Finite Volume Modeling of Borehole Electromagnetic Logging in 3-D Anisotropic Formations Using Coupled Scalar-Vector Potentials

Author

Novo, Marcela S. ; Da Silva, Luiz C. ; Teixeira, Fernando L.

Author_Institution

Pontifical Catholic Univ. of Rio de Janeiro, Rio de Janeiro

Volume

6

fYear

2007

fDate

6/29/1905 12:00:00 AM

Firstpage

549

Lastpage

552

Abstract

A cylindrical-grid finite-volume (FV) algorithm for the solution of time-harmonic Maxwell´s equations in fully three-dimensional (3-D) anisotropic media is presented. To circumvent ill-conditioning and convergence problems, Maxwell´s equations are reformulated in terms of potentials in the null space of the curl operator and its complement by applying a Helmholtz decomposition to the electric field. A staggered-grid in cylindrical coordinates is used to better conform to the typical geometries of well-logging problems. The resulting sparse linear system is solved by preconditioned Krylov-subspace methods. FV results are validated in earth formations with anisotropic conductivity against both finite-difference time-domain and numerical mode matching results.

Keywords

Helmholtz equations; Maxwell equations; anisotropic media; finite difference time-domain analysis; finite volume methods; well logging; 3-D anisotropic media; Helmholtz decomposition; Krylov-subspace method; borehole electromagnetic logging; coupled scalar-vector potential; cylindrical-grid finite-volume algorithm; finite volume modeling; finite-difference time-domain; time-harmonic Maxwell equation; well logging; Anisotropic magnetoresistance; Conductivity; Earth; Electromagnetic coupling; Electromagnetic modeling; Finite difference methods; Geometry; Linear systems; Maxwell equations; Null space; Anisotropic media; Maxwell´s equations; finite volume (FV) methods; finite volume methods; well-logging;

fLanguage

English

Journal_Title

Antennas and Wireless Propagation Letters, IEEE

Publisher

ieee

ISSN

1536-1225

Type

jour

DOI

10.1109/LAWP.2007.906301

Filename

4357949