DEPTH-DEPENDENT RHEOLOGY OF THE LITHOSPHERE

In the previous Section 4.1 we concentrated on the thermal and other physical properties of the lithosphere along the EGT. Here we concentrate on the consequences of the thermal structure for the mechanical properties of the lithosphere.

Despite the complexity of rock deformation, very simple approximations can be powerful in lithospheric studies. These approximations provide functional representations of the dependence of lithospheric properties on the most geologically significant factors. These formulations are from continuum mechanics, in which the material is treated as an aggregate with certain macroscopic features. These properties reflect, but do not explicitly deal with, the controlling physical properties. The lithosphere is modelled as two regions with different mechanical properties. In the upper region, the differential strength, which is the maximum differential stress that can be sustained, is limited by brittle fracture. For applied stresses less

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⁸²

Figure 4-8_ Depth-dependent rheologieal models for the lithosphere_

(a) Oeeanic

lithosphere,-(b) Continentallithosphere with a rheology based on quartz/diabase/olivine mineralogy_

(e) Continentallithosphere with a rheology based on quartz/diorite/olivine mineralogy_

Different curves show the effeets ofvarious geotherms_ Minima in crustal strength develop only for steep thermal gradients associated with the presenee of thinned lithosphere _ The me-ehanieally strong part ofthe erust and lithosphere are defined by the parameters MSC and MSL indicating, respeetively, the depth in the erust and the upper mantle where duetile strength beeomes smaller than 50 MPa_ Lithospheric strength is eontrolled primarily by the petrologieal layering and the temperature profile in the lithosphere while an order of magnitude variation in strain rate introduees a shift in the depth of MSL and MSC of only a few km (modified from Stephenson and Cloetingh 1991)_ The inset in (a) shows the relationship between MSL and the eoneept of EET inferredfromflexural studies_ As these loading studies adopt a uniform elastie plate with infinite strength, EET is smalter than MSL.

than the brittle strength, the material deforms elastically such that stress and strain are linearly related_ If the applied stress reaches the brittle strength, fracture occurs.

Laboratory experiments indicate that the brittle strength is a linear function of the applied normal stress and is largely insensitive to variations in temperature, strain rate, and rock type.

Thus, in the brittle regime, lithospheric strength increases linearly with press ure. In the lithosphere, within the brittle regime, the lithostatic pressure cr is a function of density p

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EUROPE'S LITHOSPHERE - PHYSICAL PROPERTlES 83

multiplied by gravity acceleration g and depth z, so that 0" = -pgz and is assumed to be one ofthe principal stresses, Ifthe rock contains a pore fluid pressure P r<z), the relations between the stresses for sliding are given in terms ofthe principal effective stress, 0"1 and 0"3' Common assumptions are that the rock is dry, P r<z)

=

0 or that the pore pressure is hydrostatic (equiva-lent to assuming that pores are connected up to the surface) so that P r<z) = -pgz where p is the fluid density. Altematively, the pore pressure can be assumed to be a fixed fraction of the lithostatic pressure. The strength of the lithosphere is defined by the maximum difference between the maximum (0"1) and minimum (0"3) effective stress that the rock can support.

Laboratory studies of rocks subject to differential stress demonstrate that, at temperatures in excess of approximately half their melting point, stresses relax by creep. Thus, with increasing depth, the effects oftemperature become dominant and ductile deformation occurs in the lower portion ofthe lithosphere. Ductile flow is described by different creep equations for various differential stresses (Goetze and Evans 1979).

A very important creep process takes place by thermally activated climb of dislocations obeying a non-linear relation between stress and strain rate

l= e;cfexp(-QIR1)

where Q is the activation energy, R the universal gas constant, 0' the differential, or deviatoric, stress (0"1 - 0'3), eOthe strain rate, T the temperature and N the exponent in the creep law (typically in the range of 2-5). For olivine, Q is 510 kJmole·l , for sigma measured in bars the value of the pre-exponential constant is 70 bar3 S·I. Power law creep holds for conditions ofhigh Tand relatively low deviatoric stresses. For stresses in excess of200 MPa, dislocation glide is the dominant creep process in olivine.

The basic equation for this process (Dom creep) is eO

=

e; exp[ -QI RT(1 -

O'/qJ

^{2 ]}

where O"p is 8500 MPa (85 kbar) and Q is 535 kJmole·l . The value of the pre-exponential constantis5.7x 10¹¹ S·I.

