The elastic characterization of anisotropic solids using group velocity data

摘要

Use of Point Source/Point Receiver (PS/PR) techniques for elastic constant determination requires the availability of methods for inverting group velocity data. The algorithms in existence invoke parametric expressions for the group velocity, and this necessitates two-step inversion schemes in which the values of the parameters are determined at each iteration of the elastic constants. In this paper we present a much simpler inversion scheme that is applicable to first arrival longitudinal wave data, and which yields acceptable 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 symmetry media. It is based on an approximate analytical equation for the directional dependence of the longitudinal group slowness that extends to quartic terms in the group velocity direction vector. Extensive calculations have shown that this inversion scheme performs well even for media of fairly high degree of anisotropy. The formula for the group slowness should also be useful in other inverse problems involving first wave arrival data, in seismology, materials characterization and elsewhere.