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V.Zakharov's Ph.D. thesis

Windows CP1251

сVladimir S.Zakharov
DYNAMIC OF RHEOLOGICALY STRATIFIED LITHOSPHERE UNDER CONTINENTAL COLLISION.
Electronic version of Ph.D. thesis

CONTENTS

Contents

INTRODUCTION

Purpose of work - constructing of quantitative model of mechanical and thermal processes occurring in the lithosphere, having simplified 3-layers construction (rigid upper, plastic lower crust, rigid mantle lithosphere), under continental collision.

Contents

1. MODEL of a CONTINENTAL COLLISION.

It is necessary to consider the rheological structure of lithosphere (fig.1) for explanation phenomena observed under collisions and constructing the model of collision.

It is possible to select on the profile, shown on fig.1 areas, corresponding to maximum of strength (brittle): nearly the whole upper crust, small part of the lower crust and undercrust mantle. Areas of maximums are divided two minimum (ductile), the most significant from which corresponds a lower crust, which material deformed according to experimental nonlinear-viscous law of crip flow:

= A sn exp(-Q/RT),                      (1)

where      - strain rate; s = s1-s3;
T - absolute temperature; R - gas constant;
A,n,Q - material constant.

The features of distribution of earthquake's hypocenter with depth are the complementary independent evidence of crust's rheologic layering.

Fig.1.
Model profiles of generalizing strength of continental lithosphere for regions with different heat flow.
1 - strength, 2 - geotherm for mode with heat flow 45 ЛбР/Л2,
3 - strength, 4 - geotherm for mode with heat flow 60 ЛбР/Л2

Fig.2. Scheme of continental collision use in our work, taking into account rheological layering of lithosphere.
a)collision; b)subduction

In our approach at early stages of a collision between continental plates there is a lockout of the upper brittle layer of a crust. The plastic properties of the bottom crust allow the upper crust and undercrust lithosphere to move rather independently. Mantle part of lithosphere continues undermoving. The matter of lower crust leading by lithosphere, driven under it, to a zone of subduction. At such fast down of a ductile material in a gap between more rigid massifs arise significant vertical forces. In result there is a swell of a crust in the area of a collision and connected with it raising of territories. During plastic deforming of matter of the bottom crust takes place dissipate heat production, which one results to heating of both crust, and underlying mantle.

A number of models of collision based on the above mentioned schema is esteemed. Basic model M1 elaborate for region with a normal heat flow and local isostasy. It is investigated, how the boundary conditions and internal properties of layers influence the deformations. The models applicable by other heat flow (л1Я, л1h), model with "retreat" of subducting mantle lithosphere (M1b), model with elastic undercrust lithosphere (л2, л4), model with erosion and sedimentation (л3, л4) are esteemed. The aspects of thermal evolution of a collision zone also are investigated.

Contents

2. DEFORMATIONS of a CRUST And THERMAL REGIME of a COLLISION OROGEN.

The 2D model of lithosphere is esteemed. Gravity acceleration suppose as a constant in considered area, g = {0,-g}. The undercrust lithosphere moves toward a zone of a collision with speed U, in a point of submergence (x=0) the speed is decrease up to 0.

Let's use the following identifications (fig. 3): thickness of lower crust H = H(x,t), upper - h = h(x,t). The position of lower boundary of a crust G1, boundary of layers I and II - G2, upper boundary of a crust G3 is described accordingly by functions z1(x,t), z2(x,t) and z3(x,t), H = z2 - z1 , h = z3 - z2. Density of a crust rc, density of undercrust lithosphere rm. At constructing mechanical model we suppose matter of a layer I has linear rheology (viscosity h=const). The influence of upper crust layer (II) upon the layer I is concluded in lithostatic pressure only. The equations of viscous flow in lower crust is:

h я2 V = яp - rcg

div V = 0.                                            (2)

where p - pressure,
V={Vx,Vz} - velocity vector.

Fig.3. The main elements of a model.

The boundary conditions:

(3)

Integrating (2) with boundary conditions (3) gives us the equation for dynamics of lower crust thickness. In case of local isostasy

rcgh + rcgH + rmgz1 = const

(4)

and constant thickness of upper layer II (h=const) we have equation for H(x,t) (model M1):

,

(5)

Model M2 takes into account elastic properties of mantle lithosphere which is considered as homogeneous thin elastic layer. Instead of condition of local isostasy we use the equation of a flexure of a homogeneous elastic lamina:

,

(6)

where D - flexural rigidity of mantle lithosphere. Equation for H(x,t):

(7)

where B/= B D/(rm-rc).

Model M3 take into account denudation and sedimentation. We use the following equation for erosion processes:

,

(8)

In this case equation for H(x,t):

,

(9)

where - changing of lower crust thickness due to rheological transformation.

Model M4 take into account elastic properties of mantle lithosphere and erosion. In this case equation for H(x,t):

,

(10)

For thermal evolution of collision zone we use the follow equations:

(11)

where t - time; T = T(x,z,t ) - temperature; u(z) - horizontal velocity of flow; k = l/rC, - thermal diffusivity of rocks, l - thermal conductivity, r - density, C - specific heat capasity; qb and qg - radiogenic heat production in layers I and II of crust;
- strain rate; s - stress.

Contents

3. NUMERICAL MODELING.

Equations (5)-(10) which describe evolution of lower crust layer in different models, as well as systems (11) for the thermal evolution was solved numerically. Calculations were made on the personal computer using programs developing by author.

Contents

4. RESULTS of NUMERICAL SIMULATION of a COLLISION.

The positions of boundaries G1, G2, G3, calculated on models л1 - л4 are shown on fig. 4 - 12. Everywhere on them, as well as on fig. 13 and 14 horizontal velocities of moving plate is directed right to left (see fig. 3).

