CHAPTER 1: INTRODUCTION ________________________________________
The problem of earthquake prediction is quite complex. It consists of consecutive, step-by-step procedure with narrowing down the time interval, area, and magnitude range where a strong earthquake can occur with maximum probability. Such a formulation is governed by both the nature of the process leading to strong earthquakes and by the practical need of earthquake preparedness. Of these, there are two main aspects which can be distinguished in the science of earthquake prediction. The first aspect is related to the study of the geophysical mechanisms that prepare and generate an earthquake as well as the possible symptoms (precursors) associated with the earthquake occurrence. The second aspect is focused on the prediction of a particular earthquake event regardless that the method is tried earlier. Earthquakes events take place because of the constant movements of the core of Earth's crust with its tectonic plates sliding past or over one another resulting in stresses build up within or between them along cracks known as faults. As they are sticky by nature, the faults tend to stay locked in place, deforming the plate nearby. They accumulate energy until they can take no more stresses or the critical level is reached, the accumulated strain is released in a sudden slip which shakes the ground for several km around. This phenomenon is known as an Earthquake.
For better estimates of the seismic potential and forecasts of future earthquakes, repeat times of large earthquakes can be used as an extensive tool. Repeat times are taken as the time intervals between the largest shocks that occur at a given place along a plate boundary or in a specific seismic zone. They vary within and between seismic zones depending not only on the rate of plate motion but also on other factors such as length of rupture along strike, downdip width and dip of the plate boundary (Kelleher et al., 1973). Therefore, if a model can make use of the available repeat times, it offers a very useful tool for long-term earthquake prediction.
Several workers (Cornell, 1968; Gardner and Knopoff, 1974; Papadopoulos and Voidomatis, 1987; Singh et al., 1994) have already reported that occurrence of earthquakes follow a Poisson distribution suggesting memoryless property of seismic-zones. Wallace (1970) and Nishenko and Singh (1987) and among others reported the time-dependent properties of earthquake generating sources for several regions.
TYPES OF MODELS
There are two kinds of time dependent models proposed:-
• Slip predictable model (Bufe et al., 1977; McNally and Minster, 1981; Singh et al, 1991 Wang et al., 1982, Kiremidjian and Anagnos, 1984). According to the slip predictable model, the size (co-seismic slip, seismic moment, magnitude etc) of future earthquake depends upon the time elapsed since the last earthquake.
• Time predictable model (Shimazaki and Nakata, 1980; Anagnos and Kiremidjian, 1984; Papazachos, 1989; Singh et al., 1992). According to this model, the time of occurrence of a future earthquake depends on the size and the time of occurrence of the last earthquake. The time predictable model is based on the theory that earthquakes in fault zones are caused by the constant build-up and release of strain in the Earth's crust. When an earthquake occurs on the fault, a certain amount of accumulated strain is released. Once the quake event is finished, strain starts building up again because of the continuous grinding of the tectonic plates. A fault is assumed to slip once the stress builds up to a certain level. As plates move at more or less constant rates, the model suggests that it should take longer for an earthquake to re-occur after a large magnitude quake than after a small one. A large quake relieves more stress on a fault, so it takes longer to build up once again to the critical level. It implies that after each quake, it should be able to predict the next one, based on how much the fault has slipped. This is only possible, however, if the fault zone is relatively simple – if, for example, there is no other active fault nearby that might also relieve local stress.
In principle, by the slip predictable model we can predict only the size of a future earthquake and by the time predictable model we can predict only the time of its occurrence. 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.
We will discuss the time predictable model in the present context. In the present study efforts have been made to develop and apply the said methodology for identification of seismogenic sources in Central Himalayas, considered for earthquake hazard prediction.
Fig.1 Earthquake Recurrence Model: a) time predictable model showing stress buildup to a certain value(τ₁) and non uniform stress drop; and b) slip predictable model illustrating non uniform stress buildup and stress drop to a certain minimum value(τ₂) ( after Shimazaki and Nakata, 1980)
METHODOLOGY PROPOSED
A) Shimazaki and Nakata(1980) Model
According to Shimazaki and Nakata (1980), a linear relation exists between the logarithm of repeat time (T) of two consecutive events and the magnitude of the preceding mainshock (Mp) is established in the form as given below:-
LogT = c Mp + a ……………………. (1)
where “c” is a positive slope of line, “a” is function of minimum magnitude of the earthquake considered the constant and “c” is the gradient of least square line with a positive value and “a” is a constant function of the magnitude.
