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Probabilistic seismic hazard analysis using kernel

density estimation technique for Chennai, India

Chethanamba Kempanna Ramanna a & G. R. Dodagoudar a

a Department of Civil Engineering , Indian Institute of T echnology Madras , Chennai , 600

036 , T amil Nadu , India

Published online: 22 Feb 2011.

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Probabilistic seismic hazard analysis using kernel density estimation technique for Chennai,India

Chethanamba Kempanna Ramanna and G.R.Dodagoudar*

Department of Civil Engineering,Indian Institute of Technology Madras,Chennai á600036,Tamil Nadu,India

(Received 20September 2009;final version received 22May 2010)

Delineation of the seismic area source zone is an important step in seismic hazard analysis which is carried out mainly on the basis of geographical,geological and/or seismotectonic characteristics of the region.Hence it requires knowledge or involvement of the experts from these fields,and yet the zonation suffers from subjectivity.This is especially true in the case of distributed seismicity where a correlation between geological features and earthquakes does not exist.One of the alternatives to the conventional method of area zoning in such cases is the zone-free approach.One of the zone-free approaches is the kernel technique of hazard estimation wherein the seismicity of a region,defined in terms of the Gutenberg áRichter (G áR)recurrence law,is replaced by a spatially smoothened activity rate probability density function.Chennai city lies in a low to moderate seismicity region and there are no major faults causing earthquakes in this region.The kernel method is used in estimating the probabilistic seismic hazard for Chennai and the results are compared with the standard Cornell áMcGuire approach.It is observed that the results match well for the annual probabilities of exceedance for different values of peak ground acceleration expected at Chennai.

Keywords:distributed seismicity;seismic source zone;kernel density estimation;probabilistic seismic hazard;peak ground acceleration

Notation

The following symbols are used in this paper:

a

010a is the mean yearly number of

earthquakes of magnitude greater then or equal to zero

b 0relative likelihood of large and

small earthquakes

c 0bandwidth parameter c 1,c 2,c 3,c 40attenuation coefficients D i 0duration for the i th time interval

d 0bandwidth parameter d 0Euclidean dimension f (x )0multivariat

e probability density function

f (x )0univariate probability density function

g 0acceleration owing to gravity

h 0bandwidth or window size K (x )0multivariate kernel function K (x )0univariate kernel function M 0earthquake magnitude M w 0moment magnitude

m j

0j th earthquake magnitude N 0number of earthquake events N M 0range of earthquake magnitudes N R 0possible range of distances from

site to source

N s 0number of seismic sources n 0number of data or sample or observation points n

0power law index

p im 0detection probability for the i th time interval

and m th magnitude R 0hypocentral distance R 0site to source distance R d 0Euclidean real space

r 0radial distance to epicentre

r k 0k th distance from site to source S a 0spectral acceleration

T i 0effective return period for i th

earthquake event X 0random variable x 0any point in space

x 0value a random variable X takes x 0vector of data set

x i 0i th data or observation or sample point

x in multivariate case

x i 0i th data or observation or sample point

in univariate case

Y 0ground motion parameter Y o 0current year

Y T 0effective historical threshold date or

reference year

y*0a particular value a ground motion

parameter Y takes d 0degree of anisotropy

*Corresponding author.Email:goudar@iitm.ac.in

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Vol.6,No.1,March 2012,1á

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ISSN 1749-9518print/ISSN 1749-9526online #2012Taylor &Francis

http://www.wendangku.net/doc/029b5f5b51e79b89690226aa.html/10.1080/17499518.2010.496073http://www.wendangku.net/doc/029b5f5b51e79b89690226aa.html

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0error term

l m 0mean annual rate of exceedance for

magnitude m

l y*0mean annual exceedance rate s

0standard deviation

y (M ,x ) spatial variation of seismic activity rate y i 0seismic activity rate for i th seismic source f

0angle subtended at r between the intersection

of the fault plane with the Earth’s surface and the epicentre location

1.Intro ductio n

Seismic hazard analysis (SHA)plays an important role in the earthquake resistant design of structures by providing a rational value of input hazard parameters such as peak ground acceleration (PGA)or the response spectrum amplitudes at different natural periods.The very first step in SHA is the identification and characterisation of earthquake sources whether the method adopted is deterministic or probabilistic.These sources may be as a point,fault or area seismic source zone.In low to moderate seismicity regions,the seismic sources are often areal source zones owing to the absence of active faults.In case of the area source zoning,the study region is divided into areas of uniform seismicity,i.e.the relative likelihood of small to large earthquakes (b value of the G áR recurrence law)is uniform.This division of the region into several areas involves a great deal of effort and time and is not advisable if the region is small,or if the purpose is to arrive at a rough estimate of the hazard value,or if it does not involve important structures such as nuclear power plants.

