Guided Waves In Slight, Azimuthally Anisotropic Formations

Abstract

A method of calculating dispersion curves for guided waves in slight, azimuthally anisotropic formations is developed with perturbation theory. The fluid is assumed to be inviscid, the formation perfectly elastic and homogeneous, and the ·borehole wall cylindrical. The first step is calculating the elastic moduli for a transversely isotropic formation whose moduli are close to those for the azimuthally anisotropic formation. The perturbative method then uses the particle displacements for a guided wave in the transversely isotropic formation and the difference between the elastic moduli in the two formations to determine a first order correction to the wavenumber. These corrections are used to calculate the perturbation in the phase velocity. To test the method, the elastic moduli of an isotropic formation were pe~turbed to make it transversely isotropic. The exact dispersion curves and those estimated by the perturbative method are very close. The perturbative method was used to calculate dispersion curves for guided waves in two different geologic settings - a formation with aligned, vertical cracks and another with a tilted bed. In both examples the dispersion curves for the guided waves appear similar to typical dispersion curves for either isotropic or transversely isotropic formations. At low frequencies, the phase velocities of the tube waves closely match the velocities predicted by Rice's formula.