Theory of Unipole Acoustic Logging Tools and their Relevance to Dipole and Quadrupole Tools for Slow Formations

Abstract

Abstract A simplistic mathematical model has been developed to study a unipole acoustic logging tool. The model allows us to quantitatively relate a unipole tool response to monopole, dipole, and quadrupole tool responses, and vice versa. The interconnections between the different forms of excitation and reception provide some useful insights into the acoustic tool physics. The model is confirmed by numerical simulations. The unipole flexural wave sensitivity to shear slowness has been carefully studied. Numerical modeling and slowness-time-coherence analysis show that unipole, dipole, and quadrupole appear to have similar sensitivity to the shear slowness of a slow formation. The dispersion results suggest that a unipole flexural wave cannot be dispersion corrected based on any standard wave mode such as a dipole mode. Instead, the dispersion effect needs to be corrected by considering the mode-mixing nature. The look-up table approach used for this study represents the first step in the development. The unipole sensitivity to azimuthal shear anisotropy is studied. Substantial sensitivity is observed from the modeled responses in an azimuthally anisotropic medium. The same is true for a simplistic dipole tool. A conceptual quadrupole tool in the same formation shows reduced variation in waveforms with the rotation angle. Dispersion correction of the unipole flexural waves from the anisotropic formations is attempted by treating the formation as being isotropic. Corrections of the slow shear waves are less satisfactory. Interesting relations among unipole, dipole, and quadrupole also are revealed from a large-borehole scenario. The models confirm that in a large borehole with excessive tool eccentricity, both dipole and quadrupole responses may approach that of a unipole tool as some of the dipole and quadrupole excitation and reception sectors lose their proximity to the borehole wall. The modeling also shows that the dispersion effect in a unipole wave will be dependent on tool standoff, implying the necessity of standoff measurement for accurate dispersion corrections.