The problems related to seismic area source zoning in the conventional Cornell áMcGuire ap-proach (e.g .Agarwal and Chawla 2006,El-Hefnawy et al .2006,Vipin et al .2009)are as follows:

First,knowledge of geology,seismology and tec-tonics of the region is a must and hence the expertise in the related areas (e.g.Kramer 1996).Geologic features causing earthquakes such as faults (normal faulting,thrust faulting or reverse faulting)may not be con-spicuous on the ground but be hidden in the form of subsurface faulting which may require the study of remote sensing imagery to identify the lineaments at the macro level or study of topographic indicators and so on.Similarly in seismology,the study of pre-instrumental and instrumental earthquakes of the region is required to detect spatial and temporal nature of the earthquakes.Knowledge of the amount of strain energy accumulated and the stress release thereof is the subject of tectonics and is required to identify the potential of the region to earthquakes.

Second,the areal extent to which the Gutenberg áRichter (G áR)recurrence law which defines the seismicity or spatial density of historical earthquakes in terms of the mean annual rate of exceedance,l m of an earthquake of magnitude m is applicable.This law is an empirical law;however Bak (1996)explained such laws as a self-organised critical (SOC)phenom-enon of large interactive systems in nature.With the help of a simple sand pile experiment Bak showed that the number of avalanches occurring owing to collapse of the sand pile of various sizes follows a power law.The experiment being synonymous with earthquake phenomenon wherein the number of earthquakes of various magnitudes occurring owing to stress release in a region is a result of large number of natural interactive systems.Bak commented that such a recurrence law is not a property of a fault but the property of the entire crust,or at the very least,a large geographical area because such large systems cannot be analysed discretely.Hence its applicability to small area is questionable (Allen et al .1965).

The third problem associated with the seismic area source zoning is the seismicity at the zonal boundary .Bender (1986)has illustrated this problem by noticing that there would be an abrupt change of seismicity just a few kilometres on either side of it.As a solution,Bender suggested that the seismicity associated with each point in the source zone be considered as normally distributed which would hence result in smooth variation of seismicity at the boundaries.Fourthly the assumption of homogeneity with regards to seismicity,i.e.the parameter b of the G áR recurrence law is uniform within the zonal area.Beauval et al .(2006a)carried out impact analysis for this assumption,specifically for low seismicity region.As a result,they concluded that the assumption of homogeneity had a bias for higher values of hazard and the effect was severe for longer return periods.For low to moderate seismicity regions where the seismicity data are scarce it would be very difficult to fit the G áR recurrence curve (Beauval and Scotti 2003).Also in the case of distributed seismicity where the seismicity cannot be assigned to a specific geolo-gical structure,the delineation of area source zones becomes subjective.It is a common practice to use the logic tree to address the problem related to subjectiv-ity.However,this does not address the fundamental validity of the zonation procedure itself (Woo 1996).The above problems can be overcome to a certain extent by using the approaches such as the zone-free or spatial smoothing techniques (e.g .Frankel 1995,Woo 1996,Lapajne et al .2003,Zolfaghari 2009).The other alternative,is modelling of the earth’s crust using numerical methods such as finite element method (Li et al .2009).As the latter approach is in

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its infancy,in the present study,the former approach of zone-free technique in particular,the fixed kernel technique suggested by Woo (1996)has been used in arriving at the PGA value for Chennai.The kernel technique is a nonparametric statistical technique of estimating the probability density function from a data set which is not zone-based,but a point-or a line-based (e.g.Silverman 1986,Wand and Jones 1995,Scott 1996,de Smith et al .2009).This technique is well suited for the present study area (Chennai)as most of the problems stated above are being encoun-tered when the conventional Cornell áMcGuire ap-proach to PSHA is followed.2.Geo lo gical and tecto nic setting

Chennai city (13.08338N,80.28338E)is located in the southern part of Peninsular India (PI)on the Coromandel Coast of Bay of Bengal.It is the fourth most populous metropolitan of 6.5million (1189km 2area)and fifth most populous city of 4.34million (176km 2area)in India according to 2001census.It is one of the fastest growing cities in the country with many industries emerging in various sectors such as information technology,telecom,automobile etc.The seismic map drawn by Bureau of Indian Standards (BIS 2002)has shifted Chennai from zone II (lower activity zone)to zone III (higher activity zone)owing to the importance the city is gaining as well as due to the increasing seismicity of PI (earthquakes such as Latur 1993M w 06.1,Jabalpur 1997M w 05.8and Bhuj 2001M w 07.7).

