The measurement of weak anisotropy with the generalized reciprocal method

Abstract

Anisotropy parameters can be determined from seismic refraction data using the generalized reciprocal method (GRM) for a layer in which the velocity can be described with the Crampin approximation for transverse isotropy. The parameters are the standard anisotropy factor, which is the horizontal velocity divided by the vertical velocity, and a second poorly determined parameter which, for weak anisotropy, is approximated by a linear relationship with the anisotropy factor. Although only one anisotropy parameter is effectively determined, the second parameter is essential to ensure that the anisotropy does not degenerate to the elliptical condition which is indeterminate using the approach described in this paper. The anisotropy factor is taken as the value for which the phase velocity at the critical angle given by the Crampin equation is equal to the average velocity computed with the optimum XY value obtained from a GRM analysis of the refraction data. The anisotropy parameters can be used to improve the estimate of the refractor velocity, which can exhibit marked dip effects when the overlying layer is anisotropic. In a model study, depths computed with the phase velocity at the critical angle are within 3% of the true values, whereas those calculated with the horizontal phase velocity (which assumes isotropy) are greater than the true depths by about 25%. Anisotropy illustrates the pitfalls of model‐based inversion strategies, which seek agreement between the travetime data and the computed response of the model. With anisotropic layers, the traveltime data provide the seismic velocity in the overlying layer in the horizontal direction, whereas the seismic velocity near the critical angle is required for depth computations. If anisotropy is applicable, then the GRM using the methods described in this paper is able to provide a good starting model for other approaches, such as refraction tomography.