Rheological structure and dynamical response of the DSS profile BALTIC in the SE Fennoscandian Shield

Tectonophysics 320 (2000) 175–194 www.elsevier.com/locate/tecto

Rheological structure and dynamical response of the DSS profile BALTIC in the SE Fennoscandian Shield K. Moisio a, *, P. Kaikkonen a, F. Beekman b a Department of Geophysics, University of Oulu, Oulu, Finland b Research Schoool of Sedimentary Geology, Vrije Universiteit, Amsterdam, Netherlands

Abstract 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 700 km long and 200 km 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. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Fennoscandian Shield; finite element modelling; geodynamics; geotherms; rheology; strength envelopes

1. Introduction The lithosphere is the strong layer of the Earth that allows the plates to move as uniform units. Deformation of the lithosphere is governed by the rheological parameters, temperature, composition and stress field. Vertical variation of the composition may result in rheological stratification of the lithosphere and produce a so-called ‘sandwich’ structure in which rheologically weak and strong layers alternate. These weak layers, especially the * Corresponding author. Fax: +358-8-5531414. E-mail addresses: [email protected] ( K. Moisio), [email protected] (P. Kaikkonen), [email protected] (F. Beekman)

one above the Moho, have been proposed to play an important role in the tectonic evolution of the crust. Cloetingh and Banda (1992) and Cloetingh and Burov (1996) presented strength profiles for the western Fennoscandian Shield within the European Geotraverse ( EGT ) project. Their strength profiles indicate quite strong lithosphere with characteristic values of the mechanically strong lithosphere (MSL) (the depth where the ductile strength is reduced to 50 MPa) in the range 80–95 km. Another important feature is the occurrence of a minimum in strength at the base of the crust underlain by a strong subcrustal lithosphere. Dragoni et al. (1993) also calculated rheological strength profiles for the Fennoscandian Shield.

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According to them a rheological thickness (the depth where the strength is reduced to 1 MPa) ranges from 120–140 km in the northeastern part of the shield to 60–80 km in the southwestern part. Also the depth of the brittle–ductile transition varies in similar fashion from 18 to 30 km in the Fennoscandian Shield. Recently Kaikkonen et al. (1999) concluded that in the central Fennoscandian Shield the lower crust is characterised by a weak ductile layer. The weak lower crustal layer and its properties at the Canadian Cordillera have been studied by Ranalli and Murphy (1987) and Lowe and Ranalli (1993), where they related these weak layers to the horizontal detachment and overthrusting. The weak lower crust has two other important consequences according to Ranalli (1995), lateral extrusion and vertical delamination. These processes have been described and modelled by Bird (1979, 1991). Using the finite element method ( FEM ), Schmeling and Marquart (1990) and Marquart (1991) have modelled the crustal thickness variations caused by a ductile lower crustal flow. They found that upwelling mantle flows may cause the ductile lower crust to squeeze out and finally result in rather strong crustal thickness variations while the surface topography remains moderate. In this paper we apply FEM modelling to the deep seismic sounding (DSS) profile BALTIC (Luosto et al., 1990) in SE Finland and its southern continuation, the northern part of the Sovetsk– Kohtla–Ja¨rve (SKJ ) profile (Sharov et al., 1989) in Estonia. The state of stress and deformation in the lithosphere, especially in the crust, is modelled by applying linear elastic and non-linear elastoplastic material behaviour to the two-dimensional model. The main interest is in how the lower crust with ductile strength will respond to mechanical loading.

2. Geology of the SE Fennoscandian Shield The Fennoscandian Shield can be divided into three domains (Fig. 1), the Archaean domain, located at the eastern part, the Svecofennian domain in the central part and the Scandinavian domain in the southwestern part (Gaa´l and

Gorbatschev, 1987). The Svecofennian domain was formed by an accretional type orogeny, called the Svecofennian, by deformation and high-grade metamorphism and by extensive crustal melting during the period 1.9–1.55 Ga ( Windley, 1992). The Svecofennian orogeny is believed to have been a collision between the Archaean Karelian craton and a Palaeoproterozoic island arc complex which produced large amounts of juvenile mantle derived crust in subduction-like processes (Huhma, 1986). The Svecofennian domain can be divided into three parts: the volcanic northern and southern Svecofennian provinces and the intervening central Svecofennian province. Most of the Svecofennian domain is occupied by granitoid intrusions which were deposited during 1.9–1.86 Ga and 1.83– 1.75 Ga. The Central Finland Granitoid Complex (CFGC ) is one example of these intrusions. During the time 1.7–1.55 Ga, Svecofennian crust experienced internal slow heating of the thickened crust which finally led to extension and collapse, and to decompression melting of the mantle and melting of previously depleted granulite lower crust ( Windley, 1993). Also unextensional models have been suggested (Stel et al., 1993). These processes resulted in a formation of anorogenic rapakivi granites, coeval mantle-derived gabbros, anorthosites and basic dykes (Haapala and Ra¨mo¨, 1990). The last tectonic event in the Svecofennian domain was the deposition of Jotnian (Mesoproterozoic) sandstones (1.5–1.2 Ga) in the central Sweden, south-western Finland and Lake Ladoga area.