The Peninsular India is considered as a Precam-brian stable continental region with the seismicity being low to moderate.Very rare earthquakes of magnitude greater than 5.0with a maximum historic event being M w 06.0which occurred in 1900at Coimbatore (Gupta 2006)in the southern part of the PI.Earthquakes in these regions are attributed to intraplate stress with pre-existing weak zones.Sub-rahmanya (1996)observed a major compressional lineament known as the Mulki áPulicat Axis (MPA)running from Mulki (approximately 138N)on the east coast to Pulicat Lake on the west coast (very close to Chennai city).This compression zone is the result of continuous spreading of the sea floor in the Indian Ocean.Subrahmanya further concluded that a large number of small earthquakes occur south of MPA whereas major earthquakes can be noticed only in the north of MPA as it acts as a major block with significant stress accumulation.Recent study of the southern PI by Ramasamy (2006)using remote sensing imageries has revealed several faults in this region (Figure 1).Seismically active regions such as Ongole (15.608N 80.108E)M w 05.2in 1959and 1967

and Coimbatore (10.8o N 76.8o E)M w 06.0in 1900are being observed on the Ongole áTamil Nadu and Kerala lineaments respectively.Also a few major earthquakes around Pondicherry (11.938N 79.838E)with maximum M w 05.6in 1867and the other off coast with M w 05.5in 2001have been observed.A numerous small earthquakes of maximum M w 04.6have been observed around Bangalore (12.978N 77.588E)region.Also near Kanchipuram (12.8338N 79.758E)a pre-instrumental earthquake of magnitude M w 05.05in 1823has been observed.

For seismic hazard analysis an influence area of 300km radius around Chennai is considered of which major earthquake zones such as Ongole,Bangalore and region closer to Coimbatore lie on the periphery whereas Pondicherry region and Kan-chipuram lie closer to Chennai.The geological and tectonic features around Chennai are shown in Figure 2(Gupta 2006).From the brief review of the geological and seismotectonic settings of the study region,it can be concluded that the city lies in a low to moderate seismicity region and there exists good earthquake records for the region.The earthquakes are attributed to intraplate stress and the seismicity is distributive,hence delineation into area source zones will bring in subjectivity.The seismicity is low in most part of the influence area and hence the assumption of homogeneity will affect the hazard values.With these points in mind,the present study is undertaken to explore the applic-ability of zone-free technique to seismic hazard analysis for Chennai as a case study.3.Kernel metho do lo gy

Starting with the basics,consider a random variable X ,the probability that X lies between two values a and b is obtained by the probability density function (PDF)f (x )as

P (a B X B b )0g

b

a

f (x )dx for all a B b

(1)

Broadly there exist two approaches for determination of PDF:parametric and nonparametric .In the para-metric approach,an assumption is made that the data are drawn from a known distribution and its para-meters are determined and hence f (x ).Using any goodness of fit tests,the PDF so obtained is checked for the hypothesis with respect to the distribution assumed.On the other hand,no such assumption is made in case of the nonparametric density estimation for f (x ).There are several nonparametric density estimation techniques starting from the simplest histogram to newer techniques such as splines and

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wavelets.Also there exists an intermediate class of nonparametric density estimation technique known as the kernel technique.

The kernel technique is a simple technique wherein a kernel of type Triangular (Conic),Normal (Gaussian),Quartic (Spherical),Uniform (Flat)or Epanechnikov (Paraboloid)density curves are placed on each sample/data/observation with a certain spread known as the bandwidth or radius of the kernel.As an illustration,in Figure 3,a

normal

Figure 1.Tectonic scenario of South India (Ramasamy 2006).

