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3-D density model of the crust of southern and central Finland obtained from joint interpretation of the SVEKALAPKO crustal P-wave velocity models and gravity data

This paper presents a computational method for the interpretation of electromagnetic (EM) profile data in the frequency domain using a thin plate model within a two-layer earth. The modelling method is based on an integral equation formulation, where the conductor is represented by a lattice structure composed of two-dimensional surface elements. Several approximations are used to simplify the theoretical basis and to decrease the computation time. The simple parametric model allows efficient use of optimization methods. We employ a linearized inversion scheme based on singular value decomposition and adaptive damping. The new forward computation method and the parameter optimization are combined in the computer program, emplates. The modelling examples demonstrate that the approximate method is capable of describing the characteristic behaviour of the EM response of a thin plate-like conductor in conductive surroundings. The efficacy of the inversion is demonstrated using both synthetic and field data. An optional depth compensation method is used to improve the interpreted values of the depth of burial. The results show that the method is cost effective and suitable for interactive interpretation of EM data.

A thin conducting plate has proven to be a versatile model in describing various relevant geologic features in crystalline bedrock. During the last few years we have developed several inversion codes for some commonly used electromagnetic (EM) measurements that are based on this model. Both when developing and when applying inversion codes, it is necessary to have a good understanding of how the properties of the model parameters affect the model response. We have studied the parameters of the plate model by using the misfit mapping technique and singular value decomposition. These studies include both time and frequency domain EM systems. We highlight the major differences between a plate model in free space and in conductive surroundings.

A thin conductive plate in free space is one of the most commonly employed models in the interpretation of transient electromagnetic (TEM) profile data. Despite the fact that such a model ignores the influence of the currents induced in the host medium, it is found to be useful to represent the late-time TEM responses which are not severely affected by the host medium. An iterative linearized inversion scheme is designed that computes the Jacobian matrix from numerical differences by forward computations. Parameter steps are solved using the singular value decomposition and an adaptive damping method. Since the computation of the forward solution for the plate model is fast, the inversion method is suitable for microcomputer environment. The parameters used in the inversion are: strike length, depth extent, x-position, depth of burial, dip angle and conductance. The sensitivity analysis of the Jacobian matrix shows that the parameters that can be resolved from TEM profile data with the greatest accuracy are: the x-position, dip angle, depth of burial and conductance. However, it is possible to obtain reasonably good estimates also for the strike length and depth extent from TEM profile data.

Electromagnetic (EM) investigations of the 1980s in the Fennoscandian (Baltic) Shield produced an unique and unified EM data set. Studies include regional investigations by the magnetovariational (MV) method with large lateral sampling distance, investigations of anomalous conductivity structures by magnetotelluric (MT) soundings and other (EM) and electrical methods (audio MT soundings, d.c. dipole-dipole and VLF resistivity profilings) with shorter sampling distance, and studies of the near-surface conductivity by airborne EM surveys. The variety of methods provide an ability to map efficiently crustal conductivity structures from a regional scale of hundreds of kilometres down to local details of some metres in the anomalous structures. The Precambrian of the Fennoscandian Shield is characterized by roughly NW-SE-directed elongated belts of conductors which separate more resistive crustal blocks. The latter serve as transparent windows through which to probe deep electrical structure and belts of conductors as tectonic markers of ancient orogenic zones including (1) the Kittila-Vetrenny Poyas conductor, (2) the Lapland Granulite Belt and Inari-Pechenga-Imandra-Varzuga conductors, (3) the Archaean-Proterozoic boundary conductor and (4) the Southern Finland Conductor. The conductive belts—orogenic conductors—indicate places where crustal masses collided and were finally sealed together. Enhanced conductivity in the orogenic conductors is caused primarily by an electronic conducting mechanism in graphite- and sulphide-bearing metasedimentary rocks. Estimations of the lower-crustal conductivity indicate a laterally heterogeneous lower crust in the Fennoscandian Shield. Archaean lower crust seems to be in general more resistive than the Early Proterozoic lower crust of the Karelian and Svecofennian Domains. The lower crust in the southwestern part of the Svecofennian Domain and in the Sveconorwegian Domain seems to be more resistive than in the central part of the Svecofennian Domain.

