A C T A G E O P H Y S I C A P O L O N I C A Vol. 53, no. 2, pp. 143-152 2005 GSHAP REVISITED FOR THE PREDICTION OF MAXIMUM CREDIBLE EARTHQUAKE IN THE SIKKIM REGION, INDIA Madhav VYAS, Sankar Kumar NATH, Indrajit PAL, Probal SENGUPTA and William K. MOHANTY Department of Geology and Geophysics, Indian Institute of Technology Kharagpur 721302, India; e-mail: nath@gg.iitkgp.ernet.in Abstract Global Seismic Hazard Assessment Program (GSHAP) has classified the Indian peninsula into several seismogenic zones. Considering the seismotectonic setting of the Sikkim Himalaya, sources 2, 3, 4, 5, 25, 26, 27 and 86 may be critical in contributing to the seismic hazard of the region. These seismogenic zones have been classified as Himalayan source (25, 86), extension of Tibetan plateau (26, 27), Burmese arc subduction zone (4, 5), Shillong plateau (3) and the Indian Shield region (2). The probabilistic seismic hazard assessment of the region necessitated prediction of Maximum Credible Earthquake magnitude for each source with 10% probability of exceedance in 50 years. Considering the widespread damages caused in the state capital of Sikkim due to the recent earthquakes of 1934 (M w = 8) and 1988 (M w = 7.2) a 50-year prediction seemed to be reasonable. Gutenberg Richter (b-value) approach and Gumbel s method of extreme value statistics have been used in the present analysis for the prediction of Maximum Credible Earthquake magnitude, results of both being comparable to each other. The maximum credible earthquake magnitude as predicted by both the methods are above 6 except for zone 26, the highest being in the Burmese arc with a magnitude of 8.5 by Gutenberg Richter approach and a magnitude of 7.7 by Gumbel s method Key words: GSHAP, seismogenic zone. 1. INTRODUCTION Earthquake prediction over the years has been a controversial issue (Sykes et al., 1999). Earthquake prediction can be categorized on the basis of time scale involved in the prediction process like long-term, short-term and so on. In the present paper, we
144 M. VYAS et al. attempt to predict the magnitude of an earthquake that has 10% probability of exceedance in 50 years, a standard used for building codes. We can see that the time scale involved corresponds to long-term prediction referring to earthquakes with a return period of the order of 500 years. Stresses are reduced below a Self Organized Critical (SOC) state at the time of large earthquakes in the regions surrounding the rupture zones. As stresses slowly start to build up, the region approaches a SOC state, the presence of such state can be regarded as a long-term precursor. Self-organized critical processes are explained by Bak et al. (1988) using the analogy of grains of sand being added slowly to a sand pile (Sykes et al., 1999). After great earthquake of San Francisco, 1906, a broad neighbouring area was quiet for greater-magnitude events (M > 5) for about 70 years (Sykes and Jaume, 1990). Shocks of that size were more numerous before the earthquake from 1883 to 1906. Thus, the greater San Francisco area can be regarded as at or close to the SOC state from 1883 to 1906 as manifested by the frequent occurrence of moderate to large earthquakes. Seismic hazard analysis is dependent upon the definition of seismogenic zones. Seismic activity within a zone is assumed to be uniform. This critical assumption of homogeneity can introduce severe errors in the estimation of seismic hazard of a region. From a study made by NGRI (Bhatia et al., 1999) based on seismotectonic considerations and compilation of tectonic features (Khattri, 1987; Khattri et al., 1984; Leloup et al., 1995; Molnar, 1992) it follows that the Indian peninsula can be subdivided into two major seismogenic provinces, namely: (1) the Himalayan arc and other plate boundary regions, and (2) the Indian Shield region. Our study is focused on the Sikkim Himalaya and it is evident from the GSHAP map (Fig. 1) that source zones 2, 3, 4, 5, 25, 26, 27, 86 are critical in the probabilistic estimation of peak ground acceleration in Sikkim. We can classify these source zones based on the nature of fault systems and associated source mechanism. Seismicity of the Himalayan zone is due to the underthrusting of Indian plate under the Eurasian plate. Main Central Thrust (MCT), Main Boundary Thrust (MBT) and Main Frontal Thrust (MFT) (Gansser, 1964) are primary faults in this area and are dipping north. Source zones 25 and 86 are classified as the Himalayan sources. Seismicity in zones 27 and 28 is the manifestation of extension of the Tibetan plateau. The Altyn Tagh, Kunlun and Xianshuihe are the three major fault systems in this region (Molnar, 1992). The distribution of earthquakes in the Burmese arc subduction zone suggests subduction of the Indian lithospheric slab beneath the Burmese plate (Verma et al., 1976; Mukhopadhyay and Dasgupta, 1988; Ni et al., 1989; Gupta et al., 1990). The seismic sources 4 and 5 cover the Burmese arc and the adjoining region. Source 3 on the west of Burmese subduction zone encompasses the Shillong Plateau. Source zone 2 is considered to be the part of Indian shield region. We made an attempt here to statistically predict the Maximum Credible Earthquake (MCE) magnitude with a specified probability of exceedance and also to estimate the probabilistic seismic hazard. We predict the magnitude of MCE using two techniques, namely, Gumbel s method (Gumbel, 1958) and b-value approach (Guten-
