The Recent Developments
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The Recent Developments
5.1 Advancement of the Plane-Wave Model We have examined the plane-wave model of the inhomogeneous Earth that offers basic invariant magnetotelluric and magnetovariational response functions: the impedance tensor [Z] and phase tensor ⌽ , the Doll and magnetic tensors [D] and [M], the Schmucker perturbation tensor [S], the Wiese–Parkinson and Vozoff tipper vectors W and V. The condition of existence of these invariant response functions is that the normal magnetic field allows for the plane-wave (one-dimensional) approximation. This actually is the case if the horizontal components of the normal magnetic field change slowly along the Earth’s surface and its vertical component is close to zero. Unfortunately, the question on physical feasibility of the plane-wave model with its one-dimensional normal magnetic field is poorly studied theoretically. Up to now we content ourselves with empirical estimates derived from the practical magnetotelluric experience. There are good grounds to believe that at middle and low latitudes (far away from the polar field sources) the magnetotelluric and magnetovariational response functions in a broad range of frequencies (from 103 to 10–4 Hz) yield to stable determination and give geologically meaningful information on the structure of the Earth’s interior. The more complicated situation is encountered in the polar zones with their dramatic electromagnetic disturbances caused by events in the ionosphere and magnetosphere. Concluding the analysis of magnetotelluric and magnetovariational response functions, we would like to consider a generalized model taking into account a source effect which may manifest itself in considerable departure of the normal magnetic field from the plane wave (specifically, with noticeable vertical magnetic component). The model to be examined is presented in Fig. 5.1. It consists of the horizontally homogeneous Earth of normal conductivity N (z) and a bounded three-dimensional inhomogeneous domain V of conductivity (x, y.z) = N (z) + ⌬(x, y, z), where ⌬(x, y, z) is an excess conductivity that varies arbitrarily in x, y, z. The Earth comes in contact with the nonconducting air, air = 0. The field is excited by M. Berdichevsky, V.I. Dmitriev, Models and Methods of Magnetotellurics, C Springer-Verlag Berlin Heidelberg 2008 DOI 10.1007/978-3-540-77814-1 5,
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5 The Recent Developments
Fig. 5.1 Illustrating the determination of the generalized impedance tensor air earth
V
primary currents of density j p closed in a source domain I located above the Earth. The centre of the domain I is at a point O, its maximum radius is r i . The electromagnetic field meets here the Maxwell equations curl H = E + j p ,
curl E = io H, z ∈ [−∞, ∞].
(5.1)
For the normal field excited in the horizontally layered Earth in the absence of the inhomogeneous domain V we have curl HN = N EN ,
curl EN = io HN , z ≥ 0.
(5.2)
5.1.1 Analysis of the Normal Magnetotelluric Field A remarkable feature of the model is that the normal cur
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