We use data from two magnetotelluric profiles, ToSca10 and ToSca'09, over the Scandinavian Mountains to study the crustal structure in southern Norway. The profiles cross the major tectonic structures of the Caledonian orogen as well as the western margin of the Precambrian Baltica. Dimensionality and strike analyses indicate generally 3-D behavior of the data. However, the majority of the used data distinguishes a preferable strike direction, which is supported by the geology of the region. Hence, we employ 2-D inversion and choose to invert the determinant of the impedance tensor to mitigate 3-D effects in the data on our 2-D models.Magnetotelluric data from both profiles are inverted using a damped least squares solution based on a singular value decomposition. We improved the solution by defining the inverse model covariance matrix through gradient or Laplacian smoothing operators.The two-dimensional inversion models of the ToSca'09 and ToSca'10 field data from southern Norway derived from the damped least squares scheme with the Laplacian inverse model covariance matrix are presented. Resistive rocks, extending to the surface, image the autochthonous Southwest Scandinavian Domain and the allochthonous Western Gneiss Region. Near-surface conductors, which are located between the resistive Caledonian nappes and Precambrian basement, delineate highly conductive shallow-sea sediments, so called alum shales. They exhibit a decollement along which the Caledonian nappes were overthrust. A deeper, upper to midcrustal conducting layer in the Southwest Scandinavian Domain may depict the remnants of closed ocean basins formed during the accretions and collisions of various Sveconorwegian terranes. In ToSca'10, the Caledonian nappes, the conducting alum shales and the deeper conductor are terminated in the west by the Faltungsgraben shear complex which represents a crustal scale boundary between the Western Gneiss Region in the west and the Southwest Scandinavian Domain in the east. (C) 2014 Elsevier B.V. All rights reserved.

We model stress fields and potential areas of deformation, use differences to analyse the possible variations in the modelling results and investigate the relations between the earthquakes and our modelling results in the POLAR profile in the northern Fennoscandian Shield. Calculated stress fields show rather uniform distribution, with significant deviations concentrated in rheologically weaker regions, mainly in the middle crust. Significant areas of deformation are also connected to these weaker regions, in the crust and also in the mantle. These regions control whether decoupled or coupled mechanical conditions exist. Further analysis shows that major differences between the stress fields calculated with dry and wet rheologies are found in the lower part of the middle crust extending from the Lapland Granulite Belt area towards the northeast. Similarly, differences between the models due to the varying heat production and the depth of the thermal lithosphere–asthenosphere boundary concentrate in rheologically weak crustal regions and in the mantle. These differences display importance of the rheological composition and thermal structure in rheological modelling. Our rheological model for reverse stress regime with typically used values of 0.35 for pore fluid factor and 0.75 for friction coefficient seems to result in too strong crust in order to explain satisfactorily the earthquakes focal depths in the POLAR profile. Most of the earthquakes can be explained by reverse stress regime if high pore pressure conditions exist. However, for the deepest events, it seems that also changes both in stress regime and in friction coefficients are needed. Rheologically, weak middle crust in the central and north-eastern parts of the POLAR could explain the absence of deep earthquakes in these parts of the profile.

Very low frequency (VLF) electromagnetic measurements are generally used to study the variations in electrical conductivity in the upper few hundred meters of the Earth’s crust. The VLF magnetic field mode, in which the tilt angle and ellipticity of the magnetic polarization ellipse, i.e., the real and imaginary anomalies respectively, are measured, has been widely used for more than 30 years. The VLF resistivity mode (VLF-R), in use since the late 1960s, is, in principle, nothing but a high frequency magnetotelluric method in which the apparent resistivity and phase are recorded.