These constants depend upon the nature of the source. Since the preceding magnitude Mp is linearly related to the logarithm of the co-seismic slip. Eq. (1) indicates that the time between the two successive main shocks in a seismogenic source is linearly related to the coseismic
slip of the previous main shock. It supports the time predictable model which predicts that the inter-event time is proportional to the co-seismic slip of the last main shock (Shimazaki
and Nakata, 1980). The repeat time (T) between two shocks shows a variation from one source to another due to a difference in the value of “a”. For the validity of the time-predictable model developed for a region for a given value of coefficient Mp, the value of c is always positive (Qin et al., 1999). The worldwide value of this coefficient has been calculated as 0.33 (Papazachos and Papadimitriou,1997). The seismic moment Mo (moment released), for an earthquake event in the sequence is calculated from the surface wave magnitude (Ms) using the following relationship (Purcaru and Berckhemer, 1978):-
LogMo=1.5Ms+16.1 …………………….. (2)
Similarly, the moment magnitude Mw (cumulative magnitude) for all the considered events in the sequence is derived from the following relation given by Hanks and Kanamori (1979):-
Mw =2/3logMo−10.7 ……………………. (3)
To find the preceding and following mainshocks, Mmin is considered in each source.
B) Papazachos (1994) Model
Most of the studies related to seismicity and seismic hazard assessment are based on time-independent models (Papazachos et al., 1994). Later the model given in 1980 by Shimazaka & Nakata was changed by adopting some new constants that had better properties of the seismogenic sources. These models are based on the Poission distribution for time and Gutenberg-Richter formula for magnitude distribution. Papazachos and Papadimitriou (1993) gave a relation based on the interevent times of strong mainshocks in various seismogenic sources :-
logTt = bMmin + cMp + dlogmₒ + t ……………………… (4)
and
Mf = BMmin + CMp + Dlogmₒ + m ……………………… (5)
where Tt is the interevent time measured in years, Mmin is the surface-wave magnitude of the smallest mainshock considered, Mp is the magnitude of the preceding mainshock, Mf is the magnitude of the following mainshock, mₒ is the moment rate in each source per year which expresses the tectonic loading exerted in the volume of each seismogenic region, and t and m are constants. The term bMmin shows that larger the threshold magnitude (Mmin),
larger are repeat times in the seismogenic region. The term cMp shows that larger the
magnitude of mainshock in a seismogenic region, the longer is the time taken for the next mainshock. The term dlogmₒ defines the tectonic loading which is released in a seismogenic region. The parameter t and m are estimated for each seismogenic region. Equation (4) and (5) represent the regional time and magnitude predictable model. Seismic moment rate (Mₒ) is an important parameter for the application of this model because it represents the tectonic loading exerted in the volume of each seismogenic region and varies from source to source. On the basis of these two equations, one can estimate the probability of occurrence and magnitude of the expected strong mainshocks in the seismogenic region.. In this study to evaluate the seismic moment rate, a procedure suggested by Molnar (1979) has been used. According to that, the number of events with seismic moment equal to or greater than Mo is given by the relation:-
.
For the determination of the model parameters (b, c, d, q, B, C, D, m) of equation (4) and (5), a well-known regression technique given by Draper and Smith (1966) & Weisberg (1980) is used. The uncertainties associated with the determination of model parameters are given in the form of standard deviation and correlation coefficient which have been derived after the application of data. In the present study efforts have been made to develop and apply the above said methodology for identification of seismogenic sources in Central Himalayas, considered for earthquake hazard prediction.
DIFFERENCE BETWEEN THE TWO PROPOSED MODELS
A well-known and most widely used ‘regional time and magnitude predictable model’ was introduced by Papazachos (1989 & 1992) which was further modified by Papazachos and Papaioannou (1993) and applied in the seismogenic regions of Aegean and its surroundings. This model was different from original time-predictable model proposed by Shimazaki and Nakata (1980) in two ways as given below:-
• Firstly, this model was applicable to broad seismogenic regions and not only to a single fault or a simple plate boundary.
• Secondly, the time of the next mainshock was not usually proportional to the preceding mainshock.
These differences extended the applicability of a simple time predictable model and allows its uses for practical purposes.
SEISMOGENIC SOURCES
The seismogenic source zones are a relatively smaller part of the lithosphere which includes the rupture zones (faults, deformation volumes) of the largest mainshock as well as the rupture zones of the smaller mainshocks (Papazachos et al. 1997.b). One of the basic requirements for the application of the regional time and magnitude predictable model is the division of study region into various seismogenic sources. It is assumed that each seismogenic source zone has its own individual characteristics from seismotectonics point of view. For the determination of prediction relations, it is necessary to find out the values of a,b, M(max) and Mo for each of the seismogenic source into which the region to be studied is divided. Values of a and b is founded using least square method whereas Mo is found out using historical and modern dataset available for each source.
