The Study Of Elastic Wave Propagation In Transversely Isotropic Layered Formation Induced By Vertical Stress

The horizontal or vertical stress often exists in the underground reservoir,among which the vertical stress will induce the transverse isotropy of the medium.Transversely isotropic media is a relatively common anisotropic model.For example,many sedimentary rocks exhibit the transversely isotropic nature.The analytical solution and numerical simulation of the elastic wavefield are mainly carried out for the layered media in the isotropic case.However,it is difficult to solve the elastic wavefield for the transversely isotropic layered medium,because of the coupling of P-SV wave,whose the elastic wavefield is mainly studied with the help of numerical methods such as finite difference or finite element.At present,the analytical solution of elastic wave field in transversely isotropic layered media induced by intrinsic or vertical stress has not been reported.Therefore,in this paper,the propagation characteristics of the elastic wavefield are analyzed by the analytical method for the formation with the vertical stress.The investigation in this paper will provide a convenient and fast analytical method and numerical algorithm for the solution and simulation of the elastic wavefield in the transversely isotropic layered media.It provides a basis for understanding the influence of the overburden stress on the acoustic field and provides the framework for obtaining the vertical stress.In this paper,the elastic wavefield of the transversely isotropic layered formation induced by the vertical stress was analytically solved.The expressions of acoustic field potential of the transversely isotropic layered induced by vertical stress were presented excited by the point source,based on the analytical solution method of the acoustic wavefield of a borehole in a transversely isotropic formation.The expression provides a new method for solving the elastic wavefield of transversely layered media.The layered boundary conditions are used to determine the coefficients of acoustic field potential,then the acoustic field reflection coefficient was obtained,and thus the acoustic field in layered model was determined,and the full wave waveform of the acoustic field in fluid media was calculated by the fast Fourier transform.In this paper,the acoustic field of isotropic layered media under different vertical stresses was investigated.Newton iterative calculation was used to obtain the dispersion curves of the mode wave.The results have shown that in the fluid-solid model,the velocity of the Scholte wave varies in different formations under the different stress,and the stress also affects the amplitude of the Scholte wave.In the fluid-solid-solid model,it can be seen that the stress has an effect on the velocity of the Scholte wave at different frequencies,and the greater the stress,the faster the velocity.The velocity,arrival time and amplitude of the wave will change with the action of different vertical stress,which indicates that the propagation characteristics of the acoustic wavefield received in the fluid layer carry the information about the vertical stress.