The ArchaeanProterozoic collisional zone is a complex mixture of the Archaean complexes [e.g. Iisalmi Complex (IC)], Proterozoic supracrustal belts [e.g. Kainuu Belt (KB) and Savo Belt (SB)] and oceanic arc lithologies in the central Fennoscandian Shield. The zone was formed in the Savo orogeny when the Keitele microcontinent collided with the Archaean Karelian craton in the Palaeoproterozoic time. The crustal architecture of this palaeosuture is studied using new broad-band magnetotelluric data from 104 sites. 2-D conductivity models across the border zone between the Palaeoproterozoic Svecofennian Domain and the Archaean Karelian province are constrained using the recent, partly collocated reflection seismic data from the Finnish Reflection Experiment (FIRE). Dimensionality analyses, in particular the Q-function analysis, show that magnetotelluric data represent reasonably well regional 2-D structure at periods <100 s, which is the longest period used in this study. Strike determinations gave a stable strike of N15W. For the inversions, the data are projected into three parallel profiles with an azimuth of N75E. The determinant inversion is selected as the most suitable method for the data set. Especially the phase data are useable only from the determinant since one of the polarizations have the out-of-quadrant phase at several sites. The interpreted final, geological more appropriate models, where smoother thick conductive areas are replaced by thinner layers, are constructed from the results of the unconstrained smooth inversions with the help of forward modelling, synthetic and prior model inversions and reflection seismic models. The two major sets of crustal conductors are identified. They have an opposite dip and together they form a bowl-shaped conductor. In the west, the eastward dipping SB conductors are located at the bottom of the formation underlain by the Keitele microcontinent. The SB conductors extend to the east possibly cutting the westward dipping conductors of the KB. The conductive KB is flanked above and below by the resistive Archaean IC/Rautavaara and Eastern Finland Complexes and represents the remnants of a basin that was squeezed between two Archaean blocks in the collision. The crustal conductors revealed by the inversion extend to the surface, where they can be associated with the near-surface conductors mapped by airborne electromagnetic surveys. Geological mapping has shown that the near-surface conductors are caused by graphite and/or sulphide-bearing metasedimentary rocks. Thus the deep conductors related with the Proterozoic KB and SB were formed on the surface and transported into the upper and middle crustal levels in the Savo orogeny. The crust in the Karelian Craton is highly resistive having only minor resistivity variations in our research area. Also the Archaean lower crust is resistive on the contrary to the conductive lower crust of the Proterozoic SB and the Keitele microcontinent.

Three-dimensional linearized nonlinear electromagnetic inversion is developed for revealing the subsurface conductivity structure using isolated very low frequency (VLF) and VLF-resistivity anomalies due to conductors that may be arbitrarily directed towards the measuring profiles and the VLF transmitter. We described the 3D model using a set of variables in terms of geometric and physical parameters. These model parameters were then optimized (parametric inversion) to obtain their best estimates to fit the observations. Two VLF transmitters, i.e., the [Formula: see text], [Formula: see text] (“E”) and the [Formula: see text], [Formula: see text] (“H”) polarizations, respectively, can be considered jointly in inversion. After inverting several noise-free and noisy synthetic data, the results revealed that the estimated model parameters and the functionality of the approach were very good and reliable. The inversion procedure also worked well for the field data. The reliability and validity of the results after the field data inversion have been checked using data from a shear zone associated with uranium mineralization.

A three-dimensional model for the central Fennoscandian Shield was constructed for analysing the thermal, the rheological and the structural conditions in the lithosphere. The mesh covers a rectangular area in the southern Finland with horizontal dimensions of 500 km × 400 km and a depth extent of 100 km. Structural boundaries are derived from the several deep seismic soundings carried out in the area. Constructed model is first used in the calculation of the thermal and the rheological models and secondly in analysing the stress and the deformational conditions with the obtained rheology. Thermal and structural models are solved with the finite element method. The calculated surface HFD is between 40 and 48 mW m−2 in the Proterozoic southern part and below 40 mW m−2 in the older and northern Archaean part of the model. The calculated rheological strength shows a layered structure with two individual rheologically weak layers in the crust and strong layer in the upper part of the lower crust. The minimum brittle–ductile transition (BDT) depth is around 10 km in the southern part of the model while in the north and north-eastern parts the BDT depth is around 45–50 km. Comparison with the focal depth data shows that as most of the earthquakes occur no deeper than the depth of 10 km are they located in the brittle regime. Resulting stress conditions and possible regions of deformation after the model is subjected to pressure of 50 MPa reveals that the stress field is quite uniformly distributed in different crustal layers and that the elastic parameters control more the state of the stress than the applied rheological structure. In the upper crust, the stress intensity has values between 42 and 45 MPa whereas in the middle crust the values are around 50 MPa. Comparison of the 3-D model with earlier 2-D models shows that some differences in the results are to be expected.

