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Spatial bias in b-value of the frequency–magnitude relation for the Hong Kong region
Journal of Asian Earth Sciences 20 (2001) 73±81
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Spatial bias in b-value of the frequency±magnitude relation for the Hong Kong region L.S. Chan a, A.M. Chandler b,* a
b
Department of Earth Sciences, The University of Hong Kong, Pokfulam Road, Hong Kong Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong Received 6 October 1999; revised 31 August 2000; accepted 23 February 2001
Abstract The onshore and offshore regions in South Guangdong around Hong Kong exhibit different b-values of the G±R relation. The two regions have yielded b-values of 0.85 and 0.67, respectively, based on the most complete seismic database for the period 1970±1995. Tests on the completeness of the seismic catalogue and dominance of local source zones suggest a fundamentally complete record for M $ 3 events and the spatial bias in the b-values cannot be explained entirely in terms of these two factors. The subcatalogue of onshore events with focal depth ^ 6 km has yielded an essentially identical b-value as that for the offshore region, thus revealing a weak upper crust with diffused seismicity overlying a relatively strong lower crust. The present study shows that spatial bias in the b-value can be resolved by a proper analysis of the seismic data. The interpretation is also consistent with the model that the relative motion between South China and the South China Sea is diffused over a broad fault zone along the coast, with a higher b-value in the upper crust and the lack of a single wrench fault. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: b-Value; Frequency±magnitude relation; Hong Kong
1. Introduction Concerns about potential earthquake hazard in the rapidly developing region of South China have led to the undertaking of several studies on the seismicity of the region in recent years (Lee et al., 1996; Chan and Zhao, 1996; Lin and Xie 1996; Pun, 1998; Chandler and Lee, 1999). Such studies have yielded crucial information for the earthquake risk assessment and may facilitate the decision whether earthquake-resistant design codes should be adopted for the region. The study area, located at latitudes 208N±268N and longitudes 1108E±1178E, is referred to in this paper as the `Hong Kong Region'. In a companion paper, Chandler et al. (2001) have presented a deterministic seismic hazard analysis. For the purpose of specifying a worst-case scenario for engineering seismic risk assessment, such an analysis requires the designation of a maximum credible earthquake (MCE). The determination of the MCE requires an accurate characterization of the frequency±magnitude relation of the
* Corresponding author. Tel.: 1852-2859-1973; fax: 1852-2559-5337. E-mail address: [email protected] (A.M. Chandler).
region. Previous studies have revealed a spatial bias in the b-value of the frequency±magnitude relation of the region (Lee et al., 1996; Pun, 1998). The onshore region appears to possess signi®cantly higher b-values than the offshore region. Since the b-value in the G±R relation plays a vital role in the formulation of realistic design earthquakes for the region, the discrepancies in the seismic parameters for the onshore and offshore region should be given a detailed analysis. Speci®cally, we need to determine if such discrepancies are statistical artifacts due to the incompleteness of the seismic record or re¯ect actual differences in the seismogenic nature of the two regions. Another important aspect concerning the estimation of the MCE is the rate of tectonic motion and whether the release moment is likely con®ned to a single fault or diffused over the region. Instantaneous plate motion data that have recently become available have shed new light on the nature of the seismicity of the region. It will become possible in the future to evaluate certain seismic parameters for the region based on kinematic data. For the time being, however, the short observation record renders it dif®cult to estimate precisely the seismic release moment based on plate motions.
1367-9120/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 1367-912 0(01)00025-6
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L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
110E
112E
113E
115E
116E
118E 26N
26N M=2.0-2.9 M=3.0-3.9 M=4.0-4.9 M=5.0-5.9
G
HF
M=6.0-6.9
Shantou
24N
24N
Latitude,deg N
Heyuan HF W
Guangzhou Zhaoqing
Haifeng Shenzhen Macau
22N
F CN
HongKong 22N
Yangjiang
Hainan
20N 110E
112E
113E
115E
116E
20N 118E
Longitude, deg E Fig. 1. Seismicity and major fault system of Hong Kong Region. (CNF: Changle±Nanao Fault, WHF: Wuhua±Haifeng Fault; GHF: Guangzhou±Heyuan Fault).
2. Physical implications of b-value Gutenberg and Richter (1956) showed that the frequency±magnitude relation (G±R relation) for a region could be represented by logN M a 2 b M
1
where N(M) is the annual number of earthquakes with magnitudes in a particular range, and aand bare constants. Although the constants are determined empirically from seismic catalogues, it is imperative to understand their physical meaning. The nature of the a-constant is well known; it is directly related to the intensity of the seismic activity of the region. The physical implication of the bvalue, however, is not as obvious. Aki (1987) suggested an association between the b-value and the fractal dimension of the fault system. Many recent studies have also shown that the b-value is a scale invariant that is related to the spacing or clustering properties of epicenters or distribution of fault segments (Huang and Turcotte, 1988; Lapenna et al., 1998; Nanjo et al., 1998). Oncel et al. (1996) reported a lower b-value associated with a higher fractal dimension, and, hence, a greater degree of clustering of epicenters. The b-value for a region not only re¯ects the relative proportion of the number of large and small earthquakes in the region, but is also related to the stress condition
over the region. Kebede and Kulhanek (1994) have shown that spatial variations in the b-values in the East African Rift system can be related to crustal stress condition, with relatively lower b-values (0.5±0.8) observed in segments of the rift system experiencing high stress. The observation is consistent with experimental results reported by Mogi (1962), Main (1992) and Main et al. (1992). Higher b-values were reported for areas of greater material heterogeneity as well as lower stress intensity (Main et al., 1992). Temporal variations in the b-value have also been linked to the occurrence of seismic quiescence (Wang and Diao, 1994; Yamashita, 1998; Chong, 1983; Apostol et al., 1985; Rotwain et al., 1997; Al-Amri et al., 1998) and aftershock sequences (Nanjo et al., 1998). An earthquake sequence occurring near Hong Kong also exhibited a reduction in the b-value from the long-term average of 1.2 to about 1.0 during the month prior to an M 4.2 event (Lin et al., 1985). The study by Njike et al., 1992 shows lower b-values (0.95±1.15) in areas of well-de®ned faults and higher b-values (1.04±1.23) where diffused seismicity exists. Their study also revealed a higher b-value (1.01±1.09) for seismicity within the upper 5 km than the b-value (0.82±0.92) for earthquakes with focal depth .10 km. Given the vital seismotectonic implications of the bvalue, it is in the interest of both geoscientists and engineers to acquire an accurate description of the G±R relation of a region. However, substantial errors in b-values can be
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
caused by an incomplete catalogue, which could in turn, lead to erroneous moment release estimates (Abe, 1995; Stein and Hanks, 1998). Seismic catalogues are inherently incomplete, and the fractions of missing events generally increase with a decreasing magnitude range, resulting in a reduction in the b-values when small magnitude events are included in the analysis. But in some cases, small earthquakes are really not as numerous as a constant b-value extrapolated from larger events would predict (Rotwain et al., 1997). A completeness test of the seismic record used is therefore conducive to the interpretation of any b-values obtained. The choice of the statistical method used for deriving the b-value is also a critical consideration. Commonly the two empirical constants in the G±R relation are derived using the linear regression method on grouped magnitude data. Bender (1983) presented a detailed analysis of the dependence of the b-value on the interval size, maximum magnitude, sample size, and the data ®tting techniques. Considerably different b-values and the associated standard errors may be obtained from the same data set because of the different assumptions regarding these parameters (Bender, 1983). While no single data ®tting technique can yield accurate b-values from an inherently incomplete seismic catalogue, it is important to ensure that the spatial variations in the b-value obtained from different data-®tting techniques are consistent with each other. 3. Seismotectonic features of the Hong Kong Region The Hong Kong Region in this study is part of the South China Maritime Fold Belt that was formed predominantly during the mid-late Mesozoic Yenshanian movements in East Asia. The dominance of east±northeast-trending structures in the area probably resulted from a collision along the eastern coast of the South China Block during the Late Jurassic through Early Cretaceous (Wang and Lu, 1997). Mesozoic volcanics formed within volcanogenic depressions along a ductile shear zone known as the Linhuashan fault zone which extends from Fujian province in eastern China in a southwesterly manner through Hong Kong. Cenozoic tectonic movements in the region are characterized by formation of fault basins developed from a north± south directed minimum stress (Li and Rao, 1994; Xia et al., 1994), probably associated with the opening of the South China Sea during the Paleocene through mid-Miocene. The fault systems are well developed in the coastal areas of the Guangdong and Fujian provinces. The northeasttrending and northwest-trending systems are particularly notable in the study area. The most important northeasttrending fault systems consist of the Changle±Nanao Fault that runs along the coastline of South China, the Wuhua± Haifeng fault extending from Hong Kong to Wuhua, and the Guangzhou±Heyuan Fault farther to the north (Fig. 1). These faults controlled the occurrence and the evolution
75
of the Pearl River Estuary exterior basin, allowing for the deposition of some 7000 m of Tertiary and about 250 m of Quaternary sediments. Sediment isopachs show an elongation along a northeasterly direction. A marine geophysical investigation conducted by the Guangzhou Marine Geology Bureau in 1992 showed that these faults cut across Quaternary deposits; but no indisputable evidence for active faulting could be recognized on any of the seismic pro®les of the intensely covered Hong Kong Harbour. We are not aware of any published geodetic measurements on the motion of the northeast-trending fault systems. Measurements of movement on one particular fault in the Shenzhen area over 1986±1987 revealed a net dextral motion of about 0.3 mm/year (Chen, 1989). The accuracy of the result, however, cannot be assessed. The northwest-trending faults in the study area are less prominent but appear to be younger than the northeasttrending ones based on crosscutting relationship. Most of the recent seismicity in the area occurred on northwesttrending faults, including four historical events with magnitude M $ 6 in the Shantou area (Zhang, 1982). Results of thermoluminescence dating revealed activity as recent as 33,300 ^ 2700 years B.P. (Ding et al., 1997; Ding and Lai, 1997; Lee et al., 1997). Focal mechanisms have revealed a predominantly sinistral motion along these faults (Wang and Lu, 1997). The offshore region of the study area is located on the continental shelf and marked by the presence of a pair of northeast-trending depressions extending from Shantou westwards to Hainan Island (Xia et al., 1994). The depressions are divided into fault blocks bounded by a system of northeast-trending faults and cut by less prominent, northwest-trending ones. Results from seismic exploration reveal a gradual seaward decrease in crustal thickness from about 30 km in Guangzhou to about 27 km in Hainan Island (Feng et al., 1981; Xia et al., 1994; Pigott and Ru, 1994). The cause of the neotectonic movements of the area is enigmatic. During the mid-Oligocene to the mid-Miocene, sea ¯oor spreading occurred in a N±S direction in the South China Sea. Little is known about the post-Miocene geodynamic setting of the margin. Finite element models have revealed a maximum principal stress directed at N688W in the Pearl River Delta area (Sun and Huang, 1995). Geodetic measurements from the GEODYSSEA project during 1994±1996 have helped to identify the existence of the Sunda Block, which exhibits a distinct differential motion with respect to the Eurasian plate (Wilson et al., 1999). Since the Sunda Block includes the South China Sea, the relative motion between Sunda Block and Eurasia must also yield an effect on the continental margin of China. The kinematic solutions have revealed plausibly a right-lateral motion between the two tectonic blocks. Such a relative motion must necessarily be absorbed by the coastal faults along Guangdong and Fujian Provinces. The inferred sense of motion is consistent with focal plane mechanism of the recent earthquakes in the area. The work by Pubellier (1998)
76
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
Fig. 2. Record of events during 1960±1995.
