962, vol. 67, no. 11, pp. 4427-4440. DOI: 10.1029/JZ067i011p04427

4. Rytov S.M. [Acoustic Properties of Fine-Layered Medium]. Akusticheskiy zhurnal, 1956, vol. 2, no. 1, pp. 71-83. (in Russian)

5. Aleksandrov P.N. [Derivation of the Eikonal Equation for Aanisotropic Inhomogeneous Media]. X Annual International Conference 'Halperin Readings - 2010'. Innovative Technologies and Fundamental Researches in 2Q, 3D VSP Well-Surface Exploration and Seismology Commemorating 90 Year Anniversary of Y.I. Galperin, Moscow, 2010, pp. 53-59. (in Russian)