Convection-generated stress concentration and seismogenic models of the Tangshan earthquake

Physics of the Earth and Hanetary Interiors, 19 (1979) 307-318 © Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

307

CONVECTION-GENERATED STRESS CONCENTRATION AND SEISMOGENIC MODELS OF THE TANGSHAN EARTHQUAKE HAN-SHOU LIU

Geodynamics Branch, Goddard Space Flight Center, Greenbelt, Maryland 20771 {U.S.A.) (Received July 4, 1978; revised and accepted October 19, 1978)

Liu, H.S., 1979. Convection-generated stress concentration and seismogenic models of the Tangshan earthquake. Phys. Earth Planet. Inter.; 19: 307-318. Despite the success of earthquake predictions in China, the complete failure of the Chinese program to predict the 1976 Tangshan earthquake in the Peking region indicates that the state of stress in China is still very poorly understood. This paper examines the subcrustal stress field due to mantle convection flows under China as inferred from the satellite gravity field of the Earth. This stress field enables us to determine the current stress regimes in the crust of the Peking region. It is shown that under the influence of this subcrustal stress field the rectangular fault system in the Peking region will cause stress concentration. Conformal transformation and mapping of the convectiongenerated stresses under North China have revealed stress concentration in the rhombic Tangshan fault block. The magnitude and direction of the concentrated stress field in the Tangshan seismic district seem to be in accord with the seismogenic models for the 1976 Tangshan earthquake developed by Guo et al., (1977) and Ding (1978).

1. Introduction The Chinese earthquake prediction program successfully predicted three major earthquakes of magnitude 7 in 1976: May 29 in Yunnan province, August 16 in Szechwan province, and November 7 in the SzechwanYunnan border region. These areas are in south China. These predictions were in addition to the extensivelydocumented prediction of the Haicheng earthquake of February 4, 1975 in north-east China. In each case, the Chinese scientists had made some kind of mediumor long-term prediction that was used as a basis for long-term scientific and disaster planning and preparation. Despite the success of these predictions, the complete failure of the Chinese program to predict the 1976 Tangshan earthquake (34-- 7.8) in the Peking region, in which 655,000 people died, indicates that the state of stress under China is still very poorly understood. In order to determine the stresses in the lower crust of China, Liu (1978) has applied gravitational field models derived from satellite tracking and surface data to calculate the tectonic forces or stresses

under China. He has also discussed the general relation between the contemporary tectonics and seismicity in China within the framework of the subcrustal stress field caused by mantle convection. While most world seismicity has been related to rigid-plate interaction, the occurrence of the seismic zone in the Peking region cannot be related in this manner. Recently, Chia (1977) has discussed the geological features and cyclic behavior of seismicity in Peking region and Guo et al., (1977) and Ding (1978) have developed seismogenic models for the 1976 Tangshan earthquake. It seems, therefore, desirable to examine the applicability of the convection-generated subcrustal stress field, as inferred from satellite gravity data, for earthquake prediction and research in Peking region.

2. The state of stress in north China The shear stress components under the crust of China exerted by mantle convection flows in the eastward and northward directions are determined (Run-

308 I n this paper, only the short-wavelength mantle convection systein is considered, Equations 1 and 2 are derived from a laminar viscous mantle flow model vOith Newtonian viscosity developed by Runcorn (1967). Several assumptions underlying the formula for finding stress from gravity data were made. Most importantly, we have assumed that the contribution from the lower boundary which niay be associated with the low-degree harmonics can be ignored. For the upper boundary we have assumed the crust above the flowing mantle to be an elastic shell, for which there is evidence in its support of mountains. For this boundary the tangential component of flow velocity vanishes. Under these boundary conditions, the diverging flow would produce tensional stresses in a weak crust and there is a correlation between the converging flow and compressional tectonics. It should be noted that a low gravity may be associated either with a sink or a rise depending on the unknown boundary conditions. This uncertainty lies in the fact that the derivation of stresses from gravity data is not unique. This

corn, 1967; Liu et al., 1 9 7 6 Liu 1977) by 25

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rn=n

S

S

Mg

{~£)n+l

2n+l

. = l ~ ,,,=o 4 ~ a ~ X

.