Long-period magnetotelluric (MT) and geomagnetic depth sounding data (GDS) have been acquired on the Fennoscandian Shield under the framework of the Baltic Electromagnetic Array Research (BEAR) project. The field campaign was carried out in the summer of 1998 when variations of the natural electromagnetic field were recorded simultaneously at 46 MT and 20 GDS stations. The key targets of the project are to investigate the electrical properties of the upper mantle and to determine the depth to the lithosphere-asthenosphere boundary in the Fennoscandian craton.A challenging task emerges from the fact that numerous highly conductive crustal bodies and local conductivity contrasts generate galvanic and inductive distortions to the calculated transfer functions in the research area. We present here a systematic decomposition and dimensionality analysis of the BEAR data and use the results of this analysis to verify regions for which 1-D inversion is justified. We argue that most of the BEAR data represent regional 2-D and 3-D structures with local galvanic distortion. The decomposition of the long-period (T > 3000 s) MT impedance tensors yield a set of smoothly varying regional strike directions. Yet strike angles vary significantly in the scale of the BEAR array and have abrupt regional changes in some areas. The spatial behaviour of strike angles cannot be connected with large-scale geological units. Moreover, strong variation of strike azimuths over the BEAR array convincingly shows that the strike angles cannot be associated with present day plate motion or mantle convection, because that would require a consistent strike azimuth over the whole array. Observed long-period strike angles indicate mainly upper mantle 2-D and 3-D structures or frozen in anisotropy induced by several Palaeoproterozoic and Archaean events.The dimensionality analysis of the BEAR data shows that in the northeastern part of the array the regional structure is approximately 1-D. 1-D inversion of selected data from the western Lapland-Kola Domain reveals a conducting layer in the middle crust. An increase of conductivity is required also at depths greater than 170 km providing a minimum estimate of the lithosphere thickness beneath the target area. Partial melts or dissolved water in olivine are most plausible sources for increased conductivity at such depths.

The calculation of the rheological structure in the deep seismic profile FENNIA in the central Fennoscandian Shield allows in addition the modelling of the present-day stress field and state of deformation. Seismic and surface heat flow data together with all other applicable information are used in the construction of the model. Derivation of the two-dimensional rheological structure requires the determination of the temperature field and the use of known rheological laws both for the brittle and the ductile mechanisms. The rheological model is furthermore subjected to compressional loading resulting in the structural model, which is solved as well as the thermal model by the finite-element method. Results show that rheologically weak crustal layers can be generated under suitable conditions in the central Fennoscandian Shield. These are more evident when assuming wet conditions for the upper and middle crust. Although these weak layers are found the application of the rheological structure to a model, where stress and deformation are derived does not generate intensive crustal deformation. In the stress field influence of the rheology is very small in the crustal part whereas in the mantle a clear effect is seen at the depth of 100km where plastic deformation begins. Uncertainties related to thermal modelling and how these affect rheological and structural modelling are also analysed in a quantitative form showing the importance of temperature in tectonic modelling.

The ground magnetic field disturbance caused by ionospheric currents can be represented by equivalent currents placed to the ionospheric plane. Equivalent currents provide valuable information about the ionospheric electrodynamics, and thus they can be used, for example, in studies of space weather, ionosphere‐magnetosphere coupling, and the magnetotelluric source effect. We derive equivalent currents by using the spherical elementary current system method. The applicability of the method for the Baltic Electromagnetic Array Research (BEAR) magnetometer array is validated by means of synthetic ionospheric current models and by investigating the goodness of the fit between the modeled and measured ground magnetic field. The applicability of the method for the sparser International Monitor for Auroral Geomagnetic Effects (IMAGE) magnetometer network is also proved. In addition, the combination of the elementary current system method and the complex image method, used for the calculation of the induced electromagnetic fields on ground, is introduced, and the combination of the methods is tested by using geoelectric field data from the BEAR project. Our special interest is in the effects that rapidly varying ionospheric currents have on technological conductor systems at the surface of the Earth due to geomagnetically induced currents. Comparison between equivalent currents and the time derivative vector of the horizontal magnetic field emphasizes the importance of small‐scale structures.