PREDICTION OF CREDIBLE EARTHQUAKE IN SIKKIM REGION, INDIA 145 Fig. 1. GSHAP seismogenic sources surrounding Sikkim. The numbers in the polygons indicate different seismic source zones as demarcated according to the Global Seismic Hazard Assessment Program norm.
146 M. VYAS et al. berg and Richter, 1954) on ISC catalogue between 1964-1999. Gumbel s method is more popular in flood frequency analysis and for other natural phenomena. Here, we applied this method to assess magnitude of an earthquake with a 10% probability of exceedance in 50 years. Results of both these techniques are compared for the classified seismogenic regions proposed under GSHAP in the Sikkim Himalaya. 2. PREDICTION OF MAXIMUM CREDIBLE EARTHQUAKE Gutenberg Richter relationship This is a recurrence relation between the number of earthquakes per year and their magnitudes, as given below: log n = a bm, (1) where n is the number of earthquakes per year with a magnitude greater or equal to M and a and b are the parameters that are the characteristics of a source zone. Once a and b are estimated, we can assess the frequency of occurrence of any magnitude in that source zone using relation (1). Moreover, probability of exceedance of a magnitude M with a frequency n in t years can be calculated by λ F( x) = 1 e t, (2) where F(x) represents the probability of exceedance and λ is the frequency of occurrence of earthquakes (same as n). F(x) has been calculated assuming Poisson s distribution (Esteva et al., 1958). In our case, F(x) = 0.1 (10% probability) and t = 50 years, we can therefore calculate the frequency using relation (2). After the frequency is established we can compute the magnitude from relation (1). The b-value is estimated by the method of maximum likelihood (Aki, 1965) as given by b = log e M M t, (3) where M is the mean of magnitude of earthquakes having magnitudes greater than M t, the threshold magnitude that is 4.0 in our case, because all events above magnitude 4.0 have been expected to be well recorded. Thereupon, a is estimated by a best-fit line of the form of eq. (1) through our data. Gumbel s method According to the theory of extreme value statistics, the extrema are a set of random variables that follow a certain distribution. There are three such distributions (Ponce, 1989), namely: type 1 (Gumbel s), type 2 (Frechet s), and type 3 (Weibull s). Here we
PREDICTION OF CREDIBLE EARTHQUAKE IN SIKKIM REGION, INDIA 147 have used type 1 distribution known as Gumbel s distribution. Gumbel s method is not applied to the whole set of data, rather we select a data series on the basis of maximum magnitude event from each year s record onto which this method has been applied. According to Gumbel s method we can define T ln ln + Ymean T 1 X = Xmean S, (4) σ where X is the magnitude, X mean is the mean of extreme value series chosen from the record, T is the return period of an earthquake of magnitude X, and S is the standard deviation of extreme value series. Y mean and σ are the mean and deviation of standard Gumble s variate. Their value is taken directly from the table (Ponce, 1989) corresponding to a record length of n = 35 years (for earthquake catalogue of 1964-1999). Once the return period is calculated it can be converted to the probability as P = 1 T. (5) This is the annual probability of exceedance. The probability of exceedance for N successive years can be estimated from P = 1 ( 1 1 ) n T. (6) In our case for a probability of 10% exceedance in 50 years, P = 0.1, and n = 50. A return period can be estimated from eq. (6) (475 years in our case), and hence the magnitude from eq. (4). Results and discussion An attempt was made to apply both the b-value and Gumbel s method for the source zones 2, 3, 4, 5, 25, 26, 27 and 86 surrounding Sikkim. For source zones 26 and 27, Gumbel s method could not be applied because of the paucity of data. For Gumbel s method, data series can be selected either as annual maxima series or as annual exceedance series. In case of annual maxima series one extreme value from each year s record is taken. For annual exceedance series all the events above a certain base value are taken regardless of their occurrence time. It is further suggested that for events with large return periods annual maxima series is used (Ponce, 1989). For sources 26 and 27 annual maxima series could not be constructed. Results obtained from these two techniques are given in Fig. 2 and listed in Table 1.