~ + ]

1

sin ~ : "

(cos ~') l-inC.,., sin(rnk) + mSn, m cos(mX)] (1)

n=13m=O

H+ 1

d X ~ ~ [Pmn ( c o s ~')l [ C n , m c o s ( f f l ~ . ) + S n , m s i n ( m X ) ] (2)

where M is the mass of the Earth, g the acceleration due to gravity, ae the radius of the Earth, a the radius of the outer spherical surface of the flowing region, Cn,rn and Sn,rn the coefficients of the harmonic terms, )t the longitude, ~ the co-latitude and pmnnn(cos f) is the associated Legendre polynomial of degree n, order m and argument cos ~'.

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LONGITUDE

Fig. 1. The crust of north China is in a state of compressive stress.

130

140

309 theoretical difficulty can only be circumvented by fitting certain tensional and compressional tectonic features. Therefore, one of the important problems of convection-generated stresses is to determine the signs in eqs. 1 and 2 from geodynamic data rather than on theoretical or specula~:ive grounds. Of course, this is a workable method which needs to be tested and justified. Recent results from studies on mantle convection patterns and tectonic features (Liu, 1977, 1978, 1979) seem to justify this approach. By introducing the harmonic coefficients Cn,rn and Sn,m of the geopotential obtained by Wagner et al., (1977) into eq. 1 and 2, the resulting sub-crustal stresses exerted by mantle convection under China are shown in Fig. 1. Figure 1 shows that the crust of north China appears to be in a state of compressive stress. The magnitudes of these stresses are in the order of 0 . 8 X 1 0 s d y n ' c m -2. As with every scientific result, satellite stress fields should not be used blindly or by themselves, but patterns from them should be analyzed in conjunction with geodynamics studies. The state of stress as inferred from gravity data and the seismological framework in Peking region (Chia, 1977; Guo et al., 1977) may provide possible explanations for the puzzling compressional force which caused the 1976 Tangshan earthquake.

Y

or Y

xy

Cr x

t O

3. Method of solution for stress in a plate with faults

Let us consider an element of plate which is in a state of compressional stress, and denote the stress function which corresponds to the given stress state by Uo(x, y). If a fault is made in this plate (see Fig. 2) it will bring about a redistribution of the stress from 0 0 0 • Ox, Oy, rxy in the unweakened plate to Ox, Oy, Txy in the weakened one. Assume the center of the coordinate system x O y to be at the center of the fault, and the stress state in the fault-free plate to be the basic state of stress. The new stress state Ox, Oy, 7xy in the plate, after weakening, can be expressed by: •

Ox =o°x+ox;

Oy = a ~ + o y *;

r x y --- r x0y + r x y*

(3)

where Ox, o~, ~-xyare additional stress components due to the presence of the fault. Two-dimensional problems in the theory of elasti-

Fig. 2. Coordinate system for stress calculation. city in the absence of body forces require a stress func tion U ( x , y ) which must satisfy the relations ax -

3 2 U(x, y ) 3 2 U(x, y ) 3y 2 ; Oy OX2 ; Txy -

a4~(x,y) Ox 4

a'v(x,y) a'u(x,y) + 2 Ox2Oy 2 + - - O y 4

- 0

~ 2 U(x, y ) 3x~y-y (4)

(5)

It is known that the biharmonic function U ( x , y ) can be expressed as

U(x,y) = 2

Re [e-q~(z)+ q,(z)J

= XO(z) + q,(z) + z~(z) + q,(z)

(6)

310 where Re means the real part of the term in the square brackets, q~(z) and qffz) are analytical functions of the complex variable z = x + iy; 2-= x - iy. Consequently, the solution of the two-dimensional problem is reduced to the determination of two anNytical fimctions qS(z) and C(z) = d ~ ( z ) / d z . Thus ~ z ) = qS°(z) + ~*(z); ~(z) = ~°(z) + ~*(z)

(7)

Tangshan seismic district can be modeled as a rhombic fault block. For regions outside the shape of a rectang.ular fault system, approximate values of the function z = co(t) can be obtained from the Schwarz- Christoffel integral (Muskhelishvili, 19631. The function is of the type z = co(t)= R ( I + 0.643~ - 0.098~ 3 -

where O*(z) and ~*(z) are functions for the stress state: 0.038~ s - 0.011~ ?)

