Application Of Rayleigh's Principle To Guided Waves In A Borehole

Abstract

The Lagrangian for guided waves in a completely general borehole model is presented. Rayleigh's principle is used to derive the first order perturbations in wavenumber and frequency due to slight perturbations in the physical properties of the model. The principle is also used to calculate perturbations in frequency due to perturbations in wavenumber. These formulas are applied to a fluid-filled borehole through an infinite, transversely isotropic formation, for which the axis of symmetry is aligned with the borehole, to calculate (1) partial derivatives of wavenumber and velocity at constant frequency, (2) partial derivatives of frequency and velocity at constant wavenumber, and (3) group velocity. These formulas are also applied to a formation with general anisotropy to calculate the velocity dispersion.