The theoretical relationship between non-local motionally induced voltages (MIV) and tidal currents is validated with observations of natural low-frequency electric field at the coast of the Throat of the White Sea (northwestern Russia). The Throat of the White Sea is a strait of 50-km width and about 500-km length with depths varying from 20 to 50 m connecting semi-closed White Sea basin with the Barents Sea. Strong tidal currents providing a reference signal for calibrating coastal measurements of non-local MIV characterize the Throat. The measurements were carried out simultaneously by means of two horizontal receiving on-land and land-sea antennas. Tidally driven MIV dominates in all time series obtained in the coastal zone of the Throat of the White Sea. Monitoring of non-local MIV within the coastal zone could be used for studies of wind tides, residual tidal circulation and temporal variability of a quasi-stationary current. MIV measurements offer an important advantage over traditional oceanographic methods (currents meters, etc.), because it works also in winter period (about 6 months) when the White Sea is covered by ice. The main disadvantage of this technique is a necessity to calibrate non-local MIV with some other oceanographic direct or remote measurements.

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Source field effects in magnetotelluric data acquired at high geomagnetic latitudes can result in erroneous interpretations of Earth conductivity structure deep within the mantle. This paper describes a simple technique most appropriate for a region that is dominantly one-dimensional (1-D) and uses the vertical magnetic field variations for identifying intervals of likely low contamination by non-uniform sources. Times are chosen when the variations stay within prescribed limits defined on the basis of a histogram of the variations for the whole recording interval. An example is given showing application of the method for data from a site under the auroral oval at a time when solar activity was at its lowest for the last solar cycle. A model derived from the responses obtained by processing all available data implies a decrease in resistivity at about 350 km to about 100Ω. m. In contrast, the model obtained from low activity interval responses shows a less rapid decrease in resistivity, without a change at around the 410 km phase boundary. The responses obtained from all data can be explained by the influence of a source with an average wavelength of 3, 000 km.

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The rotationally invariant phase sensitive skew parameter, an indicator of dimensionality of conductivity structure, is a complicated non-linear function of the impedance tensor elements. In the presence of noise in the impedance data, skew can be significantly biased, leading to a false interpretation of dimensionality. Therefore, the probability function distribution of the skew parameter is derived to obtain its confidence limit, rather than treating a conventional linear propagation error. It is well known that the latter is only appropriate if the parameter is a function of independent random variables with small relative errors. The confidence limit is estimated by deriving its conditional probability function in terms of the tensor elements density function, using the Jacobi-matrix transformation of random variables, assuming the tensor elements to be normally distributed random variables. It is shown with synthetic and experimental data that the statistical confidence limit derived here truly reflects a probability range for the skew value. Bias of skew is seen to be significant with a small 5% of random Gaussian noise added to the tensor elements. Considering the 95% confidence limit instead of the measured skew itself results in a plausible approach to analyse dimensionality. The procedure developed here to estimate the confidence limit can also be extended to other functions of the tensor elements.

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We present the fundamentals of an electromagnetic sounding with an accurately controlled source signal. In this method, the tensor transfer function between transmitted and received vector electromagnetic fields is measured. We formulated the transfer function by introducing a ray model that describes the propagation of the general electromagnetic field in the whole frequency region. The transfer function includes information of the underground structure: electromagnetic parameters, propagation distance, and boundary planes. The information of the electromagnetic parameters and the propagation distance is commonly described in all the tensor elements. It is in a form of complex functions of frequency. The information concerning the boundary planes is described as real coefficients of the complex functions. The coefficients are different for each of the tensor elements. When we use an accurately controlled signal, we can estimate the information as a linear inversion problem. A profile of the transfer function varies with the frequency region: it decays rapidly in the low-frequency region and oscillates in the high-frequency region. Such a profile can be explained by the approximate form of the transfer function: a sum of complex exponential functions in a narrow frequency band. The approximate form also provides a good model for data decomposition.

