 Let us start our today's lecture for this NPTEL video course on geotechnical earthquake engineering as we were going through in the previous lecture also. In this lecture as well we will cover module number 7 which is seismic hazard analysis. So, before we start let us do a quick recap what we have learnt in our previous lecture. If we see this slide that is how to combine the various uncertainties which are involved in the estimation of probabilistic seismic hazard analysis or PSHA. So, from total probability theorem we can easily say that probability of occurrence of any event P of A can be considered as P of A intersection another event B 1 in that domain. So, you can see over here. So, this portion is A and this part is B 1, this part B 2, this is B 3, this is B 4 and this is B 5. So, occurrence of probability of A is nothing but probability of occurrence of A intersection B 1 plus probability of occurrence of A intersection B 2 and so on up to B n which we can rewrite again using the probability theorem that probability of occurrence of A equals to probability of occurrence of A for a given B 1 multiplied with probability of occurrence of that event B 1. Similarly, for probability of occurrence of A for a given B 2 multiplied with probability of occurrence of B 2 and so on. So, using this concept applying this total probability theorem what we can say for our PSHA or probabilistic seismic hazard analysis probability of occurrence of any event what we want to find out as a hazard parameter greater than a certain number or greater than a certain event will be equals to probability of occurrence of that for a given parameter or vector x multiplied with probability of occurrence of that vector where x is a vector of parameters. Now, in our PSHA analysis or probabilistic seismic hazard analysis we assume that magnitude m and the distance r these two are the most important parameters and they are independent to each other. In that case what we can write the our probability theorem will simplify to this form that is double integral of probability of occurrence of that event y greater than y star because that is what we want to find out the above a threshold number or above a given design value we want to find out the probability for a given value of m and for a given value of r. Hence, we need to multiply them with respect to the probability of that m and r. So, if suppose the site of interest is subjected to shaking is more than one site that is for a particular site we have influence from other sites as well in that case we have to take care of all number of sites involved say total n s number of sites are involved in that case we have to do the summation of all the probabilities what we are getting or mean accidents of occurrence that we have to sum up for all sites and get the total value. Then we have seen when we combine this all uncertainties involved in this PSHA what we can write that accidents of mean accidents of annual some event lambda y star that can be represented by considering all the three independent variables that is the sites involved magnitude involved and the distance involved we can get summation of each of them and write the probability theorem in this form. So, this one as I have mentioned it takes care of all the sites involved then this one takes care of all the magnitudes involved corresponding to their weighted probability of occurrence and this one considers all possible distances which are considered contribution of each is weighted by its probability of occurrence. So, we have seen how to take care of weight weighing factor for unequal or uneven distribution or unequal distribution of the distances from site to source then this one takes care of all possible effects are considered like each weighted by its conditional probability of occurrence. So, we need to compute the conditional probability for each element on a grid form. So, what we can say suppose any attenuation relationship or any particular g m p is if we select like this suppose the magnitude we are selecting or fixing it at a particular magnitude of say m equals to m 2. Similarly for m equals to m 1 m equals to m 3 we will have different relationships and this is the variation with respect to the distance r. So, at different values of r say r 1 r 2 3 r 4 r n we will have the probability distribution along that magnitude scale like this for a particular event of occurrence greater than some mean value or some design value or some chosen value about which we are interested to know. Suppose we are interested to know that let us say this is our peak ground acceleration or spectral acceleration or peak horizontal velocity because these are the standard parameters what we want to find out. A certain given value is provided to us so that we can make a design or find out the probability of occurrence of more than that. So, in that case above this line in this shaded area of probability distribution whatever colored shedding part is given that gives us nothing but the conditional probability for that given of m equals to m 2 because this curve relates to m equals to m 2 and for that given value of r like for this one it is r equals to r 1 for this one it is r equals to r 2 for this one it is r equals to r 3 and so on. So, in that fashion what we have seen we can build the hazard by considering this conditional probability combining the uncertainties from both independent parameters of magnitude and the distance r. So, as we have already seen in the previous figure for m 2 for a given magnitude of m equals to m 2 we already obtained this probability of occurrence of y greater than that