Vol. 7 No. 3 415--425 ACTA SEISMOI.()GICA SINICA Aug. ,1994

A kinematics-uplift model for the Himalayan- Tibetan region

Xian-Jie SHEN L~ (~[i,~a~)** and Ladislaus RYBACH -'~

1 ) Institute o f Geology, Academia Sinica, Beijing 100029, China 2) lnslilute o f Ueophysh's, E T l l Zi}rh'h Ctt -8093, Switzerland

Abstract

The Lhasa-Gangdise Terrane is taken as a representative mobile terrane during the Himalayan orogeny of the In-

dia-Eurasia continental collision, for which a corresponding kinematics-uplift model is set up. The parameteriza-

tion of the model is uhimately constrained by the uplift history outlined by synthesized pateogeographic studies

with consideration of the following famors: (1) kinematic features of India-Eurasia plate convergence; (2) 3-I)

mass conservation during terrane deformations incorporating shortening, thickening, extension, uplift and ero-

sion; and (3) instantaneous vertical movement of lithospheric material under the control of isostasy. The model

study involves the following four groups of uplift-relevant parameters: ~) plate converging velocity and its varia-

tions with time; @ extent of lateral mass transfers @ crustal structure; and @ surface erosion mode. The re-

suits of calculation of 144 models of different parameter combinations have indicated the non-uniqueness of solu-

tion. Nevertheless, it is also proved that for a fixed kinematic mode of plate convergence there exists a unique

best-fitting model which may reproduce the observed uplift history, implying the uniqueness of dynamic environ-

ment of two converging plates. Therefore, the uplift of the Himalayan-Tibetan region is mainly controlled by

plate dynamics-kinemaTics and is a complicated geological process of far-reaching implications.

Key words: Himalayan-Tibetan region, plate convergence, terrane deformations, kinematics-uplift model

1 Introduction

A series of previous studies (Chang e t a l . , 1982; Xiao e t a l . , 1988; Dewey e t a l . , 1989; Wu e t a l . , 1989) all suggest that the India-Eurasia collision has led to the large amplitude uplift of both the Tibetan region north of the Yarlung-Zangbo Suture Zone and the Himalayan belt south of it. And this seems to become a commonly accepted understanding. Nevertheless, uplift of orogenic belts of continental collision type can not be understood as a purely superficial geologi- cal process or a simple vertical movement of lithospheric materials. As a matter of fact, it is a comprehensive surface manifestation of many interrelated tectonic processes at depth and of the

erosion process at surface.

In this paper the main emphasis is to reproduce the observed uplift history through parame-

terized model calculations which take into consideration the following four groups of uplift-rele-

vant processes: (~) horizontal converging-shortening as main motivation for terrane deformation;

* Received June 26, 1993; Accepted September 17, 1993. ** A visiting professor at ETH, Ziirich from the Institute of Geology, Academia Sinica, Beijing, China, July 1991-January

1992. The current paper of collaboration was completed during this visit.

416 ACTA SE1SMOLOGICA SINICA Vol. 7

@ vertical thickening of both the upper crust leading to tectonic uplift of the plateau surface and

the lower crust resulting in the development of crustal root, as well as the isostatic compensation between them; @ lateral mass transfer which may suppress tile scale of the vertical thickening-u- plift ; and @ surface erosion-denudation as the major competitor with uplift in creating surface re- lief-elevation.

The main differences between the current study and the previous investigations on the Ti-

betan uplift are tile following: 1 ) The previous works (Multi discipline Scientific Expedition Team on the Tibetan Plateau,

1981 ; Chang et al. , 1982) were mainly concentrated on the age, amplitude and form of the up- lift, whereas tile current paper addresses itself to the discussion on the possible process and mech- anism of the Tibetan uplift. In particular, the transition from horizontal convergence via vertical thickening to surface uplift constrained by both erosion and isostasy is applied in the paper as a

main line of methodology. 2) The previous studies (Wang et al. , 1982; Zhao et al. , 1985; Xiao et al. , 1988) were

mainly qualitative discussions on geological models, whereas the current work carries some quasi- quantitative character. All of the above-listed four types of uplift-relevant processes will be pa-

rameterized and then introduced into the model. The I.hasa-Gangdise (abbreviated to 1.G hereafter) Terrane is selected as the model region

mainly for two reasons: firstly, the geometry of the I .G Terrane is rather simple for a quantita- tive modelling; secondly, most of information used in model calculation comes from the I.G Ter- rane. Therefore, a model based on the I.G Terrane is representative enough for the region of

study.

