Dispersion analysis of borehole sonic measurements by Hilbert transform and band-pass filters

Abstract

Dispersion analysis of waves can reveal important mechanical properties of the formation around the borehole. The traditional dispersion analysis methods are affected by wave modes and aliasing. A new method is developed to perform dispersion analysis of borehole array acoustic logging, which combines the semblance of time-slowness coherence based on differential phase (STC-DP) processing and band-pass filters. Unlike the classic STC method, STC-DP is not sensitive to the window length. Two kinds of band-pass filters, the multiple filter technique and the finite-impulse response filter, are used. The band-pass filters can decompose the waveform signal into a series of waveforms in the frequency-time domain. In contrast to traditional dispersion analysis methods, there is no knowledge of wave modes. The new method can extract multimode dispersion curves, especially for the weak wave mode. For most dispersion analysis methods, the aliasing will appear in the high-frequency band when the scanning range of slowness is large enough. The aliased modes might interfere with other true modes, but the aliased modes are quite different from other true modes in the time-slowness grid. Therefore, aliased modes can be removed in the time-slowness grid based on the modal dispersion curves. Synthetic and field examples are used to verify the advantages of the proposed method over traditional dispersion analysis methods.