0 x, Oy, Txy.

For the determination of q~°(z), we have

~Uo(x,y) + a~Uo(x,y) ax 2

ay 2

- 4 R e [q~'°(z)]

(8)

Putting 0'° (z) = P ( x , y ) + i Q ( x , y ) , we obtain

a:Uo(x,y) + ~:Uo(x,y) ax 2

3); ~

- 4 P(x, y )

3Q(x,y)

@

ay

. aP(x,y) _

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aQ(x,y)

ax

*(z) = b o + b l + b 2 + b a

7~ 7+7

(~[G3(t)] : O ' ( t ) ;

f'/[G)(t)] : ~ l ( t ) ;

~0 [(.0(~) ] ----(~l(t);

~0 [(.D(~)] ---: ~ l ( t ) ;

~*[~(~)l =~o(t):

~*[~(~)] = ~,o(~)

(10) the functions in eq. 13 will be of the type: (~1(~) =" (,hi ( t ) -[- (])o(t)

el(t) = C'(t)+ Co(t)

"'"

+...

(11)

Let us now consider constructing the conformal transformation needed for mapping the stresses in the region outside of the fault system. Conformal transformation is the most powerful method for the analysis of stress concentration (Green and Zerna, 1960; Muskhelishvili, 1963). Guo et al., (1977) and Chia (1977) have shown that the Taihangshan-TsangtungYenshan-Szehsien fault zone in the Peking region can be regarded as a rectangular fault system and the N i n h o - L u a n h s i e n - F e n t a i - J i y u n h o fault zone in the

(14)

where

~o(t)= ~

n=,

b4

03)

Introducing the terms:

a4

~ * ( z ) = a o + - Z + Z- 2-1- j + ~ +

z

[co(t)] = ¢o [~(~)1 + ~,[~(~)]

(9)

The influence of the fault on the stress conditions in the plate is of local nature only, i.e., the stress cornponents Ox, oy, r x y attenuate rapidly with increasing distance from the fault. It thus follows that the functions q~*(z) and ~*(z) which characterize this stress state can be considered as holomorphic functions in the zone outside the fault region, i.e., as functions of the following type: a 1

where R is a real constant. On passing to the transformed region by applying the function co(t), the stress functions 4~(z) and ~(z) will be of the type:

~[,*~(t)l = ~o [co(t)] + ~* I~(~)1

The imaginary part of the function ~°(z), i.e., the function Q ( x , y ) is from the known differential equation aP(x,y)_

(12)

~n~'; C0(t) = ~

rt=l

&t n

Os)

To determine the stress components % , o0, too in the curvilinear orthogonal coordinate system, the functions ~l(t) and ~1(~) in eq. 14 are inserted into the following equations and separated into their real and imaginary parts (Green and Zerna, 1968; Muskhelishviii, / 963) % + Oo = 2[qb,(t) + ~l(t)] 2t 2 °o

°o + 2iroo -

[co(t) ~b'l(t) + w ' ( t ) q G (t)]

o ~~ ( g )

whe re

(16)

311 The conformal transformation function ~o(~) is an infinite series. By taking a finite number of terms of this series we can obtain approximate solutions for the area along the fault system.

P

4. Stress concentration

l.O0

In investigating the crustal stress problem in the Peking region, the disturbance of the original stress conditions caused by the Taihangshan-Tsangtung fault system, and the corresponding stress concentration coefficients, are of interest. The geodynamical framework in the Peking region is shown in Fig. 3. The Taihangshan, Tsangtung, Yenshan, and Szehsien faults form a rectangular fault system (Chia, 1977). By the term stress concentration coefficient we understand the ratio of any component o f the stress tensor at any point situated in the disturbed zone around the fault system, to the stress tensor component at the same point in the fault-free plate, when the external forces acting on the plate are equal in both cases.

0.70 1.00

L160

/

y

I

I

0.90

~,~'e~

/

1.30

1.00

0.70

p / 40

I i I t I I

YENSNAN FAULT

PEKING

Fig. 4. Stress concentration in the Peking region.

J z ~-

39 --

/

~38 °

/

j.

