Comment on “EM induction in elongated conductors normal to a coastline with application to geomagnetic measurements in Nigeria” by J. Chen, H. W. Dosso and S. Kang

Abstract

On the Frequency Response of Induction ArrowsThe induction frequency response of some analogue models shown in Chen, Dosso and Kang (1997; hereafter referred to as CDK), seems to be somewhat strange. The frequency behaviour of the in-phase and quadrature Parkinson arrows, shown in figures 2 and 4 of CDK, indicates that: 1) the magnitude of the in-phase arrow decreases rapidly with increasing period, and becomes negligible when T = 30 min; 2) the quadrature arrow does not change its sign in the studied inducing period from 1 min to 90 min. In order to examine the correctness of the experimental results for their models, I have carried out some 3-D numerical modelling calculations using the finite difference method. I shall devide this comment into two parts. The first part gives the numerical results of an example, a model suggested by Wannamaker et al. (1984) for demonstrating the applicability of the finite difference method. The second part shows my numerical results for the elongated parallel conductors model mentioned in CDK, indicating that their analogue result is suspect. The 3-D Finite Difference MethodThe outline of the 3-D finite difference method and the detailed algorithm can be found in Chen (1985) and Chen and Fung (1988). The accuracy obtained by our computer program has been tested by making calculations for Weidelt's model (Weidelt, 1975) and Ting and Hohmann's model (Ting and Hohmann, 1981). The comparisons of our numerical results and their results are shown in the Appendix of Chen and Fung (1988). Another comparison for Hohmann's model (Hohmann, 1983) has also been carried out (Chen and Fung, 1989), and in that model the conductivity contrast is 200. All the results obtained by different methods agree well for the most part of the response curves.Here I show another comparison with the third model constructed by Wannamaker et al. (1984). In the stated model the conductive body is a plate-like feature 1 km thick at a depth of 750 m, with the lower layer situated below 2250 m. Its width is 5 km and its strike length is 60 km (see Fig. 1 Fig. 2a). Accordingly, the 3-D and 2-D results of the quadrature induction arrow do not agree well either (see Fig. 2b). Nevertheless, it is worth noting that, if we reverse the signs both for obtaining the in-phase and quadrature arrows, the quadrature Parkinson arrows in this example (T = 1 sec) point away from the conductor. As a matter of fact, when T ≥ 7 sec, the quadrature Parkinson arrows will change their directions; in that case, they will point towards the conductor. The Elongated Parallel Conductors Model without the OceanFigure 1 of CDK shows the structure of the model and figure 2 of CDK shows the response of V y (the response of the elongated conductors without the ocean). There is a pair of surface elongated conductors (3.6 S/m): both conductors' lengths and thicknesses are 500 km and 5 km respectively, the width is 20 km for conductor b and 5 km for conductor a. The conductor separation distance (S) is 50 km. The conductivity of the first layer ...