given design value of y star for r equals to r 1 r equals to r 2 r equals to r 3 and so on. So, like that we will get all these values known similarly, we should fill up this one for other magnitudes as well then this complete cell will give us the final value of the seismic hazard curve after combining these things. So, we have to repeat the entire process and develop a pair of values of this given y star with respect to log of lambda y or in the other side of the scale can be log of t r that is rate of occurrence. Now, we have seen how to make use of this hazard curve later on for further our design like if it is known that probability of exceeding a max equals to 0.3 g it is given to us in a period of 50 year we need to compute from this hazard curve then for occurrence of it at least once this is the Poisson's distribution already we have discussed in detail. So, putting the lambda value obtained from this probabilistic seismic hazard curve how we can obtain this because a max is given to us. So, whatever p s h a curve we got corresponding to a max equals to 0.3 g we need to find out what is the lambda value and that lambda value we need to use and put it in this equation and for how many years we need to find it out that time we have to put it here. So, it gives us the probability of occurrence. Similarly, suppose if the time scale is changed to 500 years we can put 500 over here and get the value of probability like this. Another way of use of this seismic hazard curve which is a more direct use suppose what is the peak acceleration we want to know for a 10 percent of probability of being exceeded in 50 years time. So, 10 percent of probability of exceeding and even 50 years in time at least once we have already derived earlier that gives us the recurrence time interval t r as 475 years corresponding lambda value is 0.0021. So, in this seismic hazard curve you go to this lambda value of 0.0021 which is nothing but t r value of 475 then from that curve you obtain your a max value and that a max value will give you the design value for which you need to design if you want to design it for that 10 percent of probability of occurrence of exceeding in 50 years time. Suppose if it is a 2 percent of probability of being exceeded in 50 years time in that case this will change the t r value lambda also will change correspondingly we have to use that value and we will get another a max value. So, like that actually we will get a max value over here because t r will increase and lambda value will decrease. So, obviously we have to design it for a higher value of lambda because we are taking care of 2 percent of probability that is for most important structures as I have already mentioned. So, that is the use of seismic hazard curve to find out this a max value corresponding to a particular value of lambda or a particular value of t r. Now, we had also discussed in our previous lecture contributions coming from various sources that is if suppose this is the seismic total seismic hazard curve what we have obtained. Now, we want to know which sources more influential to know that what we can do we can break it down that influence of lambda with respect to a max corresponding to different sources that is instead of combining them that plus of i equals to 1 to n s we can find out for individual source also what are the curves coming and if they are crisscrossing we know that that automatically says which is having more influence right. Like for example, if we want to know the peak acceleration the lambda m x value and this is versus m x we have for different sources like intra plate events, crustal events, inter plate events like that for 2 percent in 50 years we can have a some hazard curve like this. So, we can see which one will have more influence at a higher acceleration value or at higher m x value. Now, we had also discussed in our previous lecture what is called uniform hazard spectrum or UHS. UHS is nothing but the spectral acceleration versus the time period considering the simple harmonic motion of an equivalent single degree of freedom system right which we have already discussed earlier. Now, find we need to find out the spectral acceleration values for different periods at a constant value of lambda. So, how to generate each one of these points because you will get in your seismic hazard curve like this in your seismic hazard curve like this suppose if you have the log of lambda value corresponding to m x or p g a versus this is p g a you will get this kind of result of m x corresponding to a particular value of lambda. What is that particular value of lambda that depends on what is the percent probability of occurrence or exceeding a particular year you are considering right. So, based on that you obtain a value of this that to an equivalent system of s a will give you a single point like this. So, if we say this dot that is for t equals to 0 that will correspond to nothing but at t equals to 0 means it will be the corresponding to m x value or p g a value. So, for corresponding to t equals to other time period say 0.2 seconds 2 seconds we can also have these different points calculated based on our different hazard curves which we can generate like a value corresponding to t value of 0.2 seconds a value corresponding to a t value of 2 seconds. So, like that we will get this points obviously you have to select a particular value of damping ratio to generate this type of curve because you are considering the equivalence of the single degree of freedom system. So, there a damping ratio makes a important role and typically for all calculations of this u h s estimation