Electromagnetic induction by finite wavenumber source fields in 2‐D lateral heterogeneities; the transverse electric mode

Summary. This paper describes an approach to solving the case of electromagnetic induction by a time‐varying 2‐D current source directed parallel to the strike of a 2‐D anomalous structure within the Earth; this geometry represents the transverse electric (TE, or E‐parallel) induction mode. The case when the source field itself has a finite dimension imposes additional considerations for the problem of designing adequate 2‐D models. A finite spatially harmonic source field, which may be located at some position within the modelling region, is simulated by discontinuities in the magnetic (or electric) field appropriate to the current flowing in the source. Such an approach allows us to evaluate the electromagnetic fields above current sources in the ionosphere such as might be observed by satellites. Although we basically treat the problem in the wavenumber domain, more general sources can be synthesized either before or after the solution of a set of finite difference relations, depending on the application. Our results suggest that in some cases the fields induced by finite sources tend to decouple fairly rapidly with distance to either side of vertical discontinuities. Therefore in these situations, regional gradients of the horizontal field (even where the sites span a major discontinuity) can be combined with local values of the vertical field to yield reliable estimates of 1‐D gradiometric response functions. Similar results pertain to the magnetotelluric relation. This implies that in many cases, simple 1‐D plane‐layered models may be appropriately used in interpreting field data in a‘piece‐wise’sense, even when the total structure is more complicated laterally. At satellite altitudes, the difference between the results for a uniform inducing field (e.g. from a remote source in the magnetosphere) and those for a finite source field in the ionosphere below the satellite are profound. The total horizontal magnetic field produced by the distant source is approximately unity, suggesting that the horizontal field is insensitive to the effects of lateral variations in the Earth's conductivity. On the other hand, the total horizontal field produced by an ionospheric source field is reduced by more than an order of magnitude. This is due to the fact that the satellite is above the source so that the primary and secondary horizontal magnetic field components tend to cancel and the resultant H ‐field is quite small. In contrast, the ionospheric source produces an anomalous vertical field at satellite altitudes which, while small, is of the same order of magnitude as that produced by distant magnetospheric sources.