The sonic wave fields produced by wireline and loggingwhile- drilling (LWD) monopole, dipole, and quadrupole tools often consist of multiple borehole modes. Classic frequency-semblance methods used to process this data often detect only strongly excited modes and overlook weak ones, or erroneously detect some modes.

Conventional dispersion processing methods can be separated into two groups: single- and multimode prediction algorithms. Single-mode methods are stable but only return one mode at each frequency, the most energetic one. 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 important information or encode these time differences in phase differences between adjacent frequencies. Conventional frequencysemblance approaches, which only use single frequencies independently from adjacent ones, ignore this phase information.

In this paper, we show that modifying one conventional method to incorporate the arrival time of modes, or the phase difference between adjacent frequencies, facilitates multimode dispersion analysis. We propose employing the phase differences between adjacent frequencies for this purpose.

The method begins by selecting a target slowness, a target frequency, and a frequency band surrounding it. A travel time range is then calculated based on the target slowness by integrating the slowness of the waves over the propagation path. Next, we calculate the phase differences between adjacent frequencies from the predicted travel times and remove the differences in the selected frequency band. The data, with corrected phases, are then stacked to enhance the signal-to-noise ratio (SNR) of the target signals. Finally, a DPFS equation is applied to the wave spectra after stacking to calculate semblance values. This process is repeated for different target frequencies and assumed slownesses to generate a 2D slowness-frequency semblance map. The final dispersion curves are estimated from the peaks on this map.

We validated the proposed approach with synthetic, laboratory, and field data. The results suggested the method can extract a much more comprehensive set of modes present in the sonic data. Additionally, the method provided reliable estimates, even when the number of receivers was small. Unlike the Prony and Matrix-pencil that are 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. Thus, it is more stable than other multimode algorithms and less sensitive to unbalanced receiver arrays, poor data quality, and formation heterogeneity.

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