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Regional time-predictable modeling in the Hindukush–Pamir–Himalayas region
Tectonophysics 390 (2004) 129 – 140 www.elsevier.com/locate/tecto
Regional time-predictable modeling in the Hindukush–Pamir–Himalayas region D. Shankera,*, E.E. Papadimitrioub a
Department of Earthquake Engineering, Indian Institute of Technology Roorkee (formerly University of Roorkee), Rorrkee, Uttaranchal 247667, India b Laboratory of Geophysics, University of Thessaloniki, Thessaloniki GR-54006, Greece Received 7 January 2002; received in revised form 15 April 2002; accepted 9 March 2004 Available online 26 August 2004
Abstract The seismic characteristic of Hindukush–Pamir–Himalaya (HPH) and its vicinity is very peculiar and has experienced many widely distributed large earthquakes. Recent work on the time-dependent seismicity in the Hindukush–Pamir–Himalayas is mainly based on the so-called bregional time-predictable modelQ, which is expressed by the relation log T=cM p+a, where T is the inter-event time between two successive main shocks of a region and M p is the magnitude of the preceded main shock. Parameter a is a function of the magnitude of the minimum earthquake considered and of the tectonic loading and c is positive (~0.3) constant. In 90% of the cases with sufficient data, parameter c was found to be positive, which strongly supports the validity of the model. In the present study, a different approach, which assumes no prior regionalization of the area, is attempted to check the validity of the model. Nine seismic sources were defined within the considered region and the inter-event time of strong shallow main shock were determined and used for each source in an attempt at long-term prediction, which show the clustering and occurrence of at least three earthquakes of magnitude 5.5VM sV7.5 giving two repeat times, satisfying the necessary and sufficient conditions of time-predictable model (TP model). Further, using the global applicability of the regional time- and magnitude-predictable model, the following relations have been obtained: log T t=0.19 M min+0.52M p+0.29 log m 010.63 and M f =1.31M min0.60M p0.72 log m 0+21.01, where T t is the inter-event time, measured in years; M min the surface wave magnitude of the smallest main shock considered; M p the magnitude of preceding main shock; M f the magnitude of the following main shock; and m 0 the moment rate in each source per year. These relations may be used for seismic hazard assessment in the region. Based on these relations and taking into account the time of occurrence and the magnitude of the last main shock in each seismogenic source, time-dependent conditional probabilities for the occurrence of the next large (M sz5.5) shallow main shocks during the next 20 years as well as the magnitudes of the expected main shocks are determined. D 2004 Elsevier B.V. All rights reserved. Keywords: Characteristic earthquake; Hindukush–Pamir–Himalaya; Seismogenic source; Regional time predictable modeling
* Corresponding author. Tel.: +91 1332 285128; fax: +91 1332 276899/273560. E-mail address: [email protected] (D. Shanker). 0040-1951/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2004.03.027
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D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140
1. Introduction Vulnerability of our civilization to geological disasters is rapidly growing. Today, a single earthquake with subsequent ripple effects may take up to a million lives, cause material damage, render large region uninhabitable, and trigger a localized or regional economic depression. New possibilities for prediction and management of geological and geotechnical disasters have been developed during the last few decades. The problem of earthquake prediction consists of consecutive, step by step, narrowing down the time interval, area, and magnitude range where a strong earthquake will occur. Such formulation is dictated both by the nature of the process leading to strong earthquakes and by the practical need for earthquake preparedness. Most of the earthquake-generation models currently used for seismic hazard evaluation have attracted the attention of many scientists. Several workers (Cornell, 1968; Gardner and Knopoff, 1974; Papadopoulos and Voidomatis, 1987; Singh et al., 1994) reported that occurrence of earthquakes follow a Poisson distribution, suggesting memoryless property of seismic zones. Wallace (1970) and Nishenko and Singh (1987), among others, reported timedependent properties of earthquake-generating sources for several regions. Seismic hazard prediction is an important prerequisite for comprehensive disaster prevention. Recent development in seismology and geophysics have lead to two alternative representations for earthquake recurrence patterns, which are based on physical concepts and which lead to more accurate estimates of earthquake occurrence probabilities, and are desirable in seismic hazard analysis. The proposed time-dependent recurrence models were SP model (slip-predictable model: Bufe et al., 1977; McNally and Minster, 1981; Singh et al., 1991; Wang et al., 1982, Kiremidjian and Anagnos, 1984) and TP model (time-predictable model: Shimazaki and Nakata, 1980; Anagnos and Kiremidjian, 1984; Papazachos, 1989; Singh et al., 1992). To estimate the long term probabilities for the generation of strong earthquakes on single faults, the time-predictable model seems to be more plausible than the slip-predictable model (Wesnousky et al., 1984; Astiz and Kanamori, 1984; Nishenko and Buland, 1987).
TP model discussed here also holds if the seismic source includes other small faults where smaller main shocks occur in addition to the main fault where the characteristic earthquake is generated (Papazachos, 1989). These models were based on the assumption of a constant tectonic stress accumulation rate and the association of stress relief with a sequence of earthquakes. According to the TP model, the time interval between large earthquakes is proportional to the amount of slip from the preceding earthquake, and large earthquakes occur when the stress has reached a fixed limit value. In the SP model, the time interval between large earthquakes is proportional to the slip amount of the next large earthquake. Repeat times of large earthquakes have become an extensive tool to obtain better estimates of seismic potential and better forecasts of future large shocks. Repeat times are taken to be the time intervals between the largest shocks that occur at a given place along a plate boundary or in a specific seismic zone, and they vary within and between seismic zones, depending not only on the rate of plate motion but also on other factors, i.e., length of rapture along strike, downdip width, and dip of the plate boundary (Kelleher et al., 1973). Consequently, if a model can make use of the available repeat times, it offers a very useful tool for long-term earthquake prediction. Papazachos (1988a,b; 1992) carried out an investigation to identify time-dependent relations among strong earthquakes that occurred in seismogenic sources in Greece. He proposed a model where the inter-event time T t, and magnitude, M f, of the following main shock were quantitatively expressed in relation to the magnitude, M min, of the smallest considered main shock and to the magnitude, M p, of the preceding main shock in each seismogenic source, and found that the time-predictable model holds. Papazachos and Papaioannou (1993) improved the preceding methodology to include a new term in the relations both for the inter-event time and the magnitude of the expected main shock. This term depends on the yearly moment rate in each seismogenic source. This is called the btime and magnitudepredictable modelQ. Furthermore, they applied this model to estimate the probability of occurrence of the next main shock during the next several years and the magnitude of this expected main shock in each seismogenic source.
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The basic objective of the present paper is to study the time-dependent property of earthquake generation sources to establish the validity of that model in India and its vicinity and to estimate the probability of occurrence of the next main shock, as well as its magnitude, in each seismogenic source there.
2. Regional characteristics The considered zone (278N to 378N and 688 E to 848E) includes the Hindukush, Pamir, and Karakorum regions, which lie to the north of the northern apex of the Indian subcontinent. From a seismic point of view, this region is one of the most active in the world. Because the Hindukush–Pamir seismic zone is located close to the Indian–Eurasian plate boundary, several authors have suggested that the intermediate-depth seismicity is due to the convergence of the Eurasian and Indian plate (Isacks and Molnar, 1971; Roecker et al., 1980). In this region lie the junction of several major mountains such as the Himalayas, Karakorum, Pamirs, Hindukush, and
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Kun-lun. The northern part of this mountainous region is characterized by highly folded structures. Most of the mountain systems are separated by major faults paralleling their trend as shown in Fig. 1. This region experiences a large number of shallow and intermediate-depth earthquakes (Santo, 1969; Nowroozi, 1972; Billingaton et al., 1977; Kaila et al., 1974; Kaila and Madhav Rao, 1979; Kaila, 1981; Verma et al., 1980; Singh et al., 1991; Shanker and Singh, 1995). The considered region has a V-shaped lithosphere. A few weak known faults are reported to be seismically active, and the seismicity is attributed to the Herat (north of Kabul) fault, the Chaman fault, and the mountain ranges in the Pamir knot. Owing to lack of high-quality instrumental data, it is difficult to develop an earthquake generation model for this region. However, the region shows earthquake epicenters (M sz5.5) to be very close to each other in some places, and it is difficult to decide whether any two main shocks originate on the same fault. Such zones are identified as seismogenic sources.
Fig. 1. Tectonic map of the Hindukush–Pamir–Himalaya (after Singh et al., 1991).
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3. The seismogenic sources and data used An important step for this work is to define the seismogenic sources of the shallow earthquakes in the area under study. For the purposes of the present analysis, the whole area has been separated into seismogenic sources on the basis of spatial clustering of the epicenters of strong earthquakes, seismicity level, maximum earthquake observed, type of faulting, and geomorphological criteria (Papazachos, 1989). Each seismogenic source includes the main seismic fault, where the maximum (characteristic) earthquake occurs, and possibly other smaller faults where smaller main shocks can also occur. Nine of these seismogenic sources are demarcated by elliptical boundaries, which are also shown in Fig. 2 together with the epicenters of the data selected by the following criteria: (a) in each source, at least three main shocks (two repeat times) of magnitudes M sz5.5 occurred during the period 1905–1999; (b) in each source, at least one main shock with M sz6.5 occurred during this period of time; and (c) each source is characterized by distinct seismotectonic properties in relation to
the adjacent region (same kind of faulting, high seismicity level, etc.). The earthquake catalog prepared by National Earthquake Information Center (NEIC, 1905-1999), U.S. Department of the Interior, U.S. Geological Survey, USA, was used for the period 1905–1999 with surface wave magnitude M sz5.5 (Table 1). The data before 1905 appear to be incomplete because of the lack of instrumental records. In general, a 95-year catalog duration may not be sufficient for defining recurrence intervals at these magnitudes. However, it appears to be applicable for the considered region because of its high seismic activity. The data used in such studies must be homogeneous; that is, the magnitudes of the earthquakes must be in the same scale. The magnitudes used in the present study are surface wave magnitudes with the exception of some big earthquakes for which seismic moment magnitude is used due to the saturation of surface wave magnitude. Also, use of complete data, i.e., use of a data sample that includes all earthquakes that occurred in a certain seismogenic region during a certain time period and have magnitudes larger than a certain minimum value, is necessary for such
Fig. 2. Earthquake epicenters with M sz5.5 (Table 1) for the period 1905–1999. The nine seismogenic sources are demarcated by elliptical boundaries. Filled symbols denote foreshocks/aftershocks.
