 Let us start our today's lecture for this NPTEL video course on Geotechnical Earthquake Engineering. We are going through module 7 which is on seismic hazard analysis. A quick recap what we have learnt in our previous lecture. We can see in this slide that what is the application in the code design code or seismic design code worldwide of this seismic hazard curves like UBC suggest for 10 percent probability of accidents in 50 years time. This map shows the peak acceleration values for that 475 years return period. These are the values in percent G for a Nihar based site category of B and C for U.S. Similarly, for AASHTO code the proposed map for U.S. is like this with 2 percent of probability of accidents in 50 years scale. So, that is how the seismic design codes they implement the seismic hazard analysis results for further application in design. Then in the previous lecture we had started with dealing with an example of extensive case study for a particular region which is the Gujarat state of India. And we discussed in detail we have initiated the discussion in detail for the seismic hazard study for Gujarat region of India. If we look at this slide as I have already mentioned this is the work done for the Ph.D. thesis of Dr. Jayakumar Shukla who completed his Ph.D. in 2013 at IIT Bombay under my supervision. This is the map of location of Gujarat. Gujarat is the central western most state of India as shown over here. This is the Gujarat state which is surrounded by here Arabian Sea here the neighboring country Pakistan. The urban areas of Gujarat region has been subdivided into three major regions. One is Kach region another is Saurashtra region another is Mainland Gujarat regions. And these are the 25 cities which are selected for our present case study or present analysis. Further later on 4 port sites Kandla port, Mundra port, Hazira port and the Hedge port are also considered for site specific ground estimation analysis which we will discuss in our next module of this course. Now, this is the seismic zonation map of Gujarat state of India as per Indian seismic design code IS 1893 part 1 of 2002 version that is the latest version still available. These are the four color codes like red, orange, yellow and blue. These are showing four different zones zone 4 5 zone 4 zone 3 and zone 2. Among this zone 5 is the most vulnerable one zone 4 is lesser than that zone 3 is lesser than that and zone 2 is least vulnerable in the Gujarat region. So, you can see Gujarat is the only state in India which is having all the four zones as per our IS seismic design code 1893 part 1. That is another reason why the Gujarat state has been chosen. Another reason is 2001 Buj earthquake is very well known very damaging earthquake which occurred in Buj region of Gujarat and it affected several other parts of the Gujarat as well. That is the reason why we want to find out the seismic hazard study. We want to do the seismic hazard study for the Gujarat region. Now, for any particular seismic hazard study these are the various components as shown over here. For our particular case seismic hazard study for Gujarat region we need to get first the earthquake catalog for that region then regional seismicity parameters, sensitivity analysis. Using them we can do the deterministic seismic hazard analysis and probabilistic seismic hazard analysis and finally we can do the site specific ground motion analysis for particular sites which I will discuss in the next module of this course. So, this is the seismic zonation of map of Gujarat as I have already explained and if we exaggerate this part zone 5 of Gujarat region or Kutch region this is the seismotechtonic setting of that region and if we further expand it we can see these are the points showing the epicenters of various earthquakes recorded during 2007 to 2011 as given in the ISR report 2010-11. So, from various reliable data collection units or sources like USGS, IMD, ISR we can collect ER wise number of occurrence of earthquake in different regions like we have subdivided in three regions of Gujarat. This is the way this shows typical values for 2008 so many earthquake occurred, 2009 so many earthquake occurred and their magnitude scale links are also mentioned over here which automatically shows Kutch region which is in zone 5 is experiencing more number of earthquakes than other two regions which are in zone 4 and zone 3. Hence considering a single seismicity event or single seismicity hazard study or single seismicity parameter for entire Gujarat is not justifiable we should do region specific or area specific study for Gujarat state. Now we had also seen in our previous lecture how the seismicity migrates from one region to another region. Let us look at here in this slide let us take the example of seismicity in Saurashtra region of Gujarat. This is 2006 to 2007 in Jamnagar area these are the earthquakes occurred then it shifted to more clustering in the Junagar area then it again migrated to Surendranagar area over the years 2008 and 2009. So, there is a way