2 Model design 2.1 A schematic kinematics-uplift model

The variation history of average surface elevation on the Tibetan Plateau is expressed by the solid line shown in Figure la based on the achievements of multi-discipline scientific expeditions by Academia Sinica in 1970's. And this is the major constraint for the model study. A schematic kinematics-uplift model used is shown in Figure lb. The abscissa stands for the whole time span

of continental collision from 40 Ma B.P . to the present day. Explicitly, this model shows the following three uplift-relevant processes: @ bulk crustal

thickening from an initial thickness D at 40 Ma B.P . to a time-dependent value D ( t ) at time t; Z ( t ) denotes the Moho depth below sea level; @ two-directional crusal thickening both upward and downward relative to the so-called "Introcrustal Boundary I.ayer of Deformation" (abbreviat-

ed to IBI.D hereinafter; its initial depth from sea level is denoted by d (Shen, 1992) ) ; the

downward thickening of the lower crust results in the development of crustal root, whereas the upward thickening of the upper crust leads first to tectonic uplift of the surface, and then after isostatic readjustment and erosion, to the ground surface undulation with a time-dependent eleva-

tion above sea level h ( t) at time t; and @ instantaneous isostatic balance between surface eleva- tion and crustal root at time t which leads to the vertical movement of crustal materials either downward (undercompensat ion)or upward (overcompensation) ~ this is expressed intuitively by the vertical shift of the IBLD as a reference level within the crust (see Figure l b ) ; where d ( t )

stands for the time-dependent depth of the IBLD below sea level at time t. In the meantime, the model implicitly incorporates the following uplift-relevant processes:

@ compressive crustal shortening from an initial N-S length L of the LG Terrane 40 Ma B. P. to a time-dependent terrane length L ( t ) at time t; @ lateral mass transfer in the form of E-W ex-

No. 3 SHEN ,X. J. et al. : KINEMATICS-UPLIFT M(_)DEL OF HIMALAYAN-TIBETAN REGION 417

~51- ib3 ,c,j2L~L_~_, ~-0 . . . . l+l~ t - T 3

/ . ,° I 40 30 20 10 0 40 30 20 I0 0

r/Ma t/Ma

~ 3 ~ 2

7 -

,I ,I L : L -~ ~ ' ' - J

(d) j !

40 30 20 I0 ,q ~/Ma

Figure 1 Calculation results of a best fitting kinematics-uplift model for the Himalayan-Tibetan re- gion. Ca) A close up picture of the uplift history of the Himalayan-Tibetan region; The crosses are the results of model caleulations~ I I i t ) stands for the m{Klel-ealculated tectonic height, and h ( t ) stands for the isostatic height; ( b ) A kinematics-uplift model for Hi-

m a l a y a n - T i b e t a n region. IBI.D ]ntracrustal Boundary Layer of Deformation whose o-

riginal depth from sea level is denoted by d and its time-dependent value by d ( / ) ; 1) ( t ) is the time-dependent crustal thickness increased due to shortening (initial value: D)~ Z ( l )

denotes the changing Moho depth from sea level, it describes the development of the crustal

root; (c) Two types of time-dependent uplift rate. U~ ( t ) is the tectonic uplift rate repre-

sented by single arrows ; U~ ( t ) is the isostatic uplift rate represented by double arrows ; (d)

Resultant uplift rate U ( t ) and regional average erosion rate e ( l ) ; T h e time-dependent ap-

parent uplift rate u ( t ) is implicitly shown by the differences between U ( t ) and e ( t )

tension and strike-slip sliding~ it is qunatitatively measured by a cumulative transfer ratio E&(t) which is the ratio of the cumulative mass transferred out of the model region from the onset of collision till time t to the initial crustal mass; and @ surface erosion denudation process; it is de- fined by a time- and elevation-dependent erosion rate e(h, t) while the erosion-induced mass loss is measured by a cumulative erosion ratio 5LS~(t) which is the ratio of the cumulative mass loss in the model region due to erosion from the onset of collision till time t to the initial crustal mass.