Finally, a complete regression analysis is done to find all the necessary constants (b, c, d, t, B, C, D & m) to define the predictive relation.
LONG TERM EARTHQUAKE PREDICTION
It is found that there is a considerable difference between the actual repeat times (T) and the calculated repeat times (Tt) calculated from the predictive relation. Therefore, it is preferable to estimate the probability of occurrence of the next mainshock larger than a certain magnitude and in a given time interval.
It is also found that lognormal distribution of T/Tt is more useful than the Gaussian or Weibull distributions (Papazachos, 1988b; Papazachos and Papaioannou, 1993). This distribution holds for each of the seismogenic sources. We can calculate the conditional probability (P) for the occurrence of a main shock with M ≥ Mmin during the next Δt years (from now) when the previous such earthquake occurred t years ago (from now) and had magnitude Mp, by the relation given below (Papazachos and Papaioannou, 1993):-
and F is the complementary cumulative value of the normal distribution with mean equal to zero and standard deviation equal to σ.
OBJECTIVES
I have the following objectives related to the dissertation work :-
• Study of the accuracy of the data generated from USGS and plotting of few relevant graphs
• Based on the seismogenic parameters determined, using them to obtain the predictive relation. Usage of the regression analysis and calculating the values of constants of the papazachou equation and obtaining the predictive relation
• Long term earthquake prediction
• Generating conclusions from the relations obtained and to check its validity for Central Himalayas through relevant graphs plotted
CHAPTER 2: REGIONAL CHARACTERISTICS ________________________________________
The Central Himalayas consists of the larger Himalayan thrust fault and it is the frontier of the Eurasian plate which is pushed northward by the Indian plate. Due to the northward movement of the Indian plate, the Himalayan front in south western China is subjected completely to compression resulting in an uplift and the mean P axis of direction NNE becomes almost normal to Himalayan arc (Molnar and Lyon-Caen, 1989). The present distribution of shallow seismicity in the region is due to under thrusting of the continental lithosphere of the Indian plate (Isacks etal., 1968), whereas the occurrence of intermediate depth earthquakes suggests the presence of the remnants of the old oceanic lithosphere (Mckenzie, 1969; Rastogi, 1974). The seismicity is mainly due to compressive stresses between the two plates ie. Indian Plate & Eurasian Plate. The central Himalayas lying between 27⁰ N to 33⁰ N and 70⁰ E to 90⁰ E includes the areas of Nepal and parts of Bihar and Eastern Himalaya including Darjeeling, Sikkim, Bhutan, Arunachal Pradesh and Lohit sectors, Garhwal Himalayas and parts of Pakistan .
The motivation or reason to select this region for study is influenced by several factors namely, seismically very active, availability of strong main shocks data and vulnerability of this area to earthquake disasters. The Garhwal Himalayas is bounded by latitude 29.50° to 31.0°N and longitude 77.5° to 79.5° E and constitutes the northwestern part of the Himalaya. The region is characterized by occurrence of moderate to local sized earthquakes. The high seismic activity is mainly due to the motion of the Indian plate. The instrumental seismicity is very high in a zone of 50 km width across strike in the Lesser Himalayas (India and Nepal) with a high concentration of earthquakes just lying south of the Main Central Thrust (MCT).
The precise zonation of area, calculation of the seismic moment rate, and the de-clustering of the data, are pre-requisite for the model application. However, the zonation of areas is not necessary for the results of the model, accurate zonation will just improve them (Papazachos and papadimitriou, 1997). For the purpose of the present analysis, the whole area has been divided into six seismogenic sources on the basis of following factors :-
• 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 has occured and possibly other smaller faults where smaller main shocks can also occur. The main characteristic of this seismogenic region is the interaction among its faults during the important seismic excitations (redistribution of stress etc). Therefore, zonation is the procedure of defining, as accurately as possible, the boundaries of the seismogenic regions.
Fig. 2 Journey of Indian Landmass over millions of years ago
before its collision with the Eurasian Plate
CHAPTER 3: DATA COLLECTION ________________________________________
The data for the above study is collected from the earthquake catalogue prepared by National Earthquake Information Centre (NEIC) US Department of the interior US Geological Survey (USGS), USA. The data used in this study is homogeneous; that is, the magnitudes of the earthquakes are in the same scale. The magnitudes used in the 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. The following figure Fig. 3 shows the rectangle method for choosing the desired area of Central Himalayas (27⁰ N to 33⁰ N and 70⁰ E to 90⁰ E) .