that seismic events get migrated from one place to another place within a given region that also needs to be considered when we are doing any seismic study for a particular region. Next we had also seen in our previous lecture what is called earthquake catalogue and then catalogue how to check the catalogue completeness. First earthquake catalogue is this picture which is shown below over here the bottom one that is earthquake magnitude M W scale we have taken all magnitude equal and above 4. So, that is the line you can see over here magnitude of 4 and above recordings are available from 1822, 2012. So, all data points have been collected after doing that we can either use the CUVI method as given by Tinti and Mulergya in 1985 and the steps method 1973 to get this cumulative earthquake occurrence we can add this up and get the cumulative scale with respect to time and find out whether there is any change in the slope of that variation of occurrence of number of earthquake. So, if there is a change in the slope as we can see here this is the blue line slope of this initial portion and there is a slope of the green line in the recent past there is a change in the slope at around this point. So, that point indicates where this change has occurred 1962 is the year we obtain for the present analysis which I said the details are available in the journal paper Shukla and Choudhury 2012 in natural hazards and earth system science journal this is the volume number this is the page number one can go through that paper for the detail study on this earthquake catalogue generation and to check the catalogue completeness. Now, let us continue in our today's lecture further next step to check the regional seismicity parameters. So, to check that regional seismicity parameters already we have this earthquake moment magnitude M w and we have already taken M w equals to 4 and above. So, that is why you can see all the points are 4 and above and what is log of n in the log scale n value that is the number of occurrence of that magnitude of earthquake and that we have subdivided into three regions that is scutch region, Shaurashtra region and mainland Gujarat and then we have found it out for entire Gujarat also by summing them up by adding them we have proposed it for entire Gujarat also that is what we want to see what is the variation of that Gutenberg Richter parameter for individual area or individual region compared to entire Gujarat region and which region is having more effect or influence on entire Gujarat states seismicity events or recurrence of earthquake. See if we look at this figure again Gutenberg Richter recurrence relations are derived using the least square fit method. So, least square fit method is used for preparing the earthquake catalog of M w greater than or equals to 4. Now, if you see over here regions various region like Shaurashtra mainland kutch and entire Gujarat past seismicity recordings which are used in terms of years you can see over here for Shaurashtra region data of last 135 years have been used and that value till 2011 March as I have already mentioned for mainland Gujarat last 175 years for kutch region 189 years and hence for automatically for entire Gujarat also it is last 189 years of data set have been collected. And after plotting it in this fashion what we can get the intercept A value and the slope of this line B value. So, Gutenberg Richter relationship if we propose in this form that log of n equals to that A minus B M w that will give us this equation individual equation for individual region like for Shaurashtra this region because you can see if we look minutely this is the for kutch region that is square shape dark dots. So, this is for kutch region if we look at here right. So, this slope and this A value will give for the kutch region. So, kutch region the equation is this one whereas for mainland Gujarat it is this for Shaurashtra it is this and for entire Gujarat by summing all this data points we get this line which is giving us the Gutenberg Richter relationship for entire Gujarat like this and corresponding r square value when you do the best fit curve as we already know that this is the standard way we find out whether it is a good estimation or not. You can see it is more than 0.95 in all the three cases like Shaurashtra kutch and entire Gujarat, but it is little less than 0.95 for mainland Gujarat. So, the detail study about this regional seismicity parameters of Gujarat is available in the journal paper Choudhury and Shukla 2011 in the journal Disaster Advances volume 4 issue 2 page number 47 to 59. So, if one wants to know the details about this study he or she can refer to this journal paper for further details. Now, let us look at here let us highlight this value over here. If somebody wants to compare or validate this value with other researchers result what we have done our publication came in the year 2011 as I have already shown over here. Look at the B value what we have proposed for Shaurashtra region 0.64 and the latest finding by Rastogi