| Summary: | For linear wave propagation in anisotropic media, the principle of superposition still
holds. The decomposition of the acoustic dipole log is based on this principle. In the
forward decomposition inline and crossline acoustic dipole logs at any azimuthal angle
the projection of measurements is along the principal direction of the formation.
In the inverse decomposition the measurements along the principal direction can be
constructed from the orthogonal pair of inline and crossline acoustic dipole log. The
analytic formulas for both forward and inverse decompositions of the dipole laaa sss-saog
are derived in this paper. The inverse decomposition formula is the solution in
the least-square sense. Numerical examples are demonstrated for the acoustic dipole
log decomposition in isotropic and anisotropic formations. The synthetic dipole log is
calculated by the 3-D finite difference method. The numerical examples also show that
the inverse decomposition formula works very well with noisy data. This inverse decomposition formula will be useful to process the field acoustic logging data in anisotropic formations. It can provide the direction of the formation anisotropy as well as the degree of anisotropy. Because acoustic dipole logging is in the near field distance, the particle motion is complicated. The particle motion is linearly polarized only in the principle direction. The initial particle motion with a dipole source at an arbitrary azimuthal angle tends to point in the fast shear wave direction. However, it will be difficult to use this information to find a stable estimation of a fast shear wave direction.
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