we considered 5 percent damping for the system and considering that 5 percent damping we generate this s a by t curve. So, that s a by t curve will finally give us the value or design curve or uniform hazard spectrum which is very useful for design for a particular condition of probability of accidents. So, this curve say let us say we got it for 10 percent of probability of accidents in 50 years time. Similarly, we can get another s a by t curve for 2 percent of probability of accidents in 50 years time like that it says for a constant value of lambda you can generate this s a by t curve that is how in the our any design code also the similar curve you will find in the earthquake codes or seismic codes we will discuss that as well. We had also talked about in the previous lecture what is called desegregation or deaggregation like we suppose if we want to know that a max value of the hazard parameter what we have obtained from that hazard curve it corresponds to which particular magnitude and which particular distance. So, that we know the influence is coming maximum from which value. So, if we go back to our grid points where we have initially found out individual probability and then sum it up if we look at there if we break it down the hazard curve we can see where the maximum value is occurring for example, in this given grid we can see the maximum value occurs at m equals to 7 and r equals to 75. So, that is the most influential distance and magnitude distance and magnitude corresponds to that a max value. Now, we had also discussed the logic tree methods in this logic tree why this logic tree is required to consider because there are uncertainties involved in the model which we have used for estimation of the probabilistic seismic hazard curve like there is a question always arises from the use of attenuation relationship that is it is always questionable whether the attenuation relationship which we are using for deriving at PSHA is the correct attenuation relationship or not or there are many numbers of attenuation relationship for a particular region. Let us say for our India, northeast India even the Himalayan region there are several attenuation relationships which are available which we have discussed in this course. So, now which model is correct one we do not know. So, to give different weightage or different uncertainties involved in using different attenuation relationship this logic tree concept has been proposed and magnitude distribution also another thing because we do not know which model gives us the correct magnitude prediction through either the semi empirical relationship or the seismic moment criteria or crustal plate movement various ways are there to obtain the magnitude we have seen already. So, experts may disagree on a particular model parameters which is quite possible like fault segmentation maximum magnitude etcetera. Hence, this logic tree comes into picture that is suppose in our analysis we are using different two attenuation model. This is one attenuation model BGF and another attenuation model of A and S. When we are not pretty sure about which one is more correct let us give equal weightage to each of them. So, if we have two then we can give 50 percent 50 percent weightage to each of them. Now, within each attenuation model again we can have the formula which we have been using to obtain the magnitude distribution we have already seen there are two ways commonly used like Gutenberg Richter magnitude recurrence law and another is characteristic recurrence law. So, using them suppose if we know or if we are confident from our given data sets which we are using for the estimation of earthquake recurrence model say Gutenberg Richter is a more better model. Suppose if we find it out then characteristics model then we can give a little higher weightage to Gutenberg Richter model. Let us say 70 percent we give the weightage and remaining 30 percent weightage let us give to the characteristic recurrence model. So, what we can see over here in this slide that for each of the model we have given here 70 percent let us look at the slide yes 70 percent over here and 30 percent over here. Similarly, for this model 70 percent for Gutenberg Richter and for 30 percent for characteristic recurrence law. Now, again each of that magnitude distribution or recurrence law we can obtain the different M max value using different models once again different equations once again like for estimation of M max we have several formulae we have seen like we got say 7 7.2 7.5 etcetera different values. Now, which one we want to consider as more realistic accordingly we can give proper weightage to them. Let us say we have given 60 percent weightage to this 7.2 and other 20 percent and 20 percent to this 7 and 7.5 accordingly the others also. See, if we take a particular path like this for each of this branches we will get what is the multiplying factor or coefficients we need to consider. So, that actually gives us from this logic tree. So, this is why the name logic tree because this is in the tree shape and we are applying our logic that which model is more appropriate or equally appropriate. So, like that we can see from this to find out a particular value of y we can obtain it through the weighted average of the values given in this terminal branches of the logic tree that is if we go through this root 0.5 into 0.7 into 0.2 we will get this value of weighted average of 0.07 like that this is 0.21 like that this is 0.07 Similarly, for others also we will get the weighing factor. This weighing factor we need to now consider in our estimation of the value of