et al of 2013 publication that is after our publication they recommended they also did a similar analysis for Shaurashtra region only and they recommended the B value of 0.67 which is pretty close to our value. The difference can be always due to the model which we have used like least square fit method we have used also it depends on how many data points they have used from which year they have considered all these are the reasons for the change in the value, but still you can see for a particular region this value should not vary too much among researchers if it varies a particular region needs to be obtained. So, here you can see a kind of a validation of Rastogi's result with our results of 0.64 which we have proposed in 2011. Now, this B value using another method of maximum likelihood if we want to find out using maximum likelihood method which is proposed by Aki in 1965 and Utsu again in 1965 it is another popular method to find out or to estimate the beta value one is least square fit method which gives us beta value like this another method which we are now a mentioning is maximum likelihood method. In that case we how we compute this B value this is the equation log of U minus M minimum that is it depends on what is the minimum threshold value we are using is the sampling average of the magnitude and region specific B value using this maximum likelihood methods are coming like for Kutch region 0.526 for Shaurashtra region 0.572 and for Mainland Gujarat 0.642. You can see maximum likelihood methods are giving the higher values of B compared to this least square method. Now, probability models which can be used for earthquake recurrence are discussed over here. In time predictable methodology many researchers has applied various probability models to predict the next earthquake within the specified time. Like in the beginning of this course I have already mentioned whether we can predict the earthquake scientifically we said no we cannot say exact date we cannot say exact time but yes in the sense of probability we can say chances of occurrence of probability of this much percentage within this year band that kind of estimation we can provide based on the historical or earlier earthquake data points and seismicity events and parameters involved. So, this is how we are now going to use the various probability models so that we can propose the recurrence time of earthquake using various probability distribution at a particular region which may be helpful for NGOs, government organizations, designers, practitioners everybody to understand that in this region there is a chance in this year band or in this time scale that earthquake of this magnitude may occur. So, proper measure may be taken. So, the key researchers you can see in this slide who used various probability models to predict the next earthquake in a specific band of time. It is not an exact time but band of time like Utsu in 1984, Nishenko and Boland in 1987, Cycles and Nishenko in 1984, Rikitake in 1991, Shimazaki in 2002, Kagan and Nopov in 1987 and several other researchers as you can see listed over here and specifically for Indian peninsular region the where this Gujarat state also comes from that is peninsular region of India the central part of India like Parvez and Ram in 1997 and 1999 they also proposed various probability models to predict the occurrence of next earthquake, Triparty in 2006, Jaiswal in 2006, Yadavetal in 2008. So, these are the researchers who proposed or used various probability models for earthquake recurrence estimation for Gujarat. Let us look at the various probability distributions. You can see from this curve various lines are proposed. You can see this dot are showing the earthquakes occurred in the Gujarat region with magnitude greater than equals to 5. In this model we have selected magnitude greater than equals to 5 and cumulative probability we obtained using four different probability model. If you look at here what are the various probability model, Pareto probability distribution model, Rayleigh distribution model, Weibull distribution model and exponential distribution model. These are four seismicity model parameters which are used to estimate the probability of distribution. How it has been done? Let us look at this table. These are the data points, various numbers, occurrence of these events, ER wise remember we have taken magnitude more than or equals to 5. So, that is why you will see M W equals to or greater than 5 listed over here. They are occurrence in terms of year, in terms of their month and date that is exact occurrence date when those earthquake occurred and those date can be expressed in year format like this in decimal considering month and date. Where these earthquakes occurred they are latitude and longitude and recurrence time in years we can easily find it out using Gutenberg-Richter relationship and where these earthquake occurs, we have found out in terms of location like cuts region or whether a particular name has been given whether it comes to Saurashtra region