has suggested a slip rate of about 1 cm/year between South China and the South China Sea. It is not known, however, if the inferred differential motion is distributed across a number of faults or manifests itself in the form of aseismic creep. Nevertheless, the estimated slip rate is about half to one order of magnitude less than that of western North America but substantially greater than that of the eastern North America. 4. Earthquake data for the region Two seismographic networks are operated independently in the region, one by the Hong Kong Observatory and the other by the Seismological Bureau of Guangdong Province. The Guangdong network comprises 17 seismographic stations and two local observation stations distributed over the entire province of Guangdong. The Hong Kong region began recording in 1921 (Geotechnical Control Of®ce, Table 1 b-values of Hong Kong Region for different magnitude ranges for 1973± 1995 Range
$ 4.5 $ 4.0 $ 3.5 $ 3.0 $ 2.5 $ 2.0 $ 1.5 $ 1.0
Whole region
Onshore region
Offshore region
n
b-value
n
b-value
n
b-value
36 80 247 743 2159 5050 8196 13654
0.72 0.71 0.75 0.78 0.81 0.82 0.80 0.77
28 66 204 634 1833 4362 7326 12753
0.82 0.80 0.82 0.85 0.86 0.87 0.84 0.81
8 14 43 109 326 688 870 901
0.60 0.58 0.63 0.67 0.70 0.72 0.70 0.66
1991; Pun and Ambraseys, 1992). After a series of destructive earthquakes in China in the 1960s, many seismographic stations were set up in the vicinity of the Hong Kong region and the detection capacity increased remarkably. As shown in Fig. 2, the annual earthquake frequency recorded in the Hong Kong region increased drastically in 1970. The seismic network is stated to be capable of detecting M $ 1.0 events for most parts of the Guangdong province. In terms of the completeness of the seismic record, however, the monitoring capability of the province is considered as M $ 2 for the onshore and M $ 3 for the offshore region (Jiao et al., 1990). In the present study, the earthquake record of Guangdong Province for the duration 1 January 1970±30 June 1995 from the Seismological Bureau of China was used. A total of 13,654 earthquakes were recorded during the 25-year interval. The record contains information of epicentral location, focal depth, date of occurrence, origin time, magnitude, and precision estimates for earthquakes of local magnitude M $ 1.0 that occurred within the time interval. The earthquakes in the onshore region are distributed in a broad belt about 300 km in width that runs parallel to the coast of South China (Fig. 1). Within this belt, most of the earthquake activities are concentrated in two regions near Heyuan and Yangjiang. Earthquakes that occurred near these two `source areas' account for about 80% of the recorded events onshore. The offshore region, on the other hand, is characterized by relatively fewer but larger earthquake events. Several M $ 6 earthquakes occurred in this region during the period. The number of recorded earthquake events with M , 3 is also much smaller than that of the onshore region. Because the two regions have such a different seismicity, the seismic data were divided into two
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
Fig. 3. Frequency±magnitude relations for the Hong Kong region and the two subregions. The lines are linear regression ®ts of the data.
sub-catalogues using a line that runs roughly along the coastline of South China. A G±R relation was formulated for each of the two sub-catalogues. The numbers of recorded events, according to different magnitude ranges, are shown in Table 1. 5. G±R relation of the Hong Kong Region Previous seismicity analyses have produced a range of bvalues from 0.7 to 0.9 for the region (Geotechnical Control Of®ce, 1991; Lam and Fong, 1982; Pun and Ambraseys, 1992; Editorial Committee of Seismic Zoning Map of China, 1992; Chan and Zhao, 1996). Pun and Ambraseys (1992) gave a b-value of 0.75 based on 490 years of record of MS $ 4.5 events. Lam and Fong (1982) obtained a bvalue of 0.85. Based on the instrumental record from 1973±1995, Chan and Zhao (1996) determined the bvalue to be 0.88 using maximum likelihood estimator method for earthquakes with magnitude ML $ 2.0. Wong et al. (1998) gave a b-value of 0.69 based on 100-year record of M $ 4 earthquakes. None of these studies, however, has taken into account the effects of data incompleteness or the spatial distribution of seismic events in the region on the seismic parameters. While the b-values obtained by these studies are seemingly acceptable, most of these studies were based on selected magnitude ranges or time windows and ignored earthquake records at small magnitudes. In the study by Lee et al. (1996), the area in the vicinity of Hong Kong was divided into 16 source zones. A frequency± magnitude relation of each zone was determined based on the seismicity of the zone. The source zones within the land area were grouped as the `inner' zone, while those located offshore made up the `outer' zone. The b-values obtained for the two zones are, respectively, 0.80 and 0.56 based on a
77
combination of both historical and instrumental seismicity data (Lee et al., 1996). We have re-computed the G±R relation using the presumably complete instrumental seismic record for the period 1970±1995 provided by the Center for Analysis and Prediction of the State Seismological Bureau of China. In order to carry out a meaningful statistical analysis of the seismicity of the region, we took into account the various magnitude ranges that have been used for earthquake measurements in the different reports and the developments of the instrumental network in the region. Fig. 3 shows the plots of the earthquake frequency against the magnitude for the onshore, the offshore, and the entire region. The least-square regression method was used to obtain the G±R relationships using a magnitude interval of 0.5 for the grouped data. The different magnitude ranges were de®ned based on the minimum magnitude included in the regression analysis. Based on the local magnitude scale, the G±R relations obtained have yielded b-values in the range of 0.80±0.87 for the onshore region, and 0.58±0.72 for the offshore region (Fig. 3). As shown in Table 1, the b-values of the offshore data are consistently 0.14±0.22 less than that of the onshore region for the different magnitude ranges. Such a signi®cant difference between the b-values of the onshore and the offshore region warrants a detailed examination. In the sections below, we will discuss the following possibilities that may have caused the spatial bias in the b-value: 1. 2. 3. 4.
incompleteness of the seismic catalogues; dependence of the b-value on focal depth; method of computing the b-value; and domination of the b-value by individual source zones.
