Estimating Phase Velocity and Attenuation of Guided Waves in Acoustic Logging Data

Abstract

Phase velocity and attenuation of guided waves have been estimated from multireceiver, full waveform, acoustic logging data using the extended Prony's method. Since a formation affects velocity and attenuation, estimating these quantities is important in evaluating the formation properties. The estimation is performed using an array processing technique which requires two steps: (1) the traces for all receivers are transformed into the frequency domain, and (2) for each frequency the extended Prony's method is used to determine the presence of a guided wave propagating past the array of receivers. The guided wave properties estimated by the Prony's method include amplitude, attenuation, and phase change which is related to phase velocity. An important assumption in this array processing technique is that the formation, borehole fluid, and tool are homogeneous along the receiving array. For synthetic data, the phase velocities and attenuation of the tube wave and two modes of the pseudo-Rayleigh wave are accurately estimated over many frequencies, with the exception that the low amplitude of the second mode causes its attenuation estimate to be somewhat less accurate. For laboratory data, very good estimates of the phase velocities of the tube wave and three modes of the pseudo-Rayleigh wave are obtained. Since the materials used in the laboratory experiment had very large quality factors, the attenuation could not be estimated. For field data, the dispersion of the tube wave and the velocity of the pseudo-Rayleigh wave at its cutoff are very close to those predicted by another, independent method. Accurate attenuation estimates could not be made because the data are noisy and consist of only eight traces.