Seismic triggering effect of tidal stress

Tectonophysics, 93 (1983)

Elsevier Scientific

319

319-335

Publishing

Company,

SEISMIC TRIGGERING

DING

ZHONG-YI,

Department

(Received

Amsterdam

- Printed

in The Netherlands

EFFECT OF TIDAL STRESS

JIA JIN-KANG

and WANG

REN

of Geology, Peking University, Peking (China)

September

23, 1982)

ABSTRACT

Ding, Z.. Jia, J. and Wang, (Editors),

R., 1983. Seismic triggering

Quantification

of Earthquakes.

The tidal stress field of a layered, investigate

its relationship

or near China during

fracture

symmetric

of earthquakes.

the last 24 years, we computed

focus at the time of occurrence. the earthquake

spherically

to the occurrence The normal

effect of tidal stress. In: S.J. Duda

earth

due to the sun and moon

For 70 severe earthquakes

the tidal stress in spherical

and tangential

fault plane were then found by a coordinate

is used to determine

stress components transformation.

whether

these stress components

will trigger

43 have been subjected

to a triggering

that occurred

in North

China,

14 have been triggered.

there is a significant

stress has only a small triggering conclusions

are obtained.

triggering

effect. From 72 events which occurred

Finally,

for the purpose

which the tidal stress may trigger an earthquake

of predicting

on faults in North

polar coordinates criterion

the earthquakes

in

at the

along the slip direction

It may be concluded

effect, while for oblique-slip

is used to

which occurred

Coulomb’s

results show that of the 70 earthquakes, earthquakes

and K. Aki

Tectonophysics, 93: 319-335.

on

of shear

or not. The

effect and for the 18 events that for shallow

strike-slip

and dip-slip earthquakes

the tidal

in other parts of the world similar

earthquakes

the time interval

during

China is investigated.

INTRODUCTION

Since

the nineteen-sixties

triggering (1967)

of earthquakes

many

people

by luni-solar

Ryall et al. (1968) and Heaton

have

studied

the problem

tides. Dix (1964), Knopoff (1975) used different

of possible

(1964), Simpson

approaches

to study the

problem and came to different conclusions. In China Li (1978), Du (1981) and Gao et al. (198 1) have also obtained different results from their studies. In the studies of tidal stresses, most authors used a homogeneous elastic spherical earth model. Only Heaton used the layered model of Takeuchi (195 1). The authors also used different criteria in judging the triggering effect. We used here the stress formulae of Wang and Ding (1978) obtained from the exact solution for a 15-layer spherical symmetrical elastic earth model, to calculate the lunar and solar tidal stresses. To study a particular earthquake that has already occurred, ‘we have to know first its position relative to the moon and the sun. The zenith angles 2, and 2, (subscripts m and s denote that of moon and sun, 0040-1951/83/$03.00

0 1983 Elsevier Science Publishers

B.V.

320

respectively) textbooks

and the azimuth of astronomy.

approximately,

A,

the maximum

The radial distance

and A, can be calculated

We shah take 2, difference

the focus. Then from the formulae

transformation

the two being less than

coordinate

given in I degree.

from the depth of

given by Wang and Ding (1978). the lunar

at the focus at the moment

in their respective

into a single unified

between

from the centre of the earth can be obtained

solar tidal stress components can be obtained

by the formulae

and 2, to be the polar angles 8, and t?,

spherical

coordinates.

the earthquake

They are then transformed

and their effect is superposed.

is then used to find the tangential

and

occurred

and normal

Another

coordinate

stress components

on

the fault plane. We assume the tectonic stress at the focus to be at its critical state. Using Coulomb’s fracture criterion, we can then judge whether or not these components have any triggering effect. For certain types of earthquakes, we find that there are some triggering effects that are potentially applicable for the prediction of earthquakes. TIDAL

STRESS CDMPONENTS

As stated coordinates

above,

IN THE HORIZONTAL

for any

using moon-earth

calculate the tidal stress respectively, the remaining

particular

earthquake

and sun-earth

components components

PLANE COORDINATE

by obtaining

centrelines

a,, ue, a+. rFe due to the moon being zero. In order to superimpose

polar

and sun the two.

We define the new 0’ is at the focus of

toward the east, ,v, is directed toward the north (0 being the earth’s centre). We call this the

Fig. 1. Relative position of the spherical coordinate using the earth-moon the beginning of the horizontal

spherical

as their polar axes, we can

they have to be transformed into a single unified coordinate. coordinate system 0’y,y2y3 (see Fig. 1) as follows: the origin the earthquake, the y,-axis is directed and _v, along 00’ vertically upward

SYSTEM

plane coordinate

system at the focus.

centreline as the polar axis with

321

horizontal

plane

direction

coordinate

Yl

0

sin A,,,

-cos

Y2

0

cos A,,,

sin A,

Y3

1

0

0

where A,,, is the azimuth y,-axis.

system.