3. BALTIC–SKJ profile The DSS profile BALTIC and its continuation to Estonia, the northern part of the SKJ profile, are located in the Fennoscandian Shield (Fig. 2) in SE Finland and Estonia, respectively. Seismic measurements along the BALTIC profile were done in 1982. Interpretations of this seismic profile have been done by Luosto et al. (1985, 1990). Seismic measurements and their interpretation at the northern part of the SKJ profile have been reported by Sharov et al. (1989).

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Fig. 1. Geological map of the Fennoscandia (taken from Korja et al., 1993). Archaean Domain 1–3: 1, Archaean (>2.5 Ga); 2, Early Proterozoic Granulite Complex (2.2–1.9 Ga); 3, Karelian metavolcanic and metasedimentary rocks (2.5–1.9 Ga). Svecofennian Domain 4–8: 4, Svecofennian schists (2.0–1.8 Ga); 5, Early Svecofennian granitoids (1.9–1.86 Ga); 6, Late Svecofennian granitoids (1.83– 1.75 Ga); 7, rapakivi granitoids (1.65–1.54 Ga); 8, Jotnian sandstone formation. 9, Southwestern Scandinavian Domain. 10, Caledonian. 11, Phanerozoic platform cover. 12, Thrust fault. A=Inari Terrane; B=Lapland Granulite Belt; C=Kittila¨–Karasjok Belt; D= Imandra–Varzuga Belt; E=Vetrenny–Poyas Belt; F=Skelleftea˚ volcanic district; G=Northern Ostrobothnian Schist Belt; H=Kainuu Schist Belt; J=Central Finland Granitoid Complex; K=Bergslagen volcanic district; L=Tampere Schist Belt; M=Outokumpu formation; N=Transscandinavian Igneous Belt.

3.1. Geology The DSS profile BALTIC crosses the principal lithological units of Finland. Crustal age increases from the southwestern Proterozoic area to the northeastern Archaean area, being 1.65 Ga at the Wiborg rapakivi area, 1.7–1.9 Ga at the Svecofennian area and 2.7–2.9 Ga at the Archaean area. The Archaean area mainly consists of migmatite and granitoid rocks with Late Archaean and Early Proterozoic greenstone belt lithologies (Gaa´l and Gorbatschev, 1987). The Svecofennian area is composed mainly of granitoids and schist belts with island-arc affinities (Gaa´l, 1990). The Lake Ladoga–Bothnian Bay zone (LLBB) is a

boundary between the Archaean and the Proterozoic areas. It is characterised by wrench fault deformation and comprises highly deformed and locally cataclastic granitoids and migmatites and mafic volcanic rocks ( Ekdahl, 1993). The Wiborg rapakivi area is composed of rapakivi granites, gabbro-anorthosites and mafic diabase dykes. The SKJ profile in Estonia runs in the early Proterozoic granulite area, which is covered by a thin layer of Phanerozoic sediments. 3.2. Seismic data The Moho depth variation is quite large along the profile, ranging from 40 to 65 km. The deepest

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Korja (1995a) has given a detailed upper crustal model for the BALTIC profile. The block-type velocity model implies that the exposed crustal sections have very limited depth extent and that the crustal structure is more simple at depth, which may only be apparent due to a poorer resolution at greater depths. The structure of the crust and mantle is more stratified in the south than elsewhere. In the upper crust of the southern block at depths of 8–14 km there is a high-velocity layer which seems to be thrust in a thicker layer (Luosto et al., 1990). This layer is assumed to be of anorthositic to gabbroic composition ( Korja, 1995a). 3.3. Thermal data

Fig. 2. Study area in the central Fennoscandian Shield and the DSS profile BALTIC–SKJ on the contour map of the Moho depth in kilometres. The letters a–f show the locations of the points used in Fig. 4.

parts are located in the northeastern parts of the profile. The Moho depth map of the Fennoscandian Shield (Luosto, 1991; Korja et al., 1993; Luosto, 1997) reveals the large variations in crustal thickness ( Fig. 2). A seismic model of the BALTIC profile divides the cross-section into three different blocks based on the Moho depth, the velocity increase with depth and the stratification of crust (Luosto et al., 1990). The maximum Moho depth is approximately 65 km at the Archaean middle block in comparison with the thickness of 42 km at the southern block in the rapakivi area. The high variation in the Moho depth is interpreted to be due to changes in the thickness of the high-velocity lowermost crustal layer ( Korja et al., 1993). The Moho depth in the Estonian part of the profile is around 45–50 km.

