Acoustic Wave Propagation in and around a Fluid-filled Borehole of Irregular Cross-section

Boreholes with 10% or more ellipticity are not uncommon. In this paper, we consider the coupling of an incident elastic wave into a borehole of irregular cross-section and investigate the cross-mode coupling phenomenon in sonic well logging in the presence of borehole irregularity. The mode-matching method is used. Different from its original formulation, we employ the Reichel et al. algorithm to obtain the discrete least square approximation by trigonometric polynomials, a technique closely related to the fast Fourier transform (FFT). Our method not only yields great accuracy but also gains computational speed. Our study shows that the pressure in the borehole fluid is sensitive to the irregularity of the borehole cross-section, it is larger if the incident wave is along the effective minor axis and smaller if the incident wave is along the effective major axis. In the frequency range of a typical borehole experiment, the solid displacement in the formation is much less affected by the borehole irregularity. In an elliptical borehole, a monopole source excites dipole wave trains that are characteristic of the tube waves, and a centered dipole source excites monopole wave trains that are characteristic of the flexural waves.