y. Now, let us discuss in today's lecture what are the implications of this probabilistic seismic hazard curve using all this analysis or all this concept in the codal provision that is finally, we have to propose it in the design code. So, that for a particular country for a particular locality for a particular region it can be further used by engineers or designers to implement at particular site for design. So, how we can apply this concept of probabilistic seismic hazard analysis through that derivation of that essay by T curve. So, let us see the code implications you can see over here UBC unified building code of suggest this is the 10 percent of probability of accidents in 50 years time that gives us say suppose November 1996 these are the values Nihar B and C boundary of the site there are different site classification I will come to that class site classification later on when we will talk about the ground response analysis in this course in due course of time. So, these chart shows the peak acceleration in percent g values these are percent g values with 10 percent of probability of occurrence in 50 years time which is nothing but of return period of 475 years. So, this map automatically shows us for a particular area for a particular region this is for entire US the Nihar soil site of B and C considering that UBC proposed this is the map which can be used for percent g value of the peak acceleration for design. If somebody wants to design it for a 10 percent of probability of accidents in 50 years clear that is how it is implemented in the design code. Similarly, if we take another example for AASHTO code for AASHTO with 2 percent of probability of accidents in 50 years this is the map like peak acceleration in percent g same considering Nihar of B and C boundary of soil site with 2 percent probability of accidents in 50 years this is the map for US. Now AASHTO code with that 2 percent of probability of accidents in 50 years time if we have this value say at 100 years let us take say this value is corresponding to let us say it is corresponding to 100 years 100 years of T R means lambda value will be obviously 1 by 100 so 0.01. So, we have this already hazard curve available with us for a particular region for a particular site what we have done. So, we can see from this example that 400 years interval of recurrence if we want to design our structure which event or which source is most important. You can see over here in this case which source interpolate events are not particularly important like these are interpolate right, but this one is important whereas if we go for 2500 years that is this point 2500 years of T R will corresponding to lambda value of something over 1 by 2500 over here. So, in this case you can see the importance of this event increases. Now let us come back to a case study which is applied on the Gujarat state of India. This work is done by Dr. Jayakumar Shukla. He completed PhD in 2013 at IIT Bombay. So, from his PhD thesis work now we will see how this concept of deterministic seismic hazard analysis as well as the probabilistic seismic hazard analysis we can arrive at for a particular region also how the earthquake recurrence law we can apply and can somehow mathematically estimate the chances or probability of occurrence of an earthquake in future at a particular site or a particular region that we will see through this elaborate case study for the Gujarat region of India why we have chosen Gujarat region because we all know Gujarat has experienced severe earthquake in 2001 Bhuja earthquake. So, because of that reason several researchers around the world they are doing the research on this area of Gujarat. There are other reasons as well which we will come to the explanation very soon. So, let us see now over here. See if we look at this slide where the Gujarat state is located in that country India in our country India this is the map of India Gujarat state is the central western most state here which is surrounded by Arabian sea over here and the neighboring country Pakistan over here. So, this is the Gujarat state now if we look at the colors you will see for Gujarat state of India there are four different color shadings are provided over here this dark red color this is orange color this is yellow color and this is light sky blue color. So, these four colors indicates the different four seismic zones as per the Indian seismic design code IS 1893 part one of 2002 version. Now, what are the objectives of this study of this present case study for Gujarat to review the seismicity of entire Gujarat for present as well as from historic times to develop the earthquake catalog that is the very first step we need to do that is if we want to do any seismic analysis for any particular region first step is to collect the earthquake data from historical time to the recent times all the earthquake data or earthquake catalog needs to be completed. So, that is the first step to do next is to divide the earthquake catalog for three sub regions of Gujarat why the three sub regions we will explain it very soon in subsequent slide. So, it has been divided into three subdivisions Kach, Saurashtra and Mainland Gujarat to establish the region specific seismicity parameters that is for a particular region what is the seismicity parameter like Gutenberg Richter relationship for the three sub regions of Gujarat have been arrived at. Now, to study different probability distribution models for earthquake recurrence period estimation of earthquakes in Gujarat that is various probability distribution models are available to obtain the earthquake recurrence we