11
Vot. 5 No. 2 271--281 ACTA SEISMOLOGICA SINICA May, 1992 Deep mantle flow, global tectonic pattern and the background of seismic stress field in China Rongshan Fu and Jianhua Huang l)eiDartment of Earth and Space So.rices, University of Science and Technology of China,Hefei 230026, China Abstract In this paper we investigatethe sources of two kinds of forces to form the stress field in the lithosphere.These are the drag force caused by mantle flow and the force system along plate boundaries.The results show that both forces control the basic stress pattern in China and compressive stresses can fit with the stress patterns constructed by focal mechanisms, in-s%lu stress measurementsin boreholesand that deducedfrom other geophysicaland geological observation. Key words: mantle flow, tectonic pattern, seismicstre~ field. Introduction In recent years lots of studies are interested in the investigation of lithospheric stress state. Thou- sands of stress data are come from in-situ stress measurements in boreholes, focal mechanisms ,geologi- cal structures, and other geophysical and geological observations (McNutt, 1987). Both world stress map and the stress map of China have got a remarkable improvement (Zoback, 1987; Xu et al. , 1987a; 1987b). But the stress measurements are usually limited in some special regions because of the effects of local topography and geological structures to the results of measurements. It is difficult to de- termine the regional stress state in many regions. Otherwise, the observed data of stresses only provide lithospheric stress state and they couldn r t provide the force sources which are used to construct litho- spheric stress patterns. So to build up a global or regional dynamic stress model is necessary. By using the finite element method to simulate the stress field in lithosphere is an effective way in the world (Richardson et al. , 1979; Wang and Chen, 1980; Wang and Xu, 1985; Yu et al. , 1989). Their works provide some stress patterns which can fit the observed data. But it is arbitrary to choose boundary conditions by using the finite element method to model stress patterns, particularly, for regional problems. Some studies focus their ideas on using geophysical data to investigate and cal- culate lithospheric stress. Fu and Huang (1983) take Runcorn' s (1967) stress equations as a bound- ary condition,computed the global stress field and discussed the relationship between computed stress patterns and seismic stress field in China and its vicinity (Fu and Huang, 1983). But the forces dis- tributed along plate boundaries have not been taken into account in their work. So there are iots of dif- ferences comparing with observed data. The purpose of this paper is to build up a new global lithospheric stress model which consists of: the drag force caused by mantle flow and the force system distributed along plate boundaries. Calculate some theoretical models, compare these models with observed stress map, and investigate the geody- namical background of strong earthquakes in China. * The Chineseversion of this paper appeared in the Chineseedition of Acta Seismologica Sinica, 13, 295--306, 1991.

Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

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Page 1: Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

Vot. 5 No. 2 2 7 1 - - 2 8 1 A C T A SEISMOLOGICA SINICA M a y , 1992

Deep mantle f low, global tectonic pattern and the background of seismic stress field in China Rongshan Fu and J ianhua Huang

l)eiDartment o f Earth and Space So.rices, University of Science and Technology of China,Hefei 230026, China

Abstract

In this paper we investigate the sources of two kinds of forces to form the stress field in the lithosphere. These are the drag force caused by mantle flow and the force system along plate boundaries. The results show that both forces control the basic stress pattern in China and compressive stresses can fit with the stress patterns constructed by focal mechanisms, in-s%lu stress measurements in boreholes and that deduced from other geophysical and geological observation.

Key words: mantle flow, tectonic pattern, seismic stre~ field.

Introduction

In recent years lots of studies are interested in the invest igat ion of l i thospheric stress state. Thou-

sands of stress data are come f rom i n - s i t u stress measurements in boreholes , focal mechanisms ,geologi-

cal s t ruc tures , and other geophysical and geological observat ions ( M c N u t t , 1987) . Both world stress

map and the stress map of China have got a remarkable improvemen t ( Z o b a c k , 1987; Xu et al . ,

1987a; 1987b) . But the stress measurements are usually limited in some special regions because of the

effects of local topography and geological s tructures to the results of measurements . It is diff icult to de-

te rmine the regional stress state in m a n y regions. Otherwise , the observed data of stresses only provide

l i thospheric stress state and they couldn r t provide the force sources which are used to construct litho-

spheric stress pat terns. So to build up a global or regional dynamic stress model is necessary.

