Velocity Analysis of Multi-Receiver Full Waveform Acoustic Logging Data In Open and Cased Holes

Average semblance and maximum-likelihood spectral analyses are applied to synthetic and field full waveform acoustic logging data to determine formation velocities. Of particular interest is the ability of these methods to resolve the P and shear/pseudoRayleigh arrivals in data from poorly-bonded cased boreholes. In synthetic open-hole data the velocity analyses yield results within 4% of the true velocities. Results from synthetic well-bonded cased hole data are generally as good as those from the open hole data. However, if the formation P-wave velocity is within roughly 10% of the plate velocity of the steel pipe (about 5.3-5.5 km/s), then there may be a resonance effect that appears to slow down the P wave slightly (on the order of 6%). For cased-hole models with no steel/cement bonding (the free-pipe situation), the measured P-wave velocities are typically 6 to 8% less than the actual formation velocities. If the formation S-wave velocity is greater than about 2.5 km/s, the S-wave velocity estimate may also be 6 to 8% low. Furthermore, increasing the thickness of either the cement layer or the fluid layer between the pipe and the cement further decreases the formation velocity estimates. Also, if the P-wave velocity is within roughly 15% of the velocity of the steel arrival, the P wave may not be resolved by the semblance method unless the data is first low-pass filtered. Initial tests show that this filtering process may adversely affect the final P-wave velocity estimate, but the details of this type of approach have not been studied. The P wave is resolved. by spectral analysis of the original, nnfiltered data. For cased-hole models with no cement/formation bonding (the unbonded-casing 366 Block et al. situation), formation S-wave velocities are estimated to within 3% relative error, and the formation P-wave velocity is estimated to within 2% error in a slow formation. However, for P-wave velocities between 3.4 km/s and 5.94 km/a, the P wave cannot be resolved by spectral analysis, and it is resolved by the semblance method only in the model with the low velocity (3.4 km/s).