will discuss that also to carry out the seismic hazard analysis for selected 25 urban areas or urban cities of Gujarat state and to develop the seismic hazard map both deterministic seismic hazard map as well as probabilistic seismic hazard map which are consistent with the seismotectonic setting of the Gujarat. Then to focus on deterministic and probabilistic seismic hazard analysis and obviously for probabilistic seismic hazard analysis we need to use the logic tree approach as well that is which attenuation model we are using which magnitude model we are using etcetera. Finally, once we obtain this seismic hazard curves we need to develop the uniform hazard spectra because that is the final design curve which needs to be used for further design of any structure at a particular region. So, that uniform hazard spectra either we can get it through this deterministic seismic hazard curve or we can get it through the probabilistic seismic hazard curve right. So, for each of these 25 selected urban cities the based on the fault map prepared the UHS has been developed. To test the sensitivity of the seismic hazard of Gujarat for seismicity parameter or B value what we have seen in the Gutenberg Richter relation that A and B are coefficient. So, we have to find out the sensitivity of B parameter why only B parameter because that is the slope of the line A parameter is anyway that is the intercept at the minimum magnitude. So, we are probably not that much interested about that intercept or coefficient or A parameter because it is at the minimum value of magnitude. We are more interested about the higher magnitude what are the chances or recurrence of or chances of occurrence of a particular event that is why B parameter or that slope inclination we are more interested to know about. To demonstrate implementation and use of this PSHA for generation of site specific spectra for selected 4 ports we will see that later and estimation of ground amplification and site effects for the 4 port sites based on the geotechnical site characterization. These 2 points we will cover further again after we discuss our next module which will be on this ground response analysis. So, remaining other case studies or remaining other objectives we will go through from this case study of the PHD work of Dr. Jayakumar Shukla under my supervision at IIT Bombay. So, these are the urban areas or urban cities selected total 25 numbers in the entire Gujarat region. As I have already mentioned we had divided the entire Gujarat into 3 major zones or 3 major regions based on their seismic zonation map. So, Kutch region which is most vulnerable as per our Indian seismic code based on the zone parameter, then Saurashtra which is the intermediate one and Mainland Gujarat which is the lower on the lower side. So, these are the various cities within Kutch region Anjar, Bhuj, Dhola, Veera, Gandhidham, Mandavi in the Saurashtra region, Amreli, Bhavnagar, Dholera, Dwarka, Jamnagar, Jhunagar, Morvi, Porbandar, Rajkot, Surendra Nagar, Viraval and within Mainland Gujarat, Amdabad, Varuch, Gandhinagar, Meshana, Palanpur, Patan, Surat, Vadodara, Valsad. So, these 25 cities we have selected and later on as I have already mentioned that after doing the ground response analysis we will discuss also about 4 port sites of Gujarat important 4 most important ports, Kandla port, Mundra port, Hazira port and the Hedge port. So, now these are the locations of those selected 25 cities of Gujarat region in the subdivided into 3 regions. So, Kandla as per the seismic zone map of Gujarat this is scale is showing the northing or degree north the latitude and this scale is showing the degree east degree east is this is longitude. So, within this latitude and longitude this Gujarat state lies we can see over here as per our Indian seismic code IS 1893 part 1 2002 zone 5 is most vulnerable seismically that is chances of occurrence of higher magnitude of seismicity is more in zone 5 and least or lowest in zone 2 that is how our Indian seismic code has subdivided into 4 zones which I have discussed already in one of the initial lecture of this course. So, zone 5 is most vulnerable zone 4 little lesser than that zone 3 again further little lesser than that and finally zone 2 is the least vulnerable as per seismicity is concerned. So, you can see why we have chosen this state of Gujarat not only because Bujarthquake of 2001 was most one of the most damaging earthquake in India which had occurred, but also Gujarat is the only state in India which is having all the 4 seismic zones as per our Indian seismic design code IS 1893 that is the reason if we study the seismic hazard map seismicity parameters seismicity events for Gujarat state we will do that exercise completely for all the 4 zones of all the 4 seismic zones of India. So, this is zone 5 as we have already seen this is the Kutch region next this orange part is zone 4 which is in Saurashtra region and this yellow part is in Mainland Gujarat which is in zone 3 only in zone 2 this sky blue color we have not taken any city because anyway that is the least vulnerable zone as far as seismicity is concerned. So, that is why we are more interested or confined our study for the higher seismic zone starting from zone 3 to 5 zone 3, 4 and 5. Now, what are the various components of a particular seismic hazard study that is suppose if somebody is interested to do a complete seismic hazard study what are the various components needs to be addressed let us look at this slide for example, for our case seismic hazard study for the entire Gujarat region is our final goal or final objective to do. So, what