By using the finite e lement method to simulate the stress field in l i thosphere is an effect ive way in

the wor ld (Richardson et al . , 1979; W a n g and C h e n , 1980; W a n g and X u , 1985; Yu et al . ,

1 9 8 9 ) . Their works provide some stress pat terns which can fit the observed data. But it is a rb i t ra ry to

choose boundary condit ions by using the finite e lement method to model stress pa t te rns , par t icu lar ly ,

for regional problems. Some studies focus their ideas on using geophysical data to investigate and cal-

culate l i thospheric stress. Fu and Huang ( 1 9 8 3 ) take Ru n c o r n ' s ( 1 9 6 7 ) stress equat ions as a bound-

ary c o n d i t i o n , c o m p u t e d the global stress field and discussed the relat ionship between computed stress

pat terns and seismic stress field in China and its vicini ty (Fu and H u a n g , 1983) . But the forces dis-

t r ibuted along plate boundar ies have not been taken into account in their work. So there are iots of dif-

ferences compar ing wi th observed data.

The purpose of this paper is to build up a new global l i thospheric stress model which consists o f :

the drag force caused by mant le f low and the force system distr ibuted along plate boundaries . Calculate

some theoretical mode ls , compare these models wi th observed stress m a p , and investigate the geody-

namical background of s t rong ear thquakes in China.

* The Chinese version of this paper appeared in the Chinese edition of Acta Seismologica Sinica, 13, 295--306, 1991.

Page 2: Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

272 ACTA SE1SMOLOGICA SINICA Vol. 5

Deep mantle thermal process and drag forces

The study of glacial rebounding shows that the mantle can be taken as fluid when it loads by a

long time force and the mantle viscosity structure can be estimated (Pettier, 1985; Wu and Pettier,

1983). The investigation of thermal structure of the mantle gives out that the adiabatic temperature

gradient is little smaller than the temperature gradient in the mantle (Stacey, 1977 ~ Loper, 1985).

Radioactive elements in the mantle may provide enough energy to remain the thermal process in it

(Davies, 1980; Schubert et al. , 1980). Above three statements probably are the physical background

of thermal convection in the mantle. A main subject in the study of thermal process in the mantle is to

investigate the relationship between deep mantle flow and crustal tectonics and structures and litho-

spheric stress state. Runcorn pioneerly obtained the famous correlation equations of Earth ~ s geoid

anomaly and mantle convection in 1967.

dew, 2 dw, b ...a2w~ 2 dw,) l + ~r dr " : ° - ( a ) ' * ' (~-;r~ + 7- dr I,=~

n ! __ ~-~ Mg .a ~ , + x / 2 n + l~ (1)

He suggests that since the factor of the second term of the left side of eq. (1 ) (b/a) "+1 is <<1

with increasing of degree n the stress field under the lithosphere can be written as follows

(]rE: ~ ~ ( a ' ) n+12n? 1 1 ~(Cnncosm~0-'~-~..~amsinm~o)P~(cosO) ~=z ~=04~/za a n ~- 1 sin0

. ( 2 )

= ,~=04n:/za a n ~- • ~ ( C , ~ cosmcp -[- S,~ sinmq~)P~(cosO)

where W, is potential function of velocity, a and b are upper and lower boundary radii respectively, M

is the mass of the earth ; g is the gravitational acceleration, a r is the radius of the earth ~ C,~ and ,S.~ are

the harmonic coefficients of Earths t geoid anomaly and P~ (cos0) is the associated Legendre polynomi-

al.