The heat flow density varies from low values of 20–30 mW m−2 in the Archaean areas to higher values of 40–55 mW m−2 in the Proterozoic areas. Highest heat flow values are reported in the Wiborg rapakivi area (~55 mW m−2). Heat flow density values in Finland are presented for example by Kukkonen (1989, 1993, 1998) and more generally in the Fennoscandian Shield by Cerma´k et al. (1993) and Pasquale et al. (1991) and in Estonia by Urban et al. (1991). Radiogenic heat production values in Finland are presented by Kukkonen (1989, 1993). Heat production values are increasing from the Archaean towards the Proterozoic areas. Highest values are related to the Wiborg rapakivi area (~5 mW m−3). 3.4. Gravity data There is a large negative Bouguer anomaly associated with the Wiborg rapakivi area. A pronounced regional high surrounds this anomaly and the range of values is nearly 60 mGal ( Elo and Korja, 1993). The pattern indicates that the crust is relatively thin under the rapakivi granites and the mean density of the upper crust is abnormally low. This low density is mainly due to large amounts of rapakivi granites ( Elo, 1997). The LLBB zone is characterised by positive Bouguer anomaly values that are transected by negative lineaments ( Elo, 1989). The Archaean thick crust of about 65 km is associated with Bouguer anom-

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aly highs approximately 40–50 mGal in amplitude, which is abnormal as thick crust should reduce gravity values by 100 to 200 mGal. Gravity modelling suggests that a considerable mass surplus must exist in the upper and middle crust. It is suggested that a mass transfer from the upper mantle and lower crust to the present upper and middle crust took place in association with crustal thickening or later ( Elo, 1997).

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4.3. Finite element model

Continental geotherms are the analytical steadystate temperature solutions of Fourier’s law of heat conduction for a horizontally stratified model overlying a half-space (mantle) (see e.g. Turcotte and Schubert, 1982). The one-dimensional solutions are first attained separately for each layer within its depth range z ≤z≤z . The final top bottom solution for the entire model is obtained by stacking the layer solutions. We use two crustal layers in our model. The temperature and heat flow density values at the Earth’s surface are given as the initial boundary conditions. Radiogenic heat production can be constant or exponentially decaying within a layer.

Our model is two-dimensional, 700 km long and 200 km deep, containing approximately 6000 elements and 9200 node points ( Fig. 3). A crustal part contains higher-order elements (eight-node quadrilaterals) and an upper mantle is constructed using four-node quadrilaterals. The base of the lithosphere is supported by linear elastic springs to simulate the behaviour of the asthenosphere. These springs will react to any vertical movement with a proportional but oppositely directed force. They are allowed to move freely laterally, so that the top and bottom part will always have the same amount of displacement in the same direction, i.e. the springs are always exactly vertical. The bottom of the springs is not allowed to move vertically. All other boundaries are allowed to move freely, both laterally and vertically. Boundary conditions are applied to vertical edges of the model. Numerical computations were done with the finite element package ANSYS@. Equilibrium equations are used to achieve required convergence. Parameters are expressed in SI units and the sign convention for stresses is set so that compression is negative and tension positive. Note that in the strength calculations the sign convention is opposite. The convention for principal stresses is so that s >s >s , i.e. s is maximal and least com1 2 3 1 pressional and s is minimal and most 3 compressional.

4.2. Rheology

5. Results

By calculating lithospheric strengths as a difference between maximum and minimum principal stresses at different depths, we can construct the rheological profiles (strength envelopes) for certain faulting types. These profiles can be divided into brittle and ductile regions (with different mechanical properties). In the brittle region, the strength, i.e. the maximum differential stress that can be sustained, is limited by a brittle fracture (see e.g. Ranalli, 1995). In the ductile region, the temperature becomes dominant and stresses relax by creep, i.e. a ductile deformation occurs (see e.g. Kirby, 1983; Tsenn and Carter, 1987).