5.1. Incompleteness of the seismic catalogues The detectability of a seismic network can substantially modify the b-value and the estimated average magnitude (Shi et al., 1992). It is vitally important to determine if the difference in the monitoring capability and incompleteness of the seismic record could have resulted in the observed spatial bias in the b-value of the two regions. The characteristics of the data set, as well as the method used to estimate the b-value, can both contribute to variations in the b-value obtained. Mulgaria and Tinti (1985) and Tinti and Mulgaria (1985) have devised statistical procedures to identify periods within a seismic catalogue for which the seismic record is considered complete. Unfortunately, no single method can provide a measure of the absolute completeness of the seismic catalogue based on the catalogue itself. Almost all methods for evaluating the absolute completeness of a seismic catalogue require the condition to know if the reporting system which generated seismic data had, at least for some time intervals, the capability to detect all earthquakes in a particular magnitude range. It seems reasonable, however, to assume that all largest events are
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L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
Table 2 Completeness test of seismic catalogues based on method by Rydelek and Sacks (1989) (n, number of events; R, calculated resultant vector length; Rc, p critical length for unbiased data, given by Rc 1.73 n at 95% con®dence level) Onshore region
Offshore region
M range
n
R
Rc
n
R
Rc
^ 5.0 4.5±4.9 4.0±4.4 3.5±3.9 3.0±3.4 2.5±2.9 2.0±2.4 1.5±1.9 1.0±1.4
14 15 38 138 430 1201 2530 2965 5427
0.9 0.9 1.8 8.2 15.0 104.8 58.1 40.9 193.0
6.5 9.3 14.2 24.8 43.6 74.1 114.3 148.1 127.5
4 5 6 29 66 214 361 183 30
0.2 1.5 2.1 5.1 2.2 9.9 3.9 9.0 2.7
3.5 3.9 4.2 9.3 14.1 25.3 32.9 23.4 9.5
reported, and there is a progressive decline in the seismic monitoring capacity towards the smallest events. In other words, the fractions of missing record increase with decreasing magnitude. Also, since small events are only detectable by the local seismographic network, the monitoring capability of a region depends much on the presence of local seismometers as well as the intensity level of culturally produced ambient noises and ground-transmitted vibrations. Not only do seismic catalogues tend to have a less complete record at lower magnitude ranges, they are also less complete for earlier times. The number of events recorded during 1960±1995 for the Hong Kong Region is shown in Fig. 2. The chart reveals an abrupt increase in the number of recorded event since the 1970. The particular database used in the present analysis which spans the 25year interval since 1970, however, appears to have been minimally affected by data incompleteness. We have applied two tests to determine if this particular database is suitable for the derivation of the G±R relation. The ®rst test is based on how the b-value is affected by the omission of smaller events from the database. Since there is plausibly a greater omission of lower magnitude events from the record, the b-value should become progressively smaller by inclusion of the next lower magnitude interval. Based on this assumption, the b-values were computed for different magnitude ranges. As shown in Table 1, the bvalues of the inner zone are 0.80, 0.85 and 0.87 when the minimum magnitude used was M $ 4, M $ 3 and M $ 2, respectively. For the offshore area, the b-values obtained are 0.58, 0.67 and 0.72 when the same magnitude ranges were used. There are no signi®cant changes in the b-value by the inclusion of events in the next smaller magnitude interval. In fact, the b-values actually increased slightly when a lower magnitude range was included in the calculation. The result suggests that data incompleteness has not signi®cantly affected the b-value. Rydelek and Sacks (1989) proposed a rather interesting method to evaluate the completeness of the seismic data through a statistical analysis of the diurnal bias of the
seismic record. The method is based on the assumption that more nighttime events would have been recorded when the surrounding environment is less noisy. In this method, the time of occurrence of an event is treated as a unit vector with a direction given by the time, much like the hour arm on a clock. The vectors for a particular magnitude range are then added and the total length of the resultant is determined mathematically. The null hypothesis is that these vectors are randomly distributed over a 24-h period, giving a resultant vector R with a small length. Rydelek and Sacks (1989) referred to the critical distance as a `phaseout' distance; a set of events would be considered as biased and incomplete if the resultant vector exceeds the `phaseout' distance. The test is entirely inherent in nature, and requires only an accurate knowledge of the time of occurrence and not any presumed seismic parameters or knowledge of monitoring capacity. As a second test for the data incompleteness, we have applied a similar procedure to the data set by comparing the resultant vector R computed to that expected for a random process. A reasonable value for the critical R at 95% con®dence level is given by p Rc 1:73 N 2 where N is the number of data points. The data sets for the two regions were grouped by magnitude of 0.5 intervals. The time of occurrence of each earthquake was converted into a directional vector. Each vector was then resolved into its components on the X- and Y-axes, and the length of the resultant vector was obtained by p R SX 2 1 SY 2 3 The number of events in each magnitude interval, and Rcand R-values computed based on Eqs. (2) and (3) are shown in Table 2. The computed R-values exceed the critical R at magnitude interval 2.5±3.0 for the onshore region. This strong diurnal bias for events can be taken as evidence for the incompleteness of seismic record for such a magnitude interval. While the magnitude intervals M 2.0±2.5 and 1.5±2.0 passed the completeness test, we conservatively considered the catalogue as complete only for M $ 3.0. The G±R relations obtained in the following sections are based on the subsets of data with M $ 3.0. 5.2. Dependence of b-value on focal depth A particularly interesting aspect of the seismic catalogue is the dependence of the G±R relation on the focal depth. Such a relationship between the b-value and the focal depth has also been observed in the seismic catalogue from the Pyrenees (Njike et al., 1992). In this analysis, we have divided the earthquake events in the onshore region into two groups based on the reported focal depth of the events. A G±R relation was computed for each of the two sets of data. The objective of this division is to determine the seismic parameters of the upper and lower crust events, in
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81 Table 3 Reduced b-value after removal of data from two source zones for M . 3.0 using a space window of 26 km Dataset
n
b
Onshore total Heyuan source zone events removed Yangjiang source zone events removed Heyuan space window Yiangjiang space window Both source zone events removed
634 303
0.85 0.72
483
0.75
331 151 152
0.97 0.93 0.74
4b
where b is the maximum likelihood estimator, M the mean magnitude, and Mmin the smallest threshold magnitude considered. For a signi®cantly large sample size, n, the standard error of the b-value is approximated by
s b 2:30b 2 s M
5a
where 2 =n n 2 1 s 2 M S M i 2 M
order to compare them with those of the offshore region. Of the 634 onshore events with a magnitude of M $ 3.0, 177 had a reported focal depth exceeding 6 km. As shown in Table 3, the b-value obtained for the lower crustal events is 0.63, which is similar to the b-value for the offshore region. The `shallow' events with D , 6 km, on the other hand, exhibit a b-value that is close to unity. The results thus suggest a vertical variation in the b-values in addition to the spatial bias. The results suggest that the generally larger number of small earthquake events in the upper 6 km may be due to the weaker strength of the upper crust which yields to applied stresses more readily, resulting in the more frequent occurrence of smaller earthquakes. If this is the case, the upper crust of the region probably exhibits a greater degree of hetereogeneity which favors a lower stress intensity and diffused seismicity. The lower b-value obtained for the deeper seismic data set suggests that the lower crust, on the other and, has a greater strength allowing for a relatively greater accumulation of strain energy. Seismic activities are also likely con®ned to distinct faults. We must caution, however, that the focal depths of the events may not be very well constrained. Small events with great focal depths are more dif®cult to detect, resulting in an inherently lower b-value for the deeper data sets. 5.3. Method of computation of b-value The method by which the b-value is calculated can have signi®cant bearing on the observed discrepancies between the b-value of the onshore and the offshore zones. The linear regression method commonly used by geophysicists to compute the b-value has a major disadvantage since the presence of even a few large earthquakes can in¯uence the b-value signi®cantly. Such a consideration has prompted many seismologists into developing alternative methods for its determination. A rather popular method is the maximum likelihood estimation (Aki, 1987). Shi and Bolt (1982) provided a set of equations for estimating the b-value and its associated standard errors. In that method, the b-value is given by b bloge
