Seismicity Acceleration Model and Its Application to Several Earthquake

Vol.12 No.1 (35~45) ACTA SEISMOLOGICA SINICA Jan., 1999

Seismicity acceleration model and its application to several earthquake regions in China

WEN-ZHENG YANG (~ ~i~) LI MA (~ ~) Center for Analysis and Prediction, China Seismological Bureau, Beijing i 00036, China

Abstract

With the theory of subcritical crack growth, we can deduce the fundamental equation of regional seismicity acceleration model. Applying this model to intraptate earthquake regions, we select three earthquake subplates: North China Subplate, Chuan-Dian Block and Xinjiang Subplate, and divide the three subplates into seven researched regions by the difference of seismicity and tectonic conditions. With the modified equation given by Somette and Sammis (1995), we analysis the seismicity of each region. To those strong earthquakes already occurred in these region, the model can give close fitting of magnitude and occurrence time, and the result in this article indicates that the seismicity acceleration model can also be used for describing the seismicity of intraplate. In the article, we give the magnitude and occurrence time of possible strong earthquakes in Shanxi, Ordos, Bole-Tuokexun, Ayinke- Wuqia earthquake regions. In the same subplate or block, the earthquake periods for each earthquake region are similar in time interval. The constant a in model can be used to describe the intensity of regional seismicity, and for the Chinese Mainland, a is 0.4 generally. To the seismicity in Taiwan and other regions with complex tectonic conditions, the model does not fit well at present.

Key words: seismicity acceleration model subcritical crack growth China earthquake region fit Introduction Before the occurrence of a strong regional earthquake, the seismicity in the region is commonly changed from weak to strong, this phenomenon bespeaks the process of energy release in the region. After the occurrence of strong regional earthquake and its aftershock, the seismicity in the region recovers silence, as time goes by, changed from weak to strong again, later, another strong earthquake would occur. If we call the interval time between two strong earthquakes in a region to be an earthquake period, and the seismicity in this region would be changed from weak to strong in the period, then it would be beneficial for us to acknowledge which stage is this seismicity being and to set up a model to predict the following strong earthquake. In one earthquake period, we define remain time is the end time of an earthquake (when the next strong earthquake occurs) minus the time of the earthquake event in the period (Figure 1). Pa- l~emaintime(tr__~ pazachos (1973), Jones and Monlar (1979) found the number of earthquake events in a time unit is in Figurel The definition of earthquake period direct proportion to its remain time to the minus and remain time

* Received May 28, 1998; revised September 1, 1998; accepted September 16, 1998. 36 ACTA SEISMOLOGICASINICA Vol. 12 some power. Varnes (1989) pointed out the following relationship exists between the energy of foreshock series and time d.(2 /dt = C /(tf - t)" (1) where t is the currence time of one foreshock, tf is the time of mainshock occurrence, C and n are constants, .62 is a measurable quantity which is used for describing strain. Equation (1) can also be written as X~ = A + B(t~ - t) ~ (2) where A and B are constants, m=l-n, .Ocan be gotten through the following equation lgD = cM + d (3) When M is magnitude, c=1.5, .(2 representes seismic moment, d is constant; when M is Benioff strain release or square root of moment, c=0.75, d is constant; when M is the number of earthquake events, c=0, d=0 (Bufe, et al, 1994). Varnes and Bufe found Benioff strain release to be especially useful to analysis practical catalogue, and Robinson also use Benioff strain release to analysis the seismicity of New Zealand. Equation (3) can be written as

Y_,Mo = A + B(t r - t)" (4) where Y_,Mo is the observed accumulated seismic moment, to some power a range from 0 to 1 (usually to be 0.5), at time t. A, B and m are constants to be found, along with the time of ultimate failure (tf). With equation (4), Bufe and Varnes (1993) analyzed two earthquake periods in San Francis- co Bay region of the United State (1906 San Francisco Ms=8.3 earthquake and 1989 Loma Prieta Ms=7.1 earthquake as the end earthquake event of tx, o period respectively). Using the earthquake events in each period except the last event to fit the last event with equation (4), they got accurate tf and Mf for each of the two strong earthquake in the region. Sornette and Sammis (1995) modified equation (4) by leading into the conception of normalized group, which make equation (4) be with discrete hierarchical structure, and get the following form