Flow laws can be combined with failure criteria to estimate the strength of the lithosphere as a function of depth. For this purpose astrain rate and a geothermal gradient giving temperature as a function of depth are assumed. At each depth the strengths in both brittle fracture and ductile flow are calculated, and the smaller in magnitude is the relevant strength.

At shallow depths deformation occurs in the brittle regime with a brittle strength, linearly increasing with pressure and therefore with depth, that differs for compression and tension.

In general at larger depths, due to the increase in temperature, flow is the dominant effect and the limiting strength is given by the flow law for ductile deformation.

Figure 4-8 gives strength envelopes for oceanic and continentallithosphere. The oceanic lithosphere, reflecting the olivine rheology of a cooling plate, has a much simpler structure than layered continentallithosphere where the strength depends primarily on petrological layering and thermal structure. In addition, wetness, and to a lesser extent, strain-rate also affect the strength levels that can be supported within the lithosphere. We have calculated strength profiles for continental lithosphere for several positions along EGT, constructed from extrapolation of rock mechanics data using the petrological information and the thermal structure discussed in Sections 4.1 and 4.3 respectively. The profiles are given for different locations along the EGT, corresponding to three sites in the Baltic Shield (Figure 4-9), three locations in Variscan part of central Europe (Figure 4-10) and three sites in the northem part of the Alpine belt (Figure 4-11). The rheology of the lithosphere is for a quartz/ diorite/

diabase/ pyroxenite/ olivine petrological layering (Carter and Tsenn 1987), see Table 4-1,

A CONTINENT REVEALED

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depending on the available petrological and lithospheric structure data available for the actual Iocation. We adopt astrain rate of 10.^{16 S-I} which is characteristic for long-term geodynamic processes operating on the lithosphere.

Table 4-1. Rock mechanics data: values for creep constants (after Carter and Tsenn 1987) adopted in ductileflow laws usedfor the construction ofstrength envelopes.

Balüc Variscan Alpine Q Q _{eo eo} N N

(kJmole-^l) (kJmole-^l) (Pa-N S-I) (Pa-N 8- 1) dry wet

dry wet dry wet

layer I Quartzite Quartzite 134 112-6 6.03 x 10-²⁴ 1.26 X 10-¹³ 2.72 1.9

layer2 Granite Granite 186.5 140.6 3.16x 10-²⁶ 7.94 x 10 -16 3.3 1.9

layer 3 Diabase Diabase Diabase 276 212 6.31 x 10-²⁰ 1.26 X 10-¹⁶ 3.05 2.4

layer4 Ortho 293 271 1.26 x 10-¹⁵ 1.00 x 10-¹⁹ 2.4 2.8

Pyroxenite

layer 5 Olivine! Olivine! Olivine! 510 498 7.00 x 10-¹• 3.98 X 10-²⁵ 3.0 4.5

Dunite Dunite Dunite

Power law Power law Power law

Olivine Olivine Olivine 535 5.7 x 10" Gp

Dom creep Dorn creep Dom creep 8500 MPa

Inspection of the strength profiles shows pronounced changes in the distribution of lithospheric strength with depth between northem and central Europe. The lithosphere in the northem and central parts of the Baltic Shield is, according to the model predictions, quite strong with characteristic values ofthe mechanically strong lithosphere (MSL) in the range 80-95 km. The large values ofMSL in the northem and central part of the Baltic Shield reflect the temperature distribution with low gradients in the mantle part of the lithosphere, which also leads to the presence of significant strength at subcrustallevels. In contrast, the predicted strength profiles in the southemmost part of the Baltic Shield and in the Variscan and Alpine parts of Europe show relatively low values of MSL (30-50 km) and a strong reduction in upper mantle strength. As a result of higher temperature gradients, pronounced minima in crustal strength occur, Ieading to discrete cores of strength at upper crustallevels at depths of 5-15 km in some parts of the profiles. A striking feature predicted by the rheological profiles is the occurrence of a minimum in strength at the base of the crust in Europe underlain, in most cases, by a strong subcrustallithosphere. This leads to a large difference between MSL and MSC values, corresponding to isotherms of750-800°C and 300-400°C, reflecting the creep strength of olivine and crustal rocks respectively. This feature has interesting tectonic implications as such minima in crustal strength are often the sites for crustal decollements.

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