those identification also we did. So, this study in details you can again find it out in the journal paper by Choudhury and Shukla in 2011 in the same journal Disaster Advances issue 4 number 2 volume 4 number 2 page number 47 to 59. So, let us look at the selection of the best distribution which distribution is the best one and which one we can select out of this 4 different distributions. So, these are the basic model or basic equations of this probability distribution like Weibull model is expressed by this function, Rayleigh model is expressed like this function, Exponential model is expressed by this function and Pareto model is expressed by this function. For details you can refer to any probability book for details of this individual probability model which I am not going to discuss in this course. Now, using this various probability mathematical models we can automatically find out based on maximum log likelihood values individual values they are mu delta alpha theta whatever parameters are involved in individual cases and their p values are probability of occurrences etcetera. You can see from this graph also which one is giving a better result. So, like that we can select a better model from this probability distribution of various seismicity model parameters which are involved over here. Now, next we need to see among this 4 seismicity models which one is the best for this given set of data of earthquake. Let us go back once again in this data set when we were calculating the values you can see over here the cumulative probability of their occurrence with magnitude scale of more than or equals to 5. We have plotted over here these are the earthquake data points as I have already mentioned and 4 seismicity model parameters. Now, among them which one is the closest one if we see Weibull model that is the green color curve is the best average which is going through this actual dots of this earthquake occurrence. So, Weibull model is one of the best model. Next another better model is exponential distribution that is the blue color line. If you look at that that is the next better one after Weibull distribution right. Like that you have to identify which seismicity model is acting well for or satisfying well for your given set of data of earthquake catalog. Now, in this column if we re look at this column this says recurrence time in years. Recurrence means starting from this year 1819 data up to the 2007 data what we have considered in this paper from the gap between 1819 and 1845 event is something about 25.833 years right that is if you deduct this year month and date from this year date and month you will get this value in terms of unit of year. Similarly, for all other things as you can see over here that means magnitude of 5 earthquake or more than that occurred in the interval of these many years these are actual data. Now, based on this actual bit data we are now using this seismicity model parameters to extrapolate it that is the point in this case what we are planning to make use of this known data points for further extrapolation. So, that the this extrapolated data can give us based on this probability model parameters what can be the next expected range of occurrence of magnitude more than 5 earthquake at that location at that region that is what we want to find out right. So, that is why this data set is very important. So, last one when it has been recorded and considered in our paper of this 2011 that is 2007 earthquake data which occurred on 6th of November in 2007 as you can see over here that magnitude was 5 it occurred at Junagal area of Gujarat. So, the difference between the previous occurrence of earthquake date and this date is about 1.683 years you can easily find it out right this in terms of years. So, 2007.933 minus 2006.25 that will give you 1.683 fine. So, now we want to extrapolate this using this seismicity model parameters so that when the next earthquake is expected in Gujarat region or the specific region of Gujarat like in Koth region or Saurashtra region or Mainland Gujarat of tur 2007 which will have a magnitude of 5 or more than that. So, that is how we are going to use this seismicity model parameters and we have seen which distribution is best for current data set that also we have mentioned. So, this is the recurrence estimation how we are doing now the estimation if you use this four different probability distribution model exponential model rally model Pareto model and Weibull distribution model recurrence interval you can predict that is after extrapolating you can calculate from that behavior from your equations that these are the next recurrence interval as per exponential model it says after the 2007 November next one will occur 7.853 year whereas, as per rally model it says after 16.173 years as per Pareto model it says 3.135 years whereas, as per Weibull model it gives 7.011 year now what we have mentioned for the given data set which models are better or good models exponential and Weibull model. So, the last event that occurred on that 