~M°=A+ B(tf-t)'II+Cc°s(2~ lg(tf-t)lg2 +tp )1 (5)

Where C, 2 and (p are constants to be determined. Generally, equation (5) provides a better fit to the observed seismicity data than equation (4). Robinson (1997) used equation (5) to analysis the seismicity of New Zealand systematically, and divided several hazardous regions in New Zealand for the coming years. 1 Theory of seismicity acceleration model We can build the relationship between regional seismicity and time according to existed rock mechanics theory and experiment. If we regard regianal seismicity as energy release of crack due to the tectonic block continues to grow under long time stress, the growth of crack coming to ut- most would make the rock ultimately broke, and lead to a strong earthquake, then the theory of crack growth would do more help to build seismicity-time model. About the theory of crack growth, there are detail literatures on fracture mechanics of crack, but in relationship with practi- No. I YANG, W. Z. et al: SEISMICITY ACCELERATION MODEL AND ITS APPIdCATION 37 cal seismicity, the theory of subcritical crack growth (Atkinson, 1979) may provide a better ex- planation. For crack with arbitrary mode, in a homogeneous and linear elastic medium, the stress com- ponents near the crack top are proportional to r z/2, where r is the distance measured from the crack, the coefficient of the r la term in the stress is the operator of stress intensity (k), which char- acterizes the intensity of the stress field at the end of crack. Classical fracture mechanics postu- lates that the crack in a linear elastic solid will propagate once a critical stress intensity factor Kc has been reached, however, under the circumstance of long period of loading the classical fracture mechanics approach breaks down, especially if high temperatures or reactive environments are presented. By observing in glass, engineering material, rocks and minerals individually, Atkinson (1982, 1984) found that significant rates of crack extension can occur at value k, which may be substantially lower than Kc, this phenomenon is known as subcritical crack growth. For a two-dimensional crack in any mode, the stress intensity factor is given by k = Yfr(~X) I/2 (6) where fir is the far-field stress, Y is a numerical modification factor, X is the crack length for a two- dimensional crack or the radius for a circular crack. Charles (1958) used a different stress dependence of chemical reactives involved in static fatigue of grass and arrived at the following expression for subcritical crack growth

J( = voA exp(-H / RT)k" (7)

Vo and n are constants, n>2, Aexp(-H/RT) is the constant of reaction equilibrium. This equation also fits a large number of experimental data on many different classes of materials, including rocks and minerals (Atkinson, 1982, 1984). Equation (7) is most commonly used to describe experimental data on subcritical crack growth in geological material. Combining (6) and (7)

J( = voA exp(-H / RT) x [Yf r (~ X) I/2 ]" (8)

During the subcritical crack growth, the 6~ can be treated as a constant, and v=vo, X=Xo, then v o = voA exp(-H / RT) x [Y8 r (it X o )1/2 ],, (9) Combining (8) and (9) k = vo[(XIXo)l/2]" (10) v0 is the crack velocity at time zero and Xo is the crack length at time zero. Integrating to the equation (10), we can get

i -12/(2-n) X= X~ 2-')/2 n- 2 Vot .| (11) 2 x:' l Das and Scholz (1981) simply set the quantity in brackets equal to zero, since this is where X goes to infinity at time to failure. X0 2 tf - -- -- vo n- 2 (12) tf is the failure time, which only depends on the initial condition and not on the final condition. 38 ACTA SEISMOLOGICA SINICA Vol. 12