4 C.K.Ramanna and G.R.Dodagoudar

density curve is placed on each of the sample point and the density at any point is calculated as the normalised sum effect of each of these kernels.Mathematically,for a univariate case the density estimate is expressed as

f (x )01nh X n

i 01K

x (x i

h

(2)

where n is the number of observations,h is the

bandwidth which controls the variance of the

density

Figure 2.Geological and tectonic features around Chennai (Gupta 2005).

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function K ((x áx i )/h ),x is any point and x i is the sample point.For example,if standard normal distribution is considered,the kernel function is of the form

K (x )01

??????2p

p e

(x 2(3)

For multivariate density estimation,the estimator is of the form

f (x )0

1nh d X n

i 01K 1

h

j x (x i j (4)

where d is the dimension of vector x and the

corresponding standard normal distribution kernel is of the form

K (x )0(2p )(d =2exp (1

2x 2

(5)

where K (x )is usually a radial symmetric probability density function and satisfies the normality condition:

g R d

K (x )d x 01

(6)

The most important factor in the kernel technique is the selection of the bandwidth rather than the type of kernel (Silverman 1986).Large value of h leads to over smoothing and hence the density function becomes less sensitive to the change in the observation point x i .On the other hand too small a value for bandwidth results in a series of spikes centred on the observed data.There are several methods for determining h which can be found in the literature (e.g.Breiman et al.1977,Abramson 1982,Silverman 1986,Mugdadi and Ahmad 2004).The nearest neighbourhood technique

of determining the bandwidth is used in this study (Silverman 1986,Woo 1996).

The fixed kernel technique particularly to seismic hazard analysis was applied by Woo (1996)as an earthquake recurrence model.Woo developed a computer program called KERFRACT to implement the kernel technique for hazard analysis wherein the seismic activity rate density function replaces the traditional G áR recurrence law in PSHA.The form of kernel used in KERFRACT is an anisotropic multivariate kernel suggested by Vere-Jones (1992).This kernel form takes into consideration the fractal dimension of the earthquakes.Chen et al .(1998)have used the kernel technique in a different form,wherein the bandwidth parameter of the kernel function is used in defining the influence area for each of the historical earthquakes in the process of estimating the global seismic hazard.The maximum earthquake at a site was calculated as the largest event whose hypothetical influence area extends beyond the site.This maximum magnitude so obtained was used as the upper cutoff magnitude for computing occurrence rate using G áR recurrence law.Molina et al .(2001)used the fixed kernel technique as suggested by Woo (1996)for synthetic data as well as for historical catalogues of Norway and Spain.The results from KERFRACT gave lower values for Norway as compared to Cornell áMcGuire approach,however,for Spanish catalogue both results compared well.It was finally concluded that the kernel technique was attractive in situations where good historical record exists,but in regions with poor or short historical earthquake records the classical Cornell áMcGuire approach was still preferable.

Stock and Smith (2002a)used the adaptive kernel technique by considering a variable bandwidth to develop earthquake occurrence model by smoothing the annual activity rate.The annual activity rate is determined as the number of earthquakes above cutoff magnitude divided by the number of complete-ness year.According to this technique the bandwidth varies spatially,higher values for epicentres located sparsely and lower values for epicentres located in clusters.Stock and Smith (2002b)also devised a technique for comparing the output of various kernels.Beauval et al .(2006b)have applied the fixed kernel technique to France region.It was observed that for low to moderate regions,both the kernel technique as well as the Cornell áMcGuire approach yielded similar results whereas for high seismicity regions kernel technique gave lower results.Secanell et al .(2008)have applied the fixed kernel technique along with the Cornell áMcGuire approach to the Pyrenean region (400km long mountain range lo-cated in southwest Europe along the French á

Spanish

Figure 3.Graphical representation for a univariate case.

6 C.K.Ramanna and G.R.Dodagoudar

border).Logic tree was used to arrive at the hazard for this region.Chan et al .(2008)have developed a uniform seismic hazard map for entire Europe using a hybrid zone less method wherein the kernel method was applied after forming seismic zones which are solely based on geology.For each of these zones different bandwidth and catalogue completeness time were calculated.Stanislaw and Sikora (2008)have used kernel function for source size characterisation for hazard analysis of mining induced seismicity.The kernel method of SHA has also been used for some of the LNG Plants for example in Taranto,Italy (Principia 2005).4.Seismic hazard analysis

