Dispersion Asymptotic Analysis and its Applications in Acoustic Logging

Abstract

This paper presents a new and robust method for evaluating the output from acoustic well-log waveform processing by analyzing the asymptotic behavior of dispersion curves. It is a data-driven approach which helps improve the accuracy of formation slowness measurement and identifies any need for a dispersion correction.

In acoustic well logging, many of the waves propagating inside the borehole are dispersive, such as wireline dipole and LWD quadrupole waves for the determination of formation shear slowness, and leaky P wave for compressional slowness in soft formations. Only at low frequency does the speed of these waves approach the true formation value, the wave speed being slower at higher frequencies. Slowness processing can therefore be influenced by strong high frequency waves, resulting in measured slowness values greater than the true formation values. The new method determines whether a dispersion curve is asymptotic to the true formation by calculating the coherence of the slowness at each frequency interval of the dispersion curve to indicate the level of the velocity dispersion. This coherence indicator is then plotted against the averaged slowness within the frequency interval to show how well the asymptotic slowness is approached.

The method has been applied to wireline acoustic logging dipole waves in wells with both hard and soft formations, as well as to leaky P waves in soft formations. Results show that the method not only identifies the fastest waves in the data but also identifies where additional model-based dispersion corrections are needed. When the waveform's dispersion curve has a smooth approach to its true formation slowness, the asymptotic analysis shows a high value of coherence at that slowness indicting high confidence in the measured slowness. On the other hand, when the dispersion curve lacks the low frequency asymptotic part, the analysis's low-value indicator suggests that a correction to the measured slowness is necessary.

The indicator generated by this method allows the quality of the formation slowness measurement to be assessed. Traditional data-driven dispersive QC methods can identify if the processed slowness is the slowest within the available wave energy but does not assess the result's accuracy when the asymptotic part of the dispersion is missing due to lack of low frequency energy. However, this method achieves both of these two objectives in a straightforward way.