Ultrasonic anisotropic phase velocity determination with the Radon transformation

Coplanar arrays of small longitudinal ultrasonic transducers acquire a set of waveforms which are initially plotted as an amplitude image in the offset-time domain. This amplitude image is then mapped to the intercept time-horizontal slowness (τ−p) domain via a slant-stack Radon transformation. The shape of the locus of these arrivals in τ−p space directly provides information on the propagation angle-dependent phase velocities in an anisotropic medium. The method is applied to an isotropic acrylic and an anisotropic laminate with orthorhombic symmetry. The method allows determination of the phase velocities over an 80° range of propagation angles. The acrylic is isotropic with a phase velocity of 2780 m/s which differs little from that determined in a conventional pulse transmission. The phase velocities versus propagation angle were measured in three planes of symmetry and in one off-symmetry plane in the laminate. Anisotropies of up to 22% over an 80° range of propagation angles were found in the planes perpendicular to the layering. The plane containing the layering was only weakly anisotropic with velocities dependent on the weave of the fiber mats.