An acoustic logging tool in inclined or horizontal boreholes may be placed apart from the center and produce additional complicated wavefields. We investigate the effects of an off-centered tool on monopole, dipole, and quadrupole logs due to off-centering of the tool. In recent logging tools, monopole, dipole, and quadrupole logs can be obtained by adding or subtracting responses at four monopole (pressure) receiver arrays at right angles. We examine the responses of the four monopole receiver array system for three directions of eccentricity: inline direction of the dipole source (Off [Formula: see text] case), crossline direction (Off [Formula: see text] case), and [Formula: see text] to the dipole source (Off [Formula: see text] case). To simulate responses at each receiver array, we use the discrete wavenumber method. In a dipole tool positioned on the borehole axis, the inline receiver arrays have only the flexural wave while the cross receiver arrays have zero response. However, an off-centered dipole source produces nondipole modes as well as the dipole mode. For all cases with a dipole source, the dipole mode was enhanced by subtracting responses at one of the inline receiver arrays from those of the other receiver array, and we could extract the formation shear velocity. Similar to the dipole source, an off-centered quadrupole source introduces additional nonquadrupole modes. The quadrupole mode was enhanced by subtracting the sum of responses at receiver arrays below negative poles of a quadrupole source from the sum of responses at receiver arrays below positive poles for all cases. In addition, the formation shear velocity was obtained from the time semblance calculation.
A numerical simulation of the acoustic and elastic wavefields radiated by a source on a fluid‐filled borehole embedded in a layered medium