In the calculation of the geotherms surface temperature was set to zero (0°C ) and the surface heat flow values were taken from Kukkonen and Jo˜eleht (1996). Their study also provides values for the thermal conductivity and heat production ( Table 1). In the calculation of the strength profiles we mainly apply a granitic composition for the upper crust and a dioritic one for the lower crust ( Table 2). Rheological parameters are given in Table 1. The mantle is assumed to be homogeneous and composed of olivine. The strength envelopes calculated along the BALTIC–SKJ profile at the points a–f (see Fig. 2) are shown in Fig. 4 both

4. Background theory 4.1. Thermal model

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Fig. 3. Geometry and the relevant boundaries of the finite element model. Also geological terrains are shown. Note that horizontal and vertical scales are different. Table 1 Material parameters used in geothermal and rheological calculations (from Carter and Tsenn, 1987; Ranalli, 1995; Wilks and Carter, 1990; Goetze and Evans, 1979; Kukkonen and Jo˜eleht, 1996) Petrology

Density r (kg m−3)

Power law exponent n

Activation energy E (kJ mol−1) p

Initial constant A (MPa−n s−1) p

Thermal conductivity K ( W m−1 K−1)

Heat production A (mW m−3)

Granite (wet) Granite (dry) Diorite (wet) Diabase (dry) Anorthosite (dry) Felsic granulite (dry) Olivine (dry)

2500–2800 2500–2800 2800–2900 2800–2900 2800 2800–2900 3300

1.9 3.3 2.4 3.4 3.2 3.1 3.0

140 186.5 212 260 238 243 510

2.0×10−4 2.0×10−6 3.2×10−2 2.0×10−4 3.2×10−4 8.0×10−3 4×106

2.5–3.5 2.5–3.5 2.5–2.8 2.5–2.8 2.5 3.0 4.2

0.7–3.2 0.7–3.2 0.2–0.5 0.2–0.5 0.2 0.4 0.002

Flow parameters for the Dorn law Petrology

Density r (kg m−3)

Activation energy E (kJ mol−1) D

Initial constant A (s−1) D

Dorn law stress s (GPa) D

Olivine

3300

535

5.7×1011

8.5

Strain rate e˙ (s−1)

Sliding friction coefficient m

Pore fluid factor l

3.0×10−15–3.0×10−16

0.5

0.35

Other parameters used

K. Moisio et al. / Tectonophysics 320 (2000) 175–194 Table 2 Petrology used in the strength calculations

Upper crust Middle crust Lower crust Mantle

Dry

Wet

Granite Granite, felsic granulite or anorthosite Diabase Olivine

Granite Granite or diorite Diorite Olivine

for compressive (thrust faulting) and tensile (normal faulting) cases with the dry and wet rheologies. The wet rheology here refers only to the wet crust, not the entire lithosphere. The layered model used in the calculations for each point is shown in the upper left corner and the insets show the calculated present-day geotherms which were used to calculate the strength envelopes. The geotherm and strength curves marked with letters MC refer to Monte Carlo simulation which is explained in more detail below. Rheological calculations have many possible sources of error. Values of rheological parameters themselves (e.g. Cloetingh and Burov, 1996) and non-uniform strain rate can cause uncertainties in the strength values. Uncertainties in the geothermal calculations should also be considered. Variations in the geothermal parameters, i.e. the thermal conductivity and heat production, and uncertainties in the measured surface heat flow are the sources of error. Fluid circulation in the crust can disturb the heat transfer, resulting in a nonconductive system (see e.g. Chapman and Furlong, 1992; Ranalli, 1995). However, Kukkonen (1998) has concluded in the SVEKA transect studies in the central Fennoscandian Shield that these fluid flow systems are thermally irrelevant in the crustal scale. We calculated more than 20 strength envelopes for the BALTIC–SKJ profile. These envelopes show the variation of the strength in lateral and vertical directions and suggest clear weakening of the lower crust, i.e. the transition from brittle to ductile strength, which results in the decoupling of the crustal and upper mantle parts of the lithosphere. The strength envelopes calculated with a wet rheology for the Svecofennian area show a clear rheologically layered structure for the crust