2 Mmin b 1= M
79
4a
5b
(Shi and Bolt, 1982). For any seismic catalogue, the magnitude at which the catalogue is considered `complete' can be used as the Mmin. The completeness analysis presented in above sections has also entailed the reasonable assumption to use M 3.0 as the threshold magnitude Mmin. Based on Eqs. (4a) and (4b), we have computed the seismic parameters and the associated errors for both the offshore and onshore regions. The three sets of data have yielded b-values as follows: Entire region: b 1.03; s (b) 0.05 (M 3.42; n 743) Onshore region: b 0.83; s (b) 0.03 (M 3.52; n 634) Offshore region: b 0.90; s (b) 0.10 (M 3.48; n 109) It is interesting to note that the discrepancy in the b-value has essentially vanished when the maximum likelihood method was used to estimate the b-values. Since the spatial bias in the b-value may be resolved by the use of different statistical methods, one may argue that the spatial bias in the b-value is merely a mathematical artifact. However, a dif®culty with the maximum likelihood method is that the sample size does not appear to have played a role in the determination of the b-value, and that the physical meaning of the governing equation is somewhat obscure. We are also not certain whether the b-value obtained using the maximum likelihood method has identical implications for the ratio of small to large magntiude events as that obtained by the linear regression method. Since the maximum likelihood method gives more relative weight to the data points in the middle range, it may yield less sensitive estimates of large magnitude events that are crucial for seismic risk assessment exercises. 5.4. Dominance of individual source zones Earthquakes that happened in the Heyuan and the Yangjiang areas, including aftershocks, account for over 80 and 75% of the total number of onshore events with M $ 1.0 and M $ 3.0 respectively. Because of their dominance, seismic parameters obtained from an untreated catalogue essentially represent seismogenic properties that are pertaining to the local source zones. The earthquakes in the relatively
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L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
Table 4 Difference between b-values of upper and lower crust for two data sets delineated by focal depth Dataset
n
b-value
Onshore events .6 km Onshore events ,6 km Offshore total
177 457 109
0.63 1.00 0.57
short-term catalogue which includes aftershocks from the larger events cannot be regarded as random events and the Poisson distribution that is often used in earthquake recurrence analysis would not be applicable. We have determined the b-values for the Hong Kong Region when earthquake events in these two source zones were deliberately omitted. To do so, we de®ned a space window around the epicentral zones of Heyuan and Yangjiang using a method akin to the one for aftershock removal suggested by Console et al. (1979). This space window is considered as the `in¯uence area' of a source zone. The radius of the space window in km, RW, is given by logR W 0:41M 2 1:25
6
where M is the magnitude of the largest event in the area. Since both source zones have produced M $ 6.0 earthquakes historically, a slightly more conservative value of M 6.5 was used. Based on Eq. (6), the radius of the space window obtained is 26 km. In the subsequent analysis, all events that occurred within this space window have been removed and the G±R relations were re-computed. We have not de®ned a time window as often done for aftershock removal since our objective was not to remove aftershock events but to ®nd a method to determine the in¯uence area of the two source zones. As shown in Table 4 the b-values of the onshore zone were reduced from 0.85 to 0.72 and 0.75 respectively, when events within the Heyuan or the Yangjiang space window were individually omitted from the data catalogue, and from 0.85 to 0.74 when events within both space windows were removed. The two source zones have b-values that are higher than the rest of the region. Although the reduction in the b-values by omitting events in the two source zones is still insuf®cient to account for all of the spatial bias in the bvalue between the onshore and offshore region, the higher bvalues for the onshore region can in part be attributed to the seismogenic characteristics of individual source zones. 6. Conclusions A thorough seismicity analysis requires an examination of all possible factors that may have given rise to any bias in the G±R relation. In the above analysis, we have shown that the seismic catalogue used in this study is essentially complete for M $ 3.0 for the Hong Kong Region, and data incompleteness may not have signi®cantly modi®ed
the b-values in the G±R relations. By limiting the data record to events with focal depth .6 km for the onshore region, a b-value comparable to that of the offshore region can also be obtained. It is tempting to attribute the higher bvalue to a greater structural heterogeneity of the upper crust of the onshore region than that of the lower crust. But we have also demonstrated that the spatial bias in the b-value of the onshore and offshore regions essentially disappears when the maximum likelihood estimate is used in determining the G±R relation. By isolating several local source zones, the b-value of the onshore region was also brought into a closer agreement with that of the offshore region. The observed difference between the b-values of the onshore and offshore regions probably arose from a combination of the above factors. The most important implication of the result from the present study is that such a spatial bias in the bvalue for the study region can be reconciled using a proper treatment of the seismic data. Acknowledgements The authors are indebted to the Chen Yong of the State Seismological Bureau of China for provision of seismic data. The research is supported by RGC grants awarded to LSC and AMC and a HKU-CRCG grant to LSC. The authors are also grateful to Dr David M. Perkins for a thorough review of the draft manuscript. References Abe, K., 1995. Magnitudes and moments of earthquakes. In: Ahrens, T.J. (Ed.). Global Earth Physics: A Handbook of Physical Constants. AGU, Washington, pp. 206±213. Aki, K., 1987. Maximum likelihood estimate of b value in the fomula log N a 2 bM and its con®dence limits. Bull. Earthq. Res. Inst. 43, 237± 239. Al-Amri, A.M.S., Punsalan, S.B., Uy, E.A., 1998. Spatial distribution of seismicity parameters in the Red Sea regions. Jour. Asian Earth Sci. 16 (5±6), 557±563. Apostol, A., Aresene, G., Marza, V.I., 1985, Precursory seismicity of intermediate depth earthquakes in Vrancea region, Romania, Proceed. Euro. Seismo. Com. Sym. On Earthquake prediction research, Earthquake Prediction Res., 3 (2), 105±119. Bender, B., 1983. Maximum likelihood estimation of b-values from magnitude grouped data. Bull. Seismo. Soc. Amer. 73, 831±851. Chan, L.S., Zhao, A., 1996. Frequency and time series analysis of recent earthquakes in the vicinity of Hong Kong. Hong Kong Geologist 2, 11± 19. Chandler, A.M., Lee, C.F., 1999. Quantifying seismic hazard in the Hong Kong region. Geotechnical Risk Management Seminars, HKIE Geotechnical Division, Hong Kong, 57±65. Chandler, A.M., Chan, L.S., Lam, N.T.K., 2001, Determistic seismic hazard parameters and engineering risk implications for the Hong Kong region. Journ. Asian Earth Sciences. 20, 59±72. Chen, T., 1989. Basic features and present activity of Shenzhen fracture belt. Guangdong Geology 4 (1), 51±61 (in Chinese with English Abstract). Chong, F.S., 1983. Time±space±magnitude interdependence of upper crustal earthquakes in the main seismic seismic region of New Zealand. New Zealand Journal of Geology and Geophysics 26 (1), 7±24.
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81 Console, R., Gasparini, C., De Simoni, B., Marcelli, L., Spadea, M.C., Vecchi, M., 1979. Preambolo al Catalogo Sismico Nazionale (CSN, I criteri di informazione del CSN. Annali Geo®s. 32, 37±77. Ding, Y.Z., Lai, K.W., 1997. Neotectonic fault activity in Hong Kong: evidence from seismic events and thermoluminescence dating of fault gouge. Journal of the Geological Society, London 54, 1001±1007. Ding, Y., Li, Q., Huang, R., Chen, P., Yu, Y., 1997. New activity of the faults of Hong Kong. South China Journal of Seismology 17 (2), 9±15. Editorial Committee of Seismic Intensity Zonation Map of China, 1992. The seismic intensity zoning map of China, 1990 and its introduction. Earthquake Research in China 8, 1±11. Feng, R., Zhu, J., Ding, Y., et al., 1981. Crustal structure in China from surface waves. Acta Seism. Sinica 3 (4), 336±350. Geotechnical Control Of®ce, 1991. Review of Earthquake Data for the Hong Kong Region. Government Printer, Hong Kong 115 p.. Gutenberg, B., Richter, C.F., 1956. Magnitude and energy of earthquakes. Ann. Geo®sica 9, 1±15. Huang, J., Turcotte, R., 1988. Fractal distributions of stress and strength and variations of b-value. Earth and Planetary Letters 91, 223±230. Jiao, Y., Wu, K., Yang, M., 1990. Evaluation of detectability and quality of seismic network in China. Earthquake Res. In China 6, 1±8. Kebede, F., Kulhanek, O., 1994. Spatial and temporal variations of b-values along the East African Rift System and the Southern Red Sea. Phys. Earth Planet. Int. 83 (3±4), 249±264. Lam, H.K., Fong, S.W., 1982. Statistical analysis of earthquake occurrences in the vicinity of Hong Kong, in Proc. Int. Symp. Continental Seismicity Earthquake Prediction, Beijing, pp. 177±188. Lapenna, V., Macchiato, M., Telesca, L., 1998. Fluctuations and self similarity in earthquake dynamics; observational evidences in southern Italy. Phys. Earth Planet. Int. 106 (1±2), 115±127. Lee, C.F., Ding, Y.Z., Huang, R.H., Yu, Y.B., Guo, G.A., Chen, P.L., Huang, X.H., 1996. Seismic Hazard analysis of the Hong Kong Region. Geotechnical Engineering Of®ce (GEO), H.K. Government. Lee, C.F., Hou, J.J., Ye, H., 1997. The movement potential of the major faults in Hong Kong area. Episodes 20 (4), 227±231. Li, P., Rao, C., 1994. Tectonic characteristics and evolution history of the pearl River Mouth Basin. Tectonophysics 235, 13±25. Lin, J., Xie, M., 1996. Time and space distributions of seismicity in southeastern coastal China. In: Owen, Neller, Lee (Eds.), Seismicity in Eastern Asia. Geol. Soc. Hong Kong Bull. 5, 12±22. Lin, J., Wei, B., Xue, J., 1985. The focal process of the 1981 Haifeng, Guangdong, earthquake swarmÐa `locked region' model of rupturing process in the focal region. Jour. Seism. Res. 8 (1), 1±10. Main, I.G., 1992. Damage mechanics with long-range interactions; correlation between the seismic b-value and the fractal two-point correlation dimension. Geophys. Jour. Intern. 