A continued fraction method for modeling and inversion of triaxial induction logging tool

A thorough study on the one-dimensional forward modeling and inversion algorithm for triaxial induction logging tools in multi-layered transverse isotropic formation is presented in this paper. The algorithm is incorporates two parts: the optimized forward modeling and inversion. For the forward simulation, an alternate approach involving Gauss-Quadrature algorithm and continued fraction is used instead of simple fast Hankel transform or Gauss-Quadrature method. This new approach is more precise, robust and efficient for calculate the Bessl integral formulas. Then, the modified Gauss-Newton algorithm is used to invert the layered anisotropy. The positive constant, and Armijo method are introduced to search step length to inverse the vertical conductivity and horizontal conductivity of the anisotropy formation. The algorithm is shown to agree with the theory of triaxial induction logging.