Reply to “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

Dr. P. F. Chen (hereafter PFC) has questioned two main differences between the CDK analogue model and his FDM numerical results: 1) The CDK analogue model in-phase V y fall off rapidly with increasing period, whereas his numerical H z /H y do not; 2) The CDK quadrature V y do not show a reversal, whereas his H z /H y do. Upon examining the curves in Fig. 4 carefully, it can be concluded that the CDK quadrature V y do, in fact, also indicate a reversal. It can clearly be seen from the shape of the CDK curves (dashed line), that with decreasing period each response curve is approaching a reversal, though at a period some what below 1 min, being the lowest period included in the analogue model measurements. The CDK in-phase response curves as well, are each approaching a maximum at periods well below 1 min, and should each reach a maximum at roughly the same period as the corresponding quadrature reversal, being characteristic of the specific location (y) between the conductors. These shifts to longer periods with distance indicated in the CDK results, are similar to those in the PFC (solid line) results which for sites at increasing distances from the major conductor (b), show shifts to longer periods to be roughly T c = 2, 3, and 8 min at y = −45, −40, and −30 km respectively. With respect to the more rapid fall-off in-phase response with increasing period, as well as the quadrature reversals at lower periods in the CDK 3D results as compared with the PFC results, these are precisely the characteristics that distinguish 3D from 2D responses. The CDK model for the 1-60 min period range is certainly 3D for all but the shortest periods, since for the near-end (x = 30 km) traverse the conductor length is definitely too small to satisfy the criteron for a 2D conductor in terms of host conductivity skin depths. Thus, the PFC roughly constant in-phase H z /H y over the 1-60 min range appear to show a 2D rather than what should be a 3D response.Unfortunately, PFC does not include any explanation regarding the numerical grid design, the boundary conditions, or the convergence criteria used in his finite difference numerical model for the high conductivity contrast (∼5000), and the large (1-60 min) period range for which the highly resistive host skin depth changes by nearly a factor of 8. Did he use air layers above the surface, or did he use a surface boundary condition? If he used air layers, what was the height extent? Did he use the same uniform grids for all periods, or did he change the grids for different periods where appropriate in order to enhance the accuracy? Without stating any convergence criteria, he does state that his iteration did converge, though slowly, but does this necessarily constitute proof that the numerical results are valid? If the differences between the PFC and the CDK results cannot be attributed to numerical inaccuracies in the PFC results due to possible difficulties with grid design, boundary conditions, convergence, etc., then the departure from the observed CDK 3D results might only be ...