Fu ( 1 9 8 6 ; 1 9 8 9 ) developed a physical-mathematical model of mantle convection connected with

the Earth r s geoid anomaly and proved that Runcorn ~ s equations are correct in some ways ( F u ,

1989). Runcorn ~ s stress equations will be taken as one force source to construct the stress field in the

lithosphere.

Global tectonic feature and stress system distributed along plate boundary

The plate tectonic theory gives a global tectonic feature and shows that there are three kinds of

plate boundaries,spreading or divergent center, convergent zone and transform faults. In general, the

force system along divergent boundaries drive two adjacent plates away from spreading centers and

those along convergent boundaries make two adjacent plates into either collision or subducting. Trans-

form faults reflect the relative horizontal movements between two adjacent plates. We will discuss these

forces later.

Using Cooder s method ( 1 9 6 6 ) , Liu (1985) defined a generating force function along the plate

boundaries with d functions

Page 3: Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

NO. 2 Fu ,R. S. et al. : DEEP MANTLE FLOW ,GLOBAL TECTONIC PATTERN AND BACKGROUND OF STRESS FIELD 273

1 L • ( o ,~o ) = --£~_~ ,~(o,,~,,)

The function ~ ( 0 , (p) can be expanded in a harmonic series

• = 2 / o y cosm + sinm /Py(cos0) ~ 0 m=0

(3)

(4)

where Py (cos0) is a fully normalized associated Legendre polynomials. It is easy to get

L

i ay= ~lco~mg0,Py(cos0,)/L i =

L (5)

b'~ = 2 sinmtp, Py (cos0,) /L i = I

where (0i, (pi) is the ordinate of a computed point, L is the total number of data points. If we take M as

the total number of spreading boundary data sets and ay, bY as the harmonic coefficients of these

boundaries and N , a ~ y,b r y for convergent boundaries. The harmonic coefficients of both boundaries

are

l Ay = ( M a y - - Na' y ) / ( M q- N ) (6)

B~ ---- (MbY - - NU ~ ) / ( M -}- N )

Then the generating force function along plate boundaries can be rewritten as

# ( 0 , v ) = ~ ~ {Ay cosmcp q- By sinmrp}Py(cosO) (7 ) n = 0 m=0

Considering that the main forces along either divergent or convergent boundary are caused by gravita-

tional force or thermal contraction force ,we can express the boundary force system as

F = V~(0 ,~o) (8)

This force system will be taken as an another force source to construct lithospheric stress field.

Basic equations and computed models

If we assume that the lithosphere is a homogeneous elastic spherical shell in which there are plate

boundary forces expressed by ( 9 ) , a n d ignore the self-gravitational force, the basic equation which

governs mechanical behavior of an elastic body can be written as

( k -[- # ) V O -I- /L V z S n t- F -=- 0

or (k+ /~) V O + ~ V 2 S + V ~(0,~o) = 0 (9)

where Z and # are the Lame coeff icients ,S is the displacement vector and O = V • S is the volume

strain.

If we take a special solution S = V ql into equation (9) then

V ( X -~- 2/z)V2kv ~ - V ~ = 0

VZ~5 " = - - (~1/(,~ + 2/tZ) -~- C 1 ( 1 0 )

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274 A C T A SEISMOLOGICA SINICA Vol. 5

Because constant C1 reflects a hydrostatic stress state it can be taken as C~ = 0 and we have

V2T = - - ~/()~ + 2/0 (11)

Then for the nth order solution of ke and • expanded into harmonic series equation (11) becomes

V'T. = - - ~,,/(z + 2~)

Using the formula of spherical function

V 2 ( r ~ , ) = 2(2n + 3)q5o

It is easy to show that

2(2n -[- 3 ) N , / r ' = - ~ / ( 2 , 4- 2/~)

and T,,=--r2~,,/2()~-l-2~t)(2n-[-3)

(12)

(~3)

(14)

