Numerical modeling for electrical methods

Abstract

An efficient numerical method, hybrid technique, for computing electromagnetic scattering of arbitrary 3-D local inhomogeneties in the earth has been presented (Lee et al, 1981). In this scheme the inhomogeneity is enclosed by a volume discretized by a finite element mesh whose boundary is only a slight distance away from the inhomogeneity. The scheme uses two sets of independent equations. The first is a set of finite element equations derived from a variational integral, and the second is a mathematical expression for fields at the boundary in terms of electric fields inside the boundary. Green’s function is used to derive the second set of equations. An interative algorithm has been developed to solve these two sets of equations. The solutions are the electric fields at nodes inside the finite element mesh. Scattered fields anywhere may then be obtained by performing volume integrations over the inhomogeneous region. The scheme is used for modeling 3-D inhomogeneities with plane-wave and magnetic dipole sources. Computer results are in good agreement with those obtained from the scale model using magnetic dipoles. One of the major applications of the scheme is in the magnetotelluric (MT) study. Hybrid modeling provides a useful vehicle with which we can investigate the effects on the impedance tensor and tipper vector elements caused by both inductive and current channeling phenomena. A quantitative evaluation of these effects through numerical simulations are of importance both in defining the relevant measurement parameters of a projected field survey and in understanding the distorting effects caused by small near-surface and remote heterogeneities. Near surface heterogeneous regions may greatly distort the impedance estimates of the field data and thus mask the response due to deeper targets. Through the use of appropriate models, the severity of this form of geologic noise may be evaluated and, consequently, various interpretational techniques can be developed to minimize this effect.