When

considering

cosines of the new and old coordinate

Using

the moon’s

tidal stress, the

systems are as follows:

A,,,

of the moon. It is the angle between

the transformation

formulae

al., 1979), we obtained the moon’s coordinates as in the following:

the e-direction

for the stress tensor

tidal stress components

and the

(see, e.g., Wang

in the horizontal

et

plane

t~z = uomsin2A, + uerncos2Am a,? = uemcos’A,,, + IJ+~sin2A, u3y = urrn r~=(u~-u+!“)

sinA,cosA,

m=~$‘~~~A,

‘23

m--

731

rrT

sin A,,, A, to A,, one obtains the Sun’s tidal system. The combined effect is obtained

Changing coordinate

In + (Jll = 011 712

=

TIDAL

7,“;

+

a;, )

71;,

a,, = Tz3

=

ug + ui2 r2’;

+

r;;,

STRESS IN THE FAULT

)

(133 =

731 =

stress components by superposition:

in the same

u3”;+ us3

r3”;

)

+

r;,

PLANE COORDINATE

SYSTEM

The above stress components are then transformed to the fault plane system O’ABC, where 0’ is the focus, the C-axis is perpendicular to the pointing upward, the A-axis lies in the fault plane along the direction vector, and the B-axis is chosen for O’ABC to form a right-handed

coordinate fault plane of the slip rectangular

coordinate system. Here again we have two cases. In Fig. 2 is shown the case when the slip vector induces a left-lateral movement, while Fig. 3 represents a’ right-lateral movement. In both figures D, is the dip angle of the fault, E, is the dip direction and (r is the pitch angle of the slip vector (positive upward, -0, d a G 0,). O’H is the intersection line of the plane O’AB with the horizontal plain O’y, y,. G = LAO’H, which is the rake. The direction cosines between the O’ABC system and O’y, y, y,

322

Fig. 2. Relative position left-lateral

of the horizontal

plane coordinate

slip.

Fig. 3. Same as Fig. 2, for right-lateral

slip.

system and the fault plane coordinate

system:

323

system can be represented Yl

Y2

Y3

ml

nl

B

1, I2

m2

n2

C

1,

m3

n3

A

(see

as follows:

Appendix).

I, = - cos G cos EC - sin G cos DC sin EC m,=cosGsinE,-sinGcosD,cosE, n,

=sin

Gsin

DC

I, = - cos G cos DC sin EC + sin G cos EC m2

=

-

(1)

G cos DC cos EC - sin G sin EC

cos

n2 = cos G sin DC I, = sin DC sin EC m3

=

sin DC cos EC

n3 = cos DC where ICI < 90” corresponds to the left-lateral movement (Fig. 2) and 90” < IGI < 180’ to the right-lateral movement (Fig. 3). G = 0” represents a left-lateral strike-slip earthquake, Knowing

and G = 180”-a EC, DC and

right-lateral

one.

G, for each earthquake

we can

use eqs.

1 to find

I,,

as well as the stress tensor transformation formulae to obtain the tidal m,,...,n,, stress components in the fault coordinate system. If the pitch angle (Yis known instead of the rake G. we can find G by means of (Y. In fact, for both Fig. 2 and Fig. 3, the relation between G and (Yis obtained as: sin (Y= sin G sin DC For

the ranges

(2)

of G given

(Fig. 2) we should

above,

it is obvious

take cos G = (1 - sin’G)‘/‘,

that and

for a left-lateral

movement

for a right-lateral

movement

(Fig. 3): cos G = - (1 - sin’G)i/‘.

CRITERION

FOR JUDGING

THE TRIGGERING

EFFECT

There are different ways to judge whether or not a tidal stress will trigger an earthquake. For example, Ryall et al. (1968) looked into the relationship between the frequency of earthquakes and the vertical tidal stress component. Heaton (1975) discussed the phase relation between the time of earthquake occurred and the time when tidal shear stress reached its maximum and used a probability criterion. In general, these approaches look for rules between tidal stress and the occurrence of earthquakes. If the rule is obeyed, it is considered to have a triggering effect.

324

However, the rule is not unique, and it is not surprising that different authors arrive at different conclusions about the triggering effect of tidal stress. The criterion proposed

here is based solely on mechanics.