(15) Because there isW t any body force and boundary force in dipole form so the general solution of equa-

tion (9) can be expressed as

S = ~ {A,,[-r2V¢o. + a,,o~,,r] -[- B. ( rZV~ . -[- a.co.r) -[- C~Vcp. -~- D.V~o.} -t- VW. n

where

r~&, -- R1~&, r~S~ -- RflS~ o)~ - - R o , , + I (.o~ - - r ~ + l (p,, - - R o ~ + 1 (p~ - - r ~ + l

N n = - - r 2 S ~ / 2 ( 2 @ 2 ~ ) ( 2 n - ~ - 3 )

a ~ = - - 2 nX-I- ( 3 n + 1)~

(n + 3)4 + (n + 5)/~

(16)

(n + 1))~ + (3n + 2)/~ ( 2 - - n ) z + ( 4 - - n ) ~

Sn = (A~cosm(p -t- B, TM sinrn(p) P~ (cos0)

The stresses are

o i C j where 6~j = is Kronecker delta function and

1 i = j

o = V

+ B ~ E - - 2 ( n + l ) + ~ ( 2 - - n ) ] ( )'} S ~ + V ~ , - T

(17)

(18)

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No. 2 F u , R . S. et al . :DEEP MANTLE F L O W , G L O B A L TECTONIC PATTERN AND BACKGROUND OF STRESS FIELD 275

Depending on boundary conditions and force sources ,we calculate three basic models and four testing models. These are:

Model I Drag force model

V ~ ( 0 , q , ) = 0 r = R0 a . = ~r~0 = a~ = 0 (Radius of the upper boundary of lithosphere) r = R~ (r. = pqu. and equation (2) (Radius of the lower boundary of lithosphere)

n t = ~ Mg .a . . + 1 2 n + 1 3

o',.o ~= 2 .~o ~ a e l. T ) n 7 i 30 { C~" cos m~p + sin mg0}P:'(cos0)

Mg .a . . . a 1 1 O . . . . 7 ~ - 1 sinO &p {C~" cosm(p + Smsinmq~lUg(cosO)

Model ff Boundary force model

= {A:' cos + B: sinmvle: (cosO) n 1 m 0

r = Ro, (r~ = ~7~o = o~,~ : 0 7' = Rx ~o~.~ ~ - O'T0 : 0 and (r~ = pgu~

Model $ Drag force and boundary force model Model $ = Model I + c~ Model 1[ where c~ is an arbitrary proportional coefficient ,u~ is the radial displacement and p is the density of the upper mantle. These models describe an elastic lithosphere overlaying a fluid mantle and the surface of the lithosphere is free. We suggest that the lithospheric stresses are only caused by the mantle drag forces in Model I and by the plate boundary forces in Model ff. Model Ill includes both forces and it is suggested as a linear combination of Model I and Model ~ with a factor.

By taking above conditions into equations (16) and (17) we can write

A X = B (19)

where X = ( A . , B. , C. /R~, D./R~) T,

for Model I

B = ( 0 , 0 , F . , 0) T F. = - - [ M g ( 2 n + 1 ) / 4 ~ R 2 ( n -~- 1)3 (Ro / R , ) "+~

for Model

B =

I ~ R°{) 'VeT" q- 2~tOz~F./Or2}r=R0 ]

Ro~t{ 2Oe~F./R0OrO0 - - 3T./R~O0},=%

R,~{ 2O2Tn/R,&O0 - - 3T./R~O0}r=R,

R1 {~.V2'qJn -~ 2UOeW./Or 2 - - p g a T . / a r } r : . l

a12 :

a13 -----

a14 :

and A is the coefficient matrix in which all = ~[2n + a . (3 + n ) ] + 2u(n + 1) (n ÷ a . )

- - - - + + 1 ) - -

2 n ( n - 1)tt

(R1/Ro)"+22/~(n + 2 ) ( n @ 1)

, , , = , ( 2 n + a . )

