Acoustoelastic Effects On Reflection And Transmission Of Elastic Waves And Guided Waves In A Borehole Surrounded By A Transversely Isotropic (VTI) Elastic Solid

Estimates of the underground stress field are required for a variety of subsurface activities including drilling, oil and gas production, and mining et.al. The purpose of this paper is to study the nondestructive technique in estimating the abnormal formation stress based on the acoustoelastic theory.First of all, the problems of the reflection and transmission of acoustic waves at the interface between fluid and rock with elastic-plastic deformations and between rocks in the presence of elastic-plastic deformations induced by applied uniaxial stresses are investigated, respectively, based on the acoustoelastic theory for elastic-plastic materials. The effects of statically elastic-plastic deformations on energy reflection and transmission coefficients, reflected and refracted angles are investigated. The incident wave plane can coincide with or deviate from planes of principal stresses. Elastic-plastic deformations are assumed to be locally homogeneous and to satisfy static boundary conditions. Changes in phase velocity, propagation direction, and energy reflection and refraction coefficients due to the presence of elastic-plastic strains are discussed. The velocities decrease, the energy is distributed, and the critical angles are changed when the rock undergoes elastic-plastic deformations compared with those of the statically elastic deformations. The directions of transmitted wave vectors are changed especially at relative large incident angles when rock is subjected to statically elastic or elastic-plastic deformations. The investigation is helpful for estimating the abnormal stresses and analyzing the elastic-plastic deformations.In addition, we investigate reflection coefficients of the longitudinal and shear waves at the interface between isotropic rock and anisotropic rock induced by uniaxial stress according to approximate reflection coefficients in HTI media and the weak-anisotropy approximation that directly links commonly measured anisotropic Thomsen parameters to the principal stresses. We use acoustoelastic theory to relate the anisotropic parameters to the principal stresses in intermediate coordinates and obtain the direct relations of the difference of approximate reflection coefficients between azimuthal angle and and uniaxial stress. We calculate the anisotropic parameters, the longitudinal and shear wave reflection coefficients of displacements, and stresses according to the direct relations. Numerical examples show that satisfactory agreement between weak-anisotropy approximation and predicted anisotropic parameters for small stresses, and bad agreement for large stresses. The positive and negative of anisotropic parameters 0 0900ε(V )andγcan be used as an indicator of uniaxial stress-induced anisotropy. Under the weak anisotropy induced by stresses, at small incident angle, magnitude of stress can be estimated by shear wave reflection coefficients. Study of the azimuthal variation in the longidituinal wave reflection coefficients can help us to find the orientation of stress. The relative error of estimated stress is small when the stress is not big according to the direct relation. The results offer a new method to analyze the source of anisotropy and estimate stresses.Secondly, the influences of statically deformed state including both the elastic and plastic deformations induced by applied uniaxial stresses on the Rayleigh and Love waves in layered rocks are investigated on the basis of the acoustoelastic theory for elastic-plastic materials, respectively. The phase velocity equations of the Rayleigh and Love waves are obtained by a transfer matrix method and direct boundary conditions, respectively. The acoustoelastic effects of elastic and elastic-plastic deformations in rocks caused by static stresses are discussed in detail. Acoustoelastic effects of both the Rayleigh and Love waves exhibit similar trend, acoustoelastic effect increases rapidly with the frequency-thickness product and the velocity change approximates a constant value for thick layer and high frequency limit. Elastic-plastic deformations in the Castlegate layered rock obviously modify the phase velocities of the Rayleigh and Love waves and the cutoff points for the high-order modes. The acoustoelastic effects of fundamental Love mode and second-order modes (including Sezawa modes and Love waves) exceed the value of the Rayleigh-type wave significantly. The investigation may be useful for the seismic exploration, geo-technical engineering and ultrasonic detection.Finally, this paper investigates acoustoelastic effects on Stoneley wave and flexural wave in a fluid-filled pressurized borehole surrounded by a transversely isotropic elastic solid in the presence of biaxial stresses, which has ten independent third-order elastic constants. The formulation that expresses the dependence of Stoneley velocity dispersions on the sum of biaxial stresses, borehole pressurization, and eight independent third-order elastic constants is presented. The formulation that expresses the dependence of flexural velocity dispersions on the sum of biaxial stresses, the difference of biaxial stresses, borehole pressurization, eight independent third-order elastic constants, and the azimuthal angle of mutipole source polarization is presented. The frequency dependence of sensitivity coefficients and velocity dispersions of Stoneley wave and flexural wave due to the presence of stresses and anisotropic third-order elastic constants are numerically investigated. The acoustoelastic formulations of guided waves (Stoneley and flexural waves) show that the coefficients in the presence of borehole pressurization alone relate to seven independent third-order elastic constants, the coefficient is equal to negative , and is equal to negative .Numerical results for Stoneley wave show that: at almost zero frequency, the sensitivity coefficients associated to and in the presence of borehole pressurization alone are larger than other sensitivity coefficients associated to third-order elastic constants, from two to six orders of magnitude. The sensitivity coefficients associated to , and in the presence of biaxial stresses are larger than other sensitivity coefficients associated to third-order elastic constants, from two to three orders of magnitude, and at higher frequency, the eight sensitivity coefficients are almost at the same order of magnitude. The influence of Sensitivity coefficients and on phase velocity is small and can be omitted. The change of Stoneley velocity in borehole pressurization alone is obvious not only at high frequency but also possibly at low frequency, which is different from that of isotropic formation and may be used to distinguish the material character, and is mainly dominated by the third-order elastic constants and at low frequency when seven third-order elastic constants are the same order of magnitude, even larger than and . The change of Stoneley velocity in the presence of biaxial stresses is mainly dominated by the third-order elastic constants , and at low frequency when eight third-order elastic constants are the same magnitude, even larger than C111,C222 and C112.Numerical results for flexural wave show that the sensitivity coefficients in the presence of borehole pressurization alone at higher frequency are larger than at low frequency. The sensitivity coefficients associated to and in the presence of biaxial stresses are larger than other sensitivity coefficients associated to third-order elastic constants, from one to two orders of magnitude. The change of flexural velocity in the presence of biaxial stresses is mainly dominated by the third-order elastic constants and at low frequency(c1 44c155c1 44c1 55≤5kHz) when eight third-order elastic constants are the same order of magnitude, even larger than and , and each other controlled by eight independent third-order elastic constants at high frequency. The influence of sensitivity coefficients C,and on flexural phase velocity is small and can be omitted. The flexural dispersion crossover can be used as an indicator of stress-induced anisotropy. Borehole pressurization influences on the value of velocity at the point of crossover frequency, does not influence on the point of crossover frequency. However, the anisotropic third-order elastic constants influence the flexural velocity and dispersion curves crossover. It is necessary for us to consider the anisotropy of third-order elastic constants in order to investigate the acoustoelastic effects on guided waves in a borehole surrounded by a transversely isotropic elastic solid. These results are important for estimating abnormal stresses of a transversely isotropic elastic solid.