Accordingly,

an earthquake

force. At the moment direction

as the slip vector,

effect. However,

occurs when the driving

of the earthquake,

it adds to the driving

the resistance

force overcomes

if the tidal shear stress points

the resisting in the same

force and hence has a triggering

force on the fault plane against

slippage

is related to

the normal stress acting on the plane. If the tidal normal stress is compressive, it enhances the resistance force and thus helps to oppose sliding. Therefore, to consider the triggering

effect completely,

both the normal

fault plane have to be considered We shah triggering

use Coulomb’s

stress and the shearing

stress on the

from

to judge

simultaneously.

fracture

criterion

rock

mechanics

the

effect: (3)

[~l=%-P%

where [r] is the resistance to shear, ~a is the cohesion, p is the coefficient of internal friction, ,U= tan # with # the angie of internal friction, a, is the normal stress on the plane and we consider the tension as positive. In the stress plane with the coordinates u,, rn9 eq. 3 is represented by two straight lines (shear fracture lines) (Fig. 4). Let us assume that before the earthquake occurs, the stress on the fault plane is in its critical state, i.e. the stress point lies on one of these lines. Since we have taken the A-axis in the fault plane along the slip vector, the critical shear stress along this

t

Fig. 4. Triggering effect of tidal stress components criterion.

at the fault plane in relation to Coulomb’s

fracture

325

direction

is positive

the fracture “Jcc and ?A components, shall consider fracture

and the critical

lines. For a known on the fault

stress point

earthquake,

plane.

They

will be superposed

If the tidal stress vector points it to have a triggering

P must lie on the upper

to the exterior

on the critical of the fracture

effect (Fig. 4). If it points

lines, then there is no t~ggering

branch

of

we first find the tidal stress components stress

lines. we

to the interior

of the

effect.

Four different

situations are possible as shown in Fig. 4: ucc > 0 and rcA > 0; the tidal stress vector points outward, causing a trigger(1) ing effect. (2) ucc < 0 and rc. < 0; the tidal stress vector points inward, opposing sliding. then, if 19,& $J, the tidal stress (3) ucc =Z0 and rcA > 0; let 0, = arctanlrcAI/luccl, vector points

outward;

hence it has a triggering

effect. Triggering

is fostered

when #

is small. (4) ucc x 0 and rcA < 0; using the above definition for 0,, and assuming 8, < +, the tidal stress vector points outward, and hence it has a triggering effect. Triggering is fostered

when # is large.

For the last two cases, one needs to know the angle of internal

friction

of the fault

concerned. In accordance with Jaeger and Cook (1977), we have taken p = 0.202 (9 = 11.4*) to p = 0.746 (@ = 36.7”). For the situation (I), whatever &, is, there is a triggering

effect, while for the situation

RESULTS OF CALCULATION

2 there is none.

AND ANALYSIS

For the 70 large earthquakes which have occurred in and near China since 1957 (Gao et al., 1981, modified with additional data from other earthquake information sources) the tidal stress components are calculated and the triggering effect estimated. The results are shown in Table I. We note from the table the following: (1) Among

the 70 earthquakes

studied

43 (61%) have been subjected

triggering. Since there is a variety of triggering factors, the tidal stress does have at least some triggering effect. (2) For typical

shallow (depth

H G 22 km, i.e. within

this percentage

to possible shows that

the first layer of our earth

model) strike-slip earthquakes (Ial d loo), viz. the 11 earthquakes with Nos. 15-25, 9 (82%) have experienced a triggering effect. It appears that for shallow strike-slip earthquakes,

the tidal stresses have a significant

triggering

effect.

(3) For typical dip-slip earthquakes (l&l > 35”), viz. the 9 earthquakes Nos. 13-14 and 26-32, only 3 reveal triggering effects. ‘Consequently for dip-slip earthquakes, the triggering effect is practically nonexistant. (4) For deep earthquakes in the third layer (38 km Q H d 80 km), 7 out of 8 earthquakes (Nos. 63-70) show a triggering effect. This might indicate that the tidal stresses produce a significant triggering effect for deep earthquakes, though the events considered here are only few in number. (5) For the 18 events in North

China,

viz. Nos. l-18,

14 (78%) have experienced

68

66

69

75

76

14

15

16

17

18

16

9

68

76

8

67

75

7

13

69

6

12

68

5

76

66

69

66

3

4

IO

66

fl

65

1

Yr.

07

02

07

03

OS

01

03

07

07

04

02

02

07

05

03

03

03

01

mo.

28

06

19

27

15

16

27

18

28

06

25

04

18

15

26

20

08

15

day

effect of 70 earthquakes

Time

2

North China

No.