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.

Numerical modelling was carried out to investigate the rheological structure and properties of the northern part of the deep seismic sounding (DSS) profile SVEKA. This profile is located in central Finland and it crosses the Lake Ladoga–Bothnian Bay zone (LLBB), which is the border between the Proterozoic and the Archaean domains. Data from seismic, thermal, electromagnetic and gravitational studies are used as initial parameters and also for analysing the results. Mainly DSS data are used to construct the subsurface structures. Rheological and thermal models with different material properties are calculated first. These results are then applied to the two-dimensional finite-element model of the SVEKA profile. The rheologically defined model is furthermore subjected to compressive boundary conditions and the resulting response is suggested to give some understanding of the present-day state of stress and deformational conditions in the lithosphere. The rheology of the DSS profile SVEKA seems to be fairly strong. The Proterozoic lower crust of the model is weaker than the Archaean one. Finite-element modelling shows that with moderate stress fields, the crust remains still intact, and only minor deformational areas are found. These include brittle deformation in the uppermost Proterozoic crust and plastic deformation in the lowermost crust. Lower crustal yielding present in few model cases is limited to very narrow zones at depths, which are very close to the Moho boundary. Changing the lower crustal composition from dry to wet reduces the strength in the lower crust remarkably, which enables plastic deformation in the lowermost crust. Similar results are obtained with reduction of the strain rate value.

The performances of linearized (local) and global nonlinear joint 2-D inversions of very low frequency (VLF) and VLF resistivity electromagnetic measurements are analyzed. A stable iterative inversion scheme is used in linearized inversion while the very fast simulated annealing approach is used in global nonlinear inversion. Synthetic noise‐free and noisy data due to three different models in complexity and two field examples are considered. Synthetic examples show that linearized inversion reveals the subsurface structure better than global nonlinear inversion provided the model has only a few parameters under inversion. Both linearized and global nonlinear inversions must be performed combining all available data in order to obtain the most reliable estimates of the subsurface parameters. Complex models with a large number of parameters are better to invert using global nonlinear inversion although the CPU time needed is always much longer than the one used in linearized inversion. Contrary to global nonlinear inversion, success in linearized inversion requires the good a priori information of all the model parameters under inversion. Noise in data influences the linearized inversion results more than those provided by global inversion. Linearized inversion using as an initial model the mean model due to a few global inversion runs is also a good approach. Even in this case, if there are a large number of model parameters in inversion, linearized inversion can lead to an unstable solution. To overcome such a problem, one can fix the important and stable model parameters from the first step of linearized inversion and then vary and stabilize unstable parameters in the second step.

The deep seismic sounding (DSS) profiles BALTIC, including its southern continuation, the Sovetsk–Kohtla–Järve (SKJ) profile, SVEKA, the northern part of BABEL, POLAR, FENNIA and Pechenga–Kovdor–Kostomuksha, were used in studying the present-day thermomechanical structure of the central Fennoscandian Shield. These profiles are located in different tectonic units, which represent different stages in Precambrian crustal and lithospheric growth. First, present-day geotherms were constructed for several points along the DSS profiles. Successively, strength envelopes were calculated using the obtained geotherms and rheological flow laws. Variations in strain rate were also considered in the computations of the strength envelopes. The integrated crustal and lithospheric strengths, the thicknesses of the mechanically strong crust (MSC) and mechanically strong lithosphere (MSL), and the rheological thickness of the lithosphere were derived from these strength envelopes. The obtained mechanical structures for different regions were analysed and compared with other geophysical data; e.g., seismicity-depth and isotherm-depth distributions. The rheological results show lateral variations in the lithospheric strength reflecting the geometry of the lithosphere and following roughly the same trend as the geochronological development of the Fennoscandian Shield. The mechanical structure shows distinct decoupling of the weak lower crust and the strong upper mantle, particularly with a wet rheology. This decoupling interrupts the transmission of the differential stress from the brittle upper crust to the ductile lower crust and through it to the mantle lithosphere. The weak lower crustal layer is also detected with a dry rheology in the Svecofennian area, whereas in the Archaean side, it is not distinct. The assumed frictional transition temperature of 350°C varies between the depths of 25 and 44 km with an average value of 35 km. This is in good agreement with the observed focal depth limit of 31 km. Consequently, it seems that the velocity weakening/velocity strengthening explains best the real lower boundary of seismicity.

