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In order to handle the distortion of large-scale induced electric currents by local conductivity anomalies, the problem of electromagnetic induction in non-uniform thin sheets has been reformulated in terms of an integral equation over the anomalous domain. This formulation considers in the layered substratum in addition to toroidal currents also the poloidal current mode (vertical current loops), at the expense that two scalar functions have to be determined. Simple formulas for the required kernels are derived.The algorithm is applied to model the gross features of the northern Pyrenean induction anomaly. It is suggested that this pronounced anomaly results from a conductive channel between the Atlantic Ocean and the Mediterranean Sea.

[1] Magnetospheric fields and their induced counterparts are the largest source of error in models representing the geomagnetic field. Of particular concern is the current practice of coupling the internal induced field for convenience to the external field by a real constant, independent of the frequency content of the external inducing source. The error introduced into field models by this simplified representation is of the order of 5 nT on average. Here, we propose an accurate representation of the symmetric part of the disturbance field which is easy to implement. Using a 1D conductivity model of the Earth, we split the disturbance D st index into two new indices, E st and I st , which track the transient evolution of the symmetric part of the external and induced disturbance field. The ensuing D st -based transient correction for geomagnetic field models is in remarkable agreement with the transient effect observed in CHAMP, Ørsted and SAC-C satellite magnetic measurements.

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S U M M A R YRecently, marine controlled source electromagnetics (CSEM) has shown great potential in hydrocarbon exploration, where the goal is to detect thin resistive layers at depth below the seafloor. The experiment comprises a horizontal electric dipole transmitter towed over an array of receivers at the seafloor. The transmitter emits a low-frequency signal (<1 Hz) and measurements of the electric field are made. The depth of the target layer requires transmitterreceiver separations of several kilometres. As a function of separation r, the electromagnetic signal consists of a short-ranging contribution with an exponential decay resulting from the transmission through ocean and sediment (including the reflection at all interfaces) and a longranging contribution with a dominant 1/r 3 -decay associated with the airwave guided at the air-ocean interface. Of particular interest among the exponentially decaying waves is the wave guided in the resistive target layer with a well-defined long decay length. In a shallow sea, this 'resistive-layer mode' is partly masked by the airwave.The topics of this study are the airwave and the resistive-layer mode. For a general 1-D conductivity distribution we derive the simple expression of the leading term of the airwave for arbitrary transmitter and receiver position and define a 'pure' complete airwave, which for all separations is close to the asymptotic expansion of the airwave in powers of 1/r. Whereas the treatment of the airwave can be done in terms of Bessel function integrals with real wavenumbers, the resistive-layer mode requires the complex wavenumber plane, where it is defined as the residual at the TM-mode pole with the smallest imaginary part. For sufficiently high integrated resistivity of the layer, we give a simple method to determine the position of this pole. In the complex wavenumber plane, the pure complete airwave is presented by a branch-cut integral. For a typical model, this study concludes with the remarkable result that the superposition of airwave and resistive-layer mode provides an excellent description of the electric field over a wide range of separations.