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( Fig. 4a and b). Such features are absent from the Archaean strength envelopes. With a dry rheology this feature is less visible. Also the base of the dry crust is ‘stronger’ compared with a wet crust. Strength in the lower crust is increased when moving from the Svecofennian terrain to the Archaean one, i.e. from SW to NE. The calculated brittle–ductile transition depths for the wet rheology are between 15 and 30 km, and for the dry one around 30–35 km, in agreement with estimates in the Canadian Shield (Lamontagne and Ranalli, 1996). Jokinen and Kukkonen (1997) have calculated the geotherms with a Monte Carlo type (MC ) stochastic forward simulation of a conductive lithosphere model, where uncertainties in geothermal parameters are taken into account by changing their values randomly (within their natural variation). In this method temperatures of 5°C at the surface and of 1100°C at the lithosphere–asthenosphere boundary were used as the boundary conditions. The strength values (Fig. 4) calculated using the MC simulated geotherms are slightly smaller than our results (correspondingly the geotherms are warmer than ours) in the ductile crustal part, both for wet and dry rheologies. The obtained mantle lithospheric strength values based on the MC calculations are also slightly different from our modelling results. Overall these two geothermal models correlate rather well. 5.1. Elastic model In an elastic case we study the elastic response of our model (Fig. 3) to laterally applied boundary conditions. The compressional boundary conditions with 100 m of lateral displacement are applied to the vertical edges of the profile simulating tectonic loading. Compressional boundary conditions are chosen because the dominating stress component in the Fennoscandian Shield is a NW– SE-oriented horizontal compression (Mu¨ller et al., 1992). Although the dominating stress is not oriented in the same manner as the BALTIC– SKJ profile itself (NE–SW ), we assume it is still appropriate to apply compressional conditions at the profile in question (see Chen, 1991; Kakkuri, 1993, 1997). Gravitational effects were also

Fig. 4. The strength envelopes (MPa) at the points a–f (see Fig. 2) along the BALTIC–SKJ profile for dry (upper panel ) and wet ( lower panel ) rheology. The strength envelopes were calculated with two different geothermal modelling methods: the method described in this paper (thick line) and a method based on the Monte Carlo (MC ) simulation of the geotherms (Jokinen and Kukkonen, 1997) (thin line).

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Fig. 4. (continued)

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Fig. 5. The principal stress s (MPa) — most compressive (a) and the stress intensity (b) for the elastic case. 3

studied, but as the results differed only slightly from those without the gravity we only consider the latter in this paper. A lateral displacement pattern due to the applied boundary conditions is very symmetrical and uniform (not shown here). A vertical displacement pattern is also quite uniform. The surface of the model uplifts about 20 m along the profile due to compression. The base of the model remains almost unchanged. A vertical deflection has its largest value at the middle of the profile in the Wiborg rapakivi area. A distribution of the principal stresses reveals the effect of the compressional loading. The minimal (most compressive) principal stress s has 3 largest values of more than 30 MPa in the lower crust (Fig. 5a). The intermediate principal stress

s behaves similarly to s , and they are both 2 3 horizontally oriented. The maximal principal stress s ( least compressional ) has no significant 1 magnitude. The stress intensity is a parameter which is defined as the largest of the absolute values of principal stress differences. It behaves similarly to the principal stress difference, s −s , 1 3 and can be used to estimate rock failure. In the elastic case largest values of the stress intensity ( Fig. 5b) are found in the lower crust along the entire profile. The magnitude of the stress intensity is at maximum 34 MPa, which should be considered more as a relative than an absolute value. More important is the distribution of the stress fields. Although no ‘in situ’ stress measurements are available from the area in question, the magnitude of the present-day stress field can be consid-

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ered to be relatively low due to the rareness and small magnitudes of the observed earthquakes (e.g. Ahjos and Uski, 1992). 5.2. Elasto-plastic model In the elasto-plastic models the calculated strength profiles are used as non-linear material parameters. The creep strength is translated into plastic yield stress, although physically they are different. The strength profiles calculated with both wet and dry rheologies are applied. Areas where the highest stresses are found in the elastic case might reach the yield stress in the elasto-plastic case, at least in the lower crust where the value of the strength is reduced. This would result in brittle or plastic deformation in that area. The results calculated with a wet rheology are reviewed first. Displacement patterns are slightly different from

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those in the elastic case. Lateral displacements differ mostly in the Archaean area (Fig. 6a). The vertical displacement of the model is no longer symmetric in shape ( Fig. 6b). The SW part of the model uplifts 50–55 m at the surface while the NE part remains almost unchanged or even deflects slightly downwards. Overall the Archaean area is more stable and less deformed than the Proterozoic area. The principal stresses (not shown here) for the elasto-plastic case show a very similar stress distribution as in the elastic case. The largest stress values are found in the lower crust. The minimal and intermediate principal stresses s and s , 3 2 respectively, are horizontally oriented, s in the 3 lateral direction of the model. The magnitudes of the principal stresses are about the same order as in the elastic case. The maximal principal stress s has no significant magnitude. 1

Fig. 6. Lateral (a) and vertical (b) displacement (m) for the elasto-plastic model with wet crustal rheology.

