Abstract

We apply an iterative, linearized inversion method to Stoneley waves recorded on acoustic logs in a borehole. Our objective is to assess inversion of Stoneley wave phase and group velocity as a practical technique for shear velocity logging in slow formations. Indirect techniques for shear logging are of particular importance in this case because there is no shear head wave arrival. Acoustic logs from a long-spaced sonic tool provided high-quality, low-noise data in the 1 to 10 kHz band for this experiment.A shear velocity profile estimated by inversion of a 60 ft (18.3 m) section of full-wave acoustic data correlates well with the P-wave log for the section. The inferred shear velocity ranges from 60 to 90 percent of the sound velocity of the fluid. Formal error estimates on the shear velocity are everywhere less than 5 percent. Moreover, application of the same inversion method to synthetic waveforms corroborates these error estimates. Finally, a synthetic acoustic waveform computed from inversion results is an excellent match to the observed waveform.On the basis of these results, we conclude that Stoneley-wave inversion constitutes a practical, indirect, shear-logging technique for slow formations. Success of the shear-logging method depends upon availability of high-quality, low-noise waveform data in the 1 to 4 kHz band. Given good prior estimates of compressional velocity and density of the borehole fluid, only rough estimates of borehole radius and formation density and compressional velocity are required. The existing inversion procedure also yields estimates of formation Q inferred from spectral amplitudes of Stoneley waves. This extension of the method is promising, since amplitudes of Stoneley waves in a slow formation are highly sensitive to formation Q. Attenuation caused by formation Q dominates over attenuation caused by fluid viscosity if the viscosity is less than about 0.1 N.s/m 2 . However, Stoneley-wave amplitudes are also sensitive to gradients in shear velocity in the direction of propagation. In some cases, correction for the effects of shear-velocity gradients is required to obtain the formation Q from Stoneley-wave attenuation.

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