D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140 Table 1 Information on the basic earthquake data of nine seismogenic sources of Hindukush–Pamir–Himalayas
Seismogenic source
Date
Seismogenic source
Date
Y
M
D
Y
M
D
HPH5
HPH1
1940 1956 1971 1972 1982 1984 1988 1991 1972 1972 1972 1981 1987 1987 1987 1988 1988 1988 1988 1990 1991 1993 1993 1994 1994 1995 1995 1996 1997 1997 1998 1998 1998 1905 1937 1947 1955 1974 1945 1952 1952 1955 1985 1931 1931 1956 1966 1966 1966 1995 1997
03 09 05 11 11 02 11 01 09 09 09 09 04 05 10 04 08 09 07 02 07 08 09 06 10 05 10 09 05 12 02 03 12 04 11 07 06 12 06 10 12 08 05 09 09 05 01 02 02 05 02
19 16 09 16 20 01 27 31 03 03 04 12 02 05 03 16 06 25 24 05 14 09 04 30 25 16 18 14 13 17 14 21 11 04 15 10 27 28 22 10 25 23 06 26 30 13 24 07 07 13 27
1997 1997 1997 1999 1937 1955 1959 1973 1975 1986 1986 1991 1999 1911 1966 1975 1975 1982 1932 1934 1953 1955 1961 1978 1986 1926 1930 1937 1975 1975 1975 1996
02 03 08 06 10 06 05 04 01 04 07 10 03 10 03 01 07 01 03 10 10 01 06 04 07 05 09 11 04 05 06 11
27 20 24 26 20 27 12 01 19 26 16 19 28 14 06 19 29 23 04 19 11 28 04 04 06 10 01 15 28 19 04 19
HPH2
HPH3
HPH4
HPH5
Ms
Epicenter Lat. (8N)
Long. (8E)
6.0 6.4 5.5 5.6 5.7 5.9 5.6 6.6 6.2 5.6 5.7 6.1 5.7 5.7 6.0 5.5 6.0 5.5 5.8 5.7 6.5 6.3 5.5 6.4 5.9 5.9 6.3 5.9 6.5 6.3 5.5 6.0 5.7 8.6 6.5 6.0 6.0 5.9 6.5 6.1 5.8 6.5 5.6 5.6 5.6 6.5 5.5 5.7 5.6 5.6 7.3
35.75 33.96 35.54 35.66 34.54 34.57 35.20 35.99 35.94 35.95 35.90 35.67 36.12 36.46 36.49 36.00 36.49 36.40 36.11 37.05 36.33 36.44 36.43 36.33 36.36 36.46 36.43 36.05 36.41 36.39 36.36 36.43 36.51 33.00 35.00 33.00 32.50 35.05 32.50 30.20 29.40 31.00 30.88 28.00 28.50 29.90 29.92 29.92 30.25 30.23 29.98
70.00 69.51 71.05 69.91 70.51 70.49 70.90 70.40 73.32 73.24 73.34 73.59 71.14 70.68 71.46 71.60 71.60 70.73 71.10 71.25 71.12 70.71 70.81 71.15 70.96 70.89 70.39 70.71 70.94 70.77 71.11 70.13 71.02 76.00 78.00 77.00 78.60 72.91 76.00 70.00 77.00 71.50 70.23 69.00 69.00 77.00 69.62 69.68 69.89 67.94 68.21
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Table 1 (continued )
HPH6
HPH7
HPH8
HPH9
Ms 6.0 5.9 5.6 5.7 5.5 6.0 6.3 5.6 5.8 5.6 5.7 7.0 6.6 6.7 6.0 6.2 5.5 6.0 5.6 5.6 6.5 6.4 6.0 5.5 5.8 6.3 5.6 6.5 5.8 5.5 5.6 7.1
Epicenter Lat. (8N)
Long. (8E)
29.99 30.14 30.08 30.10 31.00 32.50 32.40 32.12 31.93 32.03 30.89 30.78 30.51 31.00 31.49 32.38 32.57 31.67 33.50 34.00 32.30 33.30 34.18 32.98 34.41 35.50 35.50 35.00 35.80 35.11 35.82 35.35
67.98 68.02 68.00 69.44 78.00 78.60 78.66 77.83 78.52 76.32 77.88 78.77 79.40 80.50 80.55 78.49 78.49 82.28 81.00 88.00 82.80 82.40 81.93 82.25 80.05 78.00 81.00 78.00 79.85 80.83 79.92 78.13
work. Thus, for the seismogenic region for the considered area, the data are complete for M sz5.5 since 1950, M sz6.5 since 1930, and M sz7.0 since 1897 (Table 2). For clarity, Fig. 2 shows only earthquake epicenters of magnitude 5.5 and greater. Earthquakes of 5.5VM sV7.5 are considered within each zone for statistical derivation and the foreshocks and aftershocks are identified from the earthquake distribution in the time domain. Table 2 gives the name of sources (HPH1, HPH2, . . ., HPH9) and their relevant information. M is defined as the cumulative magnitude of each sequence; that is, the magnitude that corresponds to the total moment released by the major shocks (main shocks, and large foreshocks and aftershocks) of each
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Table 2 Earthquakes M sz5.5 used in the TP model analysis Name of Seismogenic Sources
Completeness
HPH1
1950, 5.5
HPH2
1950, 5.5
HPH3
1950, 5.5
HPH4
1950, 5.5 1930, 6.5
HPH5
1950, 5.5 1930, 6.5
Date
Epicenter
d
m
year
Lat. (8N)
Long. (8E)
16 9 16 20 1 27 31 3 3 4 12 2 5 3 16 6 25 24 5 14 9 4 30 25 16 18 14 13 17 14 21 11 4 15 27 28 22 0 25 23 6 13 24 7 7 13 27 27 20 24 26
9 5 11 11 2 11 1 9 9 9 9 4 5 10 4 8 9 7 2 7 8 9 6 10 5 10 9 5 12 2 3 12 4 11 6 12 6 10 12 8 5 5 1 2 2 5 2 2 3 8 6
1956 1971 1972 1982 1984 1988 1991 1972 1972 1972 1981 1987 1987 1987 1988 1988 1988 1988 1990 1991 1993 1993 1994 1994 1995 1995 1996 1997 1997 1998 1998 1998 1905 1937 1955 1974 1945 1952 1952 1955 1985 1956 1966 1966 1966 1995 1997 1997 1997 1997 1999
33.96 35.54 35.66 34.54 34.57 35.20 35.99 35.94 35.95 35.90 35.67 36.12 36.46 36.49 36.00 36.49 36.40 36.11 37.05 36.33 36.44 36.43 36.33 36.36 36.46 36.43 36.05 36.41 36.39 36.36 36.43 36.51 33.00 35.00 32.50 35.05 32.50 30.20 29.40 31.00 30.88 29.90 29.92 29.92 30.25 30.23 29.98 29.99 30.14 30.08 30.10
69.51 71.05 69.91 70.51 70.49 70.90 70.40 73.32 73.24 73.34 73.59 71.14 70.68 71.46 71.60 71.60 70.73 71.10 71.25 71.12 70.71 70.81 71.15 70.96 70.89 70.39 70.71 70.94 70.77 71.11 70.13 71.02 76.00 78.00 78.60 2.91 76.00 70.00 77.00 71.50 70.23 77.00 69.62 69.68 69.89 67.94 68.21 67.98 68.02 68.00 69.44
Ms
M (cumulative)
6.4 5.5 5.6 5.7 5.9 5.6 6.6 6.2 5.6 5.7 6.1 5.7 5.7 6.0 5.5 6.0 5.5 5.8 5.7 6.5 6.3 5.5 6.4 5.9 5.9 6.3 5.9 6.5 6.3 5.5 6.0 5.7 8.6 6.5 6.0 5.9 6.5 6.1 5.8 6.5 5.6 6.5 5.5 5.7 5.6 5.6 7.3 6.0 5.9 5.6 5.7
6.4 f 5.8 f 6.0 f 6.6 6.3 a a 6.3 a a a a f f f f 7.0 a a a a a a a a a a a a 8.6 6.5 6.0 5.9 6.6 a a 6.5 5.6 6.5 f 5.9 a f 7.3 a a a a
D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140
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Table 2 (continued ) Name of Seismogenic Sources
Completeness
HPH6
1950, 5.5
HPH7
1950, 5.5 1897, 7.0
HPH8
1950, 5.5
HPH9
1950, 5.5 1930, 6.5
Date
Epicenter
d
m
year
Lat. (8N)
Long. (8E)
27 12 1 19 26 16 19 28 6 19 29 23 11 28 4 4 6 15 28 19 4 19
6 5 4 1 4 7 10 3 3 1 7 1 10 1 6 4 7 11 4 5 6 11
1955 1959 1973 1975 1986 1986 1991 1999 1966 1975 1975 1982 1953 1955 1961 1978 1986 1937 1975 1975 1975 1996
32.50 32.40 32.12 31.93 32.03 30.89 30.78 30.51 31.49 32.38 32.57 31.67 32.30 33.30 34.18 32.98 34.41 35.00 35.80 35.11 35.82 35.35
78.60 78.66 77.83 78.52 76.32 77.88 78.77 79.40 80.55 78.49 78.49 82.28 82.80 82.40 81.93 82.25 80.05 78.00 79.85 80.83 79.92 78.13
Ms
M (cumulative)
6.0 6.3 5.6 5.8 5.6 5.7 7.0 6.6 6.0 6.2 5.5 6.0 6.5 6.4 6.0 5.5 5.8 6.5 5.8 5.5 5.6 7.1
6.0 6.3 f 5.9 f 5.9 7.1 a 6.0 6.3 a a 6.7 a a 5.5 5.8 6.5 6.0 a a 7.1
The last column gives decluster of catalog, i.e., main shocks, foreshocks (f), and aftershocks (a).
