STABILITY OF DETERMINATION OF COMPOSITE MODULI FROM VELOCITY DATA IN PLANES OF SYMMETRY FOR WEAK AND STRONG ANISOTROPIES

The determination of elastic constants from ultrasonic bulk wave veloc ity data taken in a plane of symmetry is studied. It is shown that the problem is well-posed, i.e., the solution is unique and stable. The d isplacement polarization factors are used to define the degree of mate rial anisotropy and represent solutions of the Christoffel equation. S uch a representation in a rotated coordinate system helps to derive si mple expressions for coefficients describing the sensitivity of ultras onic waves to different elastic constants. Thus the optimal refraction angles for velocity measurement can be determined simply. The analysi s performed shows that the elastic constants reconstructed from veloci ty data are not affected by the selection of initial guesses used in a nonlinear least-square optimization (the solution is unique). The sol ution stability is validated by performing reconstruction with differe nt levels of random scatter in the velocity data. The effect of the an gle range used for velocity measurements has been analyzed, and it is shown that, depending on the refraction-angle range, reconstruction of the longitudinal elastic constants is dominated either by the quasilo ngitudinal or by the quasitransverse velocity. The desirable range of refraction angles for determination of elastic constants with high acc uracy is determined.