Fig. 3 A rectangle encompassing the central Himalayas for locating the earthquakes in the region
The resulting earthquakes in the Central Himalayas corresponding to magnitude 5.5 (main shock) and greater during the period 1900 to 2016 are shown in figure 4. The circles shows the epicentre or location of the earthquake. Closeness of the epicentres at a particular location depicts the highly seismically active fault and vice-versa. The earthquakes are widely distributed in major areas of Nepal, China, few parts of Pakistan and Himachal Pradesh.
Fig. 4 The epicentral distribution of earthquakes for Central Himalayas (27⁰ N to 33⁰ N and 70⁰ E to 90⁰ E) during the period 1900 – 2016
On the basis of the gross seismotectonic and geological properties, a total of six seismogenic sources are selected and are demarcated by different boundaries as shown in Fig. 4 together with the epicenters of the data. These sources have been selected by the following criteria:-
a) In each source at least three main shocks (two repeat times) of magnitudes Ms ≥5.5 occurred during the considered period
b) In each source at least one mainshock with Ms ≥6.0 occurred during this period of time
c) Each source is characterized by distinct seismotectonic properties in relation to the adjacent region (same kind of faulting, high seismicity level etc.).
Fig. 5 Earthquakes distribution in central Himalayas with magnitude of 5.5 and greater for the time period 1900 – 2015 with the epicentral distribution of Six seismogenic sources
Six seismogenic sources have been identified according to properties described above. Various magnitudes of earthquakes are being depicted by 3 different colours black, yellow and red with increasing magnitude.
CHAPTER 4: DATA TREATMENT ________________________________________
For the Central Himalayas, the data has been considered complete for Ms ≥5.5 since 1950, Ms ≥ 6.0 since 1930 and Ms ≥7.0 since 1900 which means in the desired period the corresponding range of earthquakes are satisfying the required need of siesmogenic sources based on which they are defined above. Also, de-clustering and use of complete data, that is, determination of foreshocks, aftershocks and main shocks and use of a data samples which includes all earthquakes which occurred in a certain seismogenic region during a certain time period and have magnitudes larger than a certain minimum value is done.
For the purpose of determining foreshocks and aftershocks for a particular mainshock, Mogi (1985) made a statement that a pre-seismic activity ie. Foreshock is constant while the post-seismic activity ie. Aftershock depends upon the magnitude of the preceding shock. Karakaisis (1991) observed that the last phase of seismic cycle is characterised by an accelerated activity period with duration of about 2.7 years and it does not depend on the magnitude of the mainshock. For the present study on this region, above value is approximated as 3 years for all mainshocks. Moreover, the duration of aftershocks activity Ta (in years) is proportional to the magnitude of preceding mainshock (Mp) as:-
Log Ta = 0.06 + 0.13Mp ………………………………… (6)
Table 1. Mainshocks, Foreshocks (f) and Aftershocks (a) data used in each seismogenic sources. Ms and Mw represents surface wave magnitude and moment magnitude respectively.
Completeness
Siesmogenic sources Time(do-mo- year) Lat⁰ N Long⁰ E Ms