Each of these processes can further be assigned a short definition in accordance to their rele- vance to uplift, s h o r t e n i n g - driving process~ extension - - r e s t r i c t i n g process; thickening - - transition process ; erosion-competing process ; isostasy regulating process ~ and finally, uplift itself is the comprehensive surface consequence of all these processes. 2. 2 Principle of mass conservation

A rather simple terrane geometry is assumed for the model , i .e . , the initial N-S length, E W width and crustal thickness of the I.G Terrane 40 Ma B.P . are assumed to be L, W and D , respectively. The average density of crustal materials is expressed by p, assumably constant over the whole 40 Ma of plate convergence. In this case, the initial crustal mass of the terrnae can he written as LDWp. At time t the crust would be shortened to L ( t ) , thickened to D ( t ) and widened to W(t ) (see Figure 2) . However , the crustal mass L ( t ) D ( t ) W ( t ) p at t would be smaller than the initial crustal mass. The mass deficit is consumed in erosion. It can be written as

~-]3o(t) = [ L D W p - L( t )D( t )W( t )p] /LDWp

or

418 ACTA SEISMOI.OGICA SINICA Vol. 7

~.23~,(t) = 1 - - L ( t ) D ( t ) W ( t ) / L D W (1)

L ( t ) in Eq. (1) is the dynamic terrane length. It defines the crustal shortening which acts

as the primary driving force for terrane deformations, and should be determined first from the

following kinematic equations (Shen, 1993):

V ( t ) = Vo -- nt (2)

f nt z L ( t ) = L - - V ( t ) d t = L - - Vot -4- ~ - (3)

where V ( t ) stands for the decreasing convergence velocity ( k m / M a ) with a deceleration

n ( k m / M a 2) ; and V0 is the initial convergence velocity ( k m / M a ) . Eq. (3) describes a non-linear

shortening process of the LG Terrane and is the basic equation for further derivations of D ( t ) , h

( t ) , etc. For saving space, the detailed derivation of different kinematic equations is referred to

Shen (1992).

L(O

L~2~lt)

\ ~wE 6.(0

Another important item of mass conservation is the

lateral mass transfer. It restricts the final scale of uplift

since the more the mass consumed in lateral extension,

the less the mass involved in vertical thickening and up-

lift would be . However , constraint imposed on this pa-

rameter by our kinematics-uplift model is the poorest, it

is therefore necessary to assume that the cumulative

transfer ratio £ & ( t ) has increased linearly from zero 40

Ma B. P. to a fixed value £82(0) at present. Thus a se- ries of pre-selected values of £&(0 ) can be used in trial-

and-error calculations for model optimization.

After defining the mass loss by Y~&(t) and the lat- eral mass transfer by £ & ( t ) , a general equation of mass

conservation for an arbitrary time t can be derived as:

L ( t ) D ( t ) L D + )-23~(t) + ~-~3~(t) = 1 (4)

Figure 2 Schematic diagram showing 3- D terrane deformations. Re- gion hatched by single lines stands for the area where ero- sion takes place; region hatched by double lines de- notes the area undergoing lat- eral mass transfer

From Eq. ( 4 ) , the expression for the time-depen-

dent crustal thickness D ( t ) incorporating the mass loss

£ & ( t ) and mass transfer £&( t ) can be obtained as

LDE1- E&(t)- ~&(t)] D ( t ) = (5)

L ( t )

The D ( t ) vs. t relation given by Eq. (5) is shown

in Figure lb. It is an important mathematical expression characterizing the transition from hori-

zontal convergence-shortening L ( t ) to vertical uplift h ( t ) , with the principle of mass conserva- tion as its prerequisite.