A platelike conducting body in free space is used as a model to invert transient electromagnetic data using the very fast simulated annealing procedure as a global optimization tool. When the host rock conductivity is nonzero, acceptable fits between the observed and computed responses are difficult to obtain. In general, the conducting body is assigned a lower conductance, larger dimensions (strike length and depth extent) and a smaller depth than the true values. We approximate the response of a conducting host to yield reliable estimates of model parameters as well as a good fit between the observed and computed responses. Our procedure is based on the assumption that the observed electromagnetic response is the sum of the response due to the conductive target and the response due to conducting surroundings (host and overburden). It is also assumed that the host response is laterally invariant, implying a layered earth and fixed source-receiver geometry The validity of the superposition assumption is tested against the full solution for a conductive plate in a finite conducting host. The efficacy of our approach is demonstrated using noise-free and noisy synthetic data and two field examples measured in different geological conditions.

Numerical modelling was applied to study the present-day state of stress and deformation under different tectonic loading conditions at the seismic BALTIC–SKJ profile in south-eastern Finland and in Estonia. The finite element method was used to solve the numerical problem. The two-dimensional model was constructed using the results from both seismic and thermal studies along the profile. The model is 700km long and 200km deep, and is roughly divided into an inhomogeneous, laterally layered crust and a homogeneous mantle lithosphere. Both the linear elastic and non-linear elasto-plastic rheologies were used. Elasto-plasticity was achieved by calculating a rheological strength as a function of depth along the profile. Different tectonic load cases were analysed with displacement, force and pressure type boundary conditions. Also, the effect of different strain rates was investigated. The results suggest that even with relatively low compressive stress levels the lower crust deforms in a plastic manner for a wet crustal rheology. When applying a dry crustal rheology, plastic yielding is attained only with much higher stress fields.

The measurements of low-frequency electromagnetic field in the seas and oceans provide information on the variability of the currents, The results of the numerical modelling and the experimental data obtained in the Northern Finland support the possibility of the application of on-land measurements of low-frequency electric field for studying the motionally induced electric fields. Thus, the results obtained present a way of developing low-cost systems for the monitoring of the coastal currents. The method will be tested at the Strait of the White Sea.

Very low frequency (VLF and VLF-R) electromagnetic methods have been increasingly applied in the delineation of the shallow subsurface structures during last decades.

—Efficacy of the global optimisation technique is demonstrated in the inversion of time domain electromagnetic data. Transient EM responses observed using a coincident loops system along several profiles and different time channels over a plate like conducting body are inverted, using very fast simulated annealing (VFSA) as an optimisation tool. Three time channels for each profile are considered in the inversion. Study reveals that only one run of global inversion considering a single multi-channel profile is not enough to resolve all the nine model parameters of a plate-like conducting body. However, the global inversion of a single multi-channel profile with several runs yields a mean model that is quite close to the true model. Considering many profiles and time channels together in the global inversion can yield reliable estimates of all the parameters. Computationally, this is not an efficient procedure. Analysis of the results shows, however, that two distant profiles are enough to yield all the model parameters reliably, even after one run of the global inversion. Both noise-free and noisy synthetic data are used in the inversion. Finally, field data are also inverted to study the performance of the global inversion.

Global optimization with very fast simulated annealing (VFSA) in association with joint inversion is performed for 1D earth structures. The inherent problems of equivalence and suppression in electromagnetic (EM) and direct current (DC) resistivity methods are studied. Synthetic phase data from multifrequency sounding using a horizontal coplanar coil system and synthetic apparent resistivity data from Schlumberger DC resistivity measurements are inverted individually and jointly over different types of layered earth structures. Noisy data are also inverted. The study reveals that global optimization of individual data sets cannot solve inherent equivalence or suppression problems. Joint inversion of EM and DC measurements can overcome the problem of equivalence very well. However, a suppression problem cannot be solved even after combination of data sets. This study reveals that the K‐type earth structure is easiest to resolve while the A‐type is the most difficult. We also conclude that the equivalence associated with a thin resistive layer can be resolved better than that for a thin conducting layer.