Dispersion Corrections on LWD Quadrupole and Wireline Dipole Array Data Revisited

In slow formation borehole acoustic wireline logging (WL) and logging while drilling (LWD), it is common to obtain formation shear slowness from the dispersive borehole guided flexural and quadrupole wave, respectively. Due to poor signal-to-noise ratio and/or tool eccentricity effects, it is not always possible to obtain formation shear slowness directly via conventional slowness-time-coherency (STC) methods. Consequently, a dispersion correction is frequently needed to QC and/or correct the STC result. We propose a hybrid method that allows for a model-based as well as a phenomenon-based approach. The latter is ideally suited to address, identify, and overcome the limitations and dependence of the former on tool eccentricity, tool model, inaccurate knowledge of borehole fluid slowness, formation anisotropy (vertical transverse isotropy), etc. Our method minimizes the over-frequency (f) cumulative difference between two slowness dispersion curves, S...(f, Ss, ..,etc.) and S_SFC(f), in the least-squares sense. S_SFC(f) denotes the dipole (WL) or quadrupole (LWD) slowness dispersion curve as obtained from the array slowness-frequency-coherency (SFC) data and S...(f, , Ss, ..,etc.) either denotes a model-based (... = “MB”) or phenomenon-based (... = “PB”) slowness dispersion curve. The PB method uses known analytical function families that are parametrized by several—not per se physical—parameters (e.g., Scholte wave slowness, cutoff frequency, etc.) in addition to the formation shear slowness (Ss). Such functions have sufficient degrees of freedom in describing WL dipole or LWD quadrupole slowness dispersion curves under all kinds of (non-ideal) circumstances (e.g., unknown borehole fluid slowness, tool eccentricity, etc.). Typically, all parameters in such a phenomenological description require inversion. In the MB method, one assumes a very specific physical model/configuration (e.g., elastic tool centered in a fluid-filled borehole and surrounded by a homogeneous and isotropic elastic formation), which, depending on model complexity, may require a significant amount of computation. We have applied both inversion methods to a variety of LWD quadrupole data sets, where the MB inversion was characterized by an elastic tool centered in a circular fluid-filled borehole surrounded by a homogeneous isotropic elastic formation. Where the model fitted reality, both methods were in excellent agreement. Where the model did not fit reality (e.g., due to tool eccentricity/borehole rugosity, etc.), only the PB method obtained the correct answer. The proposed PB approach allows for accurate formation shear slowness inversion in a variety of practical circumstances that are not properly addressed in the MB approach (e.g., tool eccentricity/borehole rugosity, etc.). Different outcomes are indicative of what these circumstances might be.