111 (3), 531±541. Main, I.G., Meredith, P.G., Sammonds, P.R., 1992. Temporal variations in seismic event rate and b-values from stress corrosion constitutive laws. Tectonophysics 211, 233±246. Mogi, K., 1962. Magnitude-frequency relation for elastic shocks accompanying fractures of various materials and some related problems in earthquakes. Bull. Earthq. Res. Inst. 40, 831. Mulgaria, R., Tinti, S., 1985. Seismic sample area de®ned from incomplete catalogues: an application to the Italian territory. Phys. Earth Planet. Int. 74, 98±112. Nanjo, K., Nagahama, H., Satomura, M., 1998. Rates of aftershock decay
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and the fractal structure of active fault systems. Tectonophysics 287, 173±186. Njike, K., Souriau, A., Gagnepain, B., Martel, L., Vadell, M., 1992. Frequency±magnitude relationship and Poisson ratio in the Pyrenees, in relation to earthquake distribution. Tectonophysics 215 (3±4), 363± 369. Oncel, A.O., Main, I., Alptekin, O., Cowie, P., 1996. Spatial variations of the fractal properties of seismicity in the Anatolian fault zones. Tectonophysics 257, 189±202. Pigott, J.D., Ru, K., 1994. Basin superposition on the northern margin of the South China Sea. Tectonophysics 235, 27±50. Pubellier, M., 1998. Geodynamic interpretations of the Sunda Block boundaries after GEODYSSEA results, EOS Trans. AGU Fall Meeting. Pun, W.K., 1998. Seismic hazard in Hong Kong, Urban Geology Congference, 15th September 1998, unpublished proceeding, (avaliable through Dept. of Earth Sciences, HKU). Pun, W.K., Ambraseys, N.N., 1992. Earthquake data review and seismic hazard analysis for the Hong Kong Region. Earthquake Engineering and Structural Dynamics 21, 433±443. Rotwain, I., Keilis-Brook, V., Botvina, L., 1997. Premonitory transformation of steel fractureing and seismicity. Phys. Earth Planet. Int. 101 (1± 2), 61±71. Rydelek, P.A., Sacks, I.S., 1989. Testing the completeness of earthquake catalogues and the hypothesis of self similarity. Nature 337, 251±253. Shi, Y., Bolt, B., 1982. The standard error of the magnitude-frequency b value. Bull. Seism. Soc. Amer. 72 (5), 1677±1687. Shi, Y., Chen, Q., Ma, L., 1992. The in¯uence of network detectability changes on seismicity research. Earthquake Res. In China 6, 1±22. Stein, R.S., Hanks, T.C., 1998. M $ 6 earthquakes in Southern California during the 20th Century; no evidence for a seismicity or moment de®cit. Bull. Seism. Soc. Amer. 88 (3), 635±652. Sun, X., Huang, X., 1995. The structure stress ®elds of Zhujiang delta and proximal area before Honghai Bay earthquake in 1911. Acta Geophysica Sin. 38 (5), 618±626. Tinti, S., Mulargia, R., 1985. Complete analysis of a seismic catalog. Annales Geophysicae 3 (3), 407±414. Wang, H., Diao, S., 1994. The time and space dynamic evolution of three seismicity parameters before and after the Heze M5.9 earthquake. North China Earthquake Science 12, 54±61. Wang, Z., Lu, H., 1997. Evidence and dynamics for the change of strikeslip direction of the Changle±Nanqo ductile shear zone, SE China. Jour. Asian Earth Sciences 15 (6), 507±515. Wilson, P., Rais, J., Bakosurtanal, C., 1999. The GEODYSSEA Project: an investigation of the geology and geodynamics of South and Southeast Asia. EOS 79, 545±548. Wong, Y.L., Zhao, J.X., Chau, K.T., Lee, C.M., 1998. Assessment of seismicity model for Hong Kong region. Trans. Hong Kong Institution Engrs. 1 (2), 37±50. Xia, K., Huang, C., Jiang, S., Zhang, Y., Su, D., Xia, S., Chen, Z., 1994. Comparison of the tectonic and geophysics of the major structural belts between the northern and southern continental margins of the South China Sea. Tectonophysics 235, 99±116. Yamashita, T., 1998. Simulation of seismicity due to ¯uid migration in a fault zone. Geophys. Jour. Intern. 132 (3), 674±686. Zhang, H., 1982. On activity of the NW-trending fractures along the Fujian±Guangdong region. Seismology and Geology 4 (3), 17±25 (Chinese with English Abstract).
www.elsevier.com/locate/jseaes
Spatial bias in b-value of the frequency±magnitude relation for the Hong Kong region L.S. Chan a, A.M. Chandler b,* a
b
Department of Earth Sciences, The University of Hong Kong, Pokfulam Road, Hong Kong Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong Received 6 October 1999; revised 31 August 2000; accepted 23 February 2001
Abstract The onshore and offshore regions in South Guangdong around Hong Kong exhibit different b-values of the G±R relation. The two regions have yielded b-values of 0.85 and 0.67, respectively, based on the most complete seismic database for the period 1970±1995. Tests on the completeness of the seismic catalogue and dominance of local source zones suggest a fundamentally complete record for M $ 3 events and the spatial bias in the b-values cannot be explained entirely in terms of these two factors. The subcatalogue of onshore events with focal depth ^ 6 km has yielded an essentially identical b-value as that for the offshore region, thus revealing a weak upper crust with diffused seismicity overlying a relatively strong lower crust. The present study shows that spatial bias in the b-value can be resolved by a proper analysis of the seismic data. The interpretation is also consistent with the model that the relative motion between South China and the South China Sea is diffused over a broad fault zone along the coast, with a higher b-value in the upper crust and the lack of a single wrench fault. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: b-Value; Frequency±magnitude relation; Hong Kong
1. Introduction Concerns about potential earthquake hazard in the rapidly developing region of South China have led to the undertaking of several studies on the seismicity of the region in recent years (Lee et al., 1996; Chan and Zhao, 1996; Lin and Xie 1996; Pun, 1998; Chandler and Lee, 1999). Such studies have yielded crucial information for the earthquake risk assessment and may facilitate the decision whether earthquake-resistant design codes should be adopted for the region. The study area, located at latitudes 208N±268N and longitudes 1108E±1178E, is referred to in this paper as the `Hong Kong Region'. In a companion paper, Chandler et al. (2001) have presented a deterministic seismic hazard analysis. For the purpose of specifying a worst-case scenario for engineering seismic risk assessment, such an analysis requires the designation of a maximum credible earthquake (MCE). The determination of the MCE requires an accurate characterization of the frequency±magnitude relation of the
* Corresponding author. Tel.: 1852-2859-1973; fax: 1852-2559-5337. E-mail address: [email protected] (A.M. Chandler).
region. Previous studies have revealed a spatial bias in the b-value of the frequency±magnitude relation of the region (Lee et al., 1996; Pun, 1998). The onshore region appears to possess signi®cantly higher b-values than the offshore region. Since the b-value in the G±R relation plays a vital role in the formulation of realistic design earthquakes for the region, the discrepancies in the seismic parameters for the onshore and offshore region should be given a detailed analysis. Speci®cally, we need to determine if such discrepancies are statistical artifacts due to the incompleteness of the seismic record or re¯ect actual differences in the seismogenic nature of the two regions. Another important aspect concerning the estimation of the MCE is the rate of tectonic motion and whether the release moment is likely con®ned to a single fault or diffused over the region. Instantaneous plate motion data that have recently become available have shed new light on the nature of the seismicity of the region. It will become possible in the future to evaluate certain seismic parameters for the region based on kinematic data. For the time being, however, the short observation record renders it dif®cult to estimate precisely the seismic release moment based on plate motions.
1367-9120/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 1367-912 0(01)00025-6
74
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
110E
112E
113E
115E
116E
118E 26N
26N M=2.0-2.9 M=3.0-3.9 M=4.0-4.9 M=5.0-5.9
G
HF
M=6.0-6.9
Shantou
24N
24N
Latitude,deg N
Heyuan HF W
Guangzhou Zhaoqing
Haifeng Shenzhen Macau
22N
F CN
HongKong 22N
Yangjiang
Hainan
20N 110E
112E
113E
115E
116E
20N 118E
Longitude, deg E Fig. 1. Seismicity and major fault system of Hong Kong Region. (CNF: Changle±Nanao Fault, WHF: Wuhua±Haifeng Fault; GHF: Guangzhou±Heyuan Fault).