Page 6: Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

276 ACTA SEISMOLOGICA SINICA Vol. 5

a22 = I t ~ . - - 2(n -4- 1 ) J ( R 1 / R o ) "

a23 = 21z(n - - 1)

az4 ---- E-- 2#(n --[- 2)-] ( R , / R o ) "+z

a31 = ~t(2n -~- a . ) ( R I / R o ) ~+1

a3z = ~ - - 2 (n -4- 1)-]

ass = 2~(n - - 1) ( R 1 / R o ) "-1

a34 = - 2u (n + 2)

a4x : EaH - - (n + ct.)-]pgRl"](R1/Ro) "+1

a4z -~- a l z ( R o / R 1 ) " - - ~-a. - - (n + 1 ) ~pgR1

a43 ---- (a13 - - rtpgR1) (RI /Ro) "-I

a44 = a14(Ro/R~) "+~ + (n -~- 1 )pgR1

The parameters of the lithosphere are R0 = 6371 k m , R~ : 6271 k m , Z : 0. 71 X 10 'z , / t = 0. 56

X 1012 , g = 981 c m / s 2 , p = 3 . 5 3 g / c m s. Wi thou t absolute values of the boundary f o r c e s , o n e needs to

compare the computed stress patterns with the stress map constructed by observations. Four testing

models with a = 0 . 5 , 0 . 7 , 1 . 0 a n d 1. 2 are employed. These are Model $ a , Ulb, I c , rod. W e

take Lerch ' s ( 1 9 7 9 ) harmonic coefficients of the ear th ' s geoid and Chert' s boundary analys is* into

our calculat ion.

Figures 1, 2 and 3 are the lithospheric stress patterns in China for Model I , K , and $ respec-

t ive ly , in which the main compressive axes of deviator ic stress are i l luminated. F igure 3a , b , e , d are

for a = 0 . 5 , 0 . 7 , 1 . 0 and 1 . 2 respectively. W e use degree and order 1 - - 19 harmonics for Model I

and 2 - - 1 9 harmonics for Model I . The computed grid is 2 ° X 2 °.

Seismic stress background in China

The stress map in China summarized by Xu et aL ( 1 9 8 7 ) and the li thospheric geodynamic map in

China and i t r s vic ini ty edited by Ma ( 1 9 8 6 ) are employed to test our computed models. The stress

patterns of Model I (F igure 1) is similar to Fu and Huang r s ( 1 9 8 3 ) results and the comparison of

this model with observed stress map was discussed in details in that paper. Model K provides a stress

pattern in which the main compressive axes are perpendicular to plate boundar ies , for example , the

collision zone in Himalayas (Between India-Aust ra l ia plate and Eurasian p la te) and the convergen t

zones in Japanese t rench (between Pacific plate and Eurasian p l a t e ) , in Mania la t rench (be tween Pa-

cific plate and Philippine p l a t e ) , and the convergent boundary between Phil ippine Plate and Eurasian

*Chen, H. , 1987. Analysis on the correlation of plate boundary and the absolute movement of plate. Bachelor thesis of Universi- ty of Science and Technology of China.

Page 7: Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

No. 2 Fu,R. S. et al. :DEEP MANTLE FLOW,GLOBAL TECTONIC PATTERN AND BACKGROUND OF STRESS FIELD 277

plate. In the cen te r par t of these plates the s t ress pa t t e rns appear mo r e complex a n d the m a g n i t u d e of

s t ress is re la t ive ly lower. T h e m a i n compress ive s t ress a x e s be tween c o mp u t e d mode l and focal m e c h a -

n i s m s a long plate bounda r i e s can fit each other v e r y wel l , for e x a m p l e , in H i m a l a y a s , the corner of

A s s a m ( 2 0 ° N - - 3 0 ° N , 8 0 0 E - - 9 0 ° E ) , and T a i w a n of China .

82* 102 ~ 54 °

, / / . , /// x .

