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.