2. Physical implications of b-value Gutenberg and Richter (1956) showed that the frequency±magnitude relation (G±R relation) for a region could be represented by logN M a 2 b M
1
where N(M) is the annual number of earthquakes with magnitudes in a particular range, and aand bare constants. Although the constants are determined empirically from seismic catalogues, it is imperative to understand their physical meaning. The nature of the a-constant is well known; it is directly related to the intensity of the seismic activity of the region. The physical implication of the bvalue, however, is not as obvious. Aki (1987) suggested an association between the b-value and the fractal dimension of the fault system. Many recent studies have also shown that the b-value is a scale invariant that is related to the spacing or clustering properties of epicenters or distribution of fault segments (Huang and Turcotte, 1988; Lapenna et al., 1998; Nanjo et al., 1998). Oncel et al. (1996) reported a lower b-value associated with a higher fractal dimension, and, hence, a greater degree of clustering of epicenters. The b-value for a region not only re¯ects the relative proportion of the number of large and small earthquakes in the region, but is also related to the stress condition
over the region. Kebede and Kulhanek (1994) have shown that spatial variations in the b-values in the East African Rift system can be related to crustal stress condition, with relatively lower b-values (0.5±0.8) observed in segments of the rift system experiencing high stress. The observation is consistent with experimental results reported by Mogi (1962), Main (1992) and Main et al. (1992). Higher b-values were reported for areas of greater material heterogeneity as well as lower stress intensity (Main et al., 1992). Temporal variations in the b-value have also been linked to the occurrence of seismic quiescence (Wang and Diao, 1994; Yamashita, 1998; Chong, 1983; Apostol et al., 1985; Rotwain et al., 1997; Al-Amri et al., 1998) and aftershock sequences (Nanjo et al., 1998). An earthquake sequence occurring near Hong Kong also exhibited a reduction in the b-value from the long-term average of 1.2 to about 1.0 during the month prior to an M 4.2 event (Lin et al., 1985). The study by Njike et al., 1992 shows lower b-values (0.95±1.15) in areas of well-de®ned faults and higher b-values (1.04±1.23) where diffused seismicity exists. Their study also revealed a higher b-value (1.01±1.09) for seismicity within the upper 5 km than the b-value (0.82±0.92) for earthquakes with focal depth .10 km. Given the vital seismotectonic implications of the bvalue, it is in the interest of both geoscientists and engineers to acquire an accurate description of the G±R relation of a region. However, substantial errors in b-values can be
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
caused by an incomplete catalogue, which could in turn, lead to erroneous moment release estimates (Abe, 1995; Stein and Hanks, 1998). Seismic catalogues are inherently incomplete, and the fractions of missing events generally increase with a decreasing magnitude range, resulting in a reduction in the b-values when small magnitude events are included in the analysis. But in some cases, small earthquakes are really not as numerous as a constant b-value extrapolated from larger events would predict (Rotwain et al., 1997). A completeness test of the seismic record used is therefore conducive to the interpretation of any b-values obtained. The choice of the statistical method used for deriving the b-value is also a critical consideration. Commonly the two empirical constants in the G±R relation are derived using the linear regression method on grouped magnitude data. Bender (1983) presented a detailed analysis of the dependence of the b-value on the interval size, maximum magnitude, sample size, and the data ®tting techniques. Considerably different b-values and the associated standard errors may be obtained from the same data set because of the different assumptions regarding these parameters (Bender, 1983). While no single data ®tting technique can yield accurate b-values from an inherently incomplete seismic catalogue, it is important to ensure that the spatial variations in the b-value obtained from different data-®tting techniques are consistent with each other. 3. Seismotectonic features of the Hong Kong Region The Hong Kong Region in this study is part of the South China Maritime Fold Belt that was formed predominantly during the mid-late Mesozoic Yenshanian movements in East Asia. The dominance of east±northeast-trending structures in the area probably resulted from a collision along the eastern coast of the South China Block during the Late Jurassic through Early Cretaceous (Wang and Lu, 1997). Mesozoic volcanics formed within volcanogenic depressions along a ductile shear zone known as the Linhuashan fault zone which extends from Fujian province in eastern China in a southwesterly manner through Hong Kong. Cenozoic tectonic movements in the region are characterized by formation of fault basins developed from a north± south directed minimum stress (Li and Rao, 1994; Xia et al., 1994), probably associated with the opening of the South China Sea during the Paleocene through mid-Miocene. The fault systems are well developed in the coastal areas of the Guangdong and Fujian provinces. The northeasttrending and northwest-trending systems are particularly notable in the study area. The most important northeasttrending fault systems consist of the Changle±Nanao Fault that runs along the coastline of South China, the Wuhua± Haifeng fault extending from Hong Kong to Wuhua, and the Guangzhou±Heyuan Fault farther to the north (Fig. 1). These faults controlled the occurrence and the evolution
75
of the Pearl River Estuary exterior basin, allowing for the deposition of some 7000 m of Tertiary and about 250 m of Quaternary sediments. Sediment isopachs show an elongation along a northeasterly direction. A marine geophysical investigation conducted by the Guangzhou Marine Geology Bureau in 1992 showed that these faults cut across Quaternary deposits; but no indisputable evidence for active faulting could be recognized on any of the seismic pro®les of the intensely covered Hong Kong Harbour. We are not aware of any published geodetic measurements on the motion of the northeast-trending fault systems. Measurements of movement on one particular fault in the Shenzhen area over 1986±1987 revealed a net dextral motion of about 0.3 mm/year (Chen, 1989). The accuracy of the result, however, cannot be assessed. The northwest-trending faults in the study area are less prominent but appear to be younger than the northeasttrending ones based on crosscutting relationship. Most of the recent seismicity in the area occurred on northwesttrending faults, including four historical events with magnitude M $ 6 in the Shantou area (Zhang, 1982). Results of thermoluminescence dating revealed activity as recent as 33,300 ^ 2700 years B.P. (Ding et al., 1997; Ding and Lai, 1997; Lee et al., 1997). Focal mechanisms have revealed a predominantly sinistral motion along these faults (Wang and Lu, 1997). The offshore region of the study area is located on the continental shelf and marked by the presence of a pair of northeast-trending depressions extending from Shantou westwards to Hainan Island (Xia et al., 1994). The depressions are divided into fault blocks bounded by a system of northeast-trending faults and cut by less prominent, northwest-trending ones. Results from seismic exploration reveal a gradual seaward decrease in crustal thickness from about 30 km in Guangzhou to about 27 km in Hainan Island (Feng et al., 1981; Xia et al., 1994; Pigott and Ru, 1994). The cause of the neotectonic movements of the area is enigmatic. During the mid-Oligocene to the mid-Miocene, sea ¯oor spreading occurred in a N±S direction in the South China Sea. Little is known about the post-Miocene geodynamic setting of the margin. Finite element models have revealed a maximum principal stress directed at N688W in the Pearl River Delta area (Sun and Huang, 1995). Geodetic measurements from the GEODYSSEA project during 1994±1996 have helped to identify the existence of the Sunda Block, which exhibits a distinct differential motion with respect to the Eurasian plate (Wilson et al., 1999). Since the Sunda Block includes the South China Sea, the relative motion between Sunda Block and Eurasia must also yield an effect on the continental margin of China. The kinematic solutions have revealed plausibly a right-lateral motion between the two tectonic blocks. Such a relative motion must necessarily be absorbed by the coastal faults along Guangdong and Fujian Provinces. The inferred sense of motion is consistent with focal plane mechanism of the recent earthquakes in the area. The work by Pubellier (1998)
76
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
Fig. 2. Record of events during 1960±1995.
has suggested a slip rate of about 1 cm/year between South China and the South China Sea. It is not known, however, if the inferred differential motion is distributed across a number of faults or manifests itself in the form of aseismic creep. Nevertheless, the estimated slip rate is about half to one order of magnitude less than that of western North America but substantially greater than that of the eastern North America. 4. Earthquake data for the region Two seismographic networks are operated independently in the region, one by the Hong Kong Observatory and the other by the Seismological Bureau of Guangdong Province. The Guangdong network comprises 17 seismographic stations and two local observation stations distributed over the entire province of Guangdong. The Hong Kong region began recording in 1921 (Geotechnical Control Of®ce, Table 1 b-values of Hong Kong Region for different magnitude ranges for 1973± 1995 Range
$ 4.5 $ 4.0 $ 3.5 $ 3.0 $ 2.5 $ 2.0 $ 1.5 $ 1.0
Whole region
Onshore region
Offshore region
n
b-value
n
b-value
n
b-value
36 80 247 743 2159 5050 8196 13654
0.72 0.71 0.75 0.78 0.81 0.82 0.80 0.77
28 66 204 634 1833 4362 7326 12753
0.82 0.80 0.82 0.85 0.86 0.87 0.84 0.81
8 14 43 109 326 688 870 901
0.60 0.58 0.63 0.67 0.70 0.72 0.70 0.66
1991; Pun and Ambraseys, 1992). After a series of destructive earthquakes in China in the 1960s, many seismographic stations were set up in the vicinity of the Hong Kong region and the detection capacity increased remarkably. As shown in Fig. 2, the annual earthquake frequency recorded in the Hong Kong region increased drastically in 1970. The seismic network is stated to be capable of detecting M $ 1.0 events for most parts of the Guangdong province. In terms of the completeness of the seismic record, however, the monitoring capability of the province is considered as M $ 2 for the onshore and M $ 3 for the offshore region (Jiao et al., 1990). In the present study, the earthquake record of Guangdong Province for the duration 1 January 1970±30 June 1995 from the Seismological Bureau of China was used. A total of 13,654 earthquakes were recorded during the 25-year interval. The record contains information of epicentral location, focal depth, date of occurrence, origin time, magnitude, and precision estimates for earthquakes of local magnitude M $ 1.0 that occurred within the time interval. The earthquakes in the onshore region are distributed in a broad belt about 300 km in width that runs parallel to the coast of South China (Fig. 1). Within this belt, most of the earthquake activities are concentrated in two regions near Heyuan and Yangjiang. Earthquakes that occurred near these two `source areas' account for about 80% of the recorded events onshore. The offshore region, on the other hand, is characterized by relatively fewer but larger earthquake events. Several M $ 6 earthquakes occurred in this region during the period. The number of recorded earthquake events with M , 3 is also much smaller than that of the onshore region. Because the two regions have such a different seismicity, the seismic data were divided into two
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
Fig. 3. Frequency±magnitude relations for the Hong Kong region and the two subregions. The lines are linear regression ®ts of the data.