,L'

37 °

U ~

TIENJS~ "

/

ACTIVE FAULT: DASHEDWHERE ACTIVITY UNCERTAIN MODELEDBOUNDARY OF FAULT ZONE

36 °

As for stress boundary conditions at the fault system in the Peking area, the friction in the faults is assumed to be negligible. This assumption would not be justified if there were a measurable heat flow anomaly in the immediate vicinity of the faults or a velocity across the fault system. The crust of the Peking region is under the stress p, as inferred from the satellite stress pattern, in the direc tion at an angle of a = n/3 with the Ox axis of the Taihangshan-Tsangtung fault system (see Fig. 4). The basic stress conditions of the plate are defined by the following stress components o -_- p cos2o~; ao

O"x

35 °

I 115'~

I 116° LONGITUDE

I 117~

Fig. 3. Fault system in the Peking region.

I 118°

p sin2a; TOy = p sin a cos a

(17)

Thus the stress function Uo(x,y) will be o f the type P

Uo(x,y) = ~ ( x sin a - y cos a) 2

(18)

312 It follows from eqs. 17 and 9 that P(x, y ) = p/4, and, by applying eq. 10 we find Q(x,y) = 0. Hence, d~°(z) 1 dz - aP Therefore,

¢°(z) = ¼pz; ~°(z)

-

p exp(-2ic~) 2

z

(19)

For the conformal region, the final results of ¢ff~) and ~1(~) are [-0.26 + (8.090 - i ' 0.510)f g~

5. Seismogenic models of the 1976 Tangshan earthquake

¢,@) = p R | ~

+ (0.023 - i" 0.022)~ 3 + (0.012 - i • 0.009)~ s + 0.004~7]. _ 0 . 2 9 + i - 0.463

0.664~j

0.336~ 3 + 0.062~ s - 0.044~ 7

1 - 0.743~ 2 + 0,323~ 4 + 0.289~ 6 + +

0.088~ 8

i(0.380~ + 0,667~ 3 + 0.202~ s + 0.034~ 7 .-~ 1 - 0.743~ 2 + 0.323~ 4 + 0,289~j 6 + 0.088~s_]

(20) By introducing eq. 20 into eq. 16 and separating the real and imaginary parts, we obtain the stress components op, o0, rpo. Then, the values of Oma x were calculated according to the known formula Omax

= oo + oo +

2

+ roo j

Peking region under the influence of the convectiongenerated subcrustal stresses nmst be calculated, by applying the theory of plates and shells (Timoshenko and Woinowsky-Krieger, 1959; Ding, 1978). The highly-compressed area at Tangshan in Fig. 4 has provided geodynamical explanations for the seismogenic models developed by Guo et al., (1977) and Ding (1978). From a mechanical point of view, the stress concentration diagram in Fig. 4 can be verified by photoelastic experiments.

(21)

The curves of equal Omax are plotted in Fig. 4, in which the value 1 corresponds to the stress of faultfree condition. Figure 4 clearly shows that stress concentration occurs at the two ends of the Taihangshan Tsangtung fault system: in the Peking-Tangshan and Szehsien areas. The stress concentration diagram in Fig. 4 also indicates that the magnitude of stresses decreases in the area where the factor of stress concentration is less than 1 : It should be noted that Fig. 4 shows only the concentration of Omax. For comparison with focal mechanisms in this area, other stress trajectories of tension, compression and shear in the

Studies of igneous activity in the region around Bohei Sea (Minero-Petrographic Laboratory, 1978) show that Pleistocene basalts occur in mountains bordering the North China Plain and Songliao Plain. This indicates that the stress field in the Peking region may be influenced by the convection flow in the upper mantle. The seismicity in North China is conspicuous in zonation (Guo et al., 1977). The zonation of earthquakes in North China can be classified into five seismic belts: (1) Jenchung belt, (2) Shansi-Weiho belt, (3) Hopei belt (4), Tancheng--Luchiang belt, and (5) Yinshan belt. The stress field and seismic periodicity and migration in the Hopei seismic belt, which includes the Peking-Tangshan-Szehsien region, seem to be independent of other seismic belts or geological features in North China (Qiu, 1976: Chia, 1977; Guo et al., 1977; Ding, 1978). According to the theory of elasticity, stress concentration occurs in fault systems and fades away very rapidly with increasing distance from them. Therefore, it is proper to treat only the faults there, and to surround them by an infinite solid plate. Geological features and seismic data concerning the Peking region are well known and progress in the seismogenic modeling of the 1976 Tangshan earthquake has already been made by Guo et al., (1977) and Ding (1978). Based on results from stress-field analyses, geodetic measurements of crustal deformation, fault motion and focal plane solutions, Guo et al., (177) have concluded that, under the influence of a principal compressive force, the strain energy was gradually accumulated within the interlocking portion of the rhombic