Event

Tidal triggering

TABLE I

3.71

12.42

9.87

2.24

8.45

3.56

16.97

13.41

18.76

0.91

13.95

19.60

21.56

3.78

23.24

0.99

5.49

23.43

hr.

38.0 39.7 38.2 38.5 37.8 37.2 37.5 38.2 40.8 39.4

7.1 7.4 6.3 5.3 4.7 5.8 4.7 5.4 7.8

40.6

1.3 40.2

38.2

6.3

37.2

4.7 5.5 3.6

37.3 37.7

5.6

37.3

5.2

35.1

5.1 6.8

VW

Lat. Long.

15

114.8

17 15

118.1

20 122.5

119.4

20

25

114.8 115.3

22

30

115.2

116.5

4

- 10

IO

-8

-47

- 55

5

15

- 17

16 35

119.4

118.7

25

-25

6.5 18

- 15

112.2

12

122.8

15

120.5

20

119.4

- 13

24 - 20

14

115.0 20

10

115.3

II

10

- 18

(2)

Pitch angle

Depth

(km)

114.9

-

111.6

(“E)

in the last 24 years in and near China

1834

1429

1138

269

1626

- 2096

85

-2721

1395

1038

1268

- 2067

1196

712

674

- 1174

958

- 4049

%o Pa)

632

648

405

505

107

387

798

-60

-340

- 417

84

- 156 47

35

137

408

753

- 693

(Pa)

?A

Yes

Yes

Yes

Yes

Yes

no

yes

Yes “0

yes yes

yes no

yes

Yes yes

yes

IlO

effect

Trig.