148 M. VYAS et al. Fig. 2. Comparative plot for Gumbel s method (solid lines) and Gutenberg Richter approach (dotted lines) for all the GSHAP sources considered.
PREDICTION OF CREDIBLE EARTHQUAKE IN SIKKIM REGION, INDIA 149 Table 1 Predicted magnitude of Maximum Credible Earthquake (MCE) for different GSHAP sources. M PGA is the magnitude considered for PGA calculation GSHAP source zone Seismogenic zone Magnitude of MCE b-value approach Gumbel s method M PGA 2 Indian shield 7.9 7.3 7.9 3 Shillong Plateau 7.6 6.5 7.6 4 Burmese arc subduction 7.9 6.9 7.9 5 Burmese arc subduction 8.5 7.7 8.5 25 Himalayan zone 8.0 7.0 8.0 26 Tibetan Plateau extension 5.3 5.3 27 Tibetan Plateau extension 7.0 7.0 86 Himalayan zone 8.3 7.3 8.3 3. MAGNITUDE DEPENDENCE AND BOUNDARY CONDITIONS Both the methods on the account of variation of probability with magnitude tend to appear to be similar in nature, as both of them vary as negative of double exponential of the magnitude. In case of b-value approach, magnitude is logarithmically related to frequency, which in turn is exponentially related to the probability of exceedance. This leads to a double exponential relationship. In case of Gumbel s method, magnitude is proportional to double logarithm of return period, which in turn is inversely proportional to the probability, thereby establishing a double exponential relationship. However, it is observed that b-value approach is an unbounded method, that is, we can go for predicting probabilities of earthquakes of any magnitude (M > M t ) on the lower as well as higher sides. In case of Gumbel s method, we cannot estimate the probability of occurrence of any event with a return period less than one year because of its inverse proportional relationship with the return period. 4. COMPARISON OF RESULTS AND CONCLUSIONS It is evident that b-value approach leads to the prediction of higher magnitude events for a given probability as compared to Gumbel s method. A set of comparative plots for different source zones is furnished in Fig. 2. In some source zones, namely, 5 and 86, the difference is pronounced. This is due to the fact that both the methods use different parts of the data.
150 M. VYAS et al. The b-value method employs large amount of extrapolation of the defined recurrence relationship. It is believed that this recurrence relationship shows a straight line behavior only for small interval but while estimating the probability we extend this straight line in either direction. As shown in Fig. 3 (Utsu, 2002) this relation does not remain a straight line and tends to taper off on higher magnitude side generally around magnitude 8. In areas where great earthquakes (M > 8) have taken place, an exponential or logarithmic function can be defined (Utsu, 2002) that falls sharply at higher magnitudes. Such functions generally involve a term M max (characteristic earthquake magnitude). In our area of interest no such great earthquakes were recorded during 1964-1999. As a result we predict magnitude of maximum credible earthquake without using a tapered function, but extrapolating the Gutenberg Richter law. Frequency Magnitude Fig. 3. Gutenberg Richter law tends to taper off at higher magnitudes (after Utsu, 2002, modified). A c k n o w l e d g e m e n t. The Department of Science and Technology, Seismology Division, Government of India funded this investigation, vide sanction numbers DST/23(97)/ESS/95 and DST/23(218)/ESS/98. The authors gratefully acknowledge the critical review and informative suggestions of the referee that helped in better scientific exposition of the manuscript.
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