sub-catalogues using a line that runs roughly along the coastline of South China. A G±R relation was formulated for each of the two sub-catalogues. The numbers of recorded events, according to different magnitude ranges, are shown in Table 1. 5. G±R relation of the Hong Kong Region Previous seismicity analyses have produced a range of bvalues from 0.7 to 0.9 for the region (Geotechnical Control Of®ce, 1991; Lam and Fong, 1982; Pun and Ambraseys, 1992; Editorial Committee of Seismic Zoning Map of China, 1992; Chan and Zhao, 1996). Pun and Ambraseys (1992) gave a b-value of 0.75 based on 490 years of record of MS $ 4.5 events. Lam and Fong (1982) obtained a bvalue of 0.85. Based on the instrumental record from 1973±1995, Chan and Zhao (1996) determined the bvalue to be 0.88 using maximum likelihood estimator method for earthquakes with magnitude ML $ 2.0. Wong et al. (1998) gave a b-value of 0.69 based on 100-year record of M $ 4 earthquakes. None of these studies, however, has taken into account the effects of data incompleteness or the spatial distribution of seismic events in the region on the seismic parameters. While the b-values obtained by these studies are seemingly acceptable, most of these studies were based on selected magnitude ranges or time windows and ignored earthquake records at small magnitudes. In the study by Lee et al. (1996), the area in the vicinity of Hong Kong was divided into 16 source zones. A frequency± magnitude relation of each zone was determined based on the seismicity of the zone. The source zones within the land area were grouped as the `inner' zone, while those located offshore made up the `outer' zone. The b-values obtained for the two zones are, respectively, 0.80 and 0.56 based on a
77
combination of both historical and instrumental seismicity data (Lee et al., 1996). We have re-computed the G±R relation using the presumably complete instrumental seismic record for the period 1970±1995 provided by the Center for Analysis and Prediction of the State Seismological Bureau of China. In order to carry out a meaningful statistical analysis of the seismicity of the region, we took into account the various magnitude ranges that have been used for earthquake measurements in the different reports and the developments of the instrumental network in the region. Fig. 3 shows the plots of the earthquake frequency against the magnitude for the onshore, the offshore, and the entire region. The least-square regression method was used to obtain the G±R relationships using a magnitude interval of 0.5 for the grouped data. The different magnitude ranges were de®ned based on the minimum magnitude included in the regression analysis. Based on the local magnitude scale, the G±R relations obtained have yielded b-values in the range of 0.80±0.87 for the onshore region, and 0.58±0.72 for the offshore region (Fig. 3). As shown in Table 1, the b-values of the offshore data are consistently 0.14±0.22 less than that of the onshore region for the different magnitude ranges. Such a signi®cant difference between the b-values of the onshore and the offshore region warrants a detailed examination. In the sections below, we will discuss the following possibilities that may have caused the spatial bias in the b-value: 1. 2. 3. 4.
incompleteness of the seismic catalogues; dependence of the b-value on focal depth; method of computing the b-value; and domination of the b-value by individual source zones.
5.1. Incompleteness of the seismic catalogues The detectability of a seismic network can substantially modify the b-value and the estimated average magnitude (Shi et al., 1992). It is vitally important to determine if the difference in the monitoring capability and incompleteness of the seismic record could have resulted in the observed spatial bias in the b-value of the two regions. The characteristics of the data set, as well as the method used to estimate the b-value, can both contribute to variations in the b-value obtained. Mulgaria and Tinti (1985) and Tinti and Mulgaria (1985) have devised statistical procedures to identify periods within a seismic catalogue for which the seismic record is considered complete. Unfortunately, no single method can provide a measure of the absolute completeness of the seismic catalogue based on the catalogue itself. Almost all methods for evaluating the absolute completeness of a seismic catalogue require the condition to know if the reporting system which generated seismic data had, at least for some time intervals, the capability to detect all earthquakes in a particular magnitude range. It seems reasonable, however, to assume that all largest events are
78
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
Table 2 Completeness test of seismic catalogues based on method by Rydelek and Sacks (1989) (n, number of events; R, calculated resultant vector length; Rc, p critical length for unbiased data, given by Rc 1.73 n at 95% con®dence level) Onshore region
Offshore region
M range
n
R
Rc
n
R
Rc
^ 5.0 4.5±4.9 4.0±4.4 3.5±3.9 3.0±3.4 2.5±2.9 2.0±2.4 1.5±1.9 1.0±1.4
14 15 38 138 430 1201 2530 2965 5427
0.9 0.9 1.8 8.2 15.0 104.8 58.1 40.9 193.0
6.5 9.3 14.2 24.8 43.6 74.1 114.3 148.1 127.5
4 5 6 29 66 214 361 183 30
0.2 1.5 2.1 5.1 2.2 9.9 3.9 9.0 2.7
3.5 3.9 4.2 9.3 14.1 25.3 32.9 23.4 9.5
reported, and there is a progressive decline in the seismic monitoring capacity towards the smallest events. In other words, the fractions of missing record increase with decreasing magnitude. Also, since small events are only detectable by the local seismographic network, the monitoring capability of a region depends much on the presence of local seismometers as well as the intensity level of culturally produced ambient noises and ground-transmitted vibrations. Not only do seismic catalogues tend to have a less complete record at lower magnitude ranges, they are also less complete for earlier times. The number of events recorded during 1960±1995 for the Hong Kong Region is shown in Fig. 2. The chart reveals an abrupt increase in the number of recorded event since the 1970. The particular database used in the present analysis which spans the 25year interval since 1970, however, appears to have been minimally affected by data incompleteness. We have applied two tests to determine if this particular database is suitable for the derivation of the G±R relation. The ®rst test is based on how the b-value is affected by the omission of smaller events from the database. Since there is plausibly a greater omission of lower magnitude events from the record, the b-value should become progressively smaller by inclusion of the next lower magnitude interval. Based on this assumption, the b-values were computed for different magnitude ranges. As shown in Table 1, the bvalues of the inner zone are 0.80, 0.85 and 0.87 when the minimum magnitude used was M $ 4, M $ 3 and M $ 2, respectively. For the offshore area, the b-values obtained are 0.58, 0.67 and 0.72 when the same magnitude ranges were used. There are no signi®cant changes in the b-value by the inclusion of events in the next smaller magnitude interval. In fact, the b-values actually increased slightly when a lower magnitude range was included in the calculation. The result suggests that data incompleteness has not signi®cantly affected the b-value. Rydelek and Sacks (1989) proposed a rather interesting method to evaluate the completeness of the seismic data through a statistical analysis of the diurnal bias of the
seismic record. The method is based on the assumption that more nighttime events would have been recorded when the surrounding environment is less noisy. In this method, the time of occurrence of an event is treated as a unit vector with a direction given by the time, much like the hour arm on a clock. The vectors for a particular magnitude range are then added and the total length of the resultant is determined mathematically. The null hypothesis is that these vectors are randomly distributed over a 24-h period, giving a resultant vector R with a small length. Rydelek and Sacks (1989) referred to the critical distance as a `phaseout' distance; a set of events would be considered as biased and incomplete if the resultant vector exceeds the `phaseout' distance. The test is entirely inherent in nature, and requires only an accurate knowledge of the time of occurrence and not any presumed seismic parameters or knowledge of monitoring capacity. As a second test for the data incompleteness, we have applied a similar procedure to the data set by comparing the resultant vector R computed to that expected for a random process. A reasonable value for the critical R at 95% con®dence level is given by p Rc 1:73 N 2 where N is the number of data points. The data sets for the two regions were grouped by magnitude of 0.5 intervals. The time of occurrence of each earthquake was converted into a directional vector. Each vector was then resolved into its components on the X- and Y-axes, and the length of the resultant vector was obtained by p R SX 2 1 SY 2 3 The number of events in each magnitude interval, and Rcand R-values computed based on Eqs. (2) and (3) are shown in Table 2. The computed R-values exceed the critical R at magnitude interval 2.5±3.0 for the onshore region. This strong diurnal bias for events can be taken as evidence for the incompleteness of seismic record for such a magnitude interval. While the magnitude intervals M 2.0±2.5 and 1.5±2.0 passed the completeness test, we conservatively considered the catalogue as complete only for M $ 3.0. The G±R relations obtained in the following sections are based on the subsets of data with M $ 3.0. 5.2. Dependence of b-value on focal depth A particularly interesting aspect of the seismic catalogue is the dependence of the G±R relation on the focal depth. Such a relationship between the b-value and the focal depth has also been observed in the seismic catalogue from the Pyrenees (Njike et al., 1992). In this analysis, we have divided the earthquake events in the onshore region into two groups based on the reported focal depth of the events. A G±R relation was computed for each of the two sets of data. The objective of this division is to determine the seismic parameters of the upper and lower crust events, in
L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81 Table 3 Reduced b-value after removal of data from two source zones for M . 3.0 using a space window of 26 km Dataset
n
b