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In the 1-D magnetotelluric theory, a Riccati equation governs the depth variation of the impedance, or admittance, for a given distribution of the electrical conductivity. This equation can be used to compute the surface magnetotelluric functions for generally piecewise continuous conductivity profiles. In case of a simple layered medium, it provides the classical formulae for recalculating recursively the impedances between the individual layer boundaries. We present an extended version of the Riccati differential equations for generally anisotropic 1-D structures for the case of a plane wave incident field. Relation between the standard matrix propagation procedure for a layered medium and the Riccati equation approach, as a limiting case of the former, is demonstrated. In the anisotropic case, all elements of the 2 × 2 impedance tensor are present and, consequently, a system of four coupled Riccati equations has to be considered. Standard methods for the numerical solution of systems of ordinary differential equations are applied to the Riccati system, which gives an efficient alternative to the current matrix propagation procedures for the numerical evaluation of 1-D magnetotelluric impedances in anisotropic media. As an application, a synthetic study on the influence of a depth-variable regional strike on magnetotelluric decomposition results is presented, with the variable strike simulated by a variable anisotropy within the 1-D section.

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The Riccati equation approach to the analysis of magnetotelluric impedances in 1-D anisotropic structures is generalized to models with non-uniform source field excitation. The problem is solved in the horizontal wavenumber domain. General Riccati matrix equations for the spectral impedances of the medium are derived and their relation to the standard impedance propagation formulae in layered anisotropic models is discussed. Riccati equations give a full solution for the spectral impedances, comprising both the induction and galvanic mode. For a purely inductive excitation of the field, each wave-number harmonics of the magnetic field is strictly linearly polarized on the surface, and only one half of the spectral impedance tensor can be restored. Both induction and galvanic modes generally exist inside the anisotropic conductor and are coupled. A formal similarity between the Riccati equations for a 1-D anisotropic medium with non-uniform sources and those obtained for 2-D laterally inhomogeneous structures is demonstrated, which indicates a possible way of extending the Riccati impedance/admittance equations to multi-dimensional conductors.

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Galvanic distortion of magnetotelluric (MT) data is a common problem in the study of the Earth's electrical properties. These distortions are local, they affect independently each MT site, and where restricted to distortion of the electric field are manifest as vertical shifts in the apparent resistivity curves (static shift). The removal of the static shift is necessary to avoid misinterpreting MT data. We present a method that allows us to partially retrieve the regional response of the TE-mode data in a 2D case. The method determines relative changes between distortion parameters along a profile, and is based in the Faraday's law, and uses only magnetotelluric responses: measured impedance tensor and geomagnetic transfer function (tipper). The method is valid under the assumption that the variation of horizontal magnetic field can be neglected, and a test for checking this criterion has been developed. The mathematics involved in the procedure are straightforward, and can be stated as a linear regression. We present successful applications to both synthetic and real (COPROD data) datasets.

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A new three-dimensional (3D) MT modeling scheme conserving electric current and magnetic flux is developed. The scheme is based on finite difference (FD) staggered rectangular non-uniform grid formulation for the secondary electric field with continuous components of tangential electric and normal magnetic fields, in contrast to existing FD algorithms with a discontinuous E-field at the face of the cells. The scheme leads to a sparse 13-band complex symmetrical system of linear equations, which is effectively solved by fast and stable conjugate gradient (CG) methods. The preconditioning procedure was used to decrease the condition of a number of an ill-conditioned matrix system by several orders and stably and quickly solves the matrix system. The special module for the correction of divergence-free current J greatly increased the speed of convergence and accuracy, especially at low frequencies and for high-contrast resistivity or conductivity structures. A special procedure was developed to improve the accuracy of tangential magnetic and vertical electrical components at the Earth's surface and at the interface with a large conductivity contrast. The validity of the new algorithm was demonstrated for difficult models with high-contrast resistivity structures including topography and for COMMEMI project models.

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The well-known thin-sheet modeling has become a very useful interpretation tool in electromagnetic (EM) methods. The thin-sheet model approximates fairly well 3-D heterogeneities having a limited vertical dimension. This type of approximation leads to amenable computation of EM response of a relatively complex conductivity distribution. This paper describes the integration of thin-sheet forward modeling into an inversion method based on a stochastic Monte Carlo Markov Chain (MCMC) algorithm. Effective exploration of the model space is performed using a biased sampler capable to avoid entrapment to local minima frequently encountered in a such highly nonlinear problem. Results from inversion of synthetic EM data show that the algorithm can reasonably resolve the true structure. Effectiveness and limitations of the proposed inversion method is discussed with reference to the synthetic data inversions.

