High-order, finite-difference modeling of multipole logging in formations with anisotropic attenuation and elasticity

A realistic description of the formation seen by an acoustic logging tool includes intrinsic attenuation, anisotropy, and spatial variations of the formation properties. These features are included in finite-difference (FD) modeling of acoustic full waveform multipole logging. Intrinsic attenuation is included using a phenomenological model that allows for many physical causes of attenuation, including viscous fluid flow losses, to be modeled. Furthermore, the attenuation, the corresponding velocity dispersion, and the elasticity can have any type of axisymmetric anisotropy. To increase computational speed and numerical precision, high-order FD operators that fully exploit vector processing architecture are used. The problem of using these operators near the symmetry axis in cylindrical coordinates is solved using symmetry arguments. Excellent results are obtained when comparing the calculations with the discrete wavenumber method. When correctly implemented, the FD model has the same numerical precision as the discrete wavenumber method but allows more general formations to be analyzed. Incorrect staggering of the high-order FD scheme gives artifacts equivalent to the inclusion of a thin layer between the fluid and the formation.