Petrophysics of magnetic dipole fields in an anisotropic earth

Measurement-while-drilling (MWD) resistivity log data are often acquired in highly deviated or horizontal holes. The loop sensors are located on the drill collar and are approximated as magnetic dipoles. The conductivity of the earth in the vertical direction σ_v and horizontal direction σ_h are almost always different. When an MWD resistivity tool enters a new bed, the response is compared with the precomputed logs to aid in the determination of the location of the drill bit. The MWD tool response, however, is sensitive to resistivity anisotropy. An alternative method is used to derive analytical expressions for the Sommerfeld-type integrals. Numerical results give typical MWD tool response as a function of the inclination angle θ the tool makes with respect to the axes of anisotropy and also as a function of the anisotropy index κ=(σ_h/σ_v)^1/2