f Mw
1900, 7.0 CHim 1 23-08-1955 30.836 71.012 5.6
5.6
1930, 6.0 07-02-1966 30.276 70.041 6.5 6.5
06-05-1985 30.885 70.269 5.9 5.9
08-05-1985 30.91 70.31 5.6 a
1930, 6.0 CHim 2 04-04-1905 32.636 76.788 7.9 7.9
1950, 5.5 22-06-1945 32.509 76.247 6.5 6.5
12-09-1951 32.977 75.88 5.6 a
27-06-1955 32.294 78.506 6.2 6.2
12-04-1963 31.885 78.781 5.5 a
19-01-1975 32.455 78.43 6.8 6.8
19-01-1975 31.95 78.521 6 a
29-07-1975 32.555 78.457 5.5 a
28-05-1981 31.851 78.411 5.6 a
26-04-1986 32.128 76.374 5.5 5.5
16-07-1986 31.049 77.997 5.5 a
19-10-1991 30.78 78.774 6.8 6.9
28-03-1999 30.512 79.403 6.6 a
1930, 6.0 CHim 3 28-08-1916 29.73 80.745 7 7
1950, 5.5 04-06-1945 30.218 80.082 6.4 6.4
23-02-1953 29.529 81.382 5.8 a
29-08-1953 28.168 82.333 5.8 5.8
28-12-1958 29.926 79.9 6.1 6.1
05-03-1960 29.411 81.158 5.7 a
26-09-1964 29.829 80.474 5.9 f
06-03-1966 31.525 80.487 6.7 6.7
06-03-1966 31.422 80.554 6.3 a
27-06-1966 29.504 80.845 6 a
27-06-1966 29.543 80.915 5.7 a
27-06-1966 29.706 80.935 6.3 a
15-08-1966 28.565 78.961 5.6 a
20-05-1979 30.029 80.31 5.9 f
29-07-1980 29.331 81.258 5.7 f
29-07-1980 29.598 81.092 6.5 6.5
18-05-1984 29.577 81.869 5.6 a
09-12-1991 29.543 81.632 5.6 5.6
05-01-1997 29.845 80.532 5.6 a
27-11-2001 29.606 81.752 5.5 f
04-06-2002 30.595 81.44 5.6 5.7
26-10-2004 31.024 81.154 5.6 a
1930, 6.0 CHim 4 17-10-1944 31.266 83.114 6.8 6.8
1950, 5.5 29-10-1944 31.051 83.135 6.5 a
10-02-1947 31.537 85.278 6.5 a
08-10-1953 32.258 82.892 6.1 f
11-10-1953 32.116 82.786 6.5 6.5
03-12-1953 31.151 85.743 6.5 a
14-04-1957 30.521 84.348 6.4 a
22-04-1957 30.841 84.297 6 a
23-01-1958 30.622 84.133 5.5 a
28-10-1958 30.472 84.553 6.3 a
03-11-1958 30.44 84.54 5.5 a
03-05-1971 30.739 84.443 5.5 5.5
23-01-1982 31.696 82.246 6.5 6.5
23-01-1982 31.582 82.205 6 a
11-07-2004 30.694 83.672 6.2 f
07-04-2005 30.491 83.662 6.3 f
09-01-2008 32.288 85.166 6.4 f
16-01-2008 32.331 85.158 5.9 f
22-01-2008 32.349 85.262 5.5 f
25-08-2008 30.901 83.52 6.7 6.7
25-09-2008 30.836 83.487 6 a
24-07-2009 31.158 85.902 5.8 a
1930, 6.0 CHim 5 15-12-1934 31.25 89.162 7.2 7.2
1950, 5.5 03-01-1935 30.737 88.318 6.5 a
29-12-1950 32.735 87.974 6.1 6.1
07-10-1952 31.464 87.446 5.8 a
04-08-1955 30.675 86.43 5.7 a
17-06-1965 32.052 87.784 5.9 5.9
14-09-1976 29.795 89.559 5.5 f
18-11-1977 32.693 88.388 6.5 6.5
22-02-1980 30.506 88.583 6.2 a
20-06-1986 31.24 86.847 6.1 a
03-07-1996 30.147 88.189 5.7 f
31-07-1996 30.174 88.178 5.5 f
20-07-1998 30.134 88.173 5.8 f
25-08-1998 30.079 88.109 5.9 5.9
1930, 6.0 CHim 6 27-05-1936 28.397 83.311 6.8 6.8
1950, 5.5 28-05-1951 28.925 86.685 6 6
19-11-1952 29.682 86.506 5.8 a
29-08-1953 28.168 82.333 5.8 a
04-09-1954 28.169 83.825 5.9 a
12-01-1965 27.357 87.867 5.9 5.9
24-03-1974 27.727 86.11 5.7 5.7
27-09-1974 28.596 85.496 5.6 a
19-11-1980 27.394 88.752 6.1 6.1
09-08-1987 29.502 83.714 5.6 a
09-01-1990 28.225 88.163 5.5 f
20-03-1993 29.084 87.333 6.2 6.2
03-11-1997 29.078 85.383 5.5 a
03-09-1998 27.85 86.941 5.6 a
25-03-2003 27.264 89.331 5.5 5.5
07-11-2009 29.49 86.008 5.5 f
18-09-2011 27.73 88.155 6.9 6.9
The minimum magnitude was considered in each case to define the corresponding Mp, Mf and repeat time in years (Table 2). The repeat time T, denotes the time from the beginning of one seismic sequence to the initiation of the next sequence. The tp and tf represent the year of occurrence of the preceding and following mainshock, respectively.