Substituting (12) into (11), then

( t -~,,/(2-,,) -v f

In fracture mechanics, the energy release rate G is defined to be the energy flux to the crack tip zone per unit crack length advance (per unit width along crack front) and there is a relationship as following G = Ck 2 (14) where C is constant. Combining (7), (13), (14) and the definition of G, we get E= A+ B(tf -t) m (15) where A is constant, represents the total energy released from time zero to failure; B and m are constant, E is the total cumulative energy released from time zero to t. Equation (15) gives the relationship between energy and time of subcritical crack growth, and it shows the cumulative energy is proportional to the power index of the remaining time to failure. Equation (4) and equation (15) looks alike in form, but there exists some differences. E in equation (15) is the released energy of crack growth, and E is used up in elastic strain of the material in crack tip, in frictional work on the crack face, and on supplying energy to drive the extension of the crack. Only the energy used up in elastic strain is equivalent to the cumulative moment in equation (4). 2 Simulation in several subplates of China We use equation (5) as the mathematics model in researching the seismicities in several earthquake regions of China. Comparing with that of San Francisco and New Zealand, the seismicity in China appears more complex. Firstly, San Francisco region and New Zealand are sat in the great Circum-Pacific displacement fault belt, and they belong to intraplate earthquake belt (Li, 1981). China contains several kinds of plate-tectonic styles. The western part of China is to the north of Himalayan Orogenic Belt, which is located on the conjunction of India Plate and Eurasia Plate. Taiwan lies on the border tectonic belt of Circum-Pacific seismic zone and the whole of North and South China sit in Eurasia Plate. Secondly, both the San Francisco Bay region and New Zealand have obviously master control fault, plate movement is simple, while in Chinese Main- land, the fault system is more complex, the regional rock may under the stress from many directions. Thus it makes it hard to study the seismicity of the whole China with an uniform method. In this article, we use master control fault as the first criterion of dividing seismicity regions, and also consider the earthquake distribution and other geophysical characters. The regions using for studying the seismicity acceleration model are shown in Figure 2. We adopt Levenberg-Marquart non-lineal fitting method (Press, et al, 1992) to fit data. The history catalogue of China (786 BC-1980 AD, Ms_>4.5) (Min, 1995) and the appending catalogue (1981 AD-1996 AD) compiled by DA-LIN ZHENG and JIE LIU°. Before using the catalogue, we delete afiershock in it with the experimental date (Keilis-Borok, et al, 1980) as shown in Table 1. The formula we used to transfer Ms to M0 (N.m) as the following

~According to "Fast Report Earthquake Catalogue" and "Earthquake Information" of Chinese Seismological Bureau No.i YANG, W. Z. et ah SEISMICITY ACCELERATIONMODEL AND ITS APPLICATION 39 lgM o = 1.5M s +9.14 (16)

70" E 80" 90* 100" 110" 120" 130" 140"

110" 120" Figure 2 The selectionof studied regions (Ma, 1986) I Heilongjiang Subplate II. North China Subplate III. South China Subplate IV. Xinjiang Subplate V. Qing-Zang Subplate 2.1 North China Subplate The most intensive differential movement zone alone Table 1 Window algorithm for aflershock fault in the eastern part of China is North China Subplate. (Keilis-Borok, et al, 1980/ Magnitude of Ro (m) T0(m) There exist intensive differential movement around the mainshock /km /d Ordos Block in its western part, which has higher seis- 4,0-4.5 40 46 4.5~5.0 40 92 micity from history to now. The conjunction between 5.0~5.5 50 183 North China Subplate and South China Subplate is Qin- 5.5---6.5 50 365 ling Fault Belt and Dabieshan Fault Belt; its northern bor- 6.5-7.0 IO0 548 7.0~7.5 I O0 730 der runs from Hetao fault trough series in the west, across 7.5-8.0 150 913 Zhangjiakou-Bohai active tectonic belt into the Bohai Sea to the east, which is a strong seismicity belt; its western edge is the eastern part of Helanshan Fault Belt and Niushoushan Fault Belt, which is an important geomorphic division line. There are two NNE strike fault belts, i.e., the east edge of Ordos Block and Tanlu Fault Belt, which divide North China Subplate into three parts (Ma, 1987). 2.1.1 Zhangjiakou-Bohai earthquake region Zhangjiakou-Bohai earthquake region lies in the north of North China Subplate, including Xuanhua-Huaian Basin and Yanqing-Huailai Basin, along with the border of Yanshan Mountain and North China Plain Fault Trough Series, from Changping, across Fengnan, along Haihe Fault to Bohai Sea. Zhangjiakou-Bohai earthquake region is a strong seismicity region in North China Subplate. In our catalogue, there are two strong earthquakes occurred in Zhangjiakou-Bohai earthquake region (September 2, 1679 Sanhe Ms=8.0 earthquake and July 28, 1976 Tangshan Ms=7.8 earthquake in Hebei Province). Assuming the time of these two strong earthquakes to be 40 ACTA SEISMOLOGICA SINICA Vol. 12 the end of each active period, we can fit out the origin time and magnitude by analyzing the earthquake events in the two periods before each strong earthquake. The fitting curves are shown in Figure 3, the fitting results are listed in Table 2.