No. 3 SHEN,X. J. et al. : KINEMATICS UPLIFT MODEL OF HIMALAYAN-TIBETAN REGION 419

2. 3 K i n e m a t i c s o f v e r t i c a l m o v e m e n t

The kinematics-uplift model shown in Figure lb represents a complicated situation of vertical

mass movement during crustal shortening-thickening-uplifting. One must distinguish between at

least three types of vertical movements: thickening of deforming crust, isostatic readjustment

and the variation of surface elevation. Accordingly, it is necessary to define three types of uplift

rates: tectonic uplift rate U, ( t ) , isostatic uplift rate U~ (t) and the apparent uplift rate u (t) for

surface undulation (Shen, 1987; Shen, 1992).

s

I A

d 0

t=0

N Sea level

IBLD

_A3 ,/(t) /

__L_ m t

u~(t),uttt) vt

Figure 3

t=t/Ma Z

Schematic diagram showing the space-dependent tectonic uplift rate in a vertical column. The hatched area stands for the mass removed by erosion. The others are referred to the text

1) Tectonic uplift of the plateau surface is a direct consequence of thickening of deforming

crust. The distribution of U,(t) in a vertical column is shown in Figure 3. As is shown in Figure

3, when the upper crust thickens upward through pure shear, U,(t) would increase from zero at

the depth d(t) to a peak value at the surface. Similarly, it would increase from zero at the same

depth d(t) to a peak value at the crustal base during downward thickening of the lower crust,

most probably, through ductile shear (not shown in Figure 3). However, U~ ( t ) will be used

hereafter in the text to denote exclusively the peak value at the surface.

2) Vertical isostatic readjustment is

driven by the isostatic balance between the

surface elevation and crustal root. In this

case the whole crustal mass shares a com-

mon velocity and direction of movement,

either upward with a positive isostatic uplift

rate + U i ( t ) or downward with a negative

isostatic uplift rate -- U~ ( t ) , depending on

the status of isostatic compensation. A

schematic diagram showing the isostatic

balance during crustal thickening is given in

Figure 4.

In most cases, tectonic and isostatic

movements may take place simultaneously

to cause a rather complicated resultant ve-

locity field in the vertical crustal column.

The sum of U,(t) and Ui(t) can be defined

Sea level

f D

Reference level t=0

Figure 4

l ,h( t )

D _ _ ~ o(t)

t=t/Ma

Schematic diagram showing isostatic bal- ance during crustal thickening, h (t) is the isostatic height of the ground surface; b (t) is the thickness of the crustal root af- ter thickening ; while Pc and pm are the av- erage densities of the crust and the upper mantle, respectively

42o A C T A SEISMOLOGICA S1NICA Vol. 7

as the true (or absolute) uplift rate U ( t ) :

( ' ( t ) = U , ( t ) + U~(t) (6)

U ( t ) in Eq. (6) can be positive or negative, depending on lhe magnitudes and signs of its components U, (t) and Ui (t) .

3) Variation of surface elevation is described by the so-called "apparent (or relative) uplift rate" u ( t ) , which can be expressed quantitatively by the difference hetween U ( t ) and 1he region-

al average erosion rate e ( t ) , i . e . ,

u ( t ) = U ( t ) - - e ( t ) (7)

as shown in Figure ld by the vertical distance between the two curves. Similarly, u ( t ) can also

he either positive if U ( t ) 7 ~ e ( t ) , or negative if U ( t ) % e ( t ) (Figure 2d). The former case corre-

sponds to surface elevation; and the latter case corresponds to denudation-peneplanation, but the

term denudation rate should be used in place of uplift rate.