313

/

/

Fig. 5. Seismogenic model of the Tangshan earthquake and convection-generated stress concentration. The rhombic Tangshan fault block is bounded by the Ninho, Luanhsien, Fentai and Jiyunho faults. Under the action of a mysterious compressional force (arrows) the strain energy was gradually accumulated within the interlocking portion of the rhombic fault block, and a large seismic focus was then developed. As a result of compression, a right-lateral shear fracture zone was generated along the seismogenic Tangshan fault and the interlocking was overcome, so as to cause the 1976 Tangshan earthquake (Guo et al., 1977). The shaded area indicates the location of convection-generated stress concentration. The seismogenic model of the Tangshan earthquake and the location of stress concentration at Tangshan can be verified by photoelastic experiments. The direction of the mysterious compressional force seems to be related to the shaded shape of stress concentration•

Tangshan fault block, and a large seismic focus was then developed (see Fig. 5). Their conclusion was verified by numerous photoelastic tests. Where did the principal compressive force originate? We argue that the stress concentration shown in Fig. 4 may provide some clue. Conformal transformation and mapping of the convection-generated stresses under North China (derived from satellite gravity data) have revealed a stress concentration at Tangshan. The magnitude and direction of this concentrated stress field are in accord with the genetic compressional force for the 1976 Tangshan earthquake (Fig. 5). The main problem of seismogenic modelling for earthquakes in North China is to determine the state o f stress in North China from geodynamics data rather than on theoretical and speculative grounds. According to the theory of plates and shells, the state o f

stress in North China can be calculated with the presence of the existing fault systems. Under the effect of the convection-generated stresses, the stresses in the fault system in North China can be characterized as compression in a n o r t h e a s t - e a s t direction and extension in a n o r t h - n o r t h w e s t direction. The influence of faults on the stress field in relation to earthquakes has been discussed by Gzovsky et at., (1972a, b). However, Molnar and Tapponnier (1977) have suggested that tectonic stresses in eastern China are related to the I n d i a - E u r a s i a collision. It would be of interest to known by what methods they are able to transform the collision force in the Himalayas into the principal compressive force in the Tangshan seismic district.

6. Strain energy and magnitude of earthquakes in the Peking region The dilatational and distortional strain energy in a given volume Vis given by (Bullen, 1974) as

w =fff ,o2dv +fff ,.dV

(22)

where k denotes the incompressibility, 0 the cubical dilatation,/~ the modulus of rigidity and

Ei/ = (e~j - 102) 1/23 In which ei/is the strain tensor. The first and second term on the right-hand side of equation (22) represent the dilatational and distortional strain energies, respectively. In the case of a state of compressive stress, the dilatational energy is much less than the distortional energy. At points where fracture is occurring, the deviatoric stress Pi/is equal to (1/3)S, where S is the strength of the crustal rocks• At other points, P i / = (1/3)/3S 2 where 0 ~
w= fffs dv

(23)

fhe volume in question is the region of strain in the vicinity o f the focus o f an earthquake just before the earthquake occurs. If we let E be the energy release in seismic waves in an earthquake which has

314 been at breaking-point throughout the whole strained focal region, eq. 23 gives E = 5a V / 1 2 q u

(24)

The numerical relation between seismic wave energy., E, and the magnitude of earthquake, M, is governed (B~ith, 1966) by log,oE= 12.24 + 1.44M

