A hybrid three‐dimensional electromagnetic modeling scheme

Abstract

We present an efficient numerical method for computing electromagnetic (EM) scattering of arbitrary three‐dimensional (3-D) local inhomogeneities buried in a uniform or two‐layered earth. In this scheme the inhomogeneity is enclosed by a volume whose conductivity is discretized by a finite‐element mesh and 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 the fields at the boundany in terms of electric fields inside the boundary. The Green’s function is used to derive the second set of equations. An iterative algorithm has been developed to solve these two sets of equations. The solutions are the electric fields at nodes inside the finite‐element mesh. The 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. The results agree with earlier model analyses using the finite‐element technique.

Three-dimensional em modeling

“…The overshoot at the edge of the body in the 3D case is to be expected; it is due to current channeling. The 3D hybrid results of Lee et al (1981) on the other hand, differ considerably from the 2D results over the body. Figure 9 shows the same comparison for TE excitation, in which case the electric field is parallel to strike, so that there is no surface charge in the 2D case.…”

“…On the other hand, for the hybrid scheme of Figure 7b the FE solution operates in a homogeneous region, but evaluation of (60) at singular points on the surface of the mesh is very difficult. Lee et al (1981 ), developed an iterative hybrid solution, by asstiming an initial guess for Eb, the boundary field, calculating Ev, then finding a new Eb using (60), and proceeding iteratively. Their results agree with the FE and IE results shown in Figure 6 for a low-contrast (ab/a.…”

“…However, their MT results for a body with a conductivity contrast of 200 do not agree with our IE results as shown by Figures 8 and 9. Figure 8 compares TM-mode MT apparent resistivity results for a 2D body computed by the FE method with IE results of Wannamaker and Hohmann (1983) and hybrid results of Lee et al (1981) for a 3D body with the same cross section. The body has a conductivity contrast of 200, and the frequency is 0.01 Hz.…”

Magnetotelluric investigations at Mount Hood, Oregon

“…Even though temperaturegradient wells near Timberline Lodge supported this interpretation, we carried out some 3-D simulations using a modified version of the hybrid modeling scheme introduced by Scheen (1978) and described by Pridmore {1978} and Lee et al (1981). The dark stippled region in Figure 6 outlines an area where the apparent resistivity polar diagrams for the bandwidth 0.01 to 0.001 Hz indicate a north-south polarization of the electric field Subsurface resistivity distributions based on I-D inversions of MT data from clusters 1 and 2.…”

Feasibility of simplified integral equation modeling of low-frequency marine CSEM with a resistive target

“…These methods have different computational advantages and disadvantages, some of which are discussed later. Hybrid methods ͑see, e.g., Lee et al, 1981;Best et al, 1985;Gupta et al, 1987͒ can be applied also.…”