Comparing the Time-Domain EM Response of 2-D and Elongated 3-D Conductors Excited by a Rectangular Loop Source.

Abstract

We develop an algorithm for modelling the time-domain EM response of a general 2-D geometry excited by a 3-D source. A frontal solution, isoparametric finite-element method is used to solve for the y-components of the magnetic and electric fields in the frequencywavenumber (x, ky) z, w) domain where y is the direction of strike.Step response solutions are computed for 31 frequencies over the range 1 Hz to 100 kHz and transformed into the time-domain with a digital cosine filter.The response of a 2-D simple block target in a uniform half-space is compared to 3-D models of similar cross section with strike lengths of 0.5, 1, and 2 km, computed using the compact finite-element method. Further comparisons were made with the results of a 3-D time-stepping finite-difference solution for a block on the boundary of a quarter-space. In both cases the agreement between the 2.5-D and the 3-D results is close at early delay times with the 3-D target response decaying more rapidly than the 2-D target response at later times as expected. Although the late time-amplitudes differ, the profile shapes are very similar indicating that the 2.5-D model is useful for interpreting practical exploration problems.

ArjunAir: Updating and parallelizing an existing time domain electromagnetic inversion program

“…Decomposing equations 1 into their Cartesian components and Fourier transforming with respect to the along-strike coordinate leads to a set of two coupled scalar partial differential equations for the along strike components of the electric and magnetic fields in the wavenumber domain, where the fields are functions of x, z, ω and k y , where k y is the along-strike wavenumber. This set of equations is solved on a 2D mesh at 21 values of the alongstrike wavenumber, using an iso-parametric finite-element method, described by Sugeng et al (1993). The source behaviour is encompassed by the primary field, eliminating the need to explicitly include the magnetic dipole sources in the finite element scheme.…”

2-D electromagnetic modeling by finite‐element method with a dipole source and topography

“…In order to avoid undesirable effects from the boundaries, the boundaries are placed far away from the area of interest by increasing the node-spacing gradually. The finite-element method with the quadratic interpolation function allows considerble freedom in selecting the node-spacing (Sugeng et al, 1993). We can solve the global system matrix equations by either iterative or direct methods.…”

“…Higherorder interpolation functions are needed to calculate the space derivative ofÊ y andĤ y accurately in equations (6) to (9). Therefore, a quadratic element with eight nodes (Figure 2) has been adopted as in Sugeng et al (1993). In the element,Ê y and H y are represented by the quadratic interpolation function, meaning that the space derivative is described with a linear…”

“…Everett and Edwards (1992) and Unsworth et al (1993) evaluated the time-domain and frequency-domain responses, respectively, for CSEM sea-floor EM surveys. Sugeng et al (1993) used isoparametric finite elements to calculate the secondary EM fields excited by a rectangle loop. Sugeng et al (1996) also applied the isoparametric FEM to simulate the topography in airborne EM surveys.…”

2.5D inversion of airborne electromagnetic data

“…full-wave solutions to Maxwell's equations reduce to two coupled partial differential equations for the along-strike components of the secondary electric and magnetic fields, which can be solved using either finite differences (Stoyer and Greenfield, 1976) or finite elements (Everett and Edwards, 1992;Sugeng et al, 1993;Unsworth et al, 1993). The inherent stability in their solution is that both along-strike components are spatially continuous everywhere, including across discontinuous resistivity boundaries.…”