08

04

64

70

73

74

76

67

72

73

78

64

72

21

22

23

24

25

26

27

28

29

30

31

11

62

20

7.4 6.7

9.08

22.76

0.95

21.60

20.00

2.07

26

14

24

12

31

05

05

18

29

29

07

19

09

10

01

03

12

01

01

11

11

ii

10

66

66

67

67

68

70

70

70

73

76

76

77

57

57

35

36

37

38

39

40

41

42

43

44

45

46

47

48

23

07

08

12

05

13.18

18

02

66

34

22.19

19.71

10.73

17.26

19.82

1.01

6.19

11.75

5.5

5.5

5.2

4.7

5.5

5.9

7.7

5.5

5.2

5.5

6.0

5.7

5.2

6.0

4.5

23

04

17.92

22

01

78

63

5.6

5.9

5.4

4.5

6.2

6.8

7.3

7.1

7.9

5.4

5.1

32

19.78

6.7 6.4

33

12.18

15.75

09

03

13

5.82

16.67

11

03

07

12.37

20.39

3.42

18.62

21.18

10.58

4.32

18.73

4.36

30

29

II

06

31

30

19

09

16

01

08

05

05

02

07

08

03

60

19

First and second Iayer O- 22, 22 - 38 km

Other parts of China besides North China

43.2

24.0

23.4

27.5

24.5

32.9

32.2

23.9

24.3

23.3

28.4

30.2

36.8

27.5

26.0

25.8

40.9

42.3

22.6

31.9

31.4

40.3

31.6

24.4

28.9

31.2

28.5

27.5

23.7

32.8

100.2

121.9

107.5

101.1

98.7

111.5

101.3

102.7

102.7

121.4

94.4

104.1

87.5

92.7

103.2

99.5

106.9

84.5

121.3

102.9

116.2

79.0

100.3

98.6

104.0

100.7

103.6

88.4

114.7

103.7

33

33

12

15

10

9

20

14

10

13

15

4

14

20

5

16

30

25

34

12

6

10

10

22

8

17

12

1084

- 293 924

614 1071

-5

- 15

20

- 16

12

20

20

-25

-23

12

-25

- 12

- 382 338

1269 13

-352 -80

- 548

-519

- 335 -697

758

- 2573

-353

486

- 1286

606

-57

- 2375

- 435

-213

- 1731 466

-441

- 3750

620 -672

1472

- 1534

27 16

- 189

-210

- 12

- 16

- 17

- 333

- 388

- 1140 - 227

- 565

- 2672

35

915

- 2090

285

-99

- 583

945

-751

2835

740

311 - 283

733

1558 175

549

- 802

- 129

- 1621

1131

44

-4s

-48

52

-47

5

7

10

7

5

5 21

2 - 10

6

no

no

no

no

Yes no

Yes

Yes

no

IlO

no

Yes no

Yes

Yes no

Yes

Yes no

no

SlO

ye=

II0

Yes

no

YCi

yes yes

IlO

yes

7.0

19

03

28

17

02

08

03

12

08

04

04

64

65

65

65

66

66

68

68

69

71

71

71

38 - 80 km

51

52

53

54

55

56

57

58

59

60

61

62

Third

layer

6.4

2.44

15.58

20

08

10

02

78

59

64

64

65

66

67

64

65

66

67

68

69

70

06

09

03

11

04

63

63

08

33 33

103.5

6.6 5.8

2.90

5.8 6.2 5.0 5.2 5.0

9.09

8.77

9.31

18.11

15.63

16

26

18

11

02

6.4

5.0

18.42

22.93

15

16

39.8

28.2

32.1

30.0

37.0

38.7

38.3

24.2

28.9

41

103.7

45

43

87.6 75.3

50

80.6

- 12

I

0

.- 23

- 17

50

95.6

25

-57 -11

40

IO

19

1.5

-5

20

- 10

-25

-5

30

15

40

75.3

101.0

40

33

94.7 101.0

32.0

6.4

12.81

23.53

122.4

33

73.5

39.1

5.6

11.98

28

6.0

33

101.9

36.2

5.4

17.11

22

12.51

31

100.2

29.4

5.7

0.29

03

21

32

97.9

23.8

5.2

1.62

21

23.0

33

97.9

5.4

09

26

114.5

12.6 23.8

5.7

13.06

19

11.60

07

10

35

93.2

15 25

32.9

09

9 13

(aO)

34

5.2

4.16

02

Pitch angle

24

33

97.0 100.9

25

81.6

(“E)

Depth (km)

87.0

25.9

35.7

44.7

CoNI

Lat. Long.

35.1

5.4 5.5

I 8.06

21.53

13

01

21

08

04

hr.

63

day

62

mo.

50

yr.

Time

49

No.

Event

TABLE I (continuedf

160 388

109 - 157

1511

- 689

1571 3040

296

2272

-911

58

36

-816

-91

591

134

-88

-640

-56

872

975

yes

yes

yes

yes

yes

yes

yes

no

no

yes

Yes

yes

fl0

no

II0

yes

yes

yes no

174 - 233

Yes

- 794

no yes

102

effect

Trig.

- 320

?A (Pa)

- 179

3355

I827

856

- 837

1237

706

1283

- 574

136

348

- 2291

1563

- 1667

- 1550

I896

2730

%C (pa)

TABLE

II

10

03

02

05

06

1966

1966

1967

1969

1970

1973

05

04

1940

1947

04

1906

12

10

1868

08

09

1865

1933

01

1857

1932

06

1836

Shallow strike-slip

IO

06

1963

09

1963

10

19

11

21

18

21

09

09

10

earthquakes

17

31

03

04

17

27

17

18

09

15:58

04:37

01:54

06:lO

13:12

15:47

20:30

15:30

15:30

03:55

20:23

21:41

17:58

21:42

10:41

00:48

16:58

05:45

IS:08

07

1963

01

between 30 and 50 km

08

1940

day

GCT

Time

effect of 72 earthquakes

Earthquakes

mo.

Yr.

Date

Tidal triggering

6.5

7

6.3

7.3

8+

7+

7+

8+

7+

7.4

7.8

6.5

7.5

6.5

6.25

5.2

5.5

7.0

M,

which occurred

8

8

8

IO

10

10

10

10

10

49

43

33

33

38

37

33

33

33

33

(km)

Depth

worldwide Long.

116W

115.5w

118W

118W

123W

123W

123W

117.5w

123W

145.8E

78.2W

I27.4E

24.6E

78.6W

80.9E

37.4w

29.2E

8.2E

339.58

(deg.)

Lat.

35N

32.7N

33.6N

34N

38N

38N

38N

34.5N

38N

43N

9.2s

4.9N

39.2N

10.7s

29.7N

7.6N

40.9N

43.4N

44.4N

(deg.)

Rake

5

180

180

180

180

180

180

180

180

180

100

-90

60

105

90

85

-100

80

90

(deg.)

-34

-38

- 232 707

-56

655

- 224

- 572

2038 -1143

-488

- 459

-631

-981

2673

1661

-313

- 1318

469

- 578

46

1135

-941

-905

7c.4 (pa)

- 769

1973

3762

2821

- 1443

1277

1651

1818

- 122

299

- 4539

3233

751

1007

ccc (pa)

yes

II0

yes

IlO

yes

IlO

yes

yes

yes

yes

yes

yes

IlO

yes

IlO

IlO

yes

I-IO

no

effect

Trig.

Long.