o 40C .~ 800 --~. ~z NZ + 2°c

I I 1700 1800 1900 2000 ~ 1400 1550 1600 1700 Year Year Figure 3 Strong earthquake fitting curves in Zhangjiakou-Bohaiearthquake region Circle with cross symbol is earthquake event occurred in the region in the period before the last strong earthquake, cross symbol is earthquake events occurred in the region after the fitting time in this period, solid line is the fitting curve Table 2 Strong earthquake fitting in Zhangjiakou-Bohaiearthquake region Real earthquake Fitting Tr/year Fitting Mr (Ms) Catalog time/year 2~ 1679 Sanbe Ms 8.0 1679 7.56 1456-1665 1.04 1976 Tangshan Ms=7.8 1983 7.43 1861 - 1966 0.32 * 2,2 in table represents the goodness of fitting, the less, the better, so the sime in the following tables 2.1.2 Shanxi earthquake region Shanxi earthquake region lies in the North China Subplate and to the east of Ordos Block. Stretching along the Fen-Wei Graben like an "S" shape, it comes from Yanqing-Huailai Basin in northeast, across Datong, Taiyuan, Linfen, Yunhe Basin to Gushi-Xi'an Basin. This earthquake region consists of a series of NNE and NE fault basins, and it has intensify SEE and SE horizontal extension, as well as it has well-developed NWW cross fault. In history, there occurred three strong earthquakes in Shanxi earthquake region, i.e., the Zha- ocheng Ms=8.0 earthquake on September 17, 1303; the Huaxian, Shaanxi Ms=8.3 earthquake on January 23, 1556 and the Linfen Ms=7.8 earthquake on May 18, 1695. We divide three earthquake periods in Shanxi earthquake region with each strong earthquake to be the end of each period. It has been 300 years since the last strong earthquake occurred in this region, and the time interval from the last period to now is longer than each one of the three earthquake periods. Does Shanxi earthquake region is in the end of this earthquake period? We use earthquake events from 1723 to 1989 to fit the next strong earthquake, which might occur in this region. The fitting curves are shown in Figure 4 and the results are listed in Table 3. Table 3 Strong earthquake fitting in Shanxi earthquakeregion Real earthquake Fitting Tf/year Fitting Mf (M~) Catalog time/year 22 1303 Zhaocheng Ms=80 1322 7.49 712-1291 1.27 1556 Huaxian Ms=8.3 1578 8.50 1305~1554 0.8 1695 Linfen Ms=7.8 1696 7.24 1557-1688 111 9 2004 7.24 1723-1989 0.618 The longer the time from now in the history, the more incompletely the earthquake events in our catalogue, and the less correct results we can get from fitting. As shown in Figure 4d, the fitting curve appears decrease, which is impossible in reality, although it is acceptable in mathematics. a is the power index of M0, and can adjust the ultimate magnitude Mf. The fitted Mr will de- No. 1 YANG, W. Z. et al: SEISMICITY ACCELERATION MODEL AND ITS APPLICATION 41 crease if a increase. By changing the a value in our fitting for Zhangjiakou-Bohai earthquake region and Shanxi earthquake region, we get different results, and we accept a=0.4, not 0.5 as given by Bufe and Varnes 0989) to San Francisco or given by Robinson (1997) to New Zealand. In one respect, the same value of a in different region may show the similarity of seismicity of these regions, such as San Francisco region and New Zealand are belong to intraplate Benioff strain type. In another respect, the low value of a in North China may show this region lies on intraplaie, with fewer middle earthquake events (5.0