Information on electrical conductivity of the subsurface at a crustal scale is inferred mainly from magnetotelluric (MT) and magnetometer data. The latter include both magnetometer array studies (MV) and geomagnetic depth soundings (GDS). Locally, controlled source data (e.g. data from d.c. and very low frequency (VLF) resistivity surveys, frequency soundings and airborne electromagnetic mappings) provide information on near-surface structures, e.g. on exposures of deeper conductors. The variety of electromagnetic methods provides an efficient zooming ability for structures from a regional scale of hundreds of kilometres to small local details of some metres. Thus both the mapping of large-scale crustal conductivity structures and a detail study of the anomalous structures are possible. The electrical conductivity of the crust and upper mantle is described within the plate tectonic framework: examples of structures which become electrically conductive at different phases of the process are shown. Using the results of electromagnetic soundings in various tectonic environments in Europe it is shown how the crustal conductors can be interpreted as ancient and modern tectonic markers. These include structures from the Fennoscandian Shield (Precambrian extensional basins and collisional zones), the Carpathians, Scotland and Ireland (suture zones), and the Pannonian Basin (extensional basin and thrust zones), as well as conductors detected along the European Geotraverse (e.g. the terrain boundaries and the decollement of the Variscan thrusting). An example which considers the lower-crustal conductivity from the Fennoscandian Shield shows rather large lateral variations in conductance of the lower crust varying from 1 S to several hundreds of siemens. Estimates of the depth of the asthenospheric conducting layer within the European territory also vary considerably. Shallowest depths are detected beneath extensional regions (the Pannonian Basin and the Rhinegraben; 40–80 km), whereas depths of 200 km or over (or the absence of a conducting layer) are detected beneath the Alps and old Precambrian cratons. Among the key areas where electromagnetic investigations should play an essential role are the deep structure of the East European platform (boundaries of Archaean and Proterozoic terrains), the structure of the Teisseyre-Tornquist zone, the nature of the present-day continental lower crust, and the characteristics of the electrical asthenosphere beneath Europe.

Large resistive regions (ideally having a horizontal size of about 200 km) are needed to study reliably the conductivity distribution of the lower crust of the Baltic (Scandinavian) Shield by deep electromagnetic (EM) methods. The overburden of the shield consists of Quaternary sediments, and is thin with a low conductance. This makes the shield favourable for EM studies. The numerous conductive zones (e.g., schist belts) in the uppermost crust, however, require careful two-dimensional modelling in order to obtain reliable electrical cross sections of the Earth's crust. Electromagnetic methods, magnetometer array studies and magnetotelluric profiling have proven to be a useful tool in studies of the lithospheric geophysics of the shield. The crust of the Finnish and Soviet Baltic Shield can be divided into geoelectrically different blocks. In Central Finland the blocks are surrounded by narrow, highly conductive band-like formations. They are located in the middle crust, and their upper surface often occurs in the 6–10 km region. The resisitivities are typically 5–10 Ωm. The greatest anomalous crustal regions have a conductance of more than 20,000 S. The lower crust is very conductive in most parts of the shield. Two-dimensional models of long magnetotelluric profiles indicate the great variety and complexity of the geoelectric structure of the crust.

Complex lithospheric structure under the central Baltic Shield from surface wave tomography

International audience

Three groups of electromagnetic data have been considered in order to construct a preliminary geoelectrical depth model of the old basement of the Baltic shield: (i) audiomagnetotelluric data in the period range 1 3700 − 1 8 s; (ii) magnetotelluric data in the period range 25–1000 s; and (iii) global magnetovariation-sounding data in the period range >6 h . These data sets fit together on a common apparent-resistivity curve, indicating the existence of a unified geoelectrical model. This model does not support the existence of conducting crustal or asthenospheric layers.