121w 116W 122.6W 134E 136E 137E 39.7E 36.6E 33E 27.5E 31.2E

9 11 10 8 20 10 5 10 10 10 10 10 18 10

6 6.5 5.9 7.9 7.4 7.3 6.5 8 7.3 7.3 7.4 7.1 5.7 6.8 7.1 7.2

04:26

02:29

04:56

09~27

08:37

07:13

05:15

23~57

14:03

03:22

19:06

06:33

17:57

12:22

16:52

IO:48

28

09

02

07

10

28

09

26

20

01

07

26

09

19

22

31

06

04

10

03

09

06

09

12

12

02

09

05

03

08

07

08

1966

I%8

1969

1927

1943

1948

1%9

1939

1943

1944

1953

1957

1965

1966

1967

1968

6.25

13:49

15

03

1946

6.5

18:16

30

01

1934

7.6 8

x

x

8

8+

IO:30

10

1915

06:53

03

1872

5 10

7.0

Lat.

38N

118.5W

35.7N

34N 40.5N

55

-90

-90

110

0

0

13.4N

12.lN

180

180

180

180

180

180

180

180

0

0

180

0

180

175

180

165

0

117.5w 118.1W

Rake (deg.)

34N

40.7N

39.2N

39.4N

40.6N

40N

41N

50.7N

39.7N

36N

36N

36N

35.3N

38.5N

33N

37N

33.9N

(deg.)

117.5w

122.8E

86.3W

58.7E

12

6.0

26

08:30

17

1973

03

06:29

23

12

03

1972

30.8E

10

41.6E

24E

134.3E

116.4W

8

6.5

23:43

Yr.

05

(deg.)

12

GCT

1948

Depth (km)

Time

day

Ii (continued)

mo.

Date

_~~~

TABLE

803

385

1526

971

788

657

1893

- 4027

1530

2934

1970

- 1195

- 2306

175

-22

1270

-2701

1878

- 1688

2011

~ 556

806

- 1172

UC, (Pa)

~ 1146

283

568

-444

1055

182

- 942

740

164

563

43

576

326

67

-404

964

252

1004

370

392

- 464

301

158

___.-

no

yes yes

no

yes

n0

yes no

yes no

Yes IlO

Yes yes

yes “0

no

yes yes

yes

no

yes

yes

effect

-~

Trig.

TCA

(Pa) ____

07

20

09

02

02

08

09

03

12

12

05

06

07

05

09

10

07

02

09

05

02

03

03

03

05

IO

02

1970

1971

1973

1973

1923

1933

1944

1946

1964

1964

1965

1968

1971

1964

1965

1966

1966

1967

1969

1970

1964

I%5

1968

1968

1969

16

28

14

23

30

28

28

28

01

18

05

06

06

05

16

25

16

07

02

01

06

21

09

12

18

12

24

08

08

1954

21

06

1954

07

1954

1959

07

1952

6.9 7.9

02: 14

02:41

7.1

17:24

8.5

03:36 7.5

7

21:02

02:37

7.3

02:40

5.6

6.2

20:43

07:09

5.6

5.9

6

7.1

8

5.9

7.4

6.9

8.2

8

8.5

8.2

4.7

5.75

6.5

5.4

7.1

7.1

6.8

6.6

7.7

02:02

03:18

14:31

18:35

00:48

13:33

04:Ol

07:58

19:19

04:35

17:31

02:58

23:29

14:30

14:03

14:30

06:37

II:07

05:51

II:13

12:25

22

5

21

20

20

IO

22

15

16

22

20

10

22

15

16

20

22

25

25

20

30

15

18

10

10

10

8

8

8

10

55

10.6W

117E

- 480 423 - 353 - 198 203 445 974 146

524 421 125 66 - 127 - 884 1143 -34

90

701 100

36N

-611

-431

314 105 31.8s

974

1705

-460

- 543

123 484

605

882

90

-90

90

-80

-210

292

687 -70

149

566

- 554 90

38

-449

-55

-79

-517

485

- 769

772

344

- 1026

955

- 486

- 1373

2142

569

598

- 117

-431

508

- 502

- 202

- 748

875

- 265

- 1173

-90

-90

90

2216 -453

41.7s

50.3N

177.9E 171.9E

61.lN

39N

36N

39.7N

27.8N

39.1N

38.4N

39.4N

147.4w

29.5E

10.6W

21.3E

54.38

21.7E

22.4E

24E

46.5N

35

40.8N

143.2E 141.2E

- 105

41.3N

90

90

40.4N 39N

90

90

-90

135

20

56

60

54

-90

-90

-90

-90

34N

34N

39.3N

35N

34N

34N

34N

34N

44.9N

39.5N

38N

38N

35N

146.68

139E

139E

136E

136E

344.4E

140E

119w

119w

118.5W

118W

IllW

118.3W

118.3W

118.5W

119w

yes

no

I-IO

yes

IlO

yes

IlO

yes yes

IlO

“0

yes

IlO

yes

Yes

yes

Yes

“0

IlO

yes

IlO

“0

IlO

II0

yes

no

no

Yes

“0

no

332

a triggering triggering

effect.

