Approximate formulae for acoustic wave group slownesses in weakly orthorhombic media

Approximate formulae are presented for the group slownesses (inverse group velocities) of quasi-longitudinal and quasi-transverse elastic waves in wea kly orthorhombic solids. The formula for the quasi-longitudinal modes expre sses the group slowness as a truncated series in the group velocity directi on vector, with the coefficients being longitudinal elastic constants or co mbinations thereof. Even for fairly large degrees of anisotropy the approxi mate formula is generally in good agreement with exact calculations. Numeri cal examples are provided to show that this formula can accurately account for the non-ellipticity of the quasi-longitudinal group velocity surface, e ven in non-symmetry directions. This explicit formula will he of use in res olving first arrival inverse problems, materials characterization and other applications. The formula for the quasi-transverse modes, which has a simi lar form to that for the quasi-longitudinal mode, well approximates the cor responding group velocity surface in a symmetry plane in the absence of cus ps.