3 Results of model calculation

In order to distinguish a best-fitting model which may reproduce the Tibetan uplift history through identification of optimal parameter combinations, a computer-scanning calculation of too-

Table 1 The ranges of kinematic parameters

used in model calculation

L V~ n AL No

km k m / M a k m / M a 2 km

l 2300 70 1.00 2000

2 2100 55 0 .50 1800

3 50 O. 5O

4 49 0. 45

5 48 0.4O

6 1900 47 0. 35

7 46 0.31)

8 45 0 .25

9 45 0. 5O

10 44 0.45

11 1700 43 0 .40

12 42 0.35

13 41 0.3O

16OO

1400

14 40 0 . 5 0

15 1500 37 0. 35 1200

16 35 0 .25

dels with different parameter combinations is con-

ducted in this paragraph.

3. 1 Parameterization of models

The available geological and geophysical re

search achievements are applied for parameteriza-

tion of the following four groups of factors in mod- el calculation :

3. 1. 1 Plate converging velocity and its varia- tions with time

Numerous paleomagnetic researches (Lin and

Watts , ]988; Windley, 1988; Dong et al . , 1990) have constrained the shortening scale of the I.G

Terrane AL well in a range from 1200 km to about

2000 kin. With reference to the present-day N-S

length of the I.G Terrane of L ( 0 ) ~ 3 0 0 kin, the

initial N-S terrane length L may vary from 1500

km to about 2300 kin. The relation of L to V0 and

n is defined by Eq. (3). They jointly form a group

of kinematic parameters. A total of 16 combina-

tions of L , V~, and n used in model calculation are listed in Table 1.

3 . 1 . 2 Scale of lateral mass transfer

In mdoel calculation, five possible scales of lateral mass transfer ranging from 0. 40 to 0 .30

are used as trial-and-error parameters. They are:

~(0) = 0.40, 0.36, 0.34. 0.32, 0.30

No. 3 St tEN ,X. J. et al. : K 1 N E M A T I ( ' S - U P L I F T MODEL {)F H I M A L A Y A N T I B E T A N REGION 421

3 . 1 . 3 Crustal structure

Two types of parameters of this group are involved in model calculation: the initial crustal

lhickness D and the initial depth of the IBI.D below sea level d. Once a d value is given, the

crust is assumed to t)e divided at this depth into lhe upper crusl and the lower crust. Immediately

before the onset of continental collision, the thickness of the upper crust was d and that of the

lower crust was D - - d . At any time t after convergence started, the total crustal thickness is de-

noted by l ) ( t ) , and lhe thickness of the upper crust was d ( t ) + h (t) (see Figure 1 b ) , while that

of the lower crust was I ) ( t ) - d ( t ) - - h ( t ) . D and d as two initial model parameters are closely

connected with each other to define a certain mode of crustal structure. The following wdues of I)

and d have been used in model calculation:

I) = 35, 36, 37, 38, 39, 40 and 41 kin.

e l = 19.0 , 19.2, 19 .5 , 19.8, 20 .0 , 21 .0 , 21 .2 , 21 .5 , 21 .6 ,

21 .7 , 21 .8 , 2 2 . 0 , 2 2 . 2 , 22.5 , 22 .6 , 22 .7 , 22 .8 , 23 .0 ,

23 .1 , 23 .2 , 231 3, 23 .4 , 23 .5 , 23 .6 , 23 .7 , 23.8 and 24.0 km

3. 1 .4 Surface erosion mode

Surface erosion is a very complex process depending upon many factors. Therefore, simplifi- cation is necessary. An assumt)tion is made that the eroison rate is both time-dependent and ele-

vation dependent, t)eing a two component parameter. It can be expressed as

e ( k , t ) ,= e,t + m k ( l (8)

where e,,t can be called tile time dependent component and mk (t) the elevation-dependent compo-

nent. e,, represents a certain time-dependent variation of the erosion rate measured in k m / M a e

and is assumed to be constant. Its physical meaning is that the longer the surface rock subjected

to deformalion and surface weathering, the greater the effect o{ erosion on it would be. In this