This

earthquakes

(6) In addition

means

in North

tidal

among

the 28 shallow strike-slip

means

that the tidal stress produces and dip-slip

have

significant

the 72 earthquakes

( 1975), using the present

II. Rake in the table denotes

oblique-slip

stresses

influence

on

with a focal depth

less

China.

we have investigated

than 50 km given by Heaton in Table

that

The results are shown

the angle G in Fig. 2. The results show that

earthquakes,

earthquakes,

method.

18 (64%) have a triggering

some triggering only

effect. This

effect. From among

15 (44%) show a triggering

34 shallow effect. Here

triggering by tidal stress is of only minor significance. The results agree with (2) and (3) obtained above, but they contradict Heaton’s conclusion. EARTHQUAKE

TIME PREDICTION

tN NORTH

CHINA

BASED ON TIDAL

STRESS

It is concluded above that for large shallow strike-slip earthquakes in North China. tidal stress produces a significant triggering effect. In recent years it became apparent that in North China, NE striking faults are associated with right-lateral slip

and

NW

suggestion

striking

faults

concerning

with

left-lateral

the prediction

slip.

On

this basis

we make

of the time of earthquake

a simple

occurrence

in this

area. From the trend of the fault we can estimate whether an earthquake on the fault will be associated with right-lateral or left-lateral slip. Since the direction of the slippage motion,

vector

is unknown,

we assume

faults

of large dip to produce

and we take the rake to be 0” or 180”. We can then calculate

Fig. 5. Number

of triggerings

per day before and after the Xingtai

(1966.3.8.

strike-slip

the tidal stress

5:29) M, = 6.8 event

333

Number of triggering c

o-

I

18 19 20 21 22 23 24 25 26 27 July

I 29 I

I

I

I

31 I

I

I

2

3 1 Date

1

August

Fig. 6. Number of triggering per day before and after the Tangshan (1976.7.28. 3:42) MS= 7.8 event.

components

determine

at the fault

plane

by the present

method

on an hourly

the period of time when the tidal stress components

basis

and

will have a triggering

effect. This will be illustrated by the following examples. (1) Xingtai earthquake of March 8, 1966. We have possibility at hourly intervals for 18 days around March

calculated the triggering 8, 1966 and obtained the

number

effect. This is shown as a

of hours on each day with a potential

triggering

solid line in Fig. 5. As can be seen within the 18 days, the triggering hours per day range between 12-14. There are 4 days in which there are 14 potential triggering hours per day, March 8 being one of them. It may seem that 14 out of 24 hours per day is not a large number. However, if the estimates are made for a left-lateral slip then the number of potential triggering hours per day will be much less ranging from 1 to 11 per day, as shown by the dashed line in Fig. 5. By comparing these two curves it is obvious that the tidal stress here is favourable to right-lateral slip and we may consider the date with maximum triggering number as a period of time with increased

earthquake

danger.

(2) Tungshan earthquake of in Fig. 6. Within the 18 days ranges between 12- 15 per day number. A similar calculation potential triggerings.

July 28, 1976. The result of the calculation is shown around July 28, the number of potential triggerings and July 28 is among the 5 days with the maximum for left-lateral slip yields a much smaller number of

334

From

these examples,

the prediction

it appears

that the tidal stress triggering

effect may assist

of the time of the earthquake.

CONCLUSIONS

On the basis of the present method, the analysis occurred worldwide indicates the following: (1) The tidal stresses

have a significant

of 142 large earthquakes

triggering

effect for shallow

which

strike-slip

earthquakes. (2) The tidal stresses have very little or no triggering oblique-slip events. (3) The tidal depths

between

triggering 38-80

effect is particularly

effect for shallow dip-slip

pronounced

for earthquakes

or

with

km.

(4) For the events in North China, the tidal stresses have a significant triggering effect. Thus we may consider the date with a maximum of potential triggerings as a time interval

with increased

earthquake

danger.

