Novel and Stable Formulations for the Response of Horizontal-Coil Eccentric Antennas in a Cylindrically Multilayered Medium

In this paper, we present a set of novel and stable formulations to calculate the response of logging tools with horizontal-coil antennas in an eccentric borehole straddling cylindrically multilayered formations. It can be applied in fast forward computation and the inverse problem for electromagnetic (EM) well-logging in deviated and horizontal wells, where eccentric scenarios are often encountered. Our formulations are different from previous ones in following aspects. First, the tool mandrel can be cylindrically multilayered and the electrical parameters of each layer are arbitrary. Namely, it is not limited to being perfectly metallic. Second, the EM propagation in inhomogeneous medium is considered by the generalized reflection and transmission method, in place of the transfer matrices. The associated generalized reflection and transmission coefficients are expressed by the ratios of Bessel or Hankel functions that obviate the notorious overflow problem for numerical computation. Finally, a set of linear matrix functions are constructed to solve for the EM waves in a borehole based on the concept of the generalized reflection, rather than that of the fictitious boundary. Numerical results in comparison with those from other approaches have demonstrated the validity and stability of our new formulations.