The geoelectric structure of the Baltic Shield in Finland has been studied since 1980. Four types of geoelectric model have been considered so far: numerical models for the galvanic distortions of the upper 10 km; horizontal distribution of crustal inductive anomalies; vertical cross-sections above relevant crustal anomalies; and vertical conductivity profiles on a regional scale. The models are based on extensive, on-going measurements being conducted with magnetovariational, magnetotelluric and frequency sounding methods. Geoelectric studies in Finland are a part of both the international ELAS (Electrical conductivity of the asthenosphere) and the EGT (European Geotraverse) projects. In Finland, the most relevant crustal conductivity anomalies south of 67°N are a conductive band surrounding the Central Finland Granite Area in the west and south and the Oulu, Mikkeli and Outokumpu anomalies (N-S, E-W and N-S, respectively). The anomalies are located in the middle crust, typically from 6–12 km downwards. Several regional conductivity boundaries and the existence of a conductive layer in the lower crust, at least in parts of Central Finland, have also been noted. A vertical cross-section across the Oulu anomaly shows a wide crustal conductor, which seems to dip towards the west. The anomaly has exceptionally good conductivity (0.5/5 Ωm) and cannot be attributed to the known sandstone formation or the schist zone on the surface. Along the SVEKA DSS (deep seismic sounding) profile, some increases in conductivity of the upper crust correlate with the Kainuu and the Kuhmo schist zones. The upper crustal parts of the Raahe-Ladoga zone has also a higher conductivity than the surroundings. Some local conductivity anisotropies seem to coincide with deep faults located by DSS. The area east of Kuhmo seems to be more or less free of crustal conductivity anomalies, allowing electric soundings down to the upper mantle. A deep conductivity model based on the measurements in this area differs from earlier models for northern Scandinavia, where the presence of a good conductor at asthenospheric depths has been reported. Variations in the electrical conductivity of the Earth's crust and upper mantle thus yield information about the structural composition and the tectonic development of the Earth. The results now presented are only preliminary and their detailed geological-tectonic importance is not yet fully understood. Later, the models will be completed with the results from work done in both the eastern and the western parts of the Shield.

Joint Finnish—Hungarian MT (magnetotelluric) and AMT (audiomagnetotelluric) measurements were carried out in Finland in the framework of the international ELAS project. The conditions for MT measurements are favorable at these latitudes. Five MT and 150 AMT stations gave information on the electrical conductivity distribution in the area: AMT results guided the choice of MT sites with minimal near-surface distortion effects and helped the interpretation of the MT soundings; the MT measurements indicate the presence of large conductivity anomalies and can be best interpreted as lateral induction effects of near-surface dyke structures. This result is confirmed by a certain correspondence between the directions of the maximum impedances and of the tectonic zones of the area. Any information about the upper mantle would require the use of Sq harmonics because of the crustal conductivity anomalies detected by the MT measurements.

Electromagnetic soundings have been made in order to construct a geoelectrical (conductivity) model of the crust along the European Geotraverse (EGT) POLAR Profile. Forty magnetotelluric (MT) soundings, eighteen audiomagnetotelluric (AMT) soundings and ten magnetohydrodynamic (MHD) soundings were made on the main POLAR Profile (POLAR I) and ten more MT soundings on a parallel profile (POLAR II), 40 km to the southeast of the main profile. Analysis of simultaneous recordings by the EISCAT magnetometer chain, and thin-sheet modelling of the effect of the Barents Sea, indicate that neither the source field effects nor the presence of the ocean are significant at periods below 200 s in the measurement area. The magnetotelluric data have been modelled with two-dimensional models representing the regional structure along the profiles. In addition to the regional structure, a thin inhomogeneous surface layer is included in the models in order to explain some local features of the measured response functions. Although details of the surface electrical structures are poorly resolved, the gross features of the geoelectrical cross section are considered to be reliable. The results divide the POLAR Profile into three different blocks. The better conducting Karasjok-Kittila Greenstone Belt in the south has an average resistivity of less than 10 Ωm. The more resistant Lapland Granulite Belt, with a resistivity between 100 and 200 Ωm, is underlain by conductive ( The geoelectric cross section agrees, in gross detail, with the corresponding gravity, refraction seismic and reflection seismic cross sections of the POLAR Profile. All methods indicated a similar shape for the southwestern part of the Lapland Granulite Belt i.e., granulites have a gently NE-dipping boundary against the underlying Karelian Province. In the northeastern part of the granulite belt the geoelectric model and the gravimetric model show a rather steep S-dipping boundary against the Inari Terrain northeast of the granulite belt.

Theoretical calculations using a stationary ionospheric electrojet model are presented for a resistivity model of interest in studies of the Baltic Shield. The Earth model includes the undistorted East European Platform resistivity-versus-depth model, and crustal and asthenospheric conducting layers. The results show that close to the source region, for periods > 15 min, the magnetic field depends only weakly on the Earth's conductivity. Accordingly, the resolution of apparent resistivity curves obtained by the horizontal spatial gradient (HSG) technique becomes poor at longer periods close to the source region. A comparison with experimental HSG apparent resistivity from Kiruna and Kevo in northern Scandinavia supports the existence of high conductivity in the lower crust. The sharp decrease of apparent resistivity at periods > 1 h may—within the limits of experimental error—be a result of the non-uniform source rather than an indication of a good conductor in the upper mantle.