are the various things we need to do we need to prepare the earthquake catalog for Gujarat we need to consider the regional seismicity parameters for Gujarat then we need to do the sensitivity analysis of parameters based on these we can follow the deterministic seismic hazard analysis and we can also follow probabilistic seismic hazard analysis and once all these things are done we can recommend a site specific ground motions for typical site. For example, as I have already mentioned in this thesis of Dr. Jayakumar Shukla he did the work for ports 4 ports. So, that will come anyway later in our next module for this course in this module we are going to discuss elaborately how these 5 branches are addressed to obtain the seismic hazard estimation for the Gujarat region. Now, let us see once again as I have already mentioned this is the map of Gujarat various cities are marked over here various seismic zone as per the seismic code IS 1893 part 1 of 2002 version. Now, if we look at the seismotectonic settings of a particular region say let us concentrate on the kutch region which is in the zone 5 or most vulnerable region. So, this picture shows the seismotectonic setting you can see over here seismotectonic setting for that region which further we can expand or exaggerate we can see these are the epicenters of various earthquakes which are recorded only during 2007 to 2011 you can see so many numbers. Now, what are their magnitudes that we are going to address very soon in the catalogue when we are going to prepare the catalogue. So, this data are available in ISR Indian Seismological Research Institute of report 2010, 2011 this data is available. So, from that ISR report we can obtain the seismotectonic setting of a particular region we can get the faults available in that particular region we can get the number of earthquake events and their magnitudes occurred at a particular region. So, all these data will be available with us when we are starting to do the earthquake catalogue. So, if we look at the seismicity across Gujarat in this table we have shown only the data of year wise data 2008, 2009 and 2010, 11 and 11 years. Then also up to March of 2011 because Dr. Jayakumar Shukla collected all the data till 2011 March for estimating the earthquake catalogue. Obviously, before 2008 also there are several historical earthquake data just I am showing a typical example that is how year wise we can have this detailed data for each region that is this three region Kutch, Saurashtra and Mainland Gujarat. We can subdivide the table in this fashion that is number of earthquake occurs or recorded for different magnitude say magnitude greater than equals to 4, magnitude between 3 to 3.9, magnitude between 2 to 2.9, magnitude less than 2. You can see these values are very very low as already we have mentioned we are mostly not concerned about these values for our design we are mostly concerned about more than 4, 4.5 or 5 like that and also these magnitudes can only be detected by sensitive instruments only like they will not show any kind of damage like magnitude less than 2 or between 2 to 2, 3 etcetera. So, all these recorded data are collected from this ISR report and you can see that over here in Kutch region greater than magnitude 4 earthquake in 2008 that year itself in one year there were 5 such incidents. In Saurashtra region there were 2 such incidents whereas in Mainland Gujarat there were no in such incident whereas for other magnitude also you will get several numbers and you can see there are several hundreds and even several thousands of such events occurs in a particular year. But we are not so much of interested about these numbers or these values because they do not make any harm to our structures to mankind etcetera of this low magnitude. But obviously greater than 4 or etcetera we should be concerned about so that is why we have to select a lower bound when we are planning to go for next level of recurrence law we will do that very soon. Now, if we plot this ERY's pattern that is percentage of total earthquake occurred in Gujarat for ERY is this dark blue color is 2008, green color is 2009 and this red color is 2010 up to March of 2011. So, you can see for Mainland Gujarat it is extremely low which is quite expected that is why we can see from the seismic zonation map also this is in the zone 3 whereas for Saurashtra region which is in zone 4 it is intermediate whereas for Kutch region which is in zone 5 number of earthquake occurred in Gujarat is very high that automatically says that seismicity within the Gujarat state is not same whereas our seismic code propose only a single value for entire Gujarat whether that is correct or not that we need to go through. Even some of the researchers earlier researchers they also propose the single parameter for Gujarat if we talk about the recurrence law of Gutenberg Richter which is not correct as we can automatically see from this distribution of occurrence of numbers of earthquake right in the Gujarat region. So, that single seismicity parameter for entire Gujarat state it may not represent the true seismicity within the Gujarat which is quite obvious. Now, seismicity in the Saurashtra region we can see that over the years this is again from the modified ISR report of 2009 that seismicity also migrates what is migration of seismicity that is from one region slowly over the years it moves to another region as you can see from this Jamnagar area to Junaagar area then to Surendranagar area the clustering of occurrence of more number of earthquake is shifting in this fashion from 2006 to 2006 7 to 2008 then 2009. So, that