Abstract:
We present a finite-element algorithm for computing NIT responses for 3D conductivity structures. The governing differential equations in the finite-element method are derived from the T-Omega Helmholtz decomposition of the magnetic field H in Maxwell's equations, in which T is the electric vector potential and Omega is the magnetic scalar potential. The Coulomb gauge condition on T necessary to obtain a unique solution for T is incorporated into the magnetic flux density conservation equation. This decomposition has two important benefits. First, the only unknown variable in the air is the scalar value of Omega. Second, the curl-curl equation describing T is only defined in the earth. By comparison, the system of curl-curl equations for H and the electric field E are singular in the air, where the conductivity sigma is zero. Although the use of a small but nonzero value of sigma in the air and application of a divergence correction are usually necessary in the E or H formulation, the T-Omega method avoids this necessity. In the finite-element approximation, T and Omega are represented by the edge-element and nodal-element interpolation functions within each brick element, respectively. The validity of this modeling approach is investigated and confirmed by comparing modeling results with those of other numerical techniques for two 3D models.
