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We consider a general case of a magnetotelluric (MT) study to reveal three-dimensional (3D) distribution of the electrical conductivity within the Earth based on measurements of electromagnetic (EM) fields by a two-dimensional (2D) array. Such an MT array observation can be regarded as a spatially discrete sampling of the MT responses (impedances), and each observation site can be regarded as a sampling point. This means that MT array measurements must follow the Nyquist–Shannon sampling theorem. This paper discusses how the sampling theorem is applied to MT array studies and what kind of consideration is required in the application on the basis of synthetic model calculations, with special attention to spatial resolutions. With an aid of the EM scattering theory and the sampling theorem, we can show that an observation array resolves some features of the MT impedance but does not others. We call the resolvable and unresolvable features the MT signal and noise, respectively. This study introduces the spatial Fourier transform of array MT data (impedances) which helps us investigating sampling effects of lateral heterogeneity from a different angle (in the wavenumber domain). Shallow heterogeneities cause a sharp spatial change of impedance elements near structural boundaries. High wavenumber Fourier components are required to describe such a feature, which means the site spacing must be sufficiently short to be able to resolve such features. Otherwise, a set of array MT data will suffer from aliasing, which is one of the typical causes of MT distortion (MT geologic noise). Conversely, a signal due to a deep-seated conductivity anomaly will have more reduced amplitude at higher wavenumbers, which means focused imaging of such an anomaly is generally difficult. Finally, it is suggested to properly consider the sampling theorem in an observation array design, so as to have best performance in resolving MT signals. [ABSTRACT FROM AUTHOR]

Through a large number of magnetotelluric (MT) observations conducted in a study area, one can obtain regional one-dimensional (1-D) features of the subsurface electrical conductivity structure simply by taking the geometric average of determinant invariants of observed impedances. This method was proposed by Berdichevsky and coworkers, which is based on the expectation that distortion effects due to near-surface electrical heterogeneities will be statistically smoothed out. A good estimation of a regional mean 1-D model is useful, especially in recent years, to be used as a priori (or a starting) model in 3-D inversion. However, the original theory was derived before the establishment of the present knowledge on galvanic distortion. This paper, therefore, reexamines the meaning of the Berdichevsky average by using the conventional formulation of galvanic distortion. A simple derivation shows that the determinant invariant of distorted impedance and its Berdichevsky average is always downward biased by the distortion parameters of shear and splitting. This means that the regional mean 1-D model obtained from the Berdichevsky average tends to be more conductive. As an alternative rotational invariant, the sum of the squared elements (ssq) invariant is found to be less affected by bias from distortion parameters; thus, we conclude that its geometric average would be more suitable for estimating the regional structure. We find that the combination of determinant and ssq invariants provides parameters useful in dealing with a set of distorted MT impedances. [ABSTRACT FROM AUTHOR]