sequence. These cumulative magnitudes are used in this study instead of the magnitudes of the main shocks. Seismic moment is estimated by the moment– surface wave relationship of Purcaru and Berckhemer (1978). However, this estimate is valid only for the range 5.5VM sV7.5. All the considered earthquakes are within this range except one (Kangra) earthquake in source HPH3. Source HPH3 contains a large earthquake of M s=8.6 for which the seismic moment was taken as M 0=4.61027 dyn cm (Chen and Molnar, 1977). The moment magnitude for the considered events was derived by the definition of Hanks and Kanamori (1979). In Table 2, the differences between the cumulative moment magnitude (M) and the surface wave magnitude are b0.5. Hence, the derived magnitude (M) may be considered as a true representation of the size of the events. The minimum magnitude was considered in each case to define the corresponding M p, M f, and repeat time in years. The repeat time, T, denotes the time from the beginning of one seismic sequence to the initiation of the next sequence. The T p and T f represent the year of occurrence of the preceding and following main shock, respectively.
4. Relation between the repeat time and the preceding magnitude Data reveals that the relation between the repeat time and M p may be represented in the form log10 T ¼ c Mp þ a
ð1Þ
where c is the gradient of least-square line and a is a constant. The two parameters depend on such things as stress conditions and seismicity levels. As sufficient instrumental data was not available, the estimation of c may show deviation from the actual value. The parameter a depends on the seismicity of each source and the minimum (cutoff) magnitude of the main shock considered. The choice of minimum magnitude (M min) increases the number of repeat times (Table 3). The repeat time T shows variation from source to source due to different values of a among tectonic zones. Therefore, average repeat time (T¯ ) of the event for average seismicity level for all the seismogenic sources has been considered (Singh et al., 1992) for which the regression line is derived as logT¯ ¼ 0:19M p 0:41Fr
ð2Þ
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Table 3 Seismogenic source data used for parameter determination Name of seismogenic sources
M min
Mp
Mf
T
tp
tf
HPH1
5.8
6.4 5.8 6.0 6.4 6.0 6.4 6.3 6.3 6.0 6.5 6.6 6.5 5.9 6.5 6.0 6.3 5.9 5.9 6.0 6.3 6.3 6.0 6.7 6.7 5.5 6.7 6.0 6.5
5.8 6.0 6.6 6.0 6.6 6.6 6.3 7.0 5.9 5.6 6.5 5.9 7.3 7.3 6.3 5.9 5.9 7.1 6.3 7.1 7.1 6.3 6.3 5.5 5.8 5.8 7.1 7.1
16.17 11.21 7.00 27.38 7.00 34.37 9.02 9.84 19.50 29.70 10.17 9.73 31.05 40.79 3.88 15.69 11.49 5.26 3.88 32.44 32.44 8.87 63.26 24.48 8.26 32.74 21.56 59.01
1956 1972 1984 1956 1984 1956 1972 1981 1955 1955 1945 1956 1966 1956 1955 1959 1975 1986 1955 1959 1959 1966 1911 1953 1978 1953 1975 1937
1972 1984 1991 1984 1991 1991 1981 1991 1974 1985 1955 1966 1997 1997 1959 1975 1986 1991 1959 1991 1991 1975 1975 1978 1986 1986 1996 1996
6.0
HPH2 HPH3 HPH4
6.4 6.3
HPH5
5.9 5.6 6.5 5.9
HPH6
6.5 5.9
6.0
HPH7 HPH8
HPH9
6.3 6.0 6.3 5.5 5.8 6.0 6.5
Eq. (2) represents a straight line showing the correlation coefficient of 0.64. It reflects that the average repeat time increases with increasing of M p. The same data set is treated separately for establishing relation between log T¯ and the following main shock magnitude (M f). The derived least-square line is logT¯ ¼ 0:02Mf þ 2:08Fr
ð3Þ
A very low slope (0.02) and a very low correlation coefficient (0.05) fit the data (log T¯, M f) for the above equation. It demonstrates that less time is needed for larger future earthquakes, which suggests that a SP model is not valid for the region. For the derivation of Eq. (2), foreshocks and aftershocks were included in cumulative magnitude estimation. Similar analysis for the same data set was also derived excluding foreshocks and aftershocks as logT¯ ¼ 0:16 Mp 0:05Fr
ð4Þ
Another relation between seismic moment (M 0) and log T¯ was also derived showing the linear regression equation as logT¯ ¼ 0:20 logM0 3:67Fr
ð5Þ
The correlation coefficient for the Eqs. (4) and (5) are 0.62 and 0.67, respectively. The positive correlation coefficients suggest that Eqs. (2), (4), and (5) are statistically significant, while Eq. (3) is not. Eqs. (2), (4), and (5) are very similar to each other. It may be inferred from Eqs. (2), (4), and (5) that the TP model is valid for Hindukush–Pamir–Himalaya region and its vicinity. Astiz and Kanamori (1984) and Nishenko and Singh (1987) reported the relation between average recurrence time and average seismic moment for Mexico with a slope of 0.333 and 0.299, respectively. Papazachos (1989) reported the slope to be 0.28 for Greece. Singh et al. (1992) reported the slope to be 0.36 for Northeast and adjoining regions. Shimazaki and Nakata (1980) proposed a similar relation between the repeat times and coseismic slip of the preceding main shocks. Further, for long-term prediction of strong shallow earthquakes in the region considered, the following relations for the global applicability of bregional timeand magnitude-predictable modelQ (Papazachos and Papadimitriou, 1997) have been used: logTt ¼ b Mmin þ cMp þ dlogm0 t
ð6Þ
and Mf ¼ BMmin CMp Dlogm0 þ m
ð7Þ
where T t is the inter-event time measured in years, M min is the surface-wave magnitude of the smallest main shock considered, M p is the magnitude of the preceding main shock, M f is the magnitude of the following main shock, m 0 is the moment rate in each source per year that expresses the tectonic loading exerted in the volume of each seismogenic region, and t and m are constants. Table 4 lists the values of the parameters for each seismogenic source necessary to proceed. The model expressed by relations (6) and (7) has the advantage that all parameters (b, c, d, t, B, C,
D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140 Table 4 Information on the basic parameters used for every source Seismogenic source name
a
b
Mmax
log m 0 (dyne com year1)
HPH1 HPH2 HPH3 HPH4 HPH5 HPH6 HPH7 HPH8 HPH9
5.28 5.32 5.12 5.32 5.35 5.42 5.21 5.35 5.17
0.84 0.87 0.87 0.84 0.87 0.84 0.84 0.84 0.84
6.4 6.4 8.6 6.6 6.5 6.3 6.7 6.7 6.5
25.96 25.86 26.83 26.13 25.92 26.03 26.09 26.23 25.92
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where T, M min, and log m 0 and M p are the observed values. The line drawn through the data is a leastsquares fit. The positive correlation between the repeat time and the magnitude of the preceding main shock suggests that the time-predictable model hold in the area under study. The values of the parameters of Eq. (7) were determined by the use of all available information from Table 3, and the following formula was found: Mf ¼ 1:31Mmin 0:60Mp 0:72logm0 þ 21:01
The first column gives the name of every source. The constants for the Gutenberg Richter relation are given in the next two columns. In the last two columns, the maximum magnitude and the logarithm of the moment rate are given.
ð9Þ
with a correlation coefficient of 0.55 and standard deviation of 0.27. Fig. 3 displays a plot of log T*=log T0.19M min0.29log m 0+10.63 as a function of M p,
with a correlation coefficient equal to 0.73 and a standard deviation equal to 0.36. The M f*=M f 1.31M min+0.72log m 021.01, where M f, M min, and log m 0 are the observed values, is plotted versus the observed M p in Fig. 4. The straight line is a least squares fit. The negative dependence of the magnitude of the following main shock on the magnitude of the preceding main shock indicates that a large main shock is followed by a small one, and a small main shock by a large one. Most of the parameters in Eqs. (6) and (7) and their values are self-explanatory. For instance, the inclusion of the M min term in Eq. (6) is essentially the Gutenberg–Richter law, because for large cutoff magnitudes, M min, we have smaller log N (N= number of events with MNM min) and therefore larger log T~log N 1. The crucial point of Eqs. (6) and (7) is the inclusion of linear M p term and the values of constants c and C, which represent the heart of the time- and magnitude-predictable model. Hence,
Fig. 3. Dependence of repeat time, T* with the preceding main shock magnitude, M p.
Fig. 4. Dependence of the magnitude of the following main shock (M f*) on the magnitude of the preceding main shock (M p).
D, and m) of these relations are calculated by all available data for all sources. On the basis of inter-event times of strong main shocks in the nine seismogenic sources of Hindukush–Pamir–Himalayas region, the time- and magnitude-predictable relationships (Shanker and Singh, 1996; Papazachos et al., 1997) had been determined as logTt ¼ 0:19Mmin þ 0:52Mp þ 0:29logm0 10:63 ð8Þ
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the positive global c value indicates that large events lead to large inter-event times, whereas the negative value of C value indicates that large events tend to be followed by smaller events and vice versa (Papazachos and Papadimitriou, 1997). Similar results, i.e., positive correlation between M p and log T t and negative correlation between M p and M f, were also found in other areas where this model has been tested (Papazachos, 1992; Singh et al., 1992; Papazachos and Papaioannou, 1993; Karakaisis, 1993).