VLF resistivity measurements contain at each measuring point the apparent resistivity and the phase angle between the magnetic and electric field. When interpreting the pointto-point conductivity distribution by a two-layer model, one of the three model parameters has to be assumed: overburden thickness, overburden resistivity or bedrock resistivity. The mathematical algorithm for this procedure is given. When applied to two-dimensional conductive structures, the algorithm results in several typical distortions. The inversion of perpendicular-to-strike resistivities and phases, the overburden thickness increases characteristically above thin vertical conductors, but true conductivities cannot be estimated. Above thick conductors, also conductivity information can be obtained, but the depth to the conductor is interpreted wrongly. Inversion of parallel-to-strike data estimates the conductivities of vertical structures well, but the horizontal boundaries are replaced by trade-off surface towards depth, making boundary determination more uncertain. An improved 1D algorithm with simultaneous inversion of parallel and perpendicular data to obtain the parameters of a homogeneous overburden and anisotropic bedrock is indicated.

Station “Khibiny”, equipped with a powerful magnetohydrodynamic (MHD) generator and/or diesel generator, has been successfully used since 1976 to study the electrical conductivity of the Earth's crust in the northern part of the Baltic Shield. The present paper describes the techniques of measurement, data processing and interpretation of the five-component electromagnetic fields created by this source. A longitudinal conductance map for the upper 10 km of the Earth's crust has been constructed. Several blocks, with conductances varying from 0.1 to some thousands of Siemens, have been revealed on the Kola Peninsula, in northern Karelia and in northern Finland. The blocks of high conductance are connected with relatively young complexes of Early Proterozoic and Late Archean ages. In some places, they create thick and extensive conductive belts such as the Imandra-Varzuga and the Pechenga zones. More often, they appear in the shape of vast regions with enhanced conductivity (e.g., the granulite belts and the Allarechen region). The geoelectric cross-section of the Imandra-Varzuga ore-critical structure has been studied in detail, using the method of electromagnetic field migration. Its depth extent is approximately 10 km. Highly resistant blocks are associated with the most ancient geological units, of early Archean age. Resistant regions have been found in the Murmansk and Central Kola regions, as well as in the Kovdor massif and in the Central Finland granite area. These regions are the most promising ones for deep electromagnetic sounding of the lower crust and the upper mantle of the Earth.

By using two components of anomalous magnetic fields and a formulation including complex numbers it is possible to calculate the position parameters of thick plates and both magnetization and position of thin plates directly from any two or three points of anomaly profiles. The formulae (interpretation operators) allow automatic topographic corrections to be made. The new two-component operators give more reliable results than the conventional methods of interpretation. The variance of the parameter values obtained with subsequent points of an anomaly measures directly, the total error of interpretation. The application of infinite thin plate operators to a long profile results in characteristic patterns, from which the estimation of the number of plates and their approximate position is possible.

Dip and magnetic susceptibility of very deep magnetic plates can be estimated approximately from either vertical, horizontal or total field measurements. A general accuracy of 2–5 degrees is easily obtained, if the other plate parameters, most notably horizontal position of the plate, are precisely determined. For reliable interpretation, measurements around the anomaly maximum or on the dip-side flank of the anomaly should be preferred. The depth extent of the plates must be great, some ten times the plate width at least. The method is best suited to form a part of a plate interpretation scheme, where the other plate parameters are found by some other suitable means. The method can be applied to a simultaneous determination of dips of several plates, but because of its error sensitivity an iterative formulation should then be preferred.

The authors have introduced the concept of effective demagnetizing factor to be used when measuring susceptibilities of highly magnetized samples. They have used one experiment to show that the factor thus defined differs considerably from factors computed theoretically. From its definition, it seems obvious that the numerical value of the effective demagnetizing factor will depend on the measuring geometry and, more so, on the shape of the sample. Furthermore, the relation between the new demagnetizing factor and susceptibilities calculated using it on the one hand, and true magnetization on the other hand, is far from trivial.

Wait and Spies have calculated the transient step-function response of a conducting permeable sphere using the harmonic response and integral transformations. The result is given as a series of exponential functions instead of the higher functions used earlier (Wait, 1951). The exponential series solution can be obtained in another way by separating the time and spatial variables.