Borehole Sonic Data Dispersion Analysis With a Modified Differential-Phase Semblance Method

Abstract

Ruijia Wang, Richard Coates, and Jiajun Zhao The sonic wave fields produced by wireline and logging-while-drilling (LWD) monopole, dipole, and quadrupole tools often consist of multiple borehole modes. Classic frequency-slowness semblance-map methods used to process this data often detect only strongly excited modes and overlook weak ones, and erroneously detect some modes. Conventional dispersion processing methods can be separated into two groups: single-mode and multimode extraction algorithms. Single-mode methods are stable but only return one mode, the most energetic one, at each frequency. Single-mode methods include the differential-phase frequency-semblance (DPFS) method and the weighted spectral-semblance method. Multimode methods can return multiple modes at each frequency but may be unstable in some cases. Due to their assumptions about signal models, multimode methods are often sensitive to unbalanced receiver arrays, poor data quality, and formation heterogeneity. For example, in some extreme cases, such as a formation with strong heterogeneity, multimode methods may yield erroneous ghost modes or discontinuous dispersion curves for each mode. Borehole modes with different slowness have different arrival times. Converting the data to the frequency domain can obscure this critical information or encode these time differences into phase differences between adjacent frequencies. Conventional frequency-semblance approaches, which use only a single frequency independently from adjacent ones, ignore this phase information. In this paper, we propose employing the phase differences between adjacent frequencies to facilitate multimode dispersion analysis. We modify one conventional method to incorporate the arrival time of modes or the phase difference between adjacent frequencies. We validate the proposed approach with synthetic, laboratory, and field data. The results suggest the method can extract a much more comprehensive representation of modes present in the sonic data. Additionally, the method provides reliable estimates, even when the number of receivers is small. Unlike the Prony and matrix-pencil methods based on assumed signal models, the proposed approach, which we denote “Modified Differential-Phase Frequency Semblance” (MDPFS), is a modification of the single-mode differential phase approach. The MDPFS is still a semblance-based approach, and as with other semblance-based processing, it is expected to be less sensitive to unbalanced receiver arrays, poor data quality, and formation heterogeneity than other multimode algorithms.