The elastic characterization of anisotropic solids using group velocity data

Use of Point Source/Point Receiver (PS/PR) techniques for elastic constant determination requires the availability of methods for inverting group velo city data. The algorithms in existence invoke parametric expressions for th e group velocity, and this necessitates two-step inversion schemes in which the values of the parameters are determined at each iteration of the elast ic constants. In this paper we present a much simpler inversion scheme that is applicable to first arrival longitudinal wave data, and which yields ac ceptable values of the longitudinal elastic constants C-11, C-22, C-33, (C- 23+2C(44)), (C-31+2C(55)) and (C-12+2C(66)) for orthorhombic and higher sym metry media. It is based on an approximate analytical equation for the dire ctional dependence of the longitudinal group slowness that extends to quart ic terms in the group velocity direction vector. Extensive calculations hav e shown that this inversion scheme performs well even for media of fairly h igh degree of anisotropy. The formula for the group slowness should also be useful in other inverse problems involving first wave arrival data, in sei smology, materials characterization and elsewhere.