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Fig. 7. The stress intensity (MPa) (a) and the stress ratio (b) for the elasto-plastic model with wet crustal rheology.

The stress intensity pattern (Fig. 7a) shows similar features as in the elastic case. The maximum values of the stress intensities are located in the middle crust at a depth of 20–30 km in the SW and 35–45 km in the NE end of the profile. Similar high-stress values, although slightly smaller in magnitude, are also located in the centre of the model in the rapakivi area. At these depths the strength envelopes have their highest values and enable the accumulation of relatively high stresses. Values of the stress intensity in these crustal extremes are typically above 20 MPa and at maximum 38 MPa. Immediately below this extreme a clear minimum in intensity is reached through the whole profile. This minimum is located in the lower crust above the Moho at depths where the strength envelopes have very low values of strength, i.e. the accumulation of stress is limited. Due to this weak layer, strong crustal and mantle

parts are distinctly separated from each other. At the upper mantle the stress intensity has again higher values resulting from the large strength contrast at the crust and mantle boundary (Fig. 4). In the mantle the stress intensity pattern follows the behaviour of the strength profiles. The stress ratio is a parameter which is defined as the ratio between the equivalent stress and the yield stress. The equivalent stress (the ‘von Mises stress’) is the square root of the second invariant of the stress tensor and describes the deviatoric state of stress. The stress ratio reveals the areas of yielding when the ratio is equal to or greater than one (≥1), and the areas where the stress state is elastic or near failure for ratios less than one (<1). Hereafter in the figures areas with ratio >1 are shown in grey surrounded with black. Fig. 7b shows the yielded areas for the model with a wet rheology. In a crustal part yielding is concentrated

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Fig. 8. The stress intensity (MPa) (a) and the stress ratio (b) for the elasto-plastic model with dry crustal rheology.

on the lower crust following variations in the Moho depth. In the SW end and in the centre of the model yielding originates approximately at a depth of 30 km, and in the NE at a depth of 45 km extending to the Moho boundary. The pattern of yielding is as expected when compared with the strength profiles and the stress intensities. The strength envelopes show that the lower crust has ductile strength. We can conclude that the yielded areas located in the lower crust are deformed in a ductile manner, i.e. the deformation is plastic at the base of the crust under compression. No upper crustal yielding, i.e. brittle deformation, is observed. In the mantle yielding begins in the SW edge of the model approximately at a depth of 80 km, gradually increasing to 140 km at the NE. The results for the elasto-plastic model with a dry rheology and the same boundary conditions

differ slightly from the wet model. Interesting differences are observed in the lower crust. The stress intensity (Fig. 8a) has maximum values in the thick layer composed of the middle and the lower crust where stresses have accumulated. Magnitudes are about the same as in the wet model, with maximum values around 35 MPa. Minima in stress observed in the wet model and located below this maximum, and the sharp boundary between crust and mantle, are however absent in the dry model. This is probably a result of the higher ductile strength in the lower crust, which does not allow the relaxation of stresses. Effectively in the dry model the crust and upper mantle are mechanically coupled. The stress ratio ( Fig. 8b) shows that there is practically no yielding in a dry model. Only in the lowermost crust are a few very thin layers of near failure (<1) areas predicted.

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Fig. 9. The stress intensity (MPa) (a) and the stress ratio (b) for the elasto-plastic model with dry crustal rheology and a strain rate of 10−16 s−1.

At these stress levels the model with dry rheology does not result in plastic or brittle deformation, only a few near failure areas are found. In the calculations of this paper we use the strain rate value of e˙ =3.0×10−15 s−1. However, the previous model for a dry rheology is also calculated with e˙ =3.0×10−16 s−1 to see the effect of the different strain rate. The stress intensity (Fi g. 9a) and stress ratio ( Fig. 9b) show that the effect of the smaller strain rate is not very large in comparison with the previous model. The stress intensities are approximately the same. The smaller strain rate decreases the strength (see also Kaikkonen et al., 1999), and causes plastic deformation in the lowermost crust in the SW. In the wet model (not shown here) the effect is similar but slightly stronger. The yielded area in the lower

crust for a wet model is thicker with the smaller strain rate. An elasto-plastic model with MC simulated geotherms is also investigated to find out how reliable our geothermal models are. Applying the same boundary conditions as before, modelling gives quite similar results although some small differences are observed. The overall behaviour of the stress intensity and the stress ratios calculated with MC simulated geotherms (not shown here) correspond to earlier results. The main differences are deviations in the stress magnitudes, the thickness of the yielded area in the lower crust and the depth of yielding in the mantle. Different boundary conditions are also used to test if the results would be independent of these. The force and pressure boundary conditions pro-