Probabilistic seismic hazard analysis for Chennai has been carried out using the fixed kernel technique and the results are compared with the standard Cornell áMcGuire approach.The basic difference in the two approaches is in handling the uncertainties making up the average exceedance rate.The mean annual rate of exceedance l y*of the selected ground motion para-meter Y exceeding a particular value y*is given as

l y 10

X N S i 01X N M j 01X N R k 01

y i P [Y y 1?m j ;r k ]

P [M 0m j ]P [R 0r k ]

(7)

where N s is the number of sources,N M is the range of magnitudes,N R is all the possible range of distances from site to source,y i is the seismicity and/or spatial activity rate for each source defined by the G áR recurrence law or by the kernel,P [Y y*j m j ,r k ]is obtained from the attenuation relationship,P [M 0m j ]and P [R 0r k ]are obtained from the probability density function of magnitude and distance respec-tively.

In kernel approach,the seismicity rate y i is replaced by the spatial activity rate density function given as

y (M ;x )0

X N i 01

K (M ;x (x i )T i

(8)

where N is the number of earthquake events,x is the

observation point (grid point),K (M,x áx i )is as per Equation (11)and T i is the effective return period evaluated.The formal definition of the return period for a given catalogued event M is the duration of each time interval D i times the sum of the event detection probabilities p im in all centuries up to the present.Every earthquake event is associated with an ‘effec-tive’historical threshold date Y T for its observability.The return period for the event is then obtained by subtraction of this historical date from the present

date Y o (i.e.2009in the present study).The historical threshold date is qualified as ‘effective’to allow for the partial observability of the event before the threshold date,and the partial unobservability of the event after it (Woo 1996)and is calculated using the following expression:

Y T 0Y o (X

i

p im D i (9)

a numerical value is assigned to p im based on the

seismicity of the region.Details of determining the historical threshold date for Chennai is given in section 4.3.

4.1Data

Earthquake catalogue data were compiled from sources such as India Meteorological Department (IMD),U.S.Geological Survey Moment Tensor and Broadband Source Parameter Search website (USGS),The National Earthquake Information Cen-tre (NEIC),The Harvard Seismology Central Mo-ment Tensor Project,The International Seismological Centre (ISC),Jaiswal and Sinha (2007),Chandra (1977),Rao and Rao (1984)and Rao (2000).A total of 173earthquakes of M w ]3.5were compiled for a circular influence area of 300km radius around Chennai from the year 1507to 2009A.D.Foreshocks and aftershocks were removed using Gardner and Knopoff (1974)dynamic windowing technique which resulted in 151main events.This Poissonian catalo-gue has been used for the hazard analysis.The spatial distribution of epicentres around Chennai before and after declustering are shown in Figure 4a and Figure 4b respectively.

Since the objective of the present study is to test the performance of the fixed kernel technique for low to moderate seismicity region of India such as Chennai,hence only one attenuation relationship as suggested by Ragukanth and Iyengar (2007)for the southern part of the PI has been used.The functional form of the attenuation relationship is

ln y 0c 1'c 2(M (6)'c 3(M (6)2

(ln R (c 4R 'ln o

(10)

In the above equation,y 0(S a /g )stands for the ratio of spectral acceleration S a at the bedrock level to the acceleration owing to gravity,M and R are the moment magnitude and hypocentral distance respec-tively.The attenuation coefficients for zero periods are:c 101.7816,c 200.9205,c 30(0.0673,c 400.0035and s (ln )00.3136.An average hypocentral depth of 17km was considered for all epicentres in the hazard analysis (Figure 5).

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4.2Cornell á

McGuire approach

The PSHA was carried out using CRISIS 2007(Ordaz et al .2007).Only one seismic source zone,i.e.background seismicity was considered owing to rea-sons already discussed (Figure 6).The completeness

analysis was carried out using Stepp’s method (1973)for the source zone.Figure 7depicts the statistics of the Stepp’s method.The periods of completeness for each of the magnitude bins are given in Table 1.Figure 8depicts the a and

b

Figure 4a.Spatial distribution of epicentres around Chennai (before declustering).

8 C.K.Ramanna and G.R.Dodagoudar

parameters of the G áR recurrence law.The seismicity parameters as obtained from G áR recurrence law are presented in Table 2.The curve for annual probability of exceedance is generated and is depicted in Figure 9.

