All of the models formulated beforehand, which attempt to accountfor the crustal shortening, thickening, uplifting and other phenomenaof the Qinghai-Tibet plateau, can chiefly be summarized into threeclasses in terms of dynamical mechanism: (1)Underthrusting andcollision models by compression of the Indian plate. (2)Gravitationaltectonic models by the surface load both top snd bottom ofLithosphere. (3)Two-direction (horizontal and vertical) compressionmodels from the Indian plate and plateau itself. First two classes areonly one-side view, however, the third is comparatively morereasonable. Therefore, author considers the third class as startingpoint to set up the effective model.
1. Mathematical principle
The stresses caused by compression below and above can beexpressed as follows; T_(ij.i)=ρg u_(i,j)δ_(3j)-ρg u_(3,j)……(1) T_(ij)=λu_(k,k)δ_(ij+μ) (u_(i,j)+u_(j,i))……(2)Here,ρand g are the original density and acceleration of gravity;u_(ij) and T_(ij) are the displacent and stress tensor of the deforniation.By means of several wavenumber transformation the solutions ofequations (1) and (2) can be expressed as the form of propagatormatrices: W(k,o)=Q_1·Q_2……Q_n·W(k,H)……(3)where W(k,o) and W(k,H) are the stress and displacement matrices ofthe deformation, Qi is Lagrange interpolation matrix of e~(Mi(z-zi)).According to the boundary conditions of the Qinghai-Tibet plateauabout top and bottom surface load, We can obtain the stresses anddisplacements of the deformation.
The stresses under the horizontal compression can also be expressedas:σ_(xx)=-E/(1-V~2) Z d~2l/dx~2……(4) where l is the solution of the elastic plate bending equation: D(d~4)／(dx~4)+P(d~2l)／(dx~2)+△ρgl=q_a (x)……(5)where D is the flexural rigidity, P is the horizortal compressionstress, q_a (x) is the Load of the topography at x.
As a result, We can obtain the stresses and displacements of thedeformation in terms of the overlapping principle of stresses anddisplacements under the boundary conditions of the Qinghai-Tibetplateau, thereby, the maximum shear stress and fracture stress caneasily be obtained by: T_(xx)=(σ_1-σ_3)／2τ_o=σ_1／2[(f~2+1)~(1／2)-f]-σ_3／2[(f~2+1)~(1／2)+f]Here,σ_1 andσ_2 are the greatest and least principal stresses; fis the coefficient of static friction.
Bending under the Quarternary continental glacial sheet can becomputed according to the equation (5), Because of the short time ofthe isostatic adjustment, We look l in (s) as an amount of upliftingafter the glacial sheet began to dispear.
2. The distributive characteristics of stresses and theirgelogical meaning
According to the computation in this paper, author summerize thedistributive characteristics of the stresses of the Qinghai-Tibetplateau into several main points: a. The stress intensity andtheir maintaining depth at the border of the plateau are much largerthan within the plateau, b. The compression stress within theplateau at the top of lithosphere alternates with the tension stress,and at the bottom the stress becomes tensional, c. The divisionalboundary and top surface of the medium appear to be the maximum, Whichare at the side of stronger elastic medium. Within the lower velocitylayers the stresses become minimum, but the larger stresses areaccumulated at the edge of the surrounding layers. These conclusionsare suitable to the horizontal normal stress, the maximun shear stressand fracture stress, d. The horizontal normal stress T_(xx) istensional at S-N direction beneath the Ganga busin. e. Thecompressive stresses from the Indian plate, which are attenuated very rapidly, are smaller than the stresses brought about by gravitation.
The geplogical meaning of the distributive stresses in theQinghai-Tibet plateau can be drawn as follows:
(1) The distrnbutive characteristics of the stresses of theplateau represent the regularities of the current tectonic movementsand earthquake activities.
(2) The N-S trending active tectonic systems represent maximum E-Wtrending tensional stresses and between the two are zone of maximumcompressive stress.
(3) The crust in Tibet can be divided into five layers in terms ofthe relationship between stresses and lower velosity zones and theconcentrated depthes of the carthquake distribution.
(4) The spreading forces and buoyaucy of the anomalous mantlecaused by compression of Indian plate and gravitation may be mainpoints of the whole uplift Of the plateau. In the late plate collisionthe compression from the Indian plate may be concentrated in south ofthe plateau, and it causes the different uplifting and is a minoruplifting stress. The uplift of himalaya mountain higher than theother part of the plateau has a close relation with the compressionfrom the Indian plate.
(5) After the Quarternary continental glacial sheet disappeared,the uplift of the plateau is no more than 700m, which only have atrivial effect on the whole uplift of the plateau.