M p, by the relation (Papazachos and Papaioannou, 1993): F PðDt Þ ¼
X1 F r X1 1F r
X2 r
ð10Þ
where X2 ¼ log
5. Long-term prediction of the next shallow main shock
ðt þ Dt Þ ; Tt
X1 ¼ log
t Tt
and F is the complementary cumulative value of the normal distribution with mean equal to zero and standard deviation equal to r. Given the date and the magnitude of the last event in a seismogenic source as well as the uncertainty of the model expressed by its standard deviation r=0.27, the probabilities of occurrence of the next shallow main shocks with M sz6.0 during the next 20 years were computed. Table 5 gives information on the expected large shallow earthquakes based on the model expressed by relations (8) and (9). The first column gives the name of the seismogenic source. The next two columns give the magnitude of the expected main shock, M f (this magnitude has been calculated by relation (9)) and the corresponding highest probabilities, P 20, for the occurrence of large main shocks during the decades (2000–2020). One must note that the absolute values of the probabilities are of relative importance; that is, their change from source to source is significant. This is because these values may change if a larger sample of data is used.
The model tested in the present study provides a means to calculate the time of occurrence of the next large main shock in each one of the defined seismogenic sources using relation (8). However, because there is a considerable difference between repeat times, T t, estimated from relation (8), and the corresponding actual repeat times, T, it is preferable to estimate the probability of occurrence of the next main shock larger than a certain magnitude and in a given time interval. It is found that log-normal distribution of T/T t is more appropriate than the Gaussian or Weibull distributions (Papazachos, 1988b; Papazachos and Papaioannou, 1993). This distribution holds for each of the seismogenic sources. One can calculate the conditional probability, P, for the occurrence of a main shock with MzM min during the next Dt years (from now), when the previous such earthquake occurred t years ago (from now) and had magnitude
Table 5 Expected magnitude, M f, and the corresponding probabilities, P 20, for the occurrence of large (M minz5.5) shallow main shocks during the period 2000–2020 in the Hindukush–Pamir–Himalayas Seismogenic source no.
Source name
M fF0.36 (Eq. (9))
P 20 (Eq. (10)) (log-normal)
M min (Table 3)
Mp (Table 2)
t p (year of M p) (Table 3)
log m 0 (Table 4)
log T t Eq. (8)
1 2 3 4 5 6 7 8 9
HPH1 HPH2 HPH3 HPH4 HPH5 HPH6 HPH7 HPH8 HPH9
7.4 7.5 7.5 6.9 8.6 8.4 7.1 7.7 8.5
0.68 0.42 1.00 1.00 0.00 0.10 0.99 1.00 0.04
5.8 6.3 5.9 5.6 5.9 5.9 6.0 5.5 6.0
6.6 6.5 5.9 5.6 7.3 7.0 6.2 5.8 7.1
1991 1991 1974 1985 1997 1991 1975 1986 1996
25.96 25.86 26.83 26.13 25.92 26.03 26.09 26.23 25.92
1.4324 1.4464 1.3397 0.9237 1.8038 1.6797 1.3001 1.0377 1.7188
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6. Discussion and conclusion This study attempts to quantitatively assess the probabilities of occurrence and the magnitudes of future large (M sz6.0) shallow main shocks in the nine seismogenic sources into which the seismic zone of Hindukush–Pamir–Himalaya was divided. The estimation of conditional probabilities and the magnitude of the expected event were based on the time- and magnitude-predictable model expressed by relations (8) and (9). There are several cases where this model was applied on the basis of the methodology followed in the present study; that is, for the Aegean area (Papazachos, 1988a,b, 1989, Papazachos and Papaioannou, 1993); Alpine–Himalayan belt (Papazachos et al., 1997); New Guinea-bismark sea (Karakaisis, 1993); and Northeast region (Singh et al., 1992). This methodology enables the use of more inter-event times than are usually available in studies using only the recurrence times of characteristic events, because in each seismogenic source, not only the main fault but also other secondary faults, where smaller earthquakes occur, are considered. This is expressed by the term bbM minQ in relations (8) and (9). Although there are some uncertainties involved in the methodology followed in the present study, our results indicate that the time- and magnitude-predictable model can probably play an increasingly important role in earthquake prediction. Most of the reproducible results are obtained so far for the intermediate-term stage, where characteristic duration of alarms is years. The earthquake forecasts described above have a limited accuracy. Nevertheless, they are useful in earthquake hazard assessment and loss prevention. The opinion that only a precise short-term prediction and estimate of seismic hazard are practically useful that sometimes emerges in the seismological literature can lead to costly mistakes. The results of the present analysis indicate that the dependence of the repeat time on the magnitude of the preceding main shock is strong and positive, while the dependence of the following main shock on the repeat time is weak and negative. This shows that the TP model holds for the seismogenic sources of shallow to deep earthquakes in the Hindukush–Pamir–Himalaya and its vicinity and that the SP model does not hold for the same region. Eq. (8) may be used for long-
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range earthquake forecasting in the nine seismogenic sources, and to aid in earthquake hazard mitigation and other engineering purposes. The reliability of the method depends on the availability of a good amount of reliable seismicity data. The ambiguity in assessment of forthcoming earthquakes increases for seismogenic sources showing very long repeat times.
Acknowledgement The first author is indebted to the Head of the Department of Earthquake Engineering, Indian Institute of Technology Roorkee (formerly University of Roorkee), Roorkee, India, for providing necessary facilities. The authors are grateful to Chris H. Cramer and Amy Brown for their critical comment and suggestions, and to the editor, Kaye M. Shedlock, for his efforts throughout publication. This research is supported by All India Council For Technical Education (AICTE), New Delhi, under the Research & Development Project Grant No. 8020/RID/R&D129/01-02, and the part of this work was presented in the First IAGA-IASPEI-2001 at Hanoi, Vietnam.
References Anagnos, T., Kiremidjian, A.S., 1984. Stochastic time predictable model for earthquake occurrences. Bull. Seismol. Soc. Am. 74, 2593 – 2611. Astiz, L., Kanamori, H., 1984. An earthquake doublet in Ometepec, Guerreo, Mexico. Phys. Earth Planet Inter. 34, 24 – 25. Billingaton, S., Isacks, B., Barazangi, M., 1977. Spatial distribution of focal mechanisms of mantle earthquakes in the Hindukush– Pamir region—a contorted Benioff zone. Geology 5, 699 – 704. Bufe, C.G., Harsh, P.W., Buford, R.O., 1977. Steady-state seismic slip—a precise recurrence model. Geophys. Res. Lett. 4, 91 – 94. Chen, W.P., Molnar, P., 1977. Seismic moment of major earthquakes and the average rate of slip in Central Asia. J. Geophys. Res. 82, 2945 – 2969. Cornell, C.A., 1968. Engineering seismic risk analysis. Bull. Seismol. Soc. Am. 58, 1583 – 1606. Gardner, J.K., Knopoff, L., 1974. Is the sequence of earthquakes in the southern California with aftershocks removed Poissonian? Bull. Seismol. Soc. Am. 64, 1363 – 1368. Hanks, T.C., Kanamori, H., 1979. A moment-magnitude scale. J. Geophys. Res. 84, 2348 – 2350. Isacks, B.L., Molnar, P., 1971. Distribution of stresses in the descending lithosphere from a global survey of focal mechanism solutions of mantle earthquakes. Rev. Geophys. Space Phys. 9, 103 – 147.
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Kaila, K.L., 1981. Structure and sesmotectonic of the Himalayan– Pamir–Hindukush region and Indian boundary. In: Gupta, H.K., Delany, F.M. (Eds.), Zagros–Hindukush Himalayas Geodynamic Evolution, Geodyn. Ser. Am. Geophys. Union, vol. 3, pp. 217 – 293. Kaila, K.L., Madhav Rao, N., 1979. Seismotectonics of the Himalayan belt and deep tectonic features of the Pamir– Hindukush region. Geophys. Res. Bull. 17, 319 – 327. Kaila, K.L., Madhav Rao, N., Narain, H., 1974. Seismotectonic map of the SW Asia region comprising Eastern Turkey, Caucasus, Persian Plateau, Afghanistan and Hindukush. Bull. Seismol. Soc. Am. 64, 657 – 669. Karakaisis, G.F., 1993. Long term earthquake prediction in New Guinea–Bismark sea region based on the time and magnitude predictable model. J. Phys. Earth 41, 365 – 389. Kelleher, J.A., Sykes, L.R., Oliver, J., 1973. Possible criteria for predicting earthquake locations and their applications to major plate boundaries of the Pacific and Caribbean. J. Geophys. Res. 78, 2547 – 2585. Kiremidjian, A.S., Anagnos, T., 1984. Stochastic slip predictable model for earthquake occurrences. Bull. Seismol. Soc. Am. 74, 739 – 755. McNally, K.C., Minster, J.B., 1981. Non uniform seismic slip rates along the middle America trench. J. Geophys. Res. 86, 4949 – 4959. National Earthquake Information Center (NEIC), U. S. Department of the Interior U. S. Geological Survey, USA. Catalogue of earthquakes for the period 1905–1999. Nishenko, S.P., Buland, R., 1987. A generic recurrence interval distribution for earthquake forecasting. Bull. Seismol. Soc. Am. 77, 1382 – 1399. Nishenko, S.P., Singh, P., 1987. Conditional probabilities for the recurrence of large and great interplate earthquakes along the Mexican subduction zone. Bull. Seismol. Soc. Am. 77, 2094 – 2114. Nowroozi, A.A., 1972. Focal mechanism of earthquakes in Persia, Turkey, west Pakistan, and Afghanistan and plate tectonics of the middle East. Bull. Seismol. Soc. 62, 823 – 850. Papadopoulos, G.A., Voidomatis, P., 1987. Evidence for periodic seismicity in the inner Aegean seismic zone. Pure Appl. Geophys. 125, 613 – 628. Papazachos, B.C., 1988. Seismic hazard and long term earthquake prediction in Greece. European School of Earthquake Science, Course on Earthquake Hazard Assessment, Athens, Greece, 9– 16, May 1988. , pp. 1 – 10. Papazachos, B.C., 1988. Long term prediction of earthquakes in seismogenic sources of Greece. UN Sem. On prediction of Earthquakes, Lisbon, Portugal, 14–18 Nov. 1988, pp. 1 – 10. Papazachos, B.C., 1989. A time predictable model for earthquake generation in Greece. Bull. Seismol. Soc. Am. 79, 77 – 84.