400 J

0 ./ b- 1700 1800 1900 2000 1550 1600 1650 1700 Year Year 15oo1 E80C-- o~z I: I ~z ~ lOOOt- I ~24oo 5ool- ) ~E ~E c .~.= 1300 1400 1500 1600 600 800 1000 1200 Year Year Figure 4 Strong earthquake fitting curves in Shanxi earthquakeregion 2.1.3 Northern Ordos Block earthquake region North Ordos Block earthquake region lies to the northern part of Ordos Block. Its west edge from Linhe, western part of Inner Mongolia Autonomous Region, and it runs across Wuyuan, Baotou, Hohhot and Horinger to its east edge Chongli in Hebei Province. This region is under the control of Langshan-Serge-Wula-Daqingshan normal fault, and it includes two existing faults: Baotou Fault and Wuyuan Fault. Compared with other edge parts of Ordos Block, the seismicity of Northern Ordos Block is lower, and the largest earthquake occurred in this region of this cen- tury is the Baotou Ms=6.4 on May 4,1996, and the time interval between it and the former Hor- inger Ms=6.2 is 20 years, furthermore, the time interval between Horinger Ms=6.2 and its former Wuyuan Ms=6.2 is 42 years. It seems the time interval between neighbor Ms>6 earthquake is get- ting smaller as time goes by. In October 1997, an Ms=4.9 earthquake occurred in Linhe, west part of this region, three months later, an Ms=6.2 earthquake occurred in Zhangbei, east edge of this region. Does the seismicity of this earthquake region is in the end of this period? With the earthquake events from 1895 to 1996, we get the fitting results in Table 4. Table 4 Strong earthquake fitting in Northern Ordos Block eo:,nquakeregion Real earthquake Fitting Tr / year FittingMr (Ms) Catalog time / year 22 ? 2003 8.03 1895~1996 0.295 8 2.2 Chuan-Dian Block Chuan-Dian Block is a rotating block in the transform belt at the southeast edge of Qing- Zang Subplate. Its northeast border is Xianshuihe fault and the spreading of lithosphere material in 42 ACTA SEISMOLOGICA SINICA Vol. 12 its southeast part is blocked by the Yangtze Paraplatform. Its southwest spreads to SSE, thus make the block come into intense left-lateral horizontal differential movement, which built many earthquake faults and fractured zones. Compared with North China Subplate, Chuan-Dian Block be- have higher seismicity. 2.2.1 Zhenkang-Bijiang earthquake region Zhenkang-Bijiang earthquake region lies on the southeastern part of Tibet Subblock of QingZang Subplate, and its eastern edge is Nujiang fault in SN strike. The major faults in it are in NNE strike. The Longling earthquake on May 29, 1976 lies in granite rock, surrounded by Nu- jiang fault, Wanding fault and Longling fault. There had been Quaternary volcanic activity in the west part of this region, with outcropping granite everywhere (Ma, 1989). We use the earthquake events in this region from 1757 to 1973. Because not knowing a value in this region, we try three kinds of a. The results are listed in Table 5. From Table 5, we can see a =0.5 fitting is better, which demonstrates the characteristic of the seismicity region is similar to that of intraplate seismic region. Table 5 Strong earthquake fitting in Zhenkang-Bijiang earthquake region Real earthquake a Fitting Tr/year Fitting Mr(Ms) Catalog time/year 22 1976 Longling Ms=73 0.5 1977 7.8 1757~1973 0.833 Longling Ms=7.4 0.6 1984 7.61 1757-1973 0.76 0.7 1985 7.4 1757~1973 0.922 Note: There is nearly 3.972x108 N.m energy release in a Ms=7.3 earthquake, and there is nearly 4.721×108 N.m energy release in a Ms=7.4 earthquake, in addition, there is nearly 9.419x10 s N.m energy release in a Ms=7.8 earthquake 2.2.2 Gejiu-Qiaojia earthquake region Gejiu-Qiaojia earthquake region lies in the southeast of Chuan-Dian Block in Qing-Zang Subplate, the SN strike left-lateral slip Xiaojiang Fault runs through the whole region. The southwest is right-lateral slip Honghe Fault, and we divide the other boundaries according to regional seismicity. In 1970, a Tonghai Ms=7.6 earthquake occurred in NW Chuxiong-Tonghai Fault. There are three earthquakes with Ms>7 occurred in Gejiu-Qiaojia earthquake region, and they are Tonghai Ms=7.0 on August 8, 1588, Dongcuan Ms=7.8 on August 2, 1733 and Tonghai Ms=7.6 on January 5, 1970. We set the three strong earthquakes to be the end of three periods in this region. The fitting results are shown in Table 6. Table 6 Strong earthquake fitting in Gejiu-Qiaojia earthquake region Real earthquake a Fitting Yf / year Fitting Mr (Ms) Catalog time / year 22 1588 Tonghai Ms=7.0 0.35 1584 7.41 1506-1577 0.126 1733 Dongcuan Ms=7.8 0.35 1730 6.6 1599~1725 0.763 1970 Tonghai Ms=7.6 0.4 1976 7.62 1850~1969 0.365 Because the tectonic stress field of this region is complex and the energy acceleration and release in this region is effected by several directions of stress, thus the result of fitting by seismicity acceleration model is not very well. The a values change from 0.3 to 0.7. 