Table 2. Seismogenic source data used for parameter determination
Seismogenic
Sources Mmin Mp Mf T(Inter-event time) tp tf
CHim 1 5.6 5.6 6.5 10.45 1955 1966
6.5 5.9 19.23 1966 1985
CHim 2 5.5 5.5 6.9 5.54 1986 1991
6.2 6.2 6.8 19.56 1955 1975
6.8 6.9 20.83 1975 1991
6.5 6.5 6.8 29.58 1945 1975
6.8 6.9 20.83 1975 1991
6.8 6.8 6.9 20.83 1975 1991
CHim 3 5.6 5.6 5.7 10.48 1991 2002
5.8 5.8 6.1 5.33 1953 1958
6.1 6.7 7.19 1958 1966
6.7 6.5 14.39 1966 1980
6.1 6.1 6.7 7.19 1958 1966
6.7 6.5 14.39 1966 1980
6.4 6.4 6.7 20.74 1945 1966
6.7 6.5 14.39 1966 1980
CHim 4 5.5 5.5 6.6 10.72 1971 1982
6.6 6.7 26.59 1982 2008
6.5 6.5 6.6 29.28 1953 1982
6.6 6.7 26.59 1982 2008
CHim 5 5.9 5.9 6.5 12.41 1965 1977
6.5 6 20.76 1977 1998
6.1 6.1 6.5 26.88 1950 1977
CHim 6 5.5 5.5 6.9 8.48 2003 2011
5.7 5.7 6.1 6.65 1974 1980
6.1 6.2 12.32 1980 1993
6.2 6.9 18.49 1993 2011
5.9 5.9 6.1 15.85 1965 1980
6.1 6.2 12.32 1980 1993
6.2 6.9 18.49 1993 2011
6 6 6.1 29.48 1951 1980
6.1 6.2 12.32 1980 1993
6.2 6.9 18.49 1993 2011
6.1 6.1 6.2 12.32 1980 1993
6.2 6.9 18.49 1993 2011
6.2 6.2 6.9 18.49 1993 2011
6.8 6.8 6.9 75.31 1936 2011
CHAPTER 5: COMPUTATIONAL ANALYSIS ________________________________________
Papazachos and Papadimitriou (1993) gave a relation based on the inter-event times of strong mainshocks in various seismogenic sources as follows :-
logTt = bMmin + cMp + dlogmₒ + t ……………………….. (4)
and
Mf = BMmin + CMp + Dlogmₒ + m ……………………….. (5)
where Tt is the interevent time measured in years, Mmin is the surface-wave magnitude of the smallest mainshock considered, Mp is the magnitude of the preceding mainshock, Mf is the magnitude of the following mainshock, mₒ is the moment rate in each source per year which expresses the tectonic loading exerted in the volume of each seismogenic region, and t and m are constants. Table 2 lists the values of the parameters for each seismogenic source necessary to proceed. The model expressed by relations (4) and (5) has the advantage that all parameters (b, c, d, t, B, C, D and m) of these relations are calculated by all available data for all sources.
On the basis of inter-event times of strong mainshocks in the six seismogenic sources of Central Himalayas, the first of the time and magnitude predictable model relationships using the regression analysis in 37 data sets among six seismogenic sources has been determined as:
logTt = 0.13Mmin + 0.01Mp + 0.20logmₒ – 4.73 ……………………………..(7)
The above equation has a correlation coefficient equal to 0.68 and standard deviation is 0.17.
Mp Vs LogTt Relation
From the table 2, using the column that is, values corresponding to the magnitude of preceding earthquake (Mp) and Logarithm T, we obtain the following graph.n
From the graph, we can draw two major inferences:-
1. Small earthquakes have small repeat times
2. Larger earthquakes ie. Major shocks have large repeat times.
Fig. 6 Mp Vs LogTt Graph
Clearly, the trend line equation is Log Tt = 0.392Mp – 1.242 with a positive slope of 0.392 which proves the said inferences made above. The correlation coefficient is given as square root of residuals (R²) equal to 0.671. This shows that time predictable model can be applied to the study region.
The value of the parameters of equation 5 were found from values corresponding to table 2 and the following equation was found to be relevant in the study area.
Mf = 0.28 Mmin – 0.01 Mp + 0.04 logmₒ + 3.85………………….. (8)
The correlation coefficient for the above equation is 0.57 and standard deviation is 0.33.
Now, the Mf* = Mf – 0.28 Mmin – 0.04 logmₒ – 3.85, where Mf, Mmin and logmₒ are the observed values, is plotted versus the observed Mp from table 2 in Fig.7. The straight line is a least squares fit and a negative dependence (from negative slope) of the magnitude of the following main shocks with the magnitude of the preceding mainshock indicates that a small one and a small mainshock follow a large mainshock by a large one.
Fig. 7 Mp vs Mf* Graph
The above equation ( Mf* = -0.117Mp + 0.730 ) has a positive correlation coefficient Square root of residuals (R²) equal to 0.145.
Mf vs LogTt Relation
Now, Log Tt* = Log Tt – 0.13Mmin- 0.20logmₒ + 4.73 is obtained from predictive relation and the observed values of Mf are plotted and a graph is obtained.
