Multipole borehole acoustic field in a transversely isotropic medium induced by stress

A borehole multipole acoustic field in a pre-stressed formation is investigated. The pre-stressed formation is modeled as a transversely isotropic medium induced by uniaxial stress. The formation is assumed to be isotropic in absence of any static stress and then becomes anisotropic due to the applied stress parallel to the borehole axis. The approximate equivalent elastic constants of the stress-induced anisotropic medium are derived from the theory of acoustoelasticity. The nonlinear static stress-strain relation is used for both small and large static deformations. This problem can be solved analytically because of uniformity of deformation induced by static stress applied parallel to the borehole axis. The stress effects on the velocity of guided waves and amplitude of waveforms excited by monopole, dipole, and quadrupole sources are investigated. Numerical results show that the velocities of guided waves increase with uniaxial stress. The uniaxial stress affects both amplitude and arrival time of the acoustic waves in the borehole. The integral amplitude of full waveforms varies almost in a parabolic manner with the increasing stress level and thus shows sensitivity to the uniaxial stress. This result may be helpful for remote stress measurements in boreholes.