Onshore total Heyuan source zone events removed Yangjiang source zone events removed Heyuan space window Yiangjiang space window Both source zone events removed
634 303
0.85 0.72
483
0.75
331 151 152
0.97 0.93 0.74
4b
where b is the maximum likelihood estimator, M the mean magnitude, and Mmin the smallest threshold magnitude considered. For a signi®cantly large sample size, n, the standard error of the b-value is approximated by
s b 2:30b 2 s M
5a
where 2 =n n 2 1 s 2 M S M i 2 M
order to compare them with those of the offshore region. Of the 634 onshore events with a magnitude of M $ 3.0, 177 had a reported focal depth exceeding 6 km. As shown in Table 3, the b-value obtained for the lower crustal events is 0.63, which is similar to the b-value for the offshore region. The `shallow' events with D , 6 km, on the other hand, exhibit a b-value that is close to unity. The results thus suggest a vertical variation in the b-values in addition to the spatial bias. The results suggest that the generally larger number of small earthquake events in the upper 6 km may be due to the weaker strength of the upper crust which yields to applied stresses more readily, resulting in the more frequent occurrence of smaller earthquakes. If this is the case, the upper crust of the region probably exhibits a greater degree of hetereogeneity which favors a lower stress intensity and diffused seismicity. The lower b-value obtained for the deeper seismic data set suggests that the lower crust, on the other and, has a greater strength allowing for a relatively greater accumulation of strain energy. Seismic activities are also likely con®ned to distinct faults. We must caution, however, that the focal depths of the events may not be very well constrained. Small events with great focal depths are more dif®cult to detect, resulting in an inherently lower b-value for the deeper data sets. 5.3. Method of computation of b-value The method by which the b-value is calculated can have signi®cant bearing on the observed discrepancies between the b-value of the onshore and the offshore zones. The linear regression method commonly used by geophysicists to compute the b-value has a major disadvantage since the presence of even a few large earthquakes can in¯uence the b-value signi®cantly. Such a consideration has prompted many seismologists into developing alternative methods for its determination. A rather popular method is the maximum likelihood estimation (Aki, 1987). Shi and Bolt (1982) provided a set of equations for estimating the b-value and its associated standard errors. In that method, the b-value is given by b bloge
2 Mmin b 1= M
79
4a
5b
(Shi and Bolt, 1982). For any seismic catalogue, the magnitude at which the catalogue is considered `complete' can be used as the Mmin. The completeness analysis presented in above sections has also entailed the reasonable assumption to use M 3.0 as the threshold magnitude Mmin. Based on Eqs. (4a) and (4b), we have computed the seismic parameters and the associated errors for both the offshore and onshore regions. The three sets of data have yielded b-values as follows: Entire region: b 1.03; s (b) 0.05 (M 3.42; n 743) Onshore region: b 0.83; s (b) 0.03 (M 3.52; n 634) Offshore region: b 0.90; s (b) 0.10 (M 3.48; n 109) It is interesting to note that the discrepancy in the b-value has essentially vanished when the maximum likelihood method was used to estimate the b-values. Since the spatial bias in the b-value may be resolved by the use of different statistical methods, one may argue that the spatial bias in the b-value is merely a mathematical artifact. However, a dif®culty with the maximum likelihood method is that the sample size does not appear to have played a role in the determination of the b-value, and that the physical meaning of the governing equation is somewhat obscure. We are also not certain whether the b-value obtained using the maximum likelihood method has identical implications for the ratio of small to large magntiude events as that obtained by the linear regression method. Since the maximum likelihood method gives more relative weight to the data points in the middle range, it may yield less sensitive estimates of large magnitude events that are crucial for seismic risk assessment exercises. 5.4. Dominance of individual source zones Earthquakes that happened in the Heyuan and the Yangjiang areas, including aftershocks, account for over 80 and 75% of the total number of onshore events with M $ 1.0 and M $ 3.0 respectively. Because of their dominance, seismic parameters obtained from an untreated catalogue essentially represent seismogenic properties that are pertaining to the local source zones. The earthquakes in the relatively
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L.S. Chan, A.M. Chandler / Journal of Asian Earth Sciences 20 (2001) 73±81
Table 4 Difference between b-values of upper and lower crust for two data sets delineated by focal depth Dataset
n
b-value
Onshore events .6 km Onshore events ,6 km Offshore total
177 457 109
0.63 1.00 0.57
short-term catalogue which includes aftershocks from the larger events cannot be regarded as random events and the Poisson distribution that is often used in earthquake recurrence analysis would not be applicable. We have determined the b-values for the Hong Kong Region when earthquake events in these two source zones were deliberately omitted. To do so, we de®ned a space window around the epicentral zones of Heyuan and Yangjiang using a method akin to the one for aftershock removal suggested by Console et al. (1979). This space window is considered as the `in¯uence area' of a source zone. The radius of the space window in km, RW, is given by logR W 0:41M 2 1:25
6
where M is the magnitude of the largest event in the area. Since both source zones have produced M $ 6.0 earthquakes historically, a slightly more conservative value of M 6.5 was used. Based on Eq. (6), the radius of the space window obtained is 26 km. In the subsequent analysis, all events that occurred within this space window have been removed and the G±R relations were re-computed. We have not de®ned a time window as often done for aftershock removal since our objective was not to remove aftershock events but to ®nd a method to determine the in¯uence area of the two source zones. As shown in Table 4 the b-values of the onshore zone were reduced from 0.85 to 0.72 and 0.75 respectively, when events within the Heyuan or the Yangjiang space window were individually omitted from the data catalogue, and from 0.85 to 0.74 when events within both space windows were removed. The two source zones have b-values that are higher than the rest of the region. Although the reduction in the b-values by omitting events in the two source zones is still insuf®cient to account for all of the spatial bias in the bvalue between the onshore and offshore region, the higher bvalues for the onshore region can in part be attributed to the seismogenic characteristics of individual source zones. 6. Conclusions A thorough seismicity analysis requires an examination of all possible factors that may have given rise to any bias in the G±R relation. In the above analysis, we have shown that the seismic catalogue used in this study is essentially complete for M $ 3.0 for the Hong Kong Region, and data incompleteness may not have signi®cantly modi®ed
the b-values in the G±R relations. By limiting the data record to events with focal depth .6 km for the onshore region, a b-value comparable to that of the offshore region can also be obtained. It is tempting to attribute the higher bvalue to a greater structural heterogeneity of the upper crust of the onshore region than that of the lower crust. But we have also demonstrated that the spatial bias in the b-value of the onshore and offshore regions essentially disappears when the maximum likelihood estimate is used in determining the G±R relation. By isolating several local source zones, the b-value of the onshore region was also brought into a closer agreement with that of the offshore region. The observed difference between the b-values of the onshore and offshore regions probably arose from a combination of the above factors. The most important implication of the result from the present study is that such a spatial bias in the bvalue for the study region can be reconciled using a proper treatment of the seismic data. Acknowledgements The authors are indebted to the Chen Yong of the State Seismological Bureau of China for provision of seismic data. The research is supported by RGC grants awarded to LSC and AMC and a HKU-CRCG grant to LSC. The authors are also grateful to Dr David M. Perkins for a thorough review of the draft manuscript. References Abe, K., 1995. Magnitudes and moments of earthquakes. In: Ahrens, T.J. (Ed.). Global Earth Physics: A Handbook of Physical Constants. AGU, Washington, pp. 206±213. Aki, K., 1987. Maximum likelihood estimate of b value in the fomula log N a 2 bM and its con®dence limits. Bull. Earthq. Res. Inst. 43, 237± 239. Al-Amri, A.M.S., Punsalan, S.B., Uy, E.A., 1998. Spatial distribution of seismicity parameters in the Red Sea regions. Jour. Asian Earth Sci. 16 (5±6), 557±563. Apostol, A., Aresene, G., Marza, V.I., 1985, Precursory seismicity of intermediate depth earthquakes in Vrancea region, Romania, Proceed. Euro. Seismo. Com. Sym. On Earthquake prediction research, Earthquake Prediction Res., 3 (2), 105±119. Bender, B., 1983. Maximum likelihood estimation of b-values from magnitude grouped data. Bull. Seismo. Soc. Amer. 73, 831±851. Chan, L.S., Zhao, A., 1996. Frequency and time series analysis of recent earthquakes in the vicinity of Hong Kong. Hong Kong Geologist 2, 11± 19. Chandler, A.M., Lee, C.F., 1999. Quantifying seismic hazard in the Hong Kong region. Geotechnical Risk Management Seminars, HKIE Geotechnical Division, Hong Kong, 57±65. Chandler, A.M., Chan, L.S., Lam, N.T.K., 2001, Determistic seismic hazard parameters and engineering risk implications for the Hong Kong region. Journ. Asian Earth Sciences. 20, 59±72. Chen, T., 1989. Basic features and present activity of Shenzhen fracture belt. Guangdong Geology 4 (1), 51±61 (in Chinese with English Abstract). Chong, F.S., 1983. Time±space±magnitude interdependence of upper crustal earthquakes in the main seismic seismic region of New Zealand. New Zealand Journal of Geology and Geophysics 26 (1), 7±24.
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