sense, e~, can also be called a deformation-dependent factor, m represents a certain elevation-de- pendent variation of the erosion rale measured in 1/Ma and is also assumed to be constant. Its physical meaning is that the higher the elevation, the higher the erosion rate would be. In the

early stage of plate convergence when the elevation was relatively low, the erosion rate increased

slowly with time and partly with increasing elevation; later on, the elevation effect gradually ex- ceeded the deformation effect; and in the late stage of surface denudation-peneplanation the ele-

vation effect weakened while the deformation effect continued to increase with time so as to keep a certain impetus of erosion-denudation. Therefore, the two-component definition of the erosion

behavior given by Eq. (8) was based on the observed Tibetan uplift history, especially for the last

10 Ma shown in Figure la. It is clear that e0 and m are also a group of parameters. It would be

impossible to list all of the combinations of e0 and m used for model calculation because they

amount to several tens in total. Instead, only the ranges of e, and m used are listed as follows.

e0: from 0. 010 to 0. 025 km/Mae ;

m: from 0.08 to 0.45 1/Ma.

Finally, for a selected kinematics-uplift model, the following string of parameters of the

above-listed four groups must be assigned as the input of the model:

422 ACTA SEISMOLOGICA SINICA Vol. 7

L, V0, n - - ~ - ] 8 ~ ( 0 ) D, d - - c o , m

shortening extension thickening erosion 3. 2 Identification of best-fitting models

For each 1 Ma step from 40 Ma B.P. to 0 Ma, the output of model calculation is given in the form of a determinant table with the following column sequence: t, L ( t ) , D ( t ) , Z ( t ) , d

( t ) , h ( t ) , H ( t ) , U , ( t ) , U~(t), U ( t ) , e ( t ) and u(t). They can be directly used to construct Figure la through ld. ,Y,&(t), Z8, ( t ) and W ( t ) are also given in the table for reference. Figure 1 shows the results of the best-fitting model identified through computer-scanning.

The primary criterion set for identifying a best-fitting model is the solid-line curve shown in Figure la. It represents the surface elevation change history of the Tibetan Plateau during the last 40 Ma.

The best fit means that the results of model calculation meet the following characteristic ele- vations at the corresponding time periods given by the solid-line curve in Figure la: (1) k ( 0 ) ~ 5 kin; (2) h(3)-~1 km; and (3) h(9)~-~2.5 km.

There are also two subsidiary criteria to identify the best fit. They are : (1) the uplift rate U (t) must basically agree with that determined by isotopic dating for the Himalayan region (Harmet and Allegre, 1976; Virk and Kaul, 1977; Metha, 1980; Kai, 1981; Kanoeka and Konp, 1981; Zeither et al. , 1982); in particular, the average uplift rate during the time period of 25--3 Ma B.P. must range from 0. 5 to 1. 1 km/Ma, whereas the uplift rate at present should reach 3--5 km/Ma with an obvious accelerating tendency; (2) the present-day crustal thickness must approach to D(0)~-~70 km (Teng, 1985; Hirn, 1988; Lu and Wang, 1990).

A model is considered to be best-fitting if the results of calculation not only meet the primary criterion, but also satisfy the above subsidiary criteria fairly well.

After having calculated a total of 144 kinematics-uplift models, three possible best-fitting ones have been selected. The corresponding input parameters and output results in comparison with the criteria are listed in Table 2.

According to Table 2, the model No. 822 seems to be optimal among the three specially cho- sen best-fitting models and thus is shown in Figure 1.

Table 2 Calculation results of three possible best-fitting models in comparison with the pre-set criteria

Input parameters Output compared with criteria

D ( O ) h ( O ) h(3) h(9) U(0) U ( t ) "

No L - - V o - - n z..aN~ & ( 0 ) D - - d e~) - - m 70 5 1 2.5 3--5 0. 5 - -1 .1 km km km km km/Ma km/Ma

822 2 1 0 0 - 5 5 - - 0 . 5 0,32 38 .0- -23 .8 0 .025--0 .21 69.1 5.04 1.05 2.51 3.88 0 .59- -1 ,12

989 1900--50--0.5 0.32 39 .0- -23 .6 0 .020--0 .25 70.1 5.05 1.18 2.65 3.72 0 .58- -1 .01

169 1700--50--0.5 0.32 40 .0- -23 .4 0 .015--0 .29 69,8 4.90 1.17 2. 61 3. 52 0 .57- -0 .88

* for t from 25 to 3 Ma.