(25)

period of stress redistribution or decrease in the whole area, it is reasonable to expect that no major earthquake will occur at the other end of the fault system. The time required for stress to diffuse to a distance l along a fault is given approximately (Turcotte, 1977) by (26)

t = ~12/Gbd

From eqs. 1 and 2, the magnitude of the subcrustal stress under the Peking region is of the order of 0.8 X 108 dyn cm -2. From Fig. 4, the coefficient of stress concentration is larger than 10. Therefore, the concentrated stress in the Peking region could reach the breaking point of the crustal rocks. The strained volume of the interlocking portion of the rhombic fault block in Tangshan seismic district is about 1.8 X 1019 cm 3 (Guo et al., 1977; Zhu et al., 1977; Ding, 1978). Bullen (1974)has given the values of q, S, and/J. For q = 2, S = 0.5 × 10 9 dyn • cm -2, and ~ = 1012 dyn " cm -2, we obtain E = 1.9 X 1023 ergs which is equivalent to the seismic wave energy of an earthquake with M = 7.7.

where d and G are the thickness and shear modulus, respectively, of the lithosphere, and b and ~"are the thickness and viscosity, respectively, of the asthenosphere. T a k i n g / = 325 kin, G = 3 X 1011 dyn • cm -2, ~'=4Xt02°dyn.sec.cm -2,d =100km,andb = 300 kin, the value of t from eqn. 26 is 150 years. In this period, the subcrustal stresses in this area caused by mantle convection flows would tend to be damped out by the propagation of stress. The process of stress diffusion takes about 150 years. After this period, subcrustal stresses due to mantle convection flows continue to build up and the second major earthquake would occur at the other end of the fault system because a large fraction of the concentrated stress still exists in that region.

7. Cyclical behavior of stress release

8. Seismicity

Although the processes involved in the concentration and release of stress along the Taihangshan Tsangtung fault system are extremely complicated, a simple model, as inferred from satellite stress patterns, may provide important information on the cyclical processes resulting in major earthquakes in the Peking region. If the idea of the stress concentration at the two ends of the Taihangshan-Tsnagtung fault system is accepted as the primary mechanism for earthquakes in the Peking-Tangshan and Szehsien regions, a cyclical mode of behavior is suggested. The accumulated strain at the two ends of the fault associated with the concentrated stress is released in major earthquakes. Major earthquakes occur sequentially. When a major earthquake occurs on one end of the fault system, the concentrated stress on this end is released. The sudden seismic displacements will propagate in the form of a stress wave from this end into the interior of the lithosphere and asthenosphere. The propagation of the stress wave will change the distribution of the stresses in the whole area of the fault system. During the

The Chinese record of seismicity on and adjacent to the Taihangshen-Tsangtung fault system should serve as a test for the cyclical behavior of stress release. It should also provide information of the state of stress. High levels of seismicity should be indicative of high stress levels (Turcotte, 1977). Earthquakes associated with this fault system were listed by Chia (1977) and are shown in Fig. 6 as a func tion of latitude for the period 1600-1976. All earthquakes for which M ~> 4 are included. Results prior to 1600 should not be used because of inadequate data (Chia, 1977). In order to reveal some very clear trends from the seismic data, a seismic strain release map should be constructed. Seismic activity may be expressed as a function of elastic strain release per unit area (Ao) per unit time (t). A measure of the rate of the processes of crustal deformation may be defined by t

(27) F = A o t AO O

315

2 ,.J

)og

o

PEKING-TANGSHAN TIENTSIN

39 ° N

~O ~ O

172

~

•

01679

•

Oo

M = 8

o

•

o

\

o.l

r 1976

oo¢ C

o •

M = 7.8

",...p.j ~,j

o o o

•0

ODOO GO 03 O

o

SZEHSIEN

J~oo 0

•

o

1

o

din,

36 ° N

I=1830 ]

t

~ I

I

1600

I

t

t

I

m J t

1700

m J [

t

M = 7.5 t t

, i

~ l

1800

1900

i 2000

YEAR LEGEND

o M~>4

• M~>5

@ M~>6

Fig. 6. Magnitudes of earthquakes in the Taihangshan Tsangtung fault system from 1600 to 1976.