Papazachos, B.C., 1992. A time and magnitude predictable model for generation of shallow earthquakes in the Aegean area. Pure Appl. Geophys. 138, 287 – 308. Papazachos, B.C., Papaioannou, Ch.A., 1993. Long term earthquake prediction in Aegean area based on a time and magnitude predictable model. Pure Appl. Geophys. 140, 593 – 612. Papazachos, B.C., Papadimitriou, E.E., 1997. Evaluation of the global applicability of the regional time and magnitude-predictable seismicity model. Bull. Seismol. Soc. Am. 87, 799 – 808. Papazachos, B.C., Karakaisis, G.F., Papadimitriou, E.E., Papaioannou, Ch.A., 1997. The regional time and magnitude predictable model and its application to the Alpine–Himalayan belt. Tectonophysics 271, 295 – 323. Purcaru, G., Berckhemer, H., 1978. A magnitude scale for very large earthquakes. Tectonophysics 49, 189 – 198. Roecker, S.W., Sovoleva, O.V., Nersessove, L.L., Luck, A.A., Hatzfeld, D., Chatelain, J.L., Molnar, P., 1980. Seismicity and fault plane solutions of intermediate depth earthquakes in the Pamir-Hindukush region. J. Geophys. Res. 85, 1358 – 1364. Santo, T., 1969. Regional study on the characteristic seismicity of the world. Pt. 1 Hindukush region. Bull. Earthq. Res. Inst. 47, 1035 – 1048. Shimazaki, K., Nakata, T., 1980. Time-predictable recurrence model or large earthquakes. Geophys. Res. Lett. 7, 279 – 282. Singh, V.P., Shanker, D., Ram, A., 1991. Seismological approach to earthquake prediction in Himalayas. J. Sci. Res. 41B, 101 – 110. Singh, V.P., Shanker, D., Singh, J., 1992. On the validity of timepredictable model for earthquake generation in northeast India. Proc. Indian Acad. Sci., A Earth Planet Sci. 101 (4), 361 – 368. Singh, V.P., Shanker, D., Hamada, K., 1994. A study of seismicity of north-east India and adjoining areas based on statistical analysis. Curr. Sci. 66 (12), 922 – 926. Shanker, D., Singh, V.P., 1995. Earthquake distribution characteristic and seismicity rate in the Hindukush and its vicinity. Acta Geophys. Pol. 43 (4), 337 – 342. Shanker, D., Singh, V.P., 1996. Regional time-and magnitudepredictable seismicity model for north-east India and vicinity. Acta Geod. Geophys. Hung. 31 (1–2), 181 – 190. Verma, R.K., Mukhopadhyay, M., Bhanja, A.K., 1980. Seismotectonics of the Hindukush and Baluchistan arc. Tectonophyics 66, 301 – 322. Wallace, R.E., 1970. Earthquake recurrence intervals on the San Andreas Fault. Geol. Soc. Amer. Bull. 81, 2875 – 2890. Wang, S.C., McNally, K.C., Geller, R.J., 1982. Seismic strain release along the Middle America Trench, Mexico. Geophys. Res. Lett. 9, 182 – 185. Wesnousky, S.G., Jones, L.M., Scholz, C.H., Deng, Q., 1984. Historical seismicity and rates of crustal deformation along the margin of the Ordos Block, North China. Bull. Seismol. Soc. Am. 74, 1767 – 1783.
Regional time-predictable modeling in the Hindukush–Pamir–Himalayas region D. Shankera,*, E.E. Papadimitrioub a
Department of Earthquake Engineering, Indian Institute of Technology Roorkee (formerly University of Roorkee), Rorrkee, Uttaranchal 247667, India b Laboratory of Geophysics, University of Thessaloniki, Thessaloniki GR-54006, Greece Received 7 January 2002; received in revised form 15 April 2002; accepted 9 March 2004 Available online 26 August 2004
Abstract The seismic characteristic of Hindukush–Pamir–Himalaya (HPH) and its vicinity is very peculiar and has experienced many widely distributed large earthquakes. Recent work on the time-dependent seismicity in the Hindukush–Pamir–Himalayas is mainly based on the so-called bregional time-predictable modelQ, which is expressed by the relation log T=cM p+a, where T is the inter-event time between two successive main shocks of a region and M p is the magnitude of the preceded main shock. Parameter a is a function of the magnitude of the minimum earthquake considered and of the tectonic loading and c is positive (~0.3) constant. In 90% of the cases with sufficient data, parameter c was found to be positive, which strongly supports the validity of the model. In the present study, a different approach, which assumes no prior regionalization of the area, is attempted to check the validity of the model. Nine seismic sources were defined within the considered region and the inter-event time of strong shallow main shock were determined and used for each source in an attempt at long-term prediction, which show the clustering and occurrence of at least three earthquakes of magnitude 5.5VM sV7.5 giving two repeat times, satisfying the necessary and sufficient conditions of time-predictable model (TP model). Further, using the global applicability of the regional time- and magnitude-predictable model, the following relations have been obtained: log T t=0.19 M min+0.52M p+0.29 log m 010.63 and M f =1.31M min0.60M p0.72 log m 0+21.01, where T t is the inter-event time, measured in years; M min the surface wave magnitude of the smallest main shock considered; M p the magnitude of preceding main shock; M f the magnitude of the following main shock; and m 0 the moment rate in each source per year. These relations may be used for seismic hazard assessment in the region. Based on these relations and taking into account the time of occurrence and the magnitude of the last main shock in each seismogenic source, time-dependent conditional probabilities for the occurrence of the next large (M sz5.5) shallow main shocks during the next 20 years as well as the magnitudes of the expected main shocks are determined. D 2004 Elsevier B.V. All rights reserved. Keywords: Characteristic earthquake; Hindukush–Pamir–Himalaya; Seismogenic source; Regional time predictable modeling
* Corresponding author. Tel.: +91 1332 285128; fax: +91 1332 276899/273560. E-mail address: [email protected] (D. Shanker). 0040-1951/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.tecto.2004.03.027
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1. Introduction Vulnerability of our civilization to geological disasters is rapidly growing. Today, a single earthquake with subsequent ripple effects may take up to a million lives, cause material damage, render large region uninhabitable, and trigger a localized or regional economic depression. New possibilities for prediction and management of geological and geotechnical disasters have been developed during the last few decades. The problem of earthquake prediction consists of consecutive, step by step, narrowing down the time interval, area, and magnitude range where a strong earthquake will occur. Such formulation is dictated both by the nature of the process leading to strong earthquakes and by the practical need for earthquake preparedness. Most of the earthquake-generation models currently used for seismic hazard evaluation have attracted the attention of many scientists. Several workers (Cornell, 1968; Gardner and Knopoff, 1974; Papadopoulos and Voidomatis, 1987; Singh et al., 1994) reported that occurrence of earthquakes follow a Poisson distribution, suggesting memoryless property of seismic zones. Wallace (1970) and Nishenko and Singh (1987), among others, reported timedependent properties of earthquake-generating sources for several regions. Seismic hazard prediction is an important prerequisite for comprehensive disaster prevention. Recent development in seismology and geophysics have lead to two alternative representations for earthquake recurrence patterns, which are based on physical concepts and which lead to more accurate estimates of earthquake occurrence probabilities, and are desirable in seismic hazard analysis. The proposed time-dependent recurrence models were SP model (slip-predictable model: Bufe et al., 1977; McNally and Minster, 1981; Singh et al., 1991; Wang et al., 1982, Kiremidjian and Anagnos, 1984) and TP model (time-predictable model: Shimazaki and Nakata, 1980; Anagnos and Kiremidjian, 1984; Papazachos, 1989; Singh et al., 1992). To estimate the long term probabilities for the generation of strong earthquakes on single faults, the time-predictable model seems to be more plausible than the slip-predictable model (Wesnousky et al., 1984; Astiz and Kanamori, 1984; Nishenko and Buland, 1987).
TP model discussed here also holds if the seismic source includes other small faults where smaller main shocks occur in addition to the main fault where the characteristic earthquake is generated (Papazachos, 1989). These models were based on the assumption of a constant tectonic stress accumulation rate and the association of stress relief with a sequence of earthquakes. According to the TP model, the time interval between large earthquakes is proportional to the amount of slip from the preceding earthquake, and large earthquakes occur when the stress has reached a fixed limit value. In the SP model, the time interval between large earthquakes is proportional to the slip amount of the next large earthquake. Repeat times of large earthquakes have become an extensive tool to obtain better estimates of seismic potential and better forecasts of future large shocks. Repeat times are taken to be the time intervals between the largest shocks that occur at a given place along a plate boundary or in a specific seismic zone, and they vary within and between seismic zones, depending not only on the rate of plate motion but also on other factors, i.e., length of rapture along strike, downdip width, and dip of the plate boundary (Kelleher et al., 1973). Consequently, if a model can make use of the available repeat times, it offers a very useful tool for long-term earthquake prediction. Papazachos (1988a,b; 1992) carried out an investigation to identify time-dependent relations among strong earthquakes that occurred in seismogenic sources in Greece. He proposed a model where the inter-event time T t, and magnitude, M f, of the following main shock were quantitatively expressed in relation to the magnitude, M min, of the smallest considered main shock and to the magnitude, M p, of the preceding main shock in each seismogenic source, and found that the time-predictable model holds. Papazachos and Papaioannou (1993) improved the preceding methodology to include a new term in the relations both for the inter-event time and the magnitude of the expected main shock. This term depends on the yearly moment rate in each seismogenic source. This is called the btime and magnitudepredictable modelQ. Furthermore, they applied this model to estimate the probability of occurrence of the next main shock during the next several years and the magnitude of this expected main shock in each seismogenic source.