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Fig. 10. Lateral (a) and vertical (b) displacement (m) for the elasto-plastic model with wet crustal rheology and force boundary condition of 5×1010 N.

duce so-called boundary effects, which distort the results at the relevant boundaries, which should be noted in the following figures. The compressive lateral force boundary condition of 5×1010 N is applied to vertical edges of the model. Although the lateral (Fig. 10a) and vertical ( Fig. 10b) displacement patterns differ from the previous models, the main results are essentially similar. The stress intensity (Fig. 11a) is distributed in the same manner as described earlier, the maximum at the lower crust and the clear minimum below it. Also the clear upper mantle maximum is observed. Relevant maximum magnitudes in the crust are about 35 MPa. The stress ratio (Fig. 11b) also shows similar behaviour as earlier. The depth of the yielded lower crust is slightly less than in the previous models, i.e. yielding starts a few kilometres shallower.

The behaviour of the ductile lower crust under increased loading conditions can be very well predicted from the stress ratio figures. With increasing stress conditions the areas with a value of stress ratio near one will yield next. As a result the yielded lower crust will become thicker, and also some upper crustal brittle failure will develop. With decreasing stress conditions the opposite will happen.

6. Discussion Geophysical studies, e.g. seismic, electromagnetic, earthquake distribution and focal mechanisms, can provide valuable information when verifying the results of the numerical geodynamic calculations. Due to the tectonic quiescence of the

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Fig. 11. The stress intensity (MPa) (a) and the stress ratio (b) for the elasto-plastic model with wet crustal rheology and force boundary condition of 5×1010 N.

central Fennoscandian Shield, especially southern Finland, practically no information about earthquakes and their focal depths is available. An estimation of the focal depths can be derived from the overall focal depth data of the Fennoscandian Shield (Ahjos and Uski, 1992). They assumed the error in focal depth estimations to be at least 30%, which is mainly caused by the sparse distribution of seismic stations. That data shows that 80% of the earthquakes in the central Fennoscandian Shield occur below 14 km (e.g. Kaikkonen et al., 1999). If we assume the earthquakes to be a result of brittle phenomena, they are in agreement with the brittle–ductile transition depth obtained from our calculation, which is between 15 and 30 km for the wet rheology and for the dry one around 30–35 km. The stress fields derived from our mod-

elling show that the highest stress intensities are reached in the mid and lower crustal depths, especially in the early Proterozoic terrain in Estonia. Upper crustal stresses are quite low, below 15 MPa in the Proterozoic areas, but in the Archaean area they are slightly higher. However, as earthquakes are a result of fault movements, these estimates of stress fields are not directly related to them. The fault plane solutions for the Fennoscandian Shield are summarised by Slunga (1991). He concluded that the dominant type of faulting is strike–slip at subvertical fault planes, indicating that the dominant stress direction is horizontal. However, as there are only few fault plane solutions for Finland this statement is not very conclusive. We have presented the strength values for compressive and tensile faulting. The

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values for strike–slip faulting would be approximately the average of these two values in the brittle parts of the lithosphere. Electromagnetic investigations can provide interesting information concerning the possible enhanced electrical conductivity of the lower crust and its possible connection with the ductile lower crust. Unfortunately, no high-quality deep electromagnetic surveys have been carried out in our study area. It has been proposed that there is a possibility for a correlation between ductility and high electrical conductivity caused by mineralogy, presence of water or partial melting, etc. (Ranalli and Murphy, 1987). The suggested lower crustal high-conductive layer beneath the DSS profile SVEKA ( Korja and Koivukoski, 1994) is one example. Our modelling shows plastic deformation of the lower crust only for wet crustal model. For a dry crust a possible conductive layer and a ductile layer do not correlate. Comparison of the depth of the ductile layer for the wet model with the seismic model of the BALTIC–SKJ profile shows that this layer is located in the seismic highvelocity depths, i.e. in the depths where seismic P-wave velocities are over 7 km s−1. In the Fennoscandian Shield the thickness of this highvelocity layer correlates very well with the thickening of the crust ( Korja et al., 1993). This layer is assumed to be formed by mafic under- and intraplating that resulted from the lithospheric delamination of the overthickened Svecofennian lithosphere ( Korja, 1995b). As mentioned, Ranalli (1995) connects the existence of the weak lower crust to lateral extrusion and vertical delamination. The lateral extrusion is the horizontal flow of ductile lower crustal material. This process relaxes the topography of the Earth’s surface and affects the topography of the Moho. Bird (1991) showed that the effective lateral extrusion can be expected at short wavelength (100 km) scale independent of rheology but dependent on the geotherms, i.e. the coldest areas (shields and platforms) are probably not affected. At longer wavelengths lateral extrusion depends also on the rheology of the lower crust. The Moho topography is not necessarily smoothed by lateral extrusion. If there are lateral density variations in the upper mantle, the Moho topography will become more