is called a migration of seismicity event in and around a particular region this is within the Saurashtra region. So, that also needs to be considered when we are planning to do a region specific seismicity analysis. Now, what are the methodologies used the previous discussion emphasize that seismicity parameters should be region specific because we have seen for Gujarat considering a single seismicity parameter is not justified also it is not justified to consider a single seismic event at a particular region because it migrates also over the years and seismically active regions should be considered for future seismicity. In the present study the region specific seismicity parameters are derived based on the prepared earthquake catalog and further used in the seismic hazard calculations the regions which are presently active or may show future seismicity are handled using prepared possible fault map of the region. So, for the entire region what is the next we need to prepare the fault map what are the active faults or known faults in that region are available. Now, let us see earthquake catalog for Gujarat as I was mentioning from historical data to present data we need to first collect all the earthquake look at here we have reported in this slide only those earthquake moment magnitude which are 4 and above that is the lower bound we have already selected as 4 it depends on the designer if somebody is interested they can select it as 4.5 also if somebody is interested they can select it as 3.5 also, but for the from the experience of what is most vulnerable for the structures or design consideration we thought we will be selecting and based on the numbers of occurrence of earthquake the lower bound or the threshold value of earthquake moment magnitude as 4 for the entire Gujarat and you can see we have collected the data from year scale of 1820 this first data is from 1820 to 2000 of 12 that is the span through which from various sources various authentic sources like USGS ISR IMD all this various sources like you people also have collected this information in the beginning in one of the assignment that how to collect the earthquake data for a particular region suppose for India also we have collected for earthquake above 5.5 to 7 we have collected this data from various sources authentic sources like USGS IMD ISR so similarly for Gujarat also we have collected this kind of data and this is the scatter of those occurrence of earthquake over the years you can see over here these values are mentioned in this case you can see the 2001 Buj earthquake comes over here you can see this value now whether the collected earthquake catalog or earthquake data whether it is complete or not how we will know now next step is to ask yourself whether the data which you have collected for a particular region on the earthquake whether it is complete or not so that catalog completeness needs to be checked that is the next step to check the catalog completeness how we can do the catalog completeness checking there are various methods available like in the present study CUVI method as proposed by Tinti and Mullergea in 1985 is used and also another method proposed by step in 1973 that has also been used so how we can find it out the catalog completeness in short I will explain over here the earthquake magnitude versus time this data already we have collected this lower graph which is shown over here this already we have seen in the previous slide this one this only we are redrawing over here now if we want to change this y axis scale to cumulative earthquake occurrence that is we are keep on adding the numbers of earthquake over the time scale of this one then the curve will be keep on increasing because we are keep on adding these values this is a cumulative scale now whenever in your that cumulative scale it should be clustering should be uniform uniform means there should not be any gap you can see over here as expected from 1960 onwards till present date 2012 whatever data has been collected there is no such gap that means a good collection of the data set whereas in historical times there are few gaps may be there are not so much magnitude of more than 4 are available that is one possibility another possibility is may be lack of information from the historic data both can be true now if you look at this pattern of this cumulative distribution of earthquake data points you will find that from historical to present data if you want to plot a best fit linear plot of this you will get two different slope of the line can you see this was giving a particular trend whereas in recent years the trend has changed to something else this blue color dotted line is showing one trend whereas this green color dotted line is showing another trend and where that change of trend is occurring that you can easily find it out that point shows us that from this point onwards there is a shift or there is a change of number of occurrence of earthquake in this present case it is 1962 you can see over here where the change of this curve is occurring so like that we have to check the catalogue completeness details about this catalogue completeness is available in this journal publication by Shukla and Choudhury 2012 in the journal of natural hazards and earth system sciences it is published by European geophysical union EGU of Germany the volume is 12 and page numbers is 2019 to 2037 so this is a very good journal with high impact factor you can go through this paper to know about the catalogue completeness so with this we have come to the end of today's lecture we will continue further in our next lecture.