Acoustoelastic effects on guided waves in a fluid-filled pressurized borehole in a prestressed formation

Abstract

This paper investigates acoustoelastic effects on guided waves in a fluid-filled pressurized borehole in a biaxial prestressed formation, and develops a simplified formula that explicitly expresses the dependence of velocity dispersions on the stresses, the third-order elastic constants, and the azimuthal angle of multipole source polarization. The simplified formula shows that only in the flexural wave is there a crossover of the dispersion curves, and this phenomenon does not appear in every other guided wave. In particular, as a transformed result from the simplified expression, the square difference of flexural wave velocity dispersions is only dependent on the difference of the biaxial stresses, and neither the square sum of the flexural dispersions nor the velocity dispersions of the other guided waves is dependent on it. Computational results show that the sensitivity coefficients for the flexural dispersions induced by the biaxial stresses at low frequency asymptotically approach the corresponding coefficients of shear-waves in the formation, like the asymptotic behavior of velocities.

Acoustoelastic effects of Stoneley waves in a borehole surrounded by a transversely isotropic elastic solid

“…In principle, one can solve wave field problems by any equations and their corresponding boundary conditions. 12 When the equations of motion are written in the reference state, the mass density, bounding surface area and volume are known from their reference state values and need not be calculated for different magnitudes of prestress. 9 In this paper, we choose the reference configuration to describe waves propagation in prestressed medium.…”

“…1,2 An alternative approach that has been successfully applied to the estimation of stress is based on the acoustoelastic theory. 6,[9][10][11][12][13][14] The acoustoelastic effect, i.e., the velocity change of the acoustic waves in the presence of stresses, has been investigated for more than about sixty years. 15 The acoustoelastic effect is not new to rock physicists, having already been applied in various contexts such as underground mines, 16 laboratory experiments, [17][18][19][20] and boreholes.…”

“…15 The acoustoelastic effect is not new to rock physicists, having already been applied in various contexts such as underground mines, 16 laboratory experiments, [17][18][19][20] and boreholes. 6,[9][10][11][12] A nondestructive technique based on borehole cross-dipole acoustic measurements and acoustoelastic effect has been used to measure the stress magnitudes present in the earth. 6,[9][10][11][12][13][14]21 Most attempts from sonic logging assumed that the background formation is isotropic in the absence of stress.…”

“…6,[9][10][11][12] A nondestructive technique based on borehole cross-dipole acoustic measurements and acoustoelastic effect has been used to measure the stress magnitudes present in the earth. 6,[9][10][11][12][13][14]21 Most attempts from sonic logging assumed that the background formation is isotropic in the absence of stress. 6,[9][10][11][12][13][14]22 However, some rocks can exhibit anisotropy even in the absence of stress.…”

“…6,[9][10][11][12][13][14]21 Most attempts from sonic logging assumed that the background formation is isotropic in the absence of stress. 6,[9][10][11][12][13][14]22 However, some rocks can exhibit anisotropy even in the absence of stress. 23 In petroleum seismology, we often encounter one of two types of anisotropy: transverse isotropy.…”