Fig.4. Changing of crust thickness, calculated for model M1.
Values of parameters: U = 3 sm/y; h=8.1020 Pa.Я; H = 20 km, h = 20 km; rc = 2700 kg/m3, rm = 3300 kg/m3.
Numbers - a time from the beginning of collisions in m.y.

Show dynamic

Fig.5. Deformation of a crust under different velocities of plate motion
(time from the beginning of collision - 20 m.y.)

Fig.6. Thickness of crust under different heat modes
Time from the beginning of collision - 20 m.y.
1 - "cool" crust ( H = 10 km, h=1021 Paв Я);
2 - "normal" crust;
3 - "warm" crust ( H = 25 km, h=4в1020 Paв Я).

Fig.7. Thickness of crust, calculated on model taking into account retreat (1 sm/y) of undermoving plate.
Time from the beginning of collision - 20 m.y.
1 - "cool" crust;
2 - "normal" crust;
3 - "warm" crust.

Fig.8.Changing of crust thickness, calculated for model M2 with elastic undercrust lithosphere.
Flexural rigidity D=1023 Nвm.

Fig.9. Deformation of a crust under different elastic properties of undercrust lithosphere.
Time from the beginning of collision - 20 m.y.

Fig.10 Deformation of a crust, calculated from model M3, taking into account erosion and sedimentation.
Average velocity of denudation decrease exponentially from 0.03 before 0.015 mm/y.
Time from the beginning of collision - 20 m.y.
1 - sediments,
2 - a material of upper crust below rheological boundaries,
3 - a material of lower crust above rheological boundaries.

Fig.11. Deformation of a crust in postcollision stage.
Time from the end of active collision - 20 m.y.
1 - without erosion (model M1);
2 - with erosion (model M3)

Fig.12 Deformation of a crust, calculated from model M4 taking into account erosion and sedimentation and elastic properties of undercrust lithosphere. (D=4в1022 Hв m).
Time from the beginning of collision - 20 m.y.
1 - sediments,
2 - a material of upper crust below rheological boundaries,
3 - a material of lower crust above rheological boundaries.

Show dynamic

 

 

Fig. 13. Stress txz and strain rate in lower crust, calculated from model M1.
a)5 m.y.; b)20 m.y. from the beginning of collision.

 

 

Fig. 14. Velocities of viscous flow in lower crust, calculated from model M1.
a)5 m.y.;
b)20 m.y.
from the beginning of collision.

Show dynamic

 

Results of modeling of thermal evolution..

Fig. 15. Calculated geotherm for central part of collision areas under different time of collision.
Values of parameters: qb=.5в10-6 J/m3, qg=2в10-6 J/m3, (rCp)o=4в106 J/m3, (rCp)1=3в106 J/m3, (rCp)2=3в106 J/m3, lo=3.5 W/mK, l1=2 W/mK, l2=2.5 W/mK, n = 3.4, A = 3в106 (GPa.Я)-n, Q = 260 kJ/mol.
It is seen that calculated temperature on the bottom of crust reaches the temperature of melting of granite with high fluid pressure.

Show dynamic

Fig. 16. Geotherm, calculated under different velocities of plate motion
Time from the beginning of collision - 20 m.y.

Fig. 17. Geotherm, calculated under different thickness of heat productive layers Hc
Time from the beginning of collision - 20 m.y.

 

Contents

5. DISCURSION.

Each model introduced above, is characterized by the pattern and features of deformations of a crust, keeping thus the basic distinctive features of collision orogens.

The results received for model M1, give the basic features describing collision orogens. Significant (up to 2 times) the magnification of power of a crust in a collision zone results in formation of collision uplifting and equivalent formation of "roots". Characteristic lateral dimensions of formed orogens - up to 1000 km. It corresponds to lateral dimensions of real collision orogens, as well as its assymmetric form. The grade of asymmetry depends on the relative velocity of plates

The result of model which is taking into account retreat of undermoving plate - the plateau form of collision orogen (natural object - for example, Tibet).

Analyzing the calculated stress field, it is important to note presence of area with "reverse" (in relation to shear the upper crust - mantle) shear on boundary with the upper crust, that is connected to influencing gravitational spreading of collision orogen. The velocity field points active enough stirring of a material of the lower crust during a collision.

The basic result of taking into account elastic properties of mantle lithosphere is the formation depressions (100 - 200 km in lateral, up to 2 km depths) from both sides of an orogen. In model M2 this depressions are not connected with sediments.

Forming of regional sedimentary basins (not connected with troughs depicted above) - by the basic result of model M3. In the central part of orogen the matter of the lower crust is lifting above rheological boundary separating lower and upper crust. Under regional basins the matter of the upper crust is lowered below rheological boundary. Thus, "rheological metamorphism" contributes in even more significant stirring of a material of a crust, not only in the lower crust, but also interpenetration of matter of the lower and upper crust. It can result in an offset of a material of the lower crust to the surface. It is seen also the significant role of erosion processes in keeping up of existence of roots of orogens in postcollision stage.

Apparently the most realistic is the model M4, which one allows for the greatest amount of effects.

The basic results of simulation of thermal evolution of collision zone - the substantial increasing of temperature on a base of crust (on 50 - 200oC). This source of energy can explain plutonic metamorphism, and also partial melting of matter of the lower crust. The stress field on boundary of the upper and bottom crust contributes in breaking down of the upper crust in the central part of orogen. Thus, the conditions for granitoid magmatism are appear.

The heating of a top of undercrust lithosphere can result in originating so-called anomalous mantle, and also to loss of capacity to brittle failure. It can minister by an explanation of that fact, that in the majority of collision areas are absent acclinal seismofocal zones similar to zones Benioff.

REFERENCES.

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