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In this article we analyze the sensitivity of a geoelectrical modeling technique to image 2D shallow structures. Firstly, we extend a previously developed 2D method based on Rayleigh-Fourier expansions, in order to allow arbitrary locations for the electrodes and also 3D earth models. This method is an alternative to finite element and finite difference techniques and is especially suitable to model multilayered structures, with smooth irregular boundaries. Then, for simple 2D models we build up two synthetic pseudosections, one for electrode deployments parallel to a profile perpendicular to the strike, and other for deployments perpendicular to it. We analyze the advantages in using both pseudosections to model these structures. We also compare geoelectric results with the corresponding audiomagnetotelluric transverse electric and transverse magnetic responses. Finally, we perform a geoelectrical survey to image a shallow buried structure and show the goodness of the model fit obtained considering both pseudosections. For the examples studied here, we conclude that considering both pseudosections leads to a more accurate description of the structures. When a 2D anomaly is present, its effect on the perpendicular component is more focused, both in width and depth, than in the parallel component. Hence the perpendicular component helps to constrain the localization of the inhomogeneity. In addition, we find similarities between the geoelectric parallel and perpendicular responses and the corresponding audiomagnetotelluric transverse magnetic and transverse electric results, respectively. When inverting audiomagnetotelluric data using 2D codes, better resolution in the electrical imaging is obtained when both modes are considered; then it is expected that 2D imaging of geoelectric data including both arrays should lead to an optimization of the inversion process. Even more, if results of these inversions could be used in correlation with AMT results, it is clear that this kind of joint inversion should contribute to remove uncertainties allowing an improvement in the description of the actual structures.

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A priori knowledge on large-scale sub-surface conductivity structure is required in many applications investigating electrical properties of the lithosphere. A map on crustal conductivity for the Fennoscandian Shield and its surrounding oceans, sea basins and continental areas is presented. The map is based on a new database on crustal conductance, i.e. depth integrated conductivity, where all available information on the conductivity of the bedrock, sedimentary cover and seawater are compiled together for the first time for the Fennoscandian Shield. The final model consists of eight separate layers to allow a 3D description of conductivity structures. The first three layers, viz. water, sediments and the first bedrock layer, describe the combined conductance of the uppermost 10 km. The other five bedrock layers contain the data of the crustal conductance from the depth of 10 km to the depth of 60 km. The database covers an area from 0°E to 50°E and 50°N to 85°N. Water conductances are estimated from bathymetric data by converting depths to conductances and taking into account the salinity variations in the Baltic Sea. Conductance of the sedimentary cover includes estimates on the conductance of both marine and continental sediments. Bedrock conductances are extrapolated from 1D- and 2D-models. Extrapolations are based on data from magnetometer array studies, airborne electromagnetic surveys and other electromagnetic investigations as well as on other geophysical and geological data. The crustal conductivity structure appears to be very heterogeneous. Upper crust, in particular, has a very complex structure reflecting a complex geological history. Lower crust seems to be slightly more homogeneous although large regional contrasts are found in both the Archaean and Palaeoproterozoic areas.

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Electromagnetic multisheet modelling is a powerful tool for large model areas, if they can be approximated by a multilayered heterogeneous conductivity structure of small vertical dimension in comparison with the penetration depth of electromagnetic fields. In this paper, thin sheet technique is applied to the whole Fennoscandian (Baltic) Shield, whose upper mantle conductivity structure is the objective of the long period electromagnetic array experiment BEAR (Baltic Electromagnetic Array Research). Three thin sheets, each of about 120, 000 model cells with the base length of 10 km, describe a-priori crustal inhomogeneities in terms of conductances. The three sheets represent i) upper crust from surface to the depth of 10 km including continental and ocean bottom sediments and seawater, ii) middle crust ranging from 10 km to 30 km and iii) lower crust from 30 km to 60 km. Thus, modelling is taking into account distortions caused by crustal conductivity anomalies. Additionally, distortions due to inhomogeneous external current systems are investigated by introducing an equivalent current system of a polar electrojet model at ionosphere height. Modelling results are illustrated by induced current distribution at different depth levels and by various electromagnetic transfer functions. The latter demonstrate the resolution of crustal conductivity anomalies and their screening effect even at long periods. The predicted behavior of transfer functions in the very complex conductivity structure is compared with the experimental BEAR data, showing qualitatively a first order agreement for most of the sites. Modeled phases for periods of a few thousands of seconds are considerably biased in comparison with experimental data if the background 1-D model has monotonously decreasing resistivity. However, the bias from phases is removed if a conducting asthenosphere having a resistivity of 20Ωm is emplaced between the depths of 200 km and 300 km. Thus, multisheet modelling indicates a well conducting upper mantle under the Fennoscandian Shield. All modelling has been performed using a multisheet code by Avdeev, Kuvshinov and Pankratov.