2.3 Xinjiang Subplate The characters of tectonic in Xinjiang Subplate are palingenic mountain and block basin. The active fracture belt between mountain and basin thrusts to the basin with left-lateral or right-lateral slip component. The strong earthquakes are mainly distributed in the south and north sides of Tianshan Mountain. 2.3.1 Bole-Tuokexun earthquake region Bote-Tuokexun earthquake region lies between the south edge of Jungger Block and Tian- No. I YANG, W. Z. et al: SEISMICITY ACCELERATION MODEL AND ITS APPLICATION 43 shan Block, belonging to the middle section of Tianshan earthquake region. The main faults con- sist of several fault belts in NWW strike. The major active faults are Poluokeyi Fault and Qing- shuihe Subfault. There are Yining Ms=8 on March 8, 1812 and Malashi Ms=8 earthquakes on De- cember 23, 1906 occurred in this region, and the time interval is 94 years. Because of lack of history earthquake events before 1900, we use earthquake events in 1953 to 1996 in the region to fit, and get the result with a equal 0.4, 0.5, and 0.6, respectively. The fitting results are shown in Ta- ble 7. Table 7 Strong earthquake fitting in Bole-Tuokexun earthquake region a Realea~hquake FiaingTr/year FiUingMf(Ms) Ca~logtime/year 22 04 ~ 2024 7.8 1953-1996 0.827 0.5 ? 2026 8.02 1953-1996 0.642 9 0.6 ? 2014 7.15 1953-1996 103 2.3.2 Ayinke-Wuqia earthquake region Ayinke-Wuqia earthquake region lies between the north edge of Tarim Block and Tianshan Block, belonging to the southern section of Tianshan earthquake region. The major faults are Keping fault and Totehongpaiz fault in NNE strike. In history record, there had an Atusi Ms=8 on August 22, 1902 in this region. If the earthquake period of this region is similar to Bole-Tuokexun earthquake region, nearly 100 years, then this region is just in the end of this period. With the earthquake events in 1904-1996, we get the following list. Table 8 Strong earthquake fitting in Ayingke-Wuqia earthquake region Real earthquake Fitting Tr / year Fitting Mr (M~) Catalog time / year 22 1961Bachu Ms=6.6 November, 1960 6.12 1904-1960 0.568 7 Bachu Ms=6.8 November, 1960 6.5 1904~1960 0.493 2 1996 Jiashi Ms=6.9 July, 1996 6.68 1961-1995 0.703 6 ? 2028 • 9.1 190,;~i996 0.927 2 The first and second rows of Table 8 are the fitting results of Bachu Ms=6.6 and Ms=6.8 with different a. The first row with a=0.5 and second row with a=0.4. Compare with first row and second row, we set a=0.4 for the region. With the earthquake events in 1961-1995, we fit the Jiashi Ms=6.9 in 1996 (Table 8). Because Ms=6.9 is not a strong earthquake compared to Atushi Ms = 8.0 in 1902, so with earthquake events in 1904-1996, we try to fit the strong earthquake in this earthquake period, the fitting result is Ms=9.1.There will never occur a strong earthquake larger than Ms=8.6 usually, and in fact the Ms=9.1 means the expected total energy release in this region between 1996-2028. Besides the 7 regions studied above, we have tried to divide studying region in Taiwan, Bo- hai and Xianshuihe Fault Belt, but maybe the seismicity acceleration model does not fit to these regions and the fitting results seems not good. Different from the seismicity in the Chinese Mainland, the frequency of earthquake with Ms > 6 is higher in Taiwan earthquake region. Although there exist some sense of change from weak to strong in seismicity of Taiwan earthquake region, the cumulative energy release curve is nearly linear without an accelerating process in a long time from weak to strong. Therefore, we explain that the energy store in Taiwan earthquake region does not similar with which of the mainland. Taiwan earthquake region lies on the subduction belt between the Pacific Plate and the Eurasia Plate, there is no long-term store of energy in it, and it has been in a state of energy input and out- put balance. 44 ACTA SEISMOLOGICA SINICA Vol. 12