Fig. 8 Mf vs LogTt* Graph
The equation of the least square line comes to be Log Tt* = -0.076Mf + 0.536. Clearly, the slope of the equation is negative ie. There is a reverse relation between logarithm of interevent time and the magnitude of following earthquake. This shows that the slip predictable model does not hold for the area under study and the time predictable model is more working and plausible for the Central Himalayas region.
PREDICTION OF THE NEXT SHALLOW MAINSHOCK
As there is a considerable difference between the calculated inter-event times from eq. (7) and the actual repeat times, it becomes important to estimate the conditional probabilities of occurrence of a main shock in each seismogenic source with magnitude M ≥ Mmin during next few years from now.
The probability of occurrence of shock with magnitude Ms ≥ 5.5 has been estimated within a period of 30 years from now ie. in between period of 2016 – 2046. Log normal distribution is used to find the probability of shock with F being the complementary cumulative value of normal distribution with mean equal to zero and standard deviation σ = 0.17.
Table 3 gives information on the expected large shallow earthquakes based on the model expressed by relation (7) and (8). The first column gives the name of the seismogenic source.
Seismogenic Sources Mf ± 0.33 P₃₀ Mmin Mp tp
CHim 1 6.3 0.91 5.6 5.6 1985
CHim 2 6.4 0.98 5.5 6.6 1999
CHim 3 6.3 0.99 5.6 5.6 2004
CHim 4 6.3 0.99 5.5 5.8 2009
CHim 5 6.4 0.99 5.9 5.9 1998
CHim 6 6.4 0.85 5.5 6.9 2011
Table 3. Expected magnitude Mf and conditional probability P₃₀ for the occurrence of large shallow main shocks (Ms ≥ 5.5) during 2016 – 2046 in Central Himalayas
P₃₀ denotes the conditional probability of occurrence of large earthquakes during period 2016-2046 and the corresponding Mf. CHim 5 works out to be the most hazardous zone with a shock of magnitude Mf ≥ 6.4 occuring with a high probability of 0.99. However, these results may vary if a larger sample of data is used.
CHAPTER 6: CONCLUSIONS ________________________________________
Various models are available for Probabilistic eastimation of a Earthquake Hazard including the “time-predicatable” model developed by Shimazaki and Nagata (1980) which is based on the concept of elastic rebound. The concept of a earthquake cycle describes the probability of occurrence of any shock in a fault generally increases with the time elapsed since the last earthquake in that same fault. However, the originally proposed “time and slip predictable’ model was not applicable to every region and only the “time and magnitude” reccurence was found to be more plausible and valid in major regions (faults) around the world. This model is thought to encompass some of the physics behind the earthquake cycle, in that earthquake probability increases with time. The time predictable model is therefore often preferred when adequate data are available, and it is incorporated in hazard predictions for many earthquake-prone regions.
Papazachos (1989) demonstrated that this model can also be applied in several seismotectonic environments with various fault systems. The time-predictable model can be applied for earthquake predictions in earthquake-prone areas. The study of the applicability of the time-predictable model for earthquake occurrence in different regions is quite useful for long-term earthquake hazard evaluation. It is also helpful in understanding earthquake genesis under different tectonic environments.
Although, there might be some uncertainities involved in carrying out the study, it can be proven that time and magnitude dependent model can be applied for earthquake prediction. From the study, it is easily seen that small magnitude earthquakes have shorter repeat time whereas the larger have quite large repeat times. It also proves that time predictable model can be applied to the Central Himalayas region .
Moreover, the earthquake predictions in relation to magnitude and time might have a limited accuracy, but they are useful in earthquake hazard assessment and preventing loss of life and property
References
1. D. Shankar and Ashish Harbindu.(2004) “Development of Time and Magnitude predictable model and prediction of earthquake hazard in central Himalayas” August 1-6, 2004 Paper No. 3024
2. Panthi, D. Shanker, H. N. Singh, A. Kumar and H. Paudyal “Time-predictable model applicability for earthquake occurrence in northeast India and vicinity”
3. D. Shanker, A. Panthi and H. N. Singh “Long-Term Seismic Hazard Analysis in Northeast Himalaya and Its Adjoining Regions” Nat. Hazards Earth Syst. Sci., 11, 993–1002, 2011
4. Papazachos BC. “A time and magnitude predictable model for generation of shallow earthquakes in the Aegean area”. Pure Appl. Geophys. 1992; 138: 287-308.
5. Papazachos BC, Papaioannou Ch A. “Long term earthquake prediction in Aegean area based on a time and magnitude predictable model”. Pure Appl. Geophys. 1993; 140: 593-612..