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Magnetotelluric sounding data have been collected along the Lithoprobe seismic line 21 as a complement to seismic reflection in order to better constrain the structure of the Blake River Group and of the underlying crust. The presence of shallow conductive heterogeneities in an otherwise highly resistive environment typical of the Canadian Shield generates large galvanic distortion that affects the estimates of the impedance tensor. Distortion analysis and tensor decomposition techniques show that MT data support a model represented by a 2D regional model over a 2D deep structure with two different strikes direction and distorted by shallow heterogeneities. The residual static shift affecting each mode for each sounding site is determined using a combination of techniques: shifting the apparent resistivity curves to a reference curve obtained by the authors in the region using 100 km long dipoles, a shallow resistivity estimate using TDEM sounding, 2D minimum structure inversion with free static shift factors. The resulting model does not satisfy both TE and TM modes. A better fit is found by trial and error using a 2D anisotropic model. The Blake River Group is represented as an highly anisotropic resistive layer with a possible decrease in thickness from northwest to southeast. The middle crust is moderately conductive and isotropic. The lower crust and upper mantle is found to be anisotropic and conductive. The geometry of the Blake River Group obtained from the MT data is in agreement with previous gravity and seismic studies.

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Magnetotelluric (MT) soundings were carried out in the period range of 20 to 6000 s along profiles roughly orthogonal to the Campos do Jordão Railway (CJRW), in the Brazilian southeastern region. The profiles were located over two adjacent regions with contrasting conductivity, the conductive sedimentary region of the Taubaté Basin and the resistive crystalline region of the Serra da Mantiqueira. The railway operates with DC current that produces an intense electromagnetic noise but only during diurnal periods, being turned off at night. The objective of this study is to characterize the CJRW noise in order to verify its effect on MT parameters. It was inferred that the entire length of the Taubaté Basin is probably affected by the noise, whereas in the crystalline terrains the noise reaches distances in the range of 76 to 126 km. The electric channels show a strong dependence on geology which is suggestive of the potential application of the CJRW as a controlled source in geophysical studies. The data were processed with modern techniques presently available to the scientific community. Under the conditions of the present study, it was observed that the robust Single Station technique is as efficient as the robust Remote Reference to remove the kind of noise generated by the CJRW, an intense perturbation that affects only some welldefined portions of the time series. Finally, the analyses reaffirm the necessity of a careful choice of the station to be used as reference in the Remote Reference technique.

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We have re-examined the modelling of magnetotelluric and GDS soundings carried out on the Araguainha Dome, Brazil, published a few years ago, in the light of a new modelling method and with particular stress on the induction of the vertical component of the magnetic field, which had been neglected in the early publications. By careful selection of the period range of the measured data, we obtain a set of radially symmetric induction arrows. This symmetry is taken as a first order assumption of the modelling scheme. The result is an improvement of the resolution of the radial distribution of depths to the crater basement. Due to the poor MT site coverage of the crater area, this work must be considered a feasibility study rather than a final modelling contribution.

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We apply a modified genetic algorithm, the “recombinant genetic analogue” (RGA) to the inversion of magnetotelluric (MT) data from two different geothermal areas, one in El Salvador and another in Japan. An accurate 2-D forward modelling algorithm suitable for very heterogeneous models forms the core of the inverse solver. The forward solution makes use of a gridding algorithm that depends on both model structure and frequency. The RGA represents model parameters as parallel sets of bit strings, and differs from conventional genetic algorithms in the ways in which the bit strings are manipulated in order to increase the probability of convergence to a global minimum objective function model. A synthetic data set was generated from a chessboard model, and the RGA was shown capable of reconstructing the model to an acceptable tolerance. The algorithm was applied to MT data from Ahuachapán geothermal area in El Salvador and compared with other interpretations. Data from the geothermal area of Minamikayabe in Japan served as a second test case. The RGA is highly adaptable and well suited to non-linear hypothesis testing as well as to inverse modelling.