6th of June 6th of November 2007 which comes out to be in the scale of year 2007.933. So, next expected earthquake will be this value plus what is your predicted value that you can add up and you will get in the year unit what is the next expected earthquake fine. Now, the study date considered when this study was considered that is on 10th of November 2009 which comes in year scale this one that is when we started communicating the paper to this journal. So, year left from the present date present date is 10th November 2009 we considered as our present date when we communicated the paper. So, the difference between these two this is so many years. So, as per exponential model after 5.936 years there will be an earthquake magnitude 5 or more in the Gujarat region whereas, as per Rayleigh model it is after 14.256 years whereas, as per Pareto model after 1.218 years whereas, as per Weibull model it is after 5.094 years which if we add up to this value we will get the next earthquake expected before these many years. So, October 2015 as per exponential model as per Rayleigh model before February 2024 as per Pareto model before 2011 January remember our study date is 2009. So, that time we got from Pareto model it is giving before January 2011 there will be an earthquake magnitude of 5 or above. As per Weibull model the value comes out to be next earthquake probability of occurrences before 2014 December. Now this paper after communicating this got published in 2011 you can see over here this research output was published in the journal Disaster Advances in the month of August 2011 issue and it was actually validated by a real earthquake which occurred more than 5 magnitude in September 2011 in this locality. So, that again proves the actual validity of exponential and Weibull model which are better model whereas, Pareto model is very unrealistic or I should say it is overestimating that is it is predicting that it will occur very soon, but it has not happened whereas, Rayleigh model is towards an unsafe side because it is predicting that it will occur far later. So, compared to these two models for the given set of earthquake catalogue for Gujarat exponential and Weibull model are much better which we have validated through mathematical proof in the presentation as well as through actual validation of the earthquake which occurred. Though people may say this is not that scientific, but the occurrence or calculation based on probability model is really scientific. So, we can give a band we can never give this exact date of September 2011 that I want to again highlight here we are not going to predict the earthquake date we are only going to say the chances or probability of occurrence of earthquake in a span or band that is what has been proposed over here which has been validated clear. Now, let us compare this various earthquake return periods for different regions of Gujarat like return period in the year unit and this is earthquake magnitude M W above and equal to 4, but we have taken initially. So, for Saurashtra region, Kutch region entire Gujarat and Mainland Gujarat graphs have been shown over here the detail about this study can again be obtained in this journal paper. Now, let us come to the B value what is proposed by the present method and similar B values proposed by other researchers for the same region. Let us compare that how our B values proposed differ or validate or matches with other researchers findings for this Gujarat region and what is the study period or earthquake recurrence or earthquake data points have been taken for which area. So, this portion which is black shaded that is the present results that is present study we obtain these beta values as already I have discussed there are two methods we have used to obtain this B value one is least square fit method LSF method and another one is L S F method one is maximum likelihood method. So, as per least square fit method for Kutch region we have seen B value we obtain 0.417 for Saurashtra we got it as 0.64 that we have already compared in that slide with respect to Rastogi et al 2013 latest finding which is 0.67 for Saurashtra. So, you can compare these two value which compares pretty well right for mainland Gujarat 0.62 and for entire Gujarat 0.51. So, these four are obtained using least square fit method and the study period taken that is the earthquake data points taken between 1822, 2000 of 8 for these regions for Saurashtra and mainland Gujarat 0.62. It is 1872, 2008 whereas for maximum likelihood method the same study the Kutch region we got B value as 0.526 for Saurashtra region 0.572 and for mainland Gujarat it is 0.642 for the same set of data set only one extra year we have taken because this analysis was done after this least square fit method that is why one more year of earthquake data points have been taken. Now, if we compare our results of B values with respect to the other researchers result who have calculated for the same region Gujarat region like as I have already mentioned Rastogi et al 2013 value