The above investigation is limited to earthquakes on pre-existing faults. It is based on a spherically symmetric earth model and only solid-earth tides are considered. The influence of lateral inhomogeneity and the oceanic have an additional influence on the stress distribution.

tidal effect may

ACKNOWLEDGEMENT

The authors You-quan Appendix:

wish to acknowledge

and Cai Yong-en DERIVATION

their

OF EQUATIONS

intersecting

lines of the meridian

C with the horizontal

same time, this meridian the horizontal

to Mr. Wu Qing-peng,

for their valuable

Yin

comments.

1-2

In Fig. 2, O’Q and O’F are intersecting the end of the vector

gratitude

of Peking University

plane intersects

plane.

plane. O’Cy, passing

QO’F is a straight

the O’AB plane

line. At the

at O’K, the O’AB plane

plane at O’H.

O’C I O’H (C is perpendicular to the O’AB plane and O’H lies in this plane) and to the plane O’y, _I_O’H (O’H lies in the horizontal plane). :. O’H is perpendicular O’Cy,, i.e. O’H I O’Q and O’H I O’X. in order to determine the direction cosines I,, m,, ni (i = 1, 2, 3), we shall find the components

of the vectors A, B, C, in the coordinate

system O’y, .v, y3. For example,

to find A, it is not difficult to see that in the plane O’AB: Here the subscript 0 denotes the unit vector in that direction. In the plane O’Cy,, we have: 0 ‘K, = cos D,O’F, + sin 0, y3

(b)

335

In the horizontal

plane:

O’H,, = - cos ECy, + sin ECy2

(c)

O’F=

(4

-sin

E,y,

Substituting

-cos

E,y,

(b), (c) and (d) into (a), we get:

A=(-cosGcosE,-sinGcosD,sinE,)y, + (cos G sin EC - sin G cos DC cos EC ) yz + (sin G sin DC) y,

(4

The three components are I,, m ,, and n,, respectively. The derivation for the other directions is similar and we subsequently get eqs. 1. Besides, (Y is the angle between A and its projection in the horizontal plane. Resolving A along its projection and the yj direction, we get: n,=sincu. From (e) we have already: n, = sin G sin DC, hence: sina=sinGsinD,. This is eq. 2. A similar derivation

can be made from Fig. 3.

REFERENCES

Dix, C.H.,

1964. Triggering

Du Pin-ren,

of some earthquakes.

1981. On the correlation

between

Proc. Jpn. Acad., 40(6): 410-415. earth tides and earthquake.

Research

of Seismic Sciences,

Li Jian,

1981. Triggering

1: 14-20 (in Chinese). Gao

Xi-ming,

Yin

earthquake Heaton,

T.H.,

Jaeger,

Zhi-shen,

Wang

Wei-Zhong,

by the tidal stress tensor. Crustal 1975. Tidal triggering

J.C. and Cook, N.G.W.,

Huang

Li-juan

Deformation

of earthquakes.

Geophys.

1977. Fundamentals

and

and Earthquake, J.R. Astron.

of Rock Mechanics.

of

1: 4- 16 (in Chinese).

Sot., 43: 307-326. Chapman

and Hall, London,

3rd.. pp. 379. Knopoff,

L., 1964. Earth

tides as a triggering

mechanism

for earthquakes.

Bull. Seismol.

Sot. Am., 54:

1865- 1870. Li Guo-qing. Works

1978. Horizontal on Astronomy

and

components

of earth

Geodynamics.

tides and earthquakes

Shanghai

Astronomical

in North

Observatory,

China. pp.

Collected

126-132

(in

Chinese). Ryall,

A., Van Wormer,

other features

J.D. and Jones, A.E., 1968. Triggering

of the Truckee,

California,

earthquake

of microearthquakes

sequence

of September,

by Earth tides, and

1966. Bull. Seismol. Sot.

Am., 58: 215-248. Simpson,

J.F.,

1967. Earth

tides as a triggering

mechanism

for earthquakes.

Earth

Planet.

Sci. Lett., 2:

473-478. Takeuchi,

H., 1951. On the Earth tide in the compressible

Sci., Univ. Tokyo, Wang

Ren and Ding Zhong-yi,

change

of the rotation

Geodynamics.

earth of varying

density

and elasticity.

J. Fat.

Sect. II, 7(11): l-153.

Shanghai

Wang Ren. Ding Zhong-yi

1978. The stress field of a layered

rate of the earth Astronomical

Observatory,

and Yin You-quan,

Beijing, p. 200. (in Chinese).

and the tidal forces.

spherically Collected

symmetric Works

earth due to the

on Astronomy

and

pp. 8-21 (in Chinese).

1979. Fundamentals

of Solid Mechanics.

Geological

Press,