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Thirteen magnetotelluric (MT) soundings were carried out in Neoproterozoic crystalline terrains and Tertiary sediments of the Taubaté basin, southeastern Brazil. The soundings were deployed in a cross-strike profile bisecting the basin along one of its thickest sub-basins and extending over mountain plateaus to the southeast and the northwest. Occurrences of numerous alkaline plugs and aligned tectonic grabens in the region are records of intense Mesozoic-Cenozoic tectonic activity. MT analysis techniques were used to evaluate data quality, infer strike direction, and correct for near-surface distortion. As the studied area is located only some tens of kilometers away from the Atlantic Ocean and in one of the most densely populated regions of the country, the data are severely distorted by industrial interference and the coast effect. Because of such effects, the data are modelled using a 2D inversion scheme within periods shorter than 0.1 s for the Taubaté Basin sites and shorter than 1-10 s for the offbasin sites, the latter depending on the distance of the site from the coast. The main result observed in the modelling is the identification of a conducting zone below 10 km depths beneath the region. There is poor resolution in the data of structures below this conductor, which is also not imaged beneath the basin. Studies carried out in different tectonic regions of the world have also reported conductive layers at about the same depth but in the studied area it is impossible to reach any conclusion about the total conductance of the layer with the available MT data.

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Wideband magnetotelluric (MT) observation data were obtained from 91 sites along six transects in the central part of the Japan Arc. Here, a quasi-3D georesistivity distribution, in addition to other geophysical and geological parameters, is used to better understand seismicity in the region. We found that high seismicity in the Central Mountain Range is due to relatively poor fluid saturation caused by volcanism. The high conductive fracture zone in the west of the Central Basin without big earthquakes is characterized by a low Poisson ratio. It is suggested that strains cannot be accumulated in those regions. The Miyagi-ken-hokubu region with a frequent occurrence of large earthquakes, is conductive-high Poisson ratio-high Vp suggesting that the zone is relatively fluid-rich and brittle.

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Existing sets of magnetovariational data from the large numbers of sites distributed across the peninsular India and those in the Bay of Bengal are reanalysed to obtain inter-site vertical and horizontal field transfer functions. Maps of induction arrows relocate the earlier reported conductive zones beneath the Palk-Strait and a regional scale anomaly in the offshore region, immediately southwest of the southern tip of Indian Peninsula, named South India Offshore Conductivity Anomaly (SIOCA). Period dependence of the induction arrows suggests that with increasing period SIOCA tends to control the induction pattern over the entire peninsula. Presentation of the horizontal transfer functions in the form of ellipses of anomalous currents helps to characterize the period and spatial behaviour of horizontal fields at seafloor sites. Integrated thin sheet modeling of the on-land and seafloor induction features suggest that the greater part of the anomalous behaviour of the horizontal fields at seafloor sites can be attributed to the shielding effects due to seawater. The weak anisotropic behaviour of the horizontal fields at selected sites can be explained in terms of the concentration of the induced currents in the sediment filled troughs on either side of the 85°E Ridge. Several lines of geophysical evidence favour the hypothesis that SIOCA, low velocity zone, low magnetization anomaly, all centered near the southern tip of the India, are the relics of the interaction of Marion Plume outburst with Indian lithosphere.

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EM34 and SP surveys were used to delineate shallow structures associated with the mineral water springs in the Vilarelho da Raia area located NE Portugal. This spring is part of a set of CO₂-rich mineral (hot and cold) waters connected to the main Hercynian NNE-SSW fault systems. The EM34 survey was interpreted using a quasithree-dimensional inversion approach based on a smooth-regularisation algorithm. The model put into evidence the conductive overburden as well as the fractured granitic formation. A preliminary estimation of the aquifer porosity is made based on the EM34 model. The SP anomalies were interpreted considering as having their sources on the aquifer interfaces. The modelling of two SP profiles allow the characterisation of a fault connected to the spring.

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