34*

/ / / I , ' / i / ~ " / / / / , / I I "////.. 14 ~

122" 142" /

- -

Figure I The main compressive stress axes in China (except Nanhai islands) of Model l .

The line segment with circle is the solution of focal mechanism.

82*

I-- ~" i / / /

I I I I" (f / '~K,g(/Ml~l 'xf ,~l

- - . t ; "/ / > k . . : ' , I - ' " I ~ , , / , t " - , ~ " '

102. 122" 142. , ~,~', . . . . . \ , , , ////

' r ' ' ' t ' "

l I , - f ' f ( - ~ ~ \ 3 , \ , ~ ~x ~ , , ' / \ l / /

Figure 2 The main compressive stress axes (except Nanhai islands) in China of Model I .

The line segment with circle is the solution of focal mechanism.

Model ~ is a l inear c o m b i n a t i o n be tween Model I a n d Model I . F igure 3 i l l umina te s tha t the

s t ress pa t t e rns in C h i n a o n l y h a v e smal l c h a n g e s w h e n the fac tor a increases f r o m 0. 5 to 1 . 2 . T h e

m a i n d i f fe rence of these pa t t e rns are located in the zones of 100°E - 1 1 0 " E , 20°N - 35°N a n d 80°E -

9 0 ° E , 4 0 0 N - - 5 0 ° N . W e can take the focal m e c h a n i s m s of e v e r y ind iv idua l e a r t h q u a k e as our test

principle. But because of the s impl i f ica t ion of co mp u t e d models a n d the s e l f - c o n t r a d i c t i o n of focal

Page 8: Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

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Page 9: Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

No. 2 Fu, R. S. et al . . . DEEP MANTLE FLOW, GLOBAL TECTONIC PATTERN AND BACKGROUND OF STRESS FIELD 279

mechanisms the comparison of computed models observed stress pattern may be more convenient for us

to understand the nature of this geophysical phenomena.

The stress pattern in China constructed by observed data shows that the orientations Of main com-

pressive stress axes trend NNW to NEE from 70°E to 140°E. But the main compressive axes are SE of

SSE in the zone of 115°E - 120°E, 20°N - 30°N. In other words, the compressive stresses are NNW

and NNE mainly in the west of China and the compressive stresses can be expressed as a sector with a

120 ° wide centered at 100°E and 30°N. Deng et al. (1979) divided the tectonic stress field of China in-

to three parts:west of China with NNE to NE of compressive stresses, North-east of China with NE to

NEE, and south of China with NW orientations.

The stress pattern of Model 11I can more relatively fit above stress feature. Particularly, this

model illuminates a good agreement with observed data in the zone of 100°E--105°E, 20°N- -30°N,

where the stress field appears more complex and the main compressive stress axes trend NW to NE

from south to north. But there are two regions where both patterns do not fit each other. These are the

zone of l l 0 ° E - - 1 2 0 ° E , 2 0 ° N - - 3 0 ° N , where the orientation of observed compressive axes is NW

rather than the computed direction NE, and the zone of 70°E - 80°E, 40°N- -44°N, where computed

model appears a tension stress zone with a orientation of NNW and NNE. Probably, this regional

stress character reflects the divergent flow under the Tianshan mountain (Huang and Fu , 1983).

In summary, the drag force caused by deep mantle flow and the boundary force system connected

with global tectonics are the geodynamical background of the tectonic and seismic stress field in China.

Discuss ion and conclus ion

Either Model I or Model ~ do not fully explain the tectonic stress field in China. Model III im-

plies that both of the forces (drag force and boundary force) play almost the same role in construction

of tithospheric stress field. This result mainly agrees with Yu r s (1 9 8 9 ) conclusions. But as we have

mentioned that there is an arbitrary way to choose boundary conditions even though a good agreement

with observed data can be obtained. In order to get a analysis result we have rather largely simpified

our computed model, but the geodynamical background of these force sources is very clear. We

wouldn r t like to say anything about the drag forces caused by mantle flow and more words will be ad-

dressed here about plate boundary force system. Four types of forces may be regarded as the boundary

forces acting on the lithosphere. There are ridge push acting at ridge crests, slab pull acting on the sub-

duction plate at a convergent plate boundary, the trench suction caused by lack of support, and the

thermal force generated by the ocean lithosphere cooling. We don t t take these forces into account in

detail so that we fail in having the magnitude of the boundary forces. It would be improved in the fur-

ther model.