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The basic objective of the present paper is to study the time-dependent property of earthquake generation sources to establish the validity of that model in India and its vicinity and to estimate the probability of occurrence of the next main shock, as well as its magnitude, in each seismogenic source there.
2. Regional characteristics The considered zone (278N to 378N and 688 E to 848E) includes the Hindukush, Pamir, and Karakorum regions, which lie to the north of the northern apex of the Indian subcontinent. From a seismic point of view, this region is one of the most active in the world. Because the Hindukush–Pamir seismic zone is located close to the Indian–Eurasian plate boundary, several authors have suggested that the intermediate-depth seismicity is due to the convergence of the Eurasian and Indian plate (Isacks and Molnar, 1971; Roecker et al., 1980). In this region lie the junction of several major mountains such as the Himalayas, Karakorum, Pamirs, Hindukush, and
131
Kun-lun. The northern part of this mountainous region is characterized by highly folded structures. Most of the mountain systems are separated by major faults paralleling their trend as shown in Fig. 1. This region experiences a large number of shallow and intermediate-depth earthquakes (Santo, 1969; Nowroozi, 1972; Billingaton et al., 1977; Kaila et al., 1974; Kaila and Madhav Rao, 1979; Kaila, 1981; Verma et al., 1980; Singh et al., 1991; Shanker and Singh, 1995). The considered region has a V-shaped lithosphere. A few weak known faults are reported to be seismically active, and the seismicity is attributed to the Herat (north of Kabul) fault, the Chaman fault, and the mountain ranges in the Pamir knot. Owing to lack of high-quality instrumental data, it is difficult to develop an earthquake generation model for this region. However, the region shows earthquake epicenters (M sz5.5) to be very close to each other in some places, and it is difficult to decide whether any two main shocks originate on the same fault. Such zones are identified as seismogenic sources.
Fig. 1. Tectonic map of the Hindukush–Pamir–Himalaya (after Singh et al., 1991).
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3. The seismogenic sources and data used An important step for this work is to define the seismogenic sources of the shallow earthquakes in the area under study. For the purposes of the present analysis, the whole area has been separated into seismogenic sources on the basis of spatial clustering of the epicenters of strong earthquakes, seismicity level, maximum earthquake observed, type of faulting, and geomorphological criteria (Papazachos, 1989). Each seismogenic source includes the main seismic fault, where the maximum (characteristic) earthquake occurs, and possibly other smaller faults where smaller main shocks can also occur. Nine of these seismogenic sources are demarcated by elliptical boundaries, which are also shown in Fig. 2 together with the epicenters of the data selected by the following criteria: (a) in each source, at least three main shocks (two repeat times) of magnitudes M sz5.5 occurred during the period 1905–1999; (b) in each source, at least one main shock with M sz6.5 occurred during this period of time; and (c) each source is characterized by distinct seismotectonic properties in relation to
the adjacent region (same kind of faulting, high seismicity level, etc.). The earthquake catalog prepared by National Earthquake Information Center (NEIC, 1905-1999), U.S. Department of the Interior, U.S. Geological Survey, USA, was used for the period 1905–1999 with surface wave magnitude M sz5.5 (Table 1). The data before 1905 appear to be incomplete because of the lack of instrumental records. In general, a 95-year catalog duration may not be sufficient for defining recurrence intervals at these magnitudes. However, it appears to be applicable for the considered region because of its high seismic activity. The data used in such studies must be homogeneous; that is, the magnitudes of the earthquakes must be in the same scale. The magnitudes used in the present study are surface wave magnitudes with the exception of some big earthquakes for which seismic moment magnitude is used due to the saturation of surface wave magnitude. Also, use of complete data, i.e., use of a data sample that includes all earthquakes that occurred in a certain seismogenic region during a certain time period and have magnitudes larger than a certain minimum value, is necessary for such
Fig. 2. Earthquake epicenters with M sz5.5 (Table 1) for the period 1905–1999. The nine seismogenic sources are demarcated by elliptical boundaries. Filled symbols denote foreshocks/aftershocks.
D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140 Table 1 Information on the basic earthquake data of nine seismogenic sources of Hindukush–Pamir–Himalayas
Seismogenic source
Date
Seismogenic source
Date
Y
M
D
Y
M
D
HPH5
HPH1
1940 1956 1971 1972 1982 1984 1988 1991 1972 1972 1972 1981 1987 1987 1987 1988 1988 1988 1988 1990 1991 1993 1993 1994 1994 1995 1995 1996 1997 1997 1998 1998 1998 1905 1937 1947 1955 1974 1945 1952 1952 1955 1985 1931 1931 1956 1966 1966 1966 1995 1997
03 09 05 11 11 02 11 01 09 09 09 09 04 05 10 04 08 09 07 02 07 08 09 06 10 05 10 09 05 12 02 03 12 04 11 07 06 12 06 10 12 08 05 09 09 05 01 02 02 05 02
19 16 09 16 20 01 27 31 03 03 04 12 02 05 03 16 06 25 24 05 14 09 04 30 25 16 18 14 13 17 14 21 11 04 15 10 27 28 22 10 25 23 06 26 30 13 24 07 07 13 27
1997 1997 1997 1999 1937 1955 1959 1973 1975 1986 1986 1991 1999 1911 1966 1975 1975 1982 1932 1934 1953 1955 1961 1978 1986 1926 1930 1937 1975 1975 1975 1996
02 03 08 06 10 06 05 04 01 04 07 10 03 10 03 01 07 01 03 10 10 01 06 04 07 05 09 11 04 05 06 11
27 20 24 26 20 27 12 01 19 26 16 19 28 14 06 19 29 23 04 19 11 28 04 04 06 10 01 15 28 19 04 19
HPH2
HPH3
HPH4
HPH5
Ms
Epicenter Lat. (8N)
Long. (8E)
6.0 6.4 5.5 5.6 5.7 5.9 5.6 6.6 6.2 5.6 5.7 6.1 5.7 5.7 6.0 5.5 6.0 5.5 5.8 5.7 6.5 6.3 5.5 6.4 5.9 5.9 6.3 5.9 6.5 6.3 5.5 6.0 5.7 8.6 6.5 6.0 6.0 5.9 6.5 6.1 5.8 6.5 5.6 5.6 5.6 6.5 5.5 5.7 5.6 5.6 7.3
35.75 33.96 35.54 35.66 34.54 34.57 35.20 35.99 35.94 35.95 35.90 35.67 36.12 36.46 36.49 36.00 36.49 36.40 36.11 37.05 36.33 36.44 36.43 36.33 36.36 36.46 36.43 36.05 36.41 36.39 36.36 36.43 36.51 33.00 35.00 33.00 32.50 35.05 32.50 30.20 29.40 31.00 30.88 28.00 28.50 29.90 29.92 29.92 30.25 30.23 29.98
70.00 69.51 71.05 69.91 70.51 70.49 70.90 70.40 73.32 73.24 73.34 73.59 71.14 70.68 71.46 71.60 71.60 70.73 71.10 71.25 71.12 70.71 70.81 71.15 70.96 70.89 70.39 70.71 70.94 70.77 71.11 70.13 71.02 76.00 78.00 77.00 78.60 72.91 76.00 70.00 77.00 71.50 70.23 69.00 69.00 77.00 69.62 69.68 69.89 67.94 68.21
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Table 1 (continued )
HPH6
HPH7
HPH8
HPH9
Ms 6.0 5.9 5.6 5.7 5.5 6.0 6.3 5.6 5.8 5.6 5.7 7.0 6.6 6.7 6.0 6.2 5.5 6.0 5.6 5.6 6.5 6.4 6.0 5.5 5.8 6.3 5.6 6.5 5.8 5.5 5.6 7.1
Epicenter Lat. (8N)
Long. (8E)
29.99 30.14 30.08 30.10 31.00 32.50 32.40 32.12 31.93 32.03 30.89 30.78 30.51 31.00 31.49 32.38 32.57 31.67 33.50 34.00 32.30 33.30 34.18 32.98 34.41 35.50 35.50 35.00 35.80 35.11 35.82 35.35
67.98 68.02 68.00 69.44 78.00 78.60 78.66 77.83 78.52 76.32 77.88 78.77 79.40 80.50 80.55 78.49 78.49 82.28 81.00 88.00 82.80 82.40 81.93 82.25 80.05 78.00 81.00 78.00 79.85 80.83 79.92 78.13
work. Thus, for the seismogenic region for the considered area, the data are complete for M sz5.5 since 1950, M sz6.5 since 1930, and M sz7.0 since 1897 (Table 2). For clarity, Fig. 2 shows only earthquake epicenters of magnitude 5.5 and greater. Earthquakes of 5.5VM sV7.5 are considered within each zone for statistical derivation and the foreshocks and aftershocks are identified from the earthquake distribution in the time domain. Table 2 gives the name of sources (HPH1, HPH2, . . ., HPH9) and their relevant information. M is defined as the cumulative magnitude of each sequence; that is, the magnitude that corresponds to the total moment released by the major shocks (main shocks, and large foreshocks and aftershocks) of each
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Table 2 Earthquakes M sz5.5 used in the TP model analysis Name of Seismogenic Sources
Completeness
HPH1
1950, 5.5
HPH2
1950, 5.5
HPH3
1950, 5.5
HPH4
1950, 5.5 1930, 6.5
HPH5
1950, 5.5 1930, 6.5
Date
Epicenter
d
m
year
Lat. (8N)
Long. (8E)
16 9 16 20 1 27 31 3 3 4 12 2 5 3 16 6 25 24 5 14 9 4 30 25 16 18 14 13 17 14 21 11 4 15 27 28 22 0 25 23 6 13 24 7 7 13 27 27 20 24 26
9 5 11 11 2 11 1 9 9 9 9 4 5 10 4 8 9 7 2 7 8 9 6 10 5 10 9 5 12 2 3 12 4 11 6 12 6 10 12 8 5 5 1 2 2 5 2 2 3 8 6
1956 1971 1972 1982 1984 1988 1991 1972 1972 1972 1981 1987 1987 1987 1988 1988 1988 1988 1990 1991 1993 1993 1994 1994 1995 1995 1996 1997 1997 1998 1998 1998 1905 1937 1955 1974 1945 1952 1952 1955 1985 1956 1966 1966 1966 1995 1997 1997 1997 1997 1999