Evaluation o f F requires that the energy of each of the earthquakes be determined. For particular earthquakes, we have (B~th, 1966) logloE~/2 = 6.12 + 0.72Mi forM/~> 5 logloE]/2 = 5.86 + 0.84Mi f o r M / < 5

(28)

We define Ef as the energy release in an earthquake of fiducial magnitude Mr. The ratio, Nf, of the strain release in any earthquake of magnitude Mi to that of Mf is for

Mi >15

\-~ff]

= 1

\~f]

= 100"84(Mi-Mf) for Mi < 5

(29)

Therefore

El~2 t Ff = ~ F ['N}/2dAdt

Aot L

(30)

As an approximation, the integration in eq. 30 can be converted to summations

E~/2 Ff :-~ot ~ ~N~m(ti' ¢i' X/)Ati~A/ i i

(31)

where @ and k/are latitude and longitude. In order to avoid using a strain-release figure that involves the elastic constant, we express strain in terms of the equivalent numbers of M = 4 earthquakes. Thus

n4 = E~'2 ~ ~N~/:(ti, ¢/, k/) i

i

(32)

In the study of the strain release for the TaihangshanTsangtung fault system, calculations were based on the earthquake data shown in Fig. 6. A0 has been chosen as the area bounded by five minutes of latitude and five minutes of longitude. The strain release sum of eq. 31, in terms of numbers of equivalent earthquakes with M = 4, was thus assigned to each of these space blocks. The total variation in strain release from 1830 to 1976 is from 5 to 350 equivalent M = 4 earthquakes. The resulting strain release has been contoured and

317

patterned in Figs. 7 and 8. The contour intervals have been normalized to numbers of equivalent M = 4 earthquakes per 1000 km 2. The seismic strain release pattern in Fig. 7, as derived from the Chinese earthquake data, agrees well with the stress concentration pattern in Fig. 4 (calculated from the satellite stress field). Figure 8 clearly illustrates and verifies the cyclical behavior of the stress release along the Taihangshan-Tsangtung fault system. Since the correlations between the seismic data and the model results are consistent, the cyclic sequence permits us to predict major earthquakes in the Peking region as shown in Fig. 9. It indicates that a major earthquake with M = 7.7 should occur in or before 1980 in the PekingTangshan area. The 1976 Tangshan earthquake, with M = 7.8, seems to verify this result.

~"~z4rzr L

Fig. 8. Strain release along the Taihangshan-Tsangtung fault system as a function of latitude and time.

LEGEND l.,u

O

o I-

Q

ARTHQUAKE OCCURRED EARTHQUAKEPREDICTED

_1 m

1679 M=8

1976 M = 7.8__M

i

PEKING-TANGSHAN

I.J •-~

f.j

,,

<

2280 M = 7.7

1980 = 7.7

O

u.

z I

{3 <

I.--

SZEHSIEN

-=

©

Ip'

36°N =

1830 M = 7.5

1600

2130 M = 7.7

I

I

I

I

I

I

I

1700

1800

1900

2000

2100

2200

2300

YEAR

Fig. 9. Historic and predicted major earthquakes in the Peking region.

318 9. Conclusions In developing a model for the c o n c e n t r a t i o n and release o f stress or strain in the Peking region, it is necessary to consider the implications b o t h of satellite stress fields and o f stress c o n c e n t r a t i o n theory. Conformal transformation and mapping o f the convection-generated stresses under N o r t h China (derived from satellite gravity data ) have revealed stress concentration features in the P e k i n g - T a n g s h a n - S z e h s i e n region. The magnitude and direction o f the concentrated stress field in the Tangshan seismic district are in accord with the seismogeneic models for the 1976 Tangshan earthquake developed by Guo et al., (1977) and Ding (1978). The principal compressional force which caused the 1976 Tangshan earthquake may have been due to stress c o n c e n t r a t i o n resulting from mantle convection. The periodic stress c o n c e n t r a t i o n and stress release associated with the T a i h a n g s h a n Tsangtang fault system are also modeled. Analyses of the m o d e l results and seismic data indicate that a major earthquake with M = 7.7 should occur in or before 1980 in the Peking Tangshan area. A major earthquake with M = 7.8 occurred at Tangshan in 1976. The result shown in Fig. 9 also predicts that a major earthquake with M = 7.7 should occur in or before 2280 in the Peking region.

Acknowledgements The author thanks D.L. T u r c o t t e at Cornell University for discussions on stress a c c u m u l a t i o n and strain release in fault systems, and E.S. Chang, o f the System and Applied Sciences Corporation, for c o m p u t a tional assistance.

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