4.3Kernel approach

KERFRACT program has been used to carry out the hazard analysis.The main program reads the Lati-tude and Longitude of the site at which hazard is required to be calculated,the kernel parameters,

the

Figure 4b.Spatial distribution of epicentres around Chennai (after declustering).

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ground motion values,ground motion attenuation coefficients,regional earthquake depth distribution and their weights,earthquake epicentres location and magnitude along with their respective uncertainty in the form of standard deviation.A square area of 600)600km (total area 0360000km 2)encompass-ing the influence area of 300km radius is considered for density estimation.This area is divided into grids of 10)10km size and the seismic activity rate density for each magnitude range is calculated using the kernel function at these grid points [Equation (8)].The activity rate depicts the mean number of annual exceedances of a selected ground motion at the site.For example,the activity rates for M w 03.5(3.99magnitude bin and M w 04.51(5.49magnitude bin along with the spatial distribution of epicentres are shown in Figures (10a,10b,11a and 11b),respec-tively.

The option of using an anisotropic kernel is available in the program,but in the present study region,the epicentres from identifiable lineaments are absent.Hence,an isotropic kernel (radial symmetric kernel)is used in Equation (8)wherein the smoothing is independent of the direction.The anisotropic kernel is given as

K (M ;r )0n (1p h 2(M )1'd cos 2f 1'(d =2) 1' r

h (M ) 2 (n

(11)

where n is the exponent of the power law or also

known as fractal scaling index which controls the degree of spatial smoothing or in other words scales the fall-off of the kernel density,h is the bandwidth which is a function of magnitude,r is the distance to the epicentre (x áx i ),the parameter f is the angle subtended at r between the intersection of the fault plane with the Earth’s surface and the epicentre location and d is the degree of anisotropy values lying between 0and 2.A value of zero indicates isotropy and higher value signifies anisotropy.

The value of n lies between 1.5and 2indicating a cubic and quadratic decay of the probability den-sity with the epicentral distances respectively.Fault

networks and epicentre distributions are known to have fractal properties.Thus a natural way to analyse the spatial distribution of seismicity is to determine the fractal dimension and measure the degree of clustering of earthquakes (Beauval et al .2006a).It is observed that the parameter n has little effect on the results (Molina et al .2001).A value of 1.75was chosen in the present study.The bandwidth h to be applied for each kernel,which is placed on the epicentral point is a function of magnitude and is given as

h (M )0ce (dM )

(12)

where parameters c and d depend on the spatial distribution of earthquake epicentres.The parameters are calculated by forming various magnitude bins and for each earthquake event within the bin,the distance to the nearest epicentre is determined.The mean nearest distance for each bin is obtained and through a least-square fit between the magnitude and band-width,the parameters are obtained (Figure 12).

Another important input required for kernel technique is the reference year for every earthquake event which is the effective historical threshold [Equation (9)]for potentially recording it if it had occurred.This value is assigned taking into consid-eration the magnitude,epicentral location (whether offshore or onshore)and the year of occurrence.Hence earthquake events having the above same criteria will have same reference year date.To obtain this,the catalogue is divided into time intervals of equal or unequal period D i .For each interval,the probability of detecting the event of that magni-tude p im is assigned.The reference year is calculated as the difference between the current year and the effective return period.An example of assigning the probabilities for magnitude bin 4.0á4.49for onshore events is shown in Table 3.A summary of the results of reference years for each of the selected magnitude bins is presented in Table 4.

The kernel technique also provides an opportunity to add background seismicity to allow missing events in areas of poor event detectability.Epicentre location error can also be accommodated and is specified as the standard deviation for each event.Option is available in the program to specify the extent of smoothing for location error.In such a case instead of one kernel on the epicentre,several kernels within this location error are placed.However,in arriving at hazard value for Chennai,no background seismicity was considered and the flag associated with the epicentral error is set to zero.Similarly,uncertainty in magnitude in the form of standard deviation can be provided.The result of variation of the annual probability of exceedance for each of the selected peak ground acceleration values is depicted in Figure

13.

Figure 5.Focal depth distribution.

10 C.K.Ramanna and G.R.Dodagoudar

5.Discussio n and co nclusio ns

The seismic hazard curve is combined with the Poisson model to estimate probabilities of exceedance in finite time intervals.The seismic hazard at Chennai is controlled by the low to moderate magnitude earthquakes.For short return period,i.e.,475years (i.e.10%probability of exceedance in 50years exposure time)the peak ground acceleration esti-mated by the kernel method is 0.087g.As per BIS 1893:2002the corresponding PGA is 0.08g.For long return period of 2475years (i.e.2%probability of exceedance in 50years exposure time),the

moderate

Figure 6.Seismic area source zone.

