Effect of background fields on three‐dimensional finite element analysis of induction logging

Abstract

Abstract. Three-dimensional controlled-source electromagnetic induction algorithms are generally formulated in terms of secondary fields or potentials. The selection of the primary solution is somewhat arbitrary but can greatly influence the e•ciency of finite element codes. A simple induction logging problem demonstrates this statement. Responses are computed using a three-dimensional finite element method for two different selections of the primary potential, one that includes the borehole effect and one that does not. The accuracy of the numerical solution, for a given mesh size, increases dramatically when the borehole effect is included in the primary solution. This is because the sharp gradients in the electromagnetic field near the transmitter due to the presence of the borehole are coded as an analytic source term and do not have to be captured by the numerical approximation. Whenever possible, finite element analysts should select a convenient primary solution that closely matches the anticipated total solution in the immediate vicinity of the transmitter.

Three-Dimensional Wide-Band Electromagnetic Forward Modelling Using Potential Technique

“…On the other hand, we can implement the potential technique. Several investigation has adopted the use of potentials (magnetic vector A and electric scalar ϕ) in 3-D forward simulation to solve specific geo-electromagnetic problems [29][30][31][32]. Reference [33] applied the A-ϕ disintegration of the electric field using the finite volume method to solve magnetotelluric problems.…”