Body-wave speeds and polarizations in the presence of an initial deviatoric stress

SUMMARY Body-wave speeds and polarization directions in a homogeneous and isotropic medium can be influenced by the presence of an initial deviatoric stress, which is conventionally ignored in seismic-wave propagation theories. To the first order, the P-wave speed is sensitive to the initial deviatoric stress, and the P-wave polarization has a perturbation perpendicular to the propagation direction. In addition, the S waves travel at two distinct speeds, and the S-wave polarizations are in two orthogonal directions, which are constrained by the initial deviatoric stress and involve a perturbation parallel to the propagation direction. Using a subduction zone setting with an initial deviatoric stress on the order of tens of MPa, the P-wave speed perturbation, S-wave splitting time and polarization perturbation are estimated to be on the order of 0.01 per cent, 0.01 s and 0.01 per cent, respectively. While these effects are too small to be reliably resolved using seismic observations, the theory presented in this paper could be useful for ultrasonic stress measurements in engineering applications.