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earthquakes dominate the hazard at Chennai with PGA equal to 0.137g.The value of PGA with a particular probability of exceedance increases with increasing exposure time.The peak

ground

Figure 7.Period of completeness using Stepp’s method.

Table 1.Catalogue parameters.Magnitude range Completeness

year

Completeness period

(years)

3.5á3.99196840

4.0á4.491968404.5á4.99195850

5.0

1800

209

Table 2.G áR recurrence law parameters.Parameter Value l (M 003.5) 3.3a 3.8b

0.94b (02.303b) 2.1601a (02.303a)

8.7465

Figure 9.Annual probability of exceedance from Cornell áMcGuire

approach.

Figure 10a.Spatial distribution of epicentres for M w 03.5á

3.99.

Figure 10b.Spatial variation of activity rate density for M w 03.5á3.99(activity rate magni?ed by 103

).

Figure 8.Seismicity rate as obtained from G áR law.

12 C.K.Ramanna and G.R.Dodagoudar

acceleration values obtained from the present and previous studies are summarised in Table 5.It is observed that the results obtained from the Cornell á

McGuire approach and the kernel technique are similar and in agreement with the observations from the previous studies (Molina et al.2001,Beauval et al.2006b).

The best part of kernel density estimation techni-que is that it is zone-free and hence any ambiguity

or

Figure 11a.Spatial distribution of epicentres for M w 04.51á

5.49.

Figure 11b.Spatial variation of activity rate density for M w 04.51á5.49(activity rate magni?ed by 103

).

Figure 12.Bandwith curve.

Table 3.Reference year for M w 04.0á4.49(OnShore).Time period Probability (p i )

Effective return period (p im D i )

1500á18000.157.501800á18500.2512.501850á19000.3517.501900á19500.5025.001950á19600.60 6.001960á19700.757.501970á19800.858.501980á19850.88?4.401985á19900.92 4.601990á19950.95 4.751995á20000.98 4.902000á20050.98 4.902005á20080.98 2.942008á20090.98

0.98a i

p im D i 111.97

Reference year

(2009á111.97)01897.03

Table 4.Reference year.

Reference year

Magnitude range Onshore Offshore 5.5186218965.0á5.49187418974.5á4.99188519094.0á4.49189719263.5á3.99

1909

1954

Figure 13.Annual probability of exceedance from kernel technique.

Georisk

13

error in forming seismic area source zones will not be carried forward to hazard estimate for low seismicity regions.This technique provides a spatial variation of the seismic activity rate unlike the conventional approach where it is a constant for a seismic source zone.The kernel technique frees one from force fitting the G áR recurrence curve for a small region.This can be observed from Figure 8wherein the points do not lie exactly on the line.It is also interesting to note that in Figure 6,the seismic area source zone is delineated for region where earthquake records exist.However if the whole region of the circular influence area were to be considered as a seismic source zone,the hazard value would be influenced by this variation owing to smearing of the activity rate on a much larger region.The kernel technique is not influenced by such smearing effect as the spatial variation of activity rate density function is calculated by considering both magnitude and epicentral location [equation (8)]and appropri-ately included in the hazard estimates.For low to moderate seismicity regions where the earthquake data are scarce,it is difficult to carry out the completeness analysis as it induces subjectivity.In conventional PSHA,the accuracy of the hazard calculations depends very much on the correctness of the completeness analysis results.In kernel tech-nique subjectivity is introduced owing to the detec-tion probability p im which needs to be assigned for every earthquake event.However this can be over-come by careful study of the paleoseismicity and instrumental seismicity of the region and a standard detection probability chart can be arrived at for the region.A good PSHA will be valid for a number of years and will not be discredited by new theories or data that result from the occurrence of a single earthquake.Acknowledgements

Authors would like to express their sincere thanks to the India Meteorological Department,New Delhi for sharing the earthquake data relevant to the study presented in the paper.The authors also wish to thank Dr.Gordon Woo for

sharing the KERFRACT program for carrying out a part of the work presented in the paper.Finally the authors would like to thank the two anonymous reviewers for the critical reviews and useful suggestions that improved the manuscript.

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