6. Papazachos BC, Papadimitriou EE. “Evaluation of the global applicability of the regional time and magnitude-predictable seismicity model”. Bull. Seismol. Soc. Am. 1997; 87: 799-808.
7. Papadopoulos GA Voidomatis P. “Evidence for periodic seismicity in the inner Aegean seismic zone”. Pure Appl. Geophys. 1987; 125: 613-628.
8. R. B. S. Yadav, D. Shanker, S. Chopra, A. P. Singh “An application of regional time and magnitude predictable model for long-term earthquake prediction
in the vicinity of October 8, 2005 Kashmir Himalaya earthquake” Nat Hazards (2010) 54:985–1014
9. Singh VP, Shanker D, Ram A. “ Seismological approach to earthquake prediction in Himalayas”. J. Scientific Research 1991; 41(B): 101-110
10. Singh VP, Shanker D, Singh J. “On the validity of time-predictable model for earthquake generation in northeast India"Proc. Indian Acad. Sci. (Earth Planet Sci.), 1992; 101(4): 361-368.
11. Anagnos T, Kiremidjian A.S “Stochastic time predictable model for earthquake occurrences”.Bull. Seismol. Soc. Am. 1984; 74: 2593-2611.
12. Kiremidjian AS Anagnos T. “Stochastic slip predictable model for earthquake
occurrences”. Bull Seismol. Soc. Am. 1984; 74: 739-755.
13. National Earthquake Information Center (NEIC) U.S. Department of the Interior U.S. Geological Survey, USA. Catalogue of earthquakes for the period (1905-1999).
14. Nishenko SP Singh S K. “Conditional Probabilities for the recurrence of large and great
interpolate earthquakes along the Mexican subduction zone”. Bull. Seismol. Soc. Am. 1987; 77: 2094-2114.
15. Shimazaki K Nakata T. “Time-predictable recurrence model for large earthquakes”. Geophys. Res. Lett. 1980; 7: 279-282.
16. Karakaisis GF, Kourouzidis MC, Papazachos BC (1991) Behaviour of seismic activity during a single seismic cycle. In: International conference on earthquake prediction, vol 1. Strasbourg, 15–18 October, 1991, pp 47–54.
17. Mckenzie DP. its margin”. Geophys. J. Int. 1989; 99: 123-153.
18. Molnar P, Lyon-Caen H. “Fault plane solutions of earthquakes and active tectonics of the Tibetan plateau and its margin”. Geophys. J. Int. 1989; 99: 123-153.
19. Kelleher JA Sykes LR. Oliver J. “Possible criteria for predicting earthquake locations and their applications to major plate boundaries of the Pacific and Caribbean”. J. Geophys. Res. 1973; 78:2547-2585.
20. Cornell CA. “Engineering seismic risk analysis”. Bull. Seismol. Soc. Am. 1968; 58: 1583 – 1606.
21. Gardner JK Knopoff L. “Is the sequence of earthquakes in the southern California with aftershocks removed Poissonian?” Bull. Seismol. Soc. Am. 1974; 64: 1363-1368.
22. Wallace RE. “Earthquake recurrence intervals on the San Andreas Fault”. Geol. Soc. Am. Bull.1970; 81: 2875-2890.
23. Rastogi BK. “Earthquake mechanism and plate techtonics in the Himalayan region”.
Tectonophysics, 1974; 21: 47-56
24. Nishenko SP Singh S K. “Conditional Probabilities for the recurrence of large and great interpolate earthquakes along the Mexican subduction zone”. Bull. Seismol. Soc. Am. 1987; 77: 2094-2114.
25. Wang SC McNally KC Geller RJ. “Seismic strain release along the Middle America Trench, Mexico”. Geophys. Res. Lett. 1982; 9: 182-185.
26. Bufe CG, Harsh PW Buford RO. “Steady-state seismic slip-a precise recurrence model”.
Geophys. Res. Lett. (1977); 4: 91-94.
27. McNally KC Minster JB. “Non uniform seismic slip rates along the Middle America
trench”. J.Geophys. Res. 1981; 86: 4949-4959.
28. Gutenberg B, Richter CF (1954) Seismicity of the earth and associated phenomena. Princeton University. Press, New Jersey, p 310 (publ.)
29. Kanamori H (1977) The energy release in great earthquakes. J Geophys Res 82:2981–2987.
30. Ekstrom G, Dziewosnki A (1988) Evidence of basis in estimations of earthquake size. Nature 332:319–323 Gansser A (1964) Geology of the Himalayas. Inter-Science, London.
31. Mogi K (1985) Earthquake prediction. Academic, San Diego, p 355.