Wavefields in a cased hole surrounded by a formation with transverse isotropy caused by axial stresses

Understanding acoustic field characteristics in the cased hole accompanied by stress is important for acoustical logging. This study investigates the behavior of multipole wavefields of a cased hole with a perfect combination of casing, cement, and formation under the formation borehole-axial stress. The formation can be equivalent to a transversely isotropic medium when uniaxial stress acts on isotropic formation based on nonlinear elasticity theory. The effect of axial stress in the formation on multipole wavefields in cased hole is investigated. Numerical results show that the phase slowness of Stoneley, flexural, and screw waves decreases with an increase in axial compressive stress. With the increase of uniaxial stresses, the arrival times of the full waveforms decrease, and the amplitudes of the full waveforms increase. These characteristics are similar to that of the open hole. For cased holes in soft formations, the excitation curves of flexural and screw waves shift to low frequencies as the stress increases; and the dispersion curves corresponding to excitation curves also exhibit a similar shift, while open holes do not have this pattern. The wavefields excited by a dipole source and quadrupole source in the cased hole in soft formation have more prominent changes in the frequency spectra, and the changes in the integral amplitudes of the full waveforms are larger than those of the open hole. We found that responses of wavefields excited by dipole and quadrupole sources in cased holes in soft formation to the axial stress are more sensitive than those in the open hole.