for Saurashtra region matches very close or very well with our study whereas WC NDMA report of 2010 that gives for entire Gujarat remember these value is given for entire Gujarat not they have not subdivided Gujarat into difference is make zone what it should have been as I have already given the explanation. So, they have suggested 0.87 as a B value which is pretty on the higher side as you can see with a plus minus of 0.06 and they mention that they use that earthquake data from 1800 to 2009 for the analysis whereas, Tripathi et al in 2005 proposed again for entire Gujarat the value of B as 0.72 whereas, for Kutch region Ashara et al in 2006 proposed the B value as 0.43 which is again very close to our observation of 0.417. Now, Jaiswal in 2006 proposed for Kutch region the value of B value 0.71 with plus minus error of 0.03 and taken range of data of between 1842 to 2002. So, obviously as you can see as your data set point or this year increasing or changing there is always a chance that your B value will keep on change as we have already explained it earlier. Raghukant in 2010 for entire Gujarat once again it is for entire Gujarat the value as proposed between a range 0.7 to 0.9 with an error factor of 0.07 when they considered the earthquake between 1250 to 2008 and Kolathair et al in 2011 and Kutch region Ashara et al when they proposed for entire Gujarat once again two ranges of values one for the clustered catalogue I have already mentioned what is clustered clustering and another is declustered catalogue without doing the clustering of the earthquake data points considered. They are ranges they mentioned for B value 0.420.6 or 0.420.8 and they mentioned in their papers that they considered between 250 before Christ to 2010 earthquake data whereas Jaiswal and Sinha in 2007 for entire peninsular India remember this is not only for Gujarat region this is for entire peninsular. So, obviously Madhya Pradesh Maharashtra all these comes under this peninsular India. So, their value is again very high 0.92 and when they considered the earthquake between 1842 to 2002 Bhatia et al in 1999 for entire Gujarat region proposed the B value of 0.55 which is again close to our proposed value of B as you can see over here and recently Thakir et al 2012 proposed for entire Gujarat again B value which is very much on the higher side 0.89 and they considered the data set between 1880 to 2008. So, all these details one can find it out in this journal paper of natural hazards and earth system sciences. Now, let us do once this earthquake clustering data clustering and recurrence period everything we obtain next step is to carry out the hazard analysis. So, to do the seismic hazard analysis as we know first we will do the deterministic seismic hazard analysis and then we will take care of probabilistic seismic hazard analysis. So, for DSHA let us start with few salient points to carry out the deterministic seismic hazard analysis for entire Gujarat. So, already we mentioned entire Gujarat has been subdivided into three regions like Kutch, Saurashtra and Mainland Gujarat earthquake catalogue is also divided as per these three regions. So, that we can get different regions different DSHA values and only fault sources are used as seismic sources that is no other plate boundaries have been considered only the fault information has been considered for calculating this DSHA. Poisson distribution for earthquake occurrence is considered and all the faults are assumed as normal faults. This is an assumption in the present study that is when it is not known one can grossly assume like this, but if the fault characteristics for all the faults it is known accordingly the fault whether it is a normal fault, reverse faults, strike slip fault all these things should be considered. So, in the present study it has been considered and all as normal faults and their depth are ranging between 10 to 15 kilometer from the ground surface which essentially means these are shallow earthquake sources. Now, what are the requirements for carrying out this DSHA? First one is seismicity model we have to first select which seismicity model we are going to use. So, it describes the geographical distribution of potential active source zones like seismotechonic sources and distribution of magnitude in each of the sources. So, that takes care of the fault map and seismicity parameters like maximum earthquake magnitude by using proper seismicity model whereas which attenuation model has to be used as I have already mentioned there can be several attenuation relationship. So, attenuation relation model which describes effect of an earthquake originating from a specific seismotechonic source at any given site as function of the magnitude and source to site distance. So, it has to be function of both these two not only function of magnitude or only function of distance. So, that automatically means we have to take care of ground motion prediction equations as I have already mentioned GMP is in short we call these has to be identified. So, for DSHA