3 Discussion Before the occurrence of strong earthquake in a region, the level of seismicity is increased with some power index of remain time. In many regions, with the seismicity acceleration model, we can analysis the seismicity of studied region quantitatively. By studying those earthquake events in the last period, we can get some character constants of this region, such as a, then predict the strong earthquake in the future by analysis these earthquake events in this period. It indicates that this model is adapt to analysis seismicity of intraplate region as well as that of interplate region by the fitting results of several earthquake regions in China. As stated in the introduction, the seismicity acceleration model is an experiential statistical model, and researchers can not give convinced explain on the power index relationship between cumulative moment and remain time at present under this condition, which people could not get adequately comprehension of the occurrence mechanism of earthquake. In this article, we think the subcritical crack growth theory could provide a better physical explain to seismicity acceleration model, and with the subcritical crack growth theory we deduced equation (15). The seismicity acceleration model could be based on the theory of subcritical crack growth in fracture mechanics of rock, which restrains the use of the model. Firstly, selection of a region is important. We should make sure the tectonic field is steady in the earthquake region for a long period. Secondly, the selected region should have an energy store environment, and the regional rock is mainly characterized by brittle. The power index of cumulative moment a can be used to describe the character of regional seismogenic, and the value of a ranges from 0 to 1. The higher the value of a is, the higher of the seismicity in a region. The value of a in intraplate (Benioff belt) is 0.5, and the value of a in intraplate (such as North China Subplate) is 0.4, but some regions with high seismicity in intraplate may have a higher a. There exist some similarities on earthquake period between neighbouring earthquake region. In North China Subplate, the last earthquake period of Zhangiiakou-Bohai earthquake region is nearly 300 years, and so as the Shanxi earthquake region. In Xinjiang Subplate, the last earthquake period of Bole-Tuokexun earthquake region is 94 years and this period of Ayinke-Wuqia earthquake region may be 100 years. There is also similarity in the period ended time. Sanhe Ms=8 occurred in 1679 in Zhangjiakou-Bohai earthquake region, and 14 years later, Linfen Ms=7.8 earthquake occurred in Shanxi seismic region. In 1906 Malachi Ms=8 earthquake occurred in Bole-Tuokexun earthquake region, 4 years after the Atushi Ms=8 earthquake in Ayinke-Wuqia earthquake region. The completeness and correctness of earthquake catalogue are very important to the fitting results. Although our catalogue begin from 786 BC, but nearly all these earthquake events before 1900 are come from history books, thus as the time traced back, there were fewer and fewer earthquake occurred in history record, and there were nearly no record during war. Lack of history events make the fitting for historical strong earthquake more difficult, we can see it from the fitting curve for the first earthquake period of Shanxi earthquake region. We acknowledge useful discussions with the following individuals: Prof. YAO-LIN SHI, Dr. JIE LIU and LIE-YUAN ZHU, and we thank for Dr. DA-LIN ZHENG providing related earthquake catalogue. The completion of this article is benefited from Dr. R ROBINSON's more detailed re- No. 1 YANG, W. Z. et al: SEISMICITY ACCELERATION MODEL AND ITS APPLICATION 45 port. We also thank for the communication with Dr BUFE and Dr RUSSELL ROBINSON. During the modification of this article, Prof. DAVID VERE-JONES and Dr. RUSSELLROBINSON give us good advice and provide some help on communication.

This study is sponsored by Chinese Joint Seismological Science Foundation (198044), New Zealand Asia 2000 Plan and IGNS agency.

References

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