Three-dimensional numerical modeling of induction resistivity tools for well logging problems using the finite element method

In the well logging field, three-dimensional (3-D) problems have been the subject of strong interest in recent years. In this dissertation, the formation geometry consists of a borehole and a three-layer dipping bed. Induction tools are simulated in this 3-D environment. The numerical simulation is accomplished using the finite element method.; The 3-D problem domain is first divided into many polyhedra, and then tetrahedra are generated in each polyhedron. The grid generation is carried out by Geompack software.; The finite element method (FEM) is applied to solve the vector wave equation. In the numerical calculation part, the Biconjugate Gradient Method (BCGM) is used to solve a large set of linear equations. Because of the large number of unknowns and associated linear equations, an efficient matrix storage method has been developed.; The 3-D modeling results are compared with 1-D and 2-D results in special cases to check their accuracy. The agreement between the results calculated by the FEM 3-D code and those calculated by the 1-D code, the 2-D code, and the finite difference method (FDM) 3-D code is good. A user's guide is prepared for the FEM 3-D modeling code and is presented in Appendix II.