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 frequency-wavenumber (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.