4 Discussion

4. 1 Non-uniqueness of solution Table 2 indicates an obvious non-uniqueness of solution. The direct reason for the non-u-

niqueness seems to be the ambiguity of kinematic parameters. However, the fundamental reason lies in that the level of investigations on the nature of the dynamic process of plate convergence in the Himalayan-Tibetan region is still insufficient to define uniquely an essential dynamic process based on some kinematic characteristics available so far. Along with the ever-deepening under- standing on the dynamics and kinematics of Tibet, the uniqueness of solution will sooner or later

No. 3 SHEN,X. J. et al. : KINEMATICS UPLIFT MODEL OF HIMALAYAN-TIBETAN REGION 423

come true. On the other hand, the existence of some regular connection of the input parameters with the output results and certain intrinsic quantitative correlation among the four parameter groups for shortening, extension, thickening and erosion would be an objective relfection of some basic features of plate kinematics and dynamics which may imply the uniqueness of the dynamic

environment for plate convergence. First of all, the combination of input parameters L , ~ ( 0 ) and D defines not only an initial

crustal mass but also the remaining mass of an already shortened and thickened crust, and there- by places a necessary constraint on the macroscopic mass conservation in model study. That is

presumably why a sequence of 2100--1900--1700 km for L must be coupled with a correspond- ing sequence of 38 - -39 - -40 km for D. Besides, the optimal value of D is proved to be substan-

tially larger than 35 km, an initial crustal thickness usually assumed for model study. This may have some deep-reaching implications for the mass balance. Moreover, it was not a result of sub- jective parameter assignments that for all three cases Xc~(0) turned out to be the same. This may

imply that about one third of the initial crustal mass might have been accommodated by lateral extension and sliding. And this is probably more or less realistic for the Himalayan-Tibetan re-

gion. Secondly, the combination of L , Vo and n defines a velocity field. It is initially a horizontal

velocity field of decelerative crustal shortening and finally transforms into a vertical velocity field

of accelerative crustal thickening-uplifting (see the combination of the solid line before 10 Ma B.

P. and the dashed line after it in Figure l a ) . In order to meet simultaneously the criteria of h ( 9 ) = 2 . 5 km and h ( 0 ) = 5 km, the rate of crustal thickening must be known to a certain ex-

tent. This may probably explain why the n values in the three chosen models are the same though their L and Vo values are substantially different. As a matter of fact, it is n that governs

the rate of thickening and hence the rate of tectonic uplift and their variations with time. Thirdly, the coupling of d with D controls the balance between the surfaee elevation and the

crustal root. As is seen from Table 2, the d value decreases with increasing D, but the variation is relatively small. This is rather unexpected. Obviously, the mass of the lower crust below the I- BLD plays a more important role than that of the upper crust in governing the variation of surface

elevation, since an isostatically stable surface elevation is always supported by a correspondingly developed thicker crustal root. The smaller the initial mass and the slower the shortening (for in- stance, the model No. 169 in Table 1 ) , the thicker the lower crust needed for supporting the fixed surface elevations of h ( 9 ) = 2 . 5 km and h ( 0 ) = 5 km would be. The same order of magni- tude of d values probably means that a more or less certain amount of upper crustal mass is re- quired to match a known elevation history.