33.96 35.54 35.66 34.54 34.57 35.20 35.99 35.94 35.95 35.90 35.67 36.12 36.46 36.49 36.00 36.49 36.40 36.11 37.05 36.33 36.44 36.43 36.33 36.36 36.46 36.43 36.05 36.41 36.39 36.36 36.43 36.51 33.00 35.00 32.50 35.05 32.50 30.20 29.40 31.00 30.88 29.90 29.92 29.92 30.25 30.23 29.98 29.99 30.14 30.08 30.10
69.51 71.05 69.91 70.51 70.49 70.90 70.40 73.32 73.24 73.34 73.59 71.14 70.68 71.46 71.60 71.60 70.73 71.10 71.25 71.12 70.71 70.81 71.15 70.96 70.89 70.39 70.71 70.94 70.77 71.11 70.13 71.02 76.00 78.00 78.60 2.91 76.00 70.00 77.00 71.50 70.23 77.00 69.62 69.68 69.89 67.94 68.21 67.98 68.02 68.00 69.44
Ms
M (cumulative)
6.4 5.5 5.6 5.7 5.9 5.6 6.6 6.2 5.6 5.7 6.1 5.7 5.7 6.0 5.5 6.0 5.5 5.8 5.7 6.5 6.3 5.5 6.4 5.9 5.9 6.3 5.9 6.5 6.3 5.5 6.0 5.7 8.6 6.5 6.0 5.9 6.5 6.1 5.8 6.5 5.6 6.5 5.5 5.7 5.6 5.6 7.3 6.0 5.9 5.6 5.7
6.4 f 5.8 f 6.0 f 6.6 6.3 a a 6.3 a a a a f f f f 7.0 a a a a a a a a a a a a 8.6 6.5 6.0 5.9 6.6 a a 6.5 5.6 6.5 f 5.9 a f 7.3 a a a a
D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140
135
Table 2 (continued ) Name of Seismogenic Sources
Completeness
HPH6
1950, 5.5
HPH7
1950, 5.5 1897, 7.0
HPH8
1950, 5.5
HPH9
1950, 5.5 1930, 6.5
Date
Epicenter
d
m
year
Lat. (8N)
Long. (8E)
27 12 1 19 26 16 19 28 6 19 29 23 11 28 4 4 6 15 28 19 4 19
6 5 4 1 4 7 10 3 3 1 7 1 10 1 6 4 7 11 4 5 6 11
1955 1959 1973 1975 1986 1986 1991 1999 1966 1975 1975 1982 1953 1955 1961 1978 1986 1937 1975 1975 1975 1996
32.50 32.40 32.12 31.93 32.03 30.89 30.78 30.51 31.49 32.38 32.57 31.67 32.30 33.30 34.18 32.98 34.41 35.00 35.80 35.11 35.82 35.35
78.60 78.66 77.83 78.52 76.32 77.88 78.77 79.40 80.55 78.49 78.49 82.28 82.80 82.40 81.93 82.25 80.05 78.00 79.85 80.83 79.92 78.13
Ms
M (cumulative)
6.0 6.3 5.6 5.8 5.6 5.7 7.0 6.6 6.0 6.2 5.5 6.0 6.5 6.4 6.0 5.5 5.8 6.5 5.8 5.5 5.6 7.1
6.0 6.3 f 5.9 f 5.9 7.1 a 6.0 6.3 a a 6.7 a a 5.5 5.8 6.5 6.0 a a 7.1
The last column gives decluster of catalog, i.e., main shocks, foreshocks (f), and aftershocks (a).
sequence. These cumulative magnitudes are used in this study instead of the magnitudes of the main shocks. Seismic moment is estimated by the moment– surface wave relationship of Purcaru and Berckhemer (1978). However, this estimate is valid only for the range 5.5VM sV7.5. All the considered earthquakes are within this range except one (Kangra) earthquake in source HPH3. Source HPH3 contains a large earthquake of M s=8.6 for which the seismic moment was taken as M 0=4.61027 dyn cm (Chen and Molnar, 1977). The moment magnitude for the considered events was derived by the definition of Hanks and Kanamori (1979). In Table 2, the differences between the cumulative moment magnitude (M) and the surface wave magnitude are b0.5. Hence, the derived magnitude (M) may be considered as a true representation of the size of the events. The minimum magnitude was considered in each case to define the corresponding M p, M f, and repeat time in years. The repeat time, T, denotes the time from the beginning of one seismic sequence to the initiation of the next sequence. The T p and T f represent the year of occurrence of the preceding and following main shock, respectively.
4. Relation between the repeat time and the preceding magnitude Data reveals that the relation between the repeat time and M p may be represented in the form log10 T ¼ c Mp þ a
ð1Þ
where c is the gradient of least-square line and a is a constant. The two parameters depend on such things as stress conditions and seismicity levels. As sufficient instrumental data was not available, the estimation of c may show deviation from the actual value. The parameter a depends on the seismicity of each source and the minimum (cutoff) magnitude of the main shock considered. The choice of minimum magnitude (M min) increases the number of repeat times (Table 3). The repeat time T shows variation from source to source due to different values of a among tectonic zones. Therefore, average repeat time (T¯ ) of the event for average seismicity level for all the seismogenic sources has been considered (Singh et al., 1992) for which the regression line is derived as logT¯ ¼ 0:19M p 0:41Fr
ð2Þ
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Table 3 Seismogenic source data used for parameter determination Name of seismogenic sources
M min
Mp
Mf
T
tp
tf
HPH1
5.8
6.4 5.8 6.0 6.4 6.0 6.4 6.3 6.3 6.0 6.5 6.6 6.5 5.9 6.5 6.0 6.3 5.9 5.9 6.0 6.3 6.3 6.0 6.7 6.7 5.5 6.7 6.0 6.5
5.8 6.0 6.6 6.0 6.6 6.6 6.3 7.0 5.9 5.6 6.5 5.9 7.3 7.3 6.3 5.9 5.9 7.1 6.3 7.1 7.1 6.3 6.3 5.5 5.8 5.8 7.1 7.1
16.17 11.21 7.00 27.38 7.00 34.37 9.02 9.84 19.50 29.70 10.17 9.73 31.05 40.79 3.88 15.69 11.49 5.26 3.88 32.44 32.44 8.87 63.26 24.48 8.26 32.74 21.56 59.01
1956 1972 1984 1956 1984 1956 1972 1981 1955 1955 1945 1956 1966 1956 1955 1959 1975 1986 1955 1959 1959 1966 1911 1953 1978 1953 1975 1937
1972 1984 1991 1984 1991 1991 1981 1991 1974 1985 1955 1966 1997 1997 1959 1975 1986 1991 1959 1991 1991 1975 1975 1978 1986 1986 1996 1996
6.0
HPH2 HPH3 HPH4
6.4 6.3
HPH5
5.9 5.6 6.5 5.9
HPH6
6.5 5.9
6.0
HPH7 HPH8
HPH9
6.3 6.0 6.3 5.5 5.8 6.0 6.5
Eq. (2) represents a straight line showing the correlation coefficient of 0.64. It reflects that the average repeat time increases with increasing of M p. The same data set is treated separately for establishing relation between log T¯ and the following main shock magnitude (M f). The derived least-square line is logT¯ ¼ 0:02Mf þ 2:08Fr
ð3Þ
A very low slope (0.02) and a very low correlation coefficient (0.05) fit the data (log T¯, M f) for the above equation. It demonstrates that less time is needed for larger future earthquakes, which suggests that a SP model is not valid for the region. For the derivation of Eq. (2), foreshocks and aftershocks were included in cumulative magnitude estimation. Similar analysis for the same data set was also derived excluding foreshocks and aftershocks as logT¯ ¼ 0:16 Mp 0:05Fr
ð4Þ
Another relation between seismic moment (M 0) and log T¯ was also derived showing the linear regression equation as logT¯ ¼ 0:20 logM0 3:67Fr
ð5Þ
The correlation coefficient for the Eqs. (4) and (5) are 0.62 and 0.67, respectively. The positive correlation coefficients suggest that Eqs. (2), (4), and (5) are statistically significant, while Eq. (3) is not. Eqs. (2), (4), and (5) are very similar to each other. It may be inferred from Eqs. (2), (4), and (5) that the TP model is valid for Hindukush–Pamir–Himalaya region and its vicinity. Astiz and Kanamori (1984) and Nishenko and Singh (1987) reported the relation between average recurrence time and average seismic moment for Mexico with a slope of 0.333 and 0.299, respectively. Papazachos (1989) reported the slope to be 0.28 for Greece. Singh et al. (1992) reported the slope to be 0.36 for Northeast and adjoining regions. Shimazaki and Nakata (1980) proposed a similar relation between the repeat times and coseismic slip of the preceding main shocks. Further, for long-term prediction of strong shallow earthquakes in the region considered, the following relations for the global applicability of bregional timeand magnitude-predictable modelQ (Papazachos and Papadimitriou, 1997) have been used: logTt ¼ b Mmin þ cMp þ dlogm0 t
ð6Þ
and Mf ¼ BMmin CMp Dlogm0 þ m
ð7Þ
where T t is the inter-event time measured in years, M min is the surface-wave magnitude of the smallest main shock considered, M p is the magnitude of the preceding main shock, M f is the magnitude of the following main shock, m 0 is the moment rate in each source per year that expresses the tectonic loading exerted in the volume of each seismogenic region, and t and m are constants. Table 4 lists the values of the parameters for each seismogenic source necessary to proceed. The model expressed by relations (6) and (7) has the advantage that all parameters (b, c, d, t, B, C,
D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140 Table 4 Information on the basic parameters used for every source Seismogenic source name
a
b
Mmax
log m 0 (dyne com year1)
HPH1 HPH2 HPH3 HPH4 HPH5 HPH6 HPH7 HPH8 HPH9
5.28 5.32 5.12 5.32 5.35 5.42 5.21 5.35 5.17
0.84 0.87 0.87 0.84 0.87 0.84 0.84 0.84 0.84
6.4 6.4 8.6 6.6 6.5 6.3 6.7 6.7 6.5
25.96 25.86 26.83 26.13 25.92 26.03 26.09 26.23 25.92
137
where T, M min, and log m 0 and M p are the observed values. The line drawn through the data is a leastsquares fit. The positive correlation between the repeat time and the magnitude of the preceding main shock suggests that the time-predictable model hold in the area under study. The values of the parameters of Eq. (7) were determined by the use of all available information from Table 3, and the following formula was found: Mf ¼ 1:31Mmin 0:60Mp 0:72logm0 þ 21:01
The first column gives the name of every source. The constants for the Gutenberg Richter relation are given in the next two columns. In the last two columns, the maximum magnitude and the logarithm of the moment rate are given.
