Acoustoelastic effects of borehole Stoneley wave in a transversely isotropic elastic solid

This work investigates Stoneley wave in a fluid-filled pressurized borehole surrounded by a transversely isotropic elastic solid with nine independent third-order elastic constants in presence of biaxial stresses. A simplified acoustoelastic formulation of Stoneley wave is presented for the parallelism of the borehole axis and the formation axis of symmetry. Sensitivity coefficients and velocity dispersions for Stoneley wave due to the presence of stresses are numerically investigated, respectively. The acoustoelastic formulation explicitly shows that the velocity dispersions of Stoneley wave depend on seven independent third-order elastic constants in presence of biaxial stresses and on six independent third-order elastic constants in the presence of borehole pressurization alone. Numerical results of both sensitivity coefficients and velocity dispersions of Stoneley wave show that at low frequency the velocity change of Stoneley wave is sensitive to c111 and c112. Stoneley wave velocity at low frequencies in a transversely isotropic elastic solid can be simplified by 3 independent third order elastic constants (c111, c112 andc123) instead of nine constants. In presence of biaxial stresses, at low frequencies the speed of the Stoneley wave is similar to White formula for transversely isotropic medium. Stoneley dispersions in the presence of the biaxial stresses without regard to the anisotropy of third-order elastic constants. Solid and short dash dot lines denote Stoneley dispersion curves for anisotropy of third-order elastic constants and for isotropy of third-order elastic constants (c111,c112 and c123) respectively. Third order elastic constants of the formation unit:GPa. From Prioul et al.2004