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pronounced. The observed present-day features of the Moho are not necessarily a result of the last tectonic event, which should also be noted when studying the lithosphere of the Fennoscandian Shield. During the Proterozoic era, thermal and consequently rheological conditions were quite different in the Fennoscandian Shield, and the lower crust did not have any considerable strength (e.g. Pedersen et al., 1998). At that time and perhaps also later, the lateral extrusion was a possible mechanism. It would have been most effective at short wavelengths, but also longer wavelength (~300 km) features could have been affected. Bird (1991) also pointed out that at short wavelengths a flexural rigidity plays an important role which was not taken into account in his study. The seismically determined Moho in central Fennoscandia shows large variations in short distances. These features might be preserved by the flexural rigidity of the lithosphere or by a ‘strong’ rheological strength which presently can be found only for a model with a dry crustal rheology. Vertical delamination (Bird, 1979; Ranalli, 1995) of the thickened crust and lithosphere is likely to occur at the Moho due to a weak ductile layer located above it. Delamination is a process that has been physically possible due to the existence of ductile lower crust in Proterozoic times. In detachment, hot material is brought in contact with the crust and thereby increases the temperature of the crust (possible lower crustal partial melting and magmatism) and decreases the strength. Ranalli (1995) concluded that detachment of the lithospheric root generates tensional stresses of the order of tens of MPa. These tensional stresses were studied in more detail by Bott (1993). Korja (1995b) has suggested an extensional collapse together with delamination as an evolutionary model for Svecofennian lithosphere after the Svecofennian orogen. Evolution of a non-extensional, anorogenic setting first described by Stel et al. (1993) and further studied by Heeremans et al. (1996) gives an alternative model, in which asthenospheric upwelling results in underplating of the crust and finally leads to intrusion of diabase dikes and basaltic magmas. One fundamental aspect of their model is the non-existence of any significant evidence of

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crustal extension. A model of differential stretching (Royden et al., 1983), where stretching occurs only in the lower crust and the mantle while the upper crust remains mainly unaffected, is one way to explain this. Schmeling and Marquart (1990) and Marquart (1991) suggested that upwelling mantle flows may cause the ductile lower crust to squeeze out and finally result in rather strong crustal thickness variations while the topography remains moderate. A wet rheological model results in a pronounced plastically deforming layer. Considering geological evolution of the area, e.g. the last tectonic event is 1.2–1.5 Ga old, it seems unlikely that this kind of ductile layer would not give any geophysical or geological indications. This aspect favours the dry rheological model with a possible ductility in the lowermost crust in the youngest terrain of the study area. Of course, the upper crust can and probably will have interaction with fluids.

7. Conclusions The rheological structure of the BALTIC– SKJ profile suggests substantial mechanical weakening of the lower crust. The lower crust turns out to be a weak ductile layer when assuming a wet rheology, or a slightly stronger ductile layer for a dry rheology. The strength in the lower crust increases towards the Archaean area. Our numerical modelling suggests that under sufficient loading this ductile layer deforms in a plastic manner for a wet crustal rheology. For a dry crust significant plastic deformation is observed only at relatively high stress conditions. Largest stress fields are found in the mid and lower crustal depths, especially in the Proterozoic areas. Different boundary conditions produced consistent results, especially the response of the ductile lower crustal layer remained very similar. The effects of the reduced strain rate in the stress fields were rather minor, however, the plastic deformation in the lower crust increased. The importance of the weak ductile layer in present-day and past tectonics should be noted when studying the features of the lithosphere.

Acknowledgements The authors would like to thank J. Jokinen for providing the Monte Carlo simulated geotherms. We thank S. Cloetingh for making possible the visits of PK and KM to Amsterdam, and for his support and interest in this study. KM has worked at the Lithosphere Graduate School funded by the Academy of Finland. We thank the two journal reviewers T. Pedersen and G. Ranalli for their helpful comments and suggestions. ANSYS is a trademark of Swanson Analysis System Inc.

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