ð9Þ
with a correlation coefficient of 0.55 and standard deviation of 0.27. Fig. 3 displays a plot of log T*=log T0.19M min0.29log m 0+10.63 as a function of M p,
with a correlation coefficient equal to 0.73 and a standard deviation equal to 0.36. The M f*=M f 1.31M min+0.72log m 021.01, where M f, M min, and log m 0 are the observed values, is plotted versus the observed M p in Fig. 4. The straight line is a least squares fit. The negative dependence of the magnitude of the following main shock on the magnitude of the preceding main shock indicates that a large main shock is followed by a small one, and a small main shock by a large one. Most of the parameters in Eqs. (6) and (7) and their values are self-explanatory. For instance, the inclusion of the M min term in Eq. (6) is essentially the Gutenberg–Richter law, because for large cutoff magnitudes, M min, we have smaller log N (N= number of events with MNM min) and therefore larger log T~log N 1. The crucial point of Eqs. (6) and (7) is the inclusion of linear M p term and the values of constants c and C, which represent the heart of the time- and magnitude-predictable model. Hence,
Fig. 3. Dependence of repeat time, T* with the preceding main shock magnitude, M p.
Fig. 4. Dependence of the magnitude of the following main shock (M f*) on the magnitude of the preceding main shock (M p).
D, and m) of these relations are calculated by all available data for all sources. On the basis of inter-event times of strong main shocks in the nine seismogenic sources of Hindukush–Pamir–Himalayas region, the time- and magnitude-predictable relationships (Shanker and Singh, 1996; Papazachos et al., 1997) had been determined as logTt ¼ 0:19Mmin þ 0:52Mp þ 0:29logm0 10:63 ð8Þ
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D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140
the positive global c value indicates that large events lead to large inter-event times, whereas the negative value of C value indicates that large events tend to be followed by smaller events and vice versa (Papazachos and Papadimitriou, 1997). Similar results, i.e., positive correlation between M p and log T t and negative correlation between M p and M f, were also found in other areas where this model has been tested (Papazachos, 1992; Singh et al., 1992; Papazachos and Papaioannou, 1993; Karakaisis, 1993).
M p, by the relation (Papazachos and Papaioannou, 1993): F PðDt Þ ¼
X1 F r X1 1F r
X2 r
ð10Þ
where X2 ¼ log
5. Long-term prediction of the next shallow main shock
ðt þ Dt Þ ; Tt
X1 ¼ log
t Tt
and F is the complementary cumulative value of the normal distribution with mean equal to zero and standard deviation equal to r. Given the date and the magnitude of the last event in a seismogenic source as well as the uncertainty of the model expressed by its standard deviation r=0.27, the probabilities of occurrence of the next shallow main shocks with M sz6.0 during the next 20 years were computed. Table 5 gives information on the expected large shallow earthquakes based on the model expressed by relations (8) and (9). The first column gives the name of the seismogenic source. The next two columns give the magnitude of the expected main shock, M f (this magnitude has been calculated by relation (9)) and the corresponding highest probabilities, P 20, for the occurrence of large main shocks during the decades (2000–2020). One must note that the absolute values of the probabilities are of relative importance; that is, their change from source to source is significant. This is because these values may change if a larger sample of data is used.
The model tested in the present study provides a means to calculate the time of occurrence of the next large main shock in each one of the defined seismogenic sources using relation (8). However, because there is a considerable difference between repeat times, T t, estimated from relation (8), and the corresponding actual repeat times, T, it is preferable to estimate the probability of occurrence of the next main shock larger than a certain magnitude and in a given time interval. It is found that log-normal distribution of T/T t is more appropriate than the Gaussian or Weibull distributions (Papazachos, 1988b; Papazachos and Papaioannou, 1993). This distribution holds for each of the seismogenic sources. One can calculate the conditional probability, P, for the occurrence of a main shock with MzM min during the next Dt years (from now), when the previous such earthquake occurred t years ago (from now) and had magnitude
Table 5 Expected magnitude, M f, and the corresponding probabilities, P 20, for the occurrence of large (M minz5.5) shallow main shocks during the period 2000–2020 in the Hindukush–Pamir–Himalayas Seismogenic source no.
Source name
M fF0.36 (Eq. (9))
P 20 (Eq. (10)) (log-normal)
M min (Table 3)
Mp (Table 2)
t p (year of M p) (Table 3)
log m 0 (Table 4)
log T t Eq. (8)
1 2 3 4 5 6 7 8 9
HPH1 HPH2 HPH3 HPH4 HPH5 HPH6 HPH7 HPH8 HPH9
7.4 7.5 7.5 6.9 8.6 8.4 7.1 7.7 8.5
0.68 0.42 1.00 1.00 0.00 0.10 0.99 1.00 0.04
5.8 6.3 5.9 5.6 5.9 5.9 6.0 5.5 6.0
6.6 6.5 5.9 5.6 7.3 7.0 6.2 5.8 7.1
1991 1991 1974 1985 1997 1991 1975 1986 1996
25.96 25.86 26.83 26.13 25.92 26.03 26.09 26.23 25.92
1.4324 1.4464 1.3397 0.9237 1.8038 1.6797 1.3001 1.0377 1.7188
D. Shanker, E.E. Papadimitriou / Tectonophysics 390 (2004) 129–140
6. Discussion and conclusion This study attempts to quantitatively assess the probabilities of occurrence and the magnitudes of future large (M sz6.0) shallow main shocks in the nine seismogenic sources into which the seismic zone of Hindukush–Pamir–Himalaya was divided. The estimation of conditional probabilities and the magnitude of the expected event were based on the time- and magnitude-predictable model expressed by relations (8) and (9). There are several cases where this model was applied on the basis of the methodology followed in the present study; that is, for the Aegean area (Papazachos, 1988a,b, 1989, Papazachos and Papaioannou, 1993); Alpine–Himalayan belt (Papazachos et al., 1997); New Guinea-bismark sea (Karakaisis, 1993); and Northeast region (Singh et al., 1992). This methodology enables the use of more inter-event times than are usually available in studies using only the recurrence times of characteristic events, because in each seismogenic source, not only the main fault but also other secondary faults, where smaller earthquakes occur, are considered. This is expressed by the term bbM minQ in relations (8) and (9). Although there are some uncertainties involved in the methodology followed in the present study, our results indicate that the time- and magnitude-predictable model can probably play an increasingly important role in earthquake prediction. Most of the reproducible results are obtained so far for the intermediate-term stage, where characteristic duration of alarms is years. The earthquake forecasts described above have a limited accuracy. Nevertheless, they are useful in earthquake hazard assessment and loss prevention. The opinion that only a precise short-term prediction and estimate of seismic hazard are practically useful that sometimes emerges in the seismological literature can lead to costly mistakes. The results of the present analysis indicate that the dependence of the repeat time on the magnitude of the preceding main shock is strong and positive, while the dependence of the following main shock on the repeat time is weak and negative. This shows that the TP model holds for the seismogenic sources of shallow to deep earthquakes in the Hindukush–Pamir–Himalaya and its vicinity and that the SP model does not hold for the same region. Eq. (8) may be used for long-
139
range earthquake forecasting in the nine seismogenic sources, and to aid in earthquake hazard mitigation and other engineering purposes. The reliability of the method depends on the availability of a good amount of reliable seismicity data. The ambiguity in assessment of forthcoming earthquakes increases for seismogenic sources showing very long repeat times.
Acknowledgement The first author is indebted to the Head of the Department of Earthquake Engineering, Indian Institute of Technology Roorkee (formerly University of Roorkee), Roorkee, India, for providing necessary facilities. The authors are grateful to Chris H. Cramer and Amy Brown for their critical comment and suggestions, and to the editor, Kaye M. Shedlock, for his efforts throughout publication. This research is supported by All India Council For Technical Education (AICTE), New Delhi, under the Research & Development Project Grant No. 8020/RID/R&D129/01-02, and the part of this work was presented in the First IAGA-IASPEI-2001 at Hanoi, Vietnam.
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