Finally, the surface erosion mode is a direct factor affecting surface elevation development, although the parameters of the first three groups seem to be more essential in mass control. Any- how, erosion is the final "sculptor" of the surface relief and elevation. The three combinations of e0 and m listed in Table 2 seem to keep some balance between the two components cot and mh (t)

in Eq. (8) : e0 decreases with increasing m. However, they are different from each other not only

in the time-dependent distribution of the erosion rate; but also in the bulk effect of erosion: X6"o

(0) equals 0. 42, 0 .40 and 0 .37 for models No. 822, No. 989 and No. 169, respectively. It is

obvious that the larger the initial crustal mass (correspondingly, the larger the scale of deforma-

t ion) , the more the mass consumed by erosion (and the larger the deformation-dependent com-

ponent of the erosion rate) would he.

4 . 2 The nature of denudation in uplift history a puzzle The reference curve for the uplift history of the Himalayan-Tibetan region shown in Figure

424 ACTA SEISMOLOGICA S1N1CA Vol. 7

la intuitively demonstrates the existence of an intensified denudation period from 9 to about 3 Ma B.P. What is the cause for such a prominent denudation period in the Tibetan uplift history?

A recent comparative study ~ indicates that a similar cycle of uplift--denudation--uplift is observed in the Alpine region too. No satisfactory answer to this question has been reached yet.

Nevertheless, a logical analysis suggests two possible ways to explain this cyclic phe- nomenon, temporary interruption of vertical movement or delamination of crustal root at its base. According to the explanation by delamination the vertical isostatic compensation still actively gov- erns the surface elevation. Therefore, the elevation lowering is caused not solely by intensified surface erosion, but rather by isostatic subsidence induced by the delamination of the crustal root. But it does not seem to apply to the Himalayan-Tibetan region with an extremely thick crust. In case of the first explanation the vertical isostatic readjustment was somehow temporarily interrupted about 9 Ma B.P. for some unknown reasons, then a long-lasting erosion process of two-component nature defined by Eq. (8) may still roughly reproduce the observed denudation episode in the Tibetan uplift history. This is one of the reasons for its acceptance in the current paper. But, a more important reason is as follows. According to this explanation large isostatic upwelling potential had been accumulated in the period of denudation-peneplanation (see the dashed line in Figure la) . Then, a sudden release of this potential would explain fairly well how the Tibetan Plateau was rapidly uplifted from a paleopeneplain about 3--2 Ma B. P. to a huge plateau with an average elevation of 5 km above sea level. And this is an especially attractive point for the Tibetan Plateau. But, in fact, the real nature of this phenomenon still remains a puzzle.

5 Conclusions

1) The uplift history of an orogenic belt in a continental collision zone mainly reflects the kinematic features of vertical crustal deformations induced by horizontal plate convergence and is constrained by the scale of lateral mass transfer. Genetically, it is closely related both to the crustal thickening caused by terrane shortening, and to the localized mode of erosion-denudation. Thus, a pure uplift model would suggestively be replaced by a 3-D kinematics-uplift model.

2) The non-uniqueness of solution in this paper mainly lies in the relatively low level of in- vestigations on the plate dynamics and regional kinematics of the region. As soon as the kinemat- ics is better understood, the understanding of the mechanism of plate dynamics would be greatly deepened, thus the non-uniqueness could be minimized.

3) The successful application of the uplift history determined by comprehensive paleo- geographic studies as a constrain to the kinematics-uplift model has promoted phenomenological investigations on the nature of the Himalayan-Tibetan uplift a step forward towards a genetic study.

The first author gratefully acknowledges the support of Kuan-Cheng WANG Education Foundation, Hong Kong, which has made the current joint research possible and the Chinese National Natural Science Foundation. Thanks are also addressed to Dr. D. Werner, Dr. R. Freeman and N. Okaya (all from the Institute of Geophysics, ETH Ztirich) for their construc- tive discussions and suggestions for the improvements of an original manuscript.

* Shen, X. J. and Werner, D. , Uplift histories of the Himalayas and the Alps a comparison. Tectonophysics (in press).

No. 3 SHEN ,X. J. et al. : KINEMATICS-UPLIFT MODEL OF HIMALAYAN-TIBETAN REGION 425

T h i s E n g l i s h ve r s i on is i m p r o v e d by P r o f e s s o r J i e - F a n H U A N G of P e k i n g U n i v e r s i t y .

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