There still are some problems in modeling the tectonic stress field in south of China. Our three

models do not fit observed data and form a stress field with the orientation of NW in this region.

Yu ~ s (1989) model has got a good agreement in this region. But when we look at his model it is easy

to find that he put four point force of 1. 286)< 108 Pa with an orientation of SW at the corner of As-

sam. It is obvious that these forces play important role in forming the stress features in this region.

However , where these four point forces are come from? There are not enough evidences in Yu ~ s

explanations. The gravitational slip caused by the topography of the Tibet plateau may play a crucial

role to control the stress pattern in the southeast of China.

The effects of different plate boundaries to continental stress state are different, for example, the

forces in Himalayia zone caused by the collision between India-Australian plate and Eurasian plate

may be larger than that from the convergent of Pacific plate to Eurasian plate. But the fact is that there

occur large earthquakes with magnitude more than 7 .5 . This may show that almost same magnitude of

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280 ACTA SEISMOLOGICA SINICA Vol. 5

strain energy will be built up in both regions and both forces from these two regions are not too much

different. However, in order to get more realistic model of boundary forces a good way is to have dif-

ferent weight for different plate boundaries expanded into harmonics.

It should be addressed that the basic model in this paper is very simple. It ignored the heterogene-

ity of the lithosphere, the effects of plate boundaries and the effects of intercept error of harmonic ex-

pansion to computed models.

At the end, the Earth' s lithosphere is a mechanical element, it is divided into several large

plates, and these plates act each other. So when we try to model the stress field in a special region the

boundary conditions must be arbitrary. In order to solve this problem a global model is necessary either

in analysis modeling or in finite element modeling. Our model is very simple, but it can agree with the

observed global stress map (Zoback, 1987) as well as the stress patterns in China. It may conclude

that the drag force caused by mantle flow and the boundary force system connected with global tecton-

ic features basically control the lithospheric stress state.

The authors thank Prof. Zhonghuai Xu for his stress map of China and useful discussions. This

research is sponsored by the Chinese Joint Seismological Science Fundation.

References

Coode, A . M . , 1966. An analysis of major tectonic features. C-co:phys. J . g . as/r. Soc. , 12, 55- -66 .

Davies,G. F. , 1 9 8 0. Thermal histories of convection earth models and constraints on radiogenic heat production in the earth.

J . Geohys. Res. , 85, 2517--2530.

Deng ,G.D. , Z h a n g , Y . M. , X u , G . L. and F a n , F . T . , 1 9 7 9 . On the tectonic stress field in China and its relation to

plate movement. Se/smo/ogy a~id Geo/ogy, 1.. 11- -12 (in Chinese).

Fu ,R. S. and Huang,P. H. , 1983. The global stress field in the lithosphere obtained from the satellite gravitational harmonics. Phys.

Earth. Pla,et b ~ r . , 31, 269--276.

Fu,R. S. and Huang,P. H. 1983. The stress field within the lithosphere in China and its vicinity obtained from satellite gravitational

harmonics. Acla Geophysics Sinica, 28, Supp. 641- -651( in Chinese).

Fu, R. S. , 1986. A numerical study of the effects of boundary conditions on mantle convection models constrained to fit the low degree

geoid coefficients. Phys. Earth. Inter. , 44, 257--263.

Fu,R. P. , 1989a. The earth' s geoid anomalies and the physical mathematical model of mantle convection. Acts Geophyswa 8inica. (in

Chinese, in printing).

