| Summary: | Phase velocity and attenuation of guided waves have been estimated from acoustic logging
data recorded by a receiving array. The method uses data from multiple sources
and successive depths yielding more accurate estimates than could be obtained with
data from one source and one depth. The inversion requires two steps: (1) all traces are
transformed into the frequency domain with a fast Fourier transform, and (2) at each
frequency a modification of Prony's method is used to estimate the guided waves' characteristics which include amplitude, attenuation coefficient, and wavenumber (which
yields the phase velocity). An important assumption underlying this technique is that
the formation, borehole fluid, and tool are homogeneous along the receiving array.
Application of this method to synthetic data shows that the phase velocity and attenuation of the tube and pseudo-Rayleigh waves are accurately estimated at many
frequencies. With noisy synthetic data, the phase velocities are correctly determined,
but the attenuation estimates, being sensitive to noise, are accurate only when the amplitudes are high. Using data from multiple sources and successive depths suppresses
the noise effects and improves both estimates. The amplitude estimates are important
because they roughly indicate the reliability of the velocity and attenuation estimates.
From laboratory and field data, the velocities for the guided waves are accurately predicted even when the amplitudes are low. The attenuation estimates are good when
the amplitudes are high but degrade as the amplitudes diminish.
|
|---|