Group versus phase velocity in laboratory measurements on orthorhombic samples

Robert W. Vestrum, R. James Brown

In laboratory measurements of traveltimes across anisotropic materials, there can be a significant difference between the group and phase velocities when the measurements are made in an off-symmetry direction. Ideally, to measure group velocity one should use waves generated by a point source and recorded with a point receiver; and one should use plane waves to measure phase velocity. In the actual laboratory condition we are dealing with an intermediate situation. There is some question, therefore, as to which of group or phase traveltimes across the medium in these directions is measured.

Forward models have been generated showing the wavefronts propagating through Phenolic CE, an orthorhombic-isotropic medium currently used in physical modelling experiments at The University of Calgary. These models have been interpreted and an assessment has been made to determine whether the traveltimes will invert to yield phase or group velocities or, in fact, something between the two. Further geometrical analysis has revealed an additional method of determining true group and phase velocities from the observed traveltimes.

From the modelling and geometrical analysis, it was determined that traveltimes due to phase velocity of the phenolic were measured in most of the off-symmetry-axis measurements reported by Cheadle et al. The group velocity appears difficult to determine given the finite size of the source and receiver transducers and the dimensions of the samples that were used.