if we carry out the DSHA it describes the potential for dangerous earthquake related natural phenomenon that is the maximum credible earthquake or maximum considered earthquake maximum credible earthquake we call at MCE that is the earthquake which we consider for our DSHA or deterministic seismic hazard analysis already I have mentioned this in the beginning of DSHA. So, the earthquake hazard for the site is a peak ground acceleration of let us say 0.57 G which is resulting from an earthquake magnitude of say 5.7 on a particular fault which has been obtained say Narmadasan fault at a distance of 11.42 kilometer from the site. So, in other words as we mentioned the final result sometimes the deterministic scenario we call it an magnitude and distance pair in this form that is 5.7 and 11.42 that shows that this is the maximum magnitude is going to occur at a site which is located 11.42 kilometer from the Narmadasan fault. This is just for one particular site remember. So, this type this way we can mention the DSHA result for any other site in the entire Gujarat region. Now, let us see how we apply this for all the selected 25 urban areas or urban cities in distributed in this three major seismic zones of Gujarat. Next is to study the fault map of the entire region because unless we have the complete picture of the fault map we cannot start our seismic hazard calculation. So, this slide shows us how the faults have been mapped in the entire Gujarat region. You can see there are total about more than 40 faults you can see the numbers over here fault numbers this F 18, F 48, F 49, F 23, F 5 these indicates the fault numbers this nth fault is F n. So, among all these faults only total 40 major faults are considered in the analysis and length derived from referred literature and maps that is from the available literature these length of each fault has been obtained or from the seismologist or geologist you need to collect this fault data when you are starting your seismic hazard analysis. Now, maximum earthquake magnitude which is calculated from relationships recommended by previous researchers considered that one-third length of the rupture surface needs to be taken care of when we are doing the calculation. That means suppose for F 24 this is the actual length one-third of its length will be actually taken when we are doing the hazard calculation. Now, let us see which GMPs we need to select to do the seismic hazard analysis. So, these are the various GMPs there are seven ground motion prediction equations are mentioned over here Abrahamson and Silva 1997, Bore et al 1997, Campbell 1997, Sadiq 1997, Toro et al 1997, Frankel et al 1996 and Raghukant and Aayanga 2007. So, among these seven ground motion prediction equations or attenuation relationships which we are now planning to use for our seismic hazard analysis only the last one is for peninsular India remaining all other from worldwide data not from Indian data like from the Abrahamson and Silva's data it is worldwide shallow crustal earthquake whereas for Bore et al's attenuation relationship is valid for shallow crustal earthquake of western North America region. For Campbell it is worldwide shallow earthquake data and this is valid it is also mentioned for MW greater than 5 and sites with distance to seismogenic rupture within the 60 kilometer in the active tectonic region. Whereas Sadiq data is valid for shallow crustal earthquake of California region where moment magnitude between 4 to 8 are considered and distance within 100 kilometer. Because we have already seen when we discussed in detail various attenuation relationship about their validity or limit. So, these are the limits Toro et al mentioned their attenuation relationship or GMPs are for crustal earthquake of intraplet region in eastern and central North America and for spectral period less than 0.2 second values limited to 1.5 g and periods less than 1 seconds are limited to 3 g whereas Frankel et al data is valid for intraplet region of central and eastern North America. Whereas Raghukant and Einger's attenuation relationship of 2007 or GMPs of 2007 is valid for peninsular India which is logically should be more correct to use for doing the seismic hazard analysis for Gujarat region which is also in the peninsular India region. But the validation or the limit for that GMP is for sites with shear wave velocity of v s greater than equals to 3.6 kilometer per second. So, that is the crustal velocity. So, let us now look at this various GMPs what we have already mentioned this 7 GMPs they are now represented in the form of spectral acceleration in y axis in terms of g. So, this is 0.1 g like that and x axis is distance from the hypo center in kilometer unit. So, these are various attenuation relationship 7 attenuation relationship as proposed by these 7 attenuation equations or ground motion prediction equations. Now, these results we will be going to use for our deterministic seismic hazard analysis. So, we will continue further in the next lecture on this DSHA for Gujarat region.