Joint inversion of formation radial shear-velocity profiles by dipole acoustic logging while drilling

Abstract

Formation properties near a borehole are frequently altered by mechanical damage from drilling, leading to variations of formation elastic velocities in the radial direction. Inversions of radial shear profiles are necessary for a real-time evaluation of the drilling conditions. In this study, we investigate acoustic wave propagation in a logging-while-drilling (LWD) model excited by a dipole transducer in cylindrically layered media. It is revealed that the dispersion characteristics of the dipole waves of the LWD are sensitive to the radial formation velocity variation. Accordingly, we develop a joint inversion method that evaluates radial shear-velocity profiles using the dipole modes of the first and second orders. The propagation of these two modes is strongly influenced by formation alterations, but the inversion results obtained using a single dipole mode indicate ambiguity caused by the nonuniqueness problem. Through our joint inversion, the additional second-order dipole wave can effectively help address the nonuniqueness issue in dipole acoustic logging, although its dispersion features differ in fast and slow formations. It is validated that the joint inversion has considerably improved convergence and accuracy in evaluating the thickness and shear velocity of the altered zone, compared with the estimation by a single acoustic mode. Furthermore, we develop numerical results based on synthetic logging data to demonstrate the feasibility of this inversion in a continuously varying profile, regardless of whether the formation surrounding the borehole is fast or slow. Even when strong drilling noises of low frequencies are added to the receiver signal arrays, the means of joint inversion can remain stable, and the shear-velocity profiles can be evaluated with good precision.