Fu ,R. S. , 1989b. Earth' s geoid anomaly, mantle convection and stress field under the lithosphere. Phys. Earth. Planet. Inter. 54, 50- -

54.

Huang, P. H. and Fu, R. S. , 1983. Mantle convection pattern under lithosphere of China. Aeta Geophysics Simca, 26, 39- -47 (in

Chinese).

Lerch, F . J . , Klosko, S .W. , Laubscher, R.E. and Wagner, C.A. , 1979. Gravity model improvement using Geos 3 (GEM 9 and

10 ) , J. Geophys. Res. , 54, 3897--3904.

Liu ,H. S. , 1985. Geodynamical basis for crustal deformation under the Tibetan plateau. Phys. Earth. Planet. l~er. , 40, 43-- 60.

Loper,D. E. , 1985. A simple model of whole mantle convection. J. C, eophys. Res. , 90, 1809-- 1836.

Ma,X. Y. , 1986. bY~spherw Geodynamical Map of China and Its Vicinity. Geological Press of China (in Chinese).

McNutt,M. , 1987. Lithospheric stress and deformation. Rev. Geophys. , 25, 1245--1253.

Pettier,W. R. , 1985. Mantle convection and viscoelasticity. Ann. Rev. Fluid Mech. , 17, 561--608.

Richardson, R. M. , Solomon, S. C. and Sleep, N. H. , 1979. Tectonic stress in the plates. Rev. Geophys. 8pace Phys. , 17, 981- -

1019.

Runcorn, S. K. , 1957. Flow in the mantle inferred from the low degree harmonics of the geopotential. Geo?hys. J. R. astv. Soc.,

14, 375--384.

Schubert, G. , Stevenson, D. and Cassen, P. , 1980. Whole planet cooling and the radiogenic heat source contents of the earth and

moon. J. Geophys. Res. , 85, 2531--2538.

Stacey,F. D. , 1977. Physics of the Earth, 2nd Ed, Wiley, New York.

Wang,S. Y. , and Chen, P. S. , 19 8 0. A numerical simulation of the present tectonic stress field of China and its vicinity. Acta

C, eophyswa 8inica, 23, 1, 35- -45( in Chinese).

Wang,S. Y. and Xu,Z. H. , 1985. Seismo-tectonic stress field in east China. Ads Seismologica Sinica, 7, 1, 17 - -31( in Chinese).

Page 11: Deep mantle flow, global tectonic pattern and the background of seismic stress field in China

No. 2 Fu, R. S. et al. :DEEP MANTLE FLOW, GLOBAL TECTONIC PATTERN AND BACKGROUND OF STRESS FIELD 281

Wu,P . and Pettier, W . R . , 1 9 8 3 . Glacial isostatie adjustment and the free air gravity anomaly as a constraint on deep

mantle viscosity. Geophys. J . R. astr. Soc . , 74, 377--450.

Xu,Z . H. , Wang,S. Y. , Huang,Y. R. and Gao,A. J. , 1987. Tectonic stress field of China' s continent deduced from a large number

earthquakes. Abstracts, 3, 1115, IUGG X1X General Assembly, Aug. , 9 - - 2 2 , Vancouver,Canada.

X u , Z . H . , W a n 8 , S . Y. , Huang , Y. R. , G a o , A . J . , J i n , X . F. and C h a n g , X . D. , 1 9 8 7 . Directions of main stress axes

in southwestern China deduced from mieroearthquake data. Acts Geophysica 8iaica, 30, 5, 467- -486( in Chinese).

Yu,Y. X. , Xu,Z. H. and Wang,S. Y. , 1989. Investigation of force sources of crustal stress feild in China. Master Thesis,Institute

of Geophysics, SSB (in Chinese).

Zobaek, M. L. , 1987. Global pattern of tectonic intraplate stresses. Abstracts, 3, 1116, IUGG XIX General Assembly, Aug. 9 - - 2 2 ,

Vancouver, Canada.