Michael P. Ekstrom
Schlumberger Austin Res., 8311 North RR620, Austin, TX 78720-0015
C. J. Randall
SciComp, Inc., Austin, TX 78731
The response of an acoustic logging tool in a fluid-filled borehole is quite complex, being composed of multiple interferring components. Each component has unique velocity dispersion and attenuation characteristics which are related to properties of the formation surrounding the borehole. Robust and accurate methods to decompose the borehole signals and to analyze the components have been the subjects of much interest. In this paper, a new hybrid spectral estimator is introduced to estimate the velocity dispersion and attenuation of space-time wave fields from borehole array sensor data. This high-resolution estimator is based on an eigensystem decomposition of a matrix pencil, and provides an enhanced statistical performance while avoiding the severe ill conditioning of the classical Prony's method [Lang et al., Geophysics 52, 530--544 (1987)]. This improvement in spectral resolution allows the estimated wave-number-frequency spectrum to be decomposed into its constitutive parts for subsequent individual analysis and wave field reconstruction. These estimation and decomposition procedures are mechanized in a set of MATLAB routines, and will be first validated by processing model waveforms for a homogeneous formation, then demonstrated with a variety of both model and field-acquired data [C. J. Randall, J. Acoust. Soc. Am. 90, 1620--1631 (1991)].