Slowness estimation from sonic logging waveforms

Along with the introduction of full waveform sonic logging tools has come a variety of associated digital signal processing techniques designed to estimate the formation compressional and shear slownesses (Δt, inverse velocity, travel time). In this paper, we have described these techniques and applied them, for the most part, to the same set of field waveforms. We have divided our treatment into those techniques associated with traditional two-received tools, and those associated with the recent multi-receiver array tools.

The processing associated with two-receiver tools generally consists of methods which make use of time windows and coherence measures. Specifically, time windows are positioned on each trace, and the coherence of the windowed signals is computed. The window positions which result in the highest coherence can be used to derive an estimate of the wave slowness. Issues associated with two-receiver processing seem to be focused on methods for locating the arrival time of the waves at the receivers. The semblance coherence measure seems to be more popular in the literature than either cross-correlation methods or cross-spectral techniques. In implementing these methods, we have found the resulting estimates to be somewhat sensitive to issues such as the shape and duration of the time window. The estimation of the shear slowness from two-receiver data is more difficult than the estimation of compressional slowness, due to interference from other arrivals including mode conversions from bed boundaries and fractures, and due to dispersion. Some techniques address the difficulties associated with shear estimation more than others.

With the recent commercial introduction of multi-receiver sonic array tools, a number of processing techniques have appeared in the literature. Analogous to windowed coherence methods developed for two-receiver tools, multi-receiver windowed coherence methods have developed for array tools. Again, semblance processing seems to be particularly useful. Because longer array apertures can lead to a reduced ability to resolve thin beds in the formation, a new technique has been developed which extracts sub-arrays from the full arryas associated with successive firings of the source transducer. The shorter arrays result in higher resolution, and the multiplicity of sub-arrays provide added stability. Frequency domain techniques have also been developed which are able to handle dispersive wave propagation and can aid in situations where waves are overlapped in space and time due to close slownesses. These two situations can cause coherence based methods to perform poorly. An assumption common to all processing techniques is that the formation is homogeneous across the aperture of the (sub-)array. This causes the performance of these techniques to degrade when there is a bed boundary or fracture within the aperture. An area of future research is likely to be in the area of processing for arrays in inhomogeneous media.