 Let us start our today's lecture of this NPTEL video course on Geotechnical Earthquake Engineering. Let us look at the slide here. In this video course on Geotechnical Earthquake Engineering, we were going through module number 4, which is on strong ground motion. And we had started in the previous lecture about the attenuation relationship. So, a very quick recap what we have learnt in our previous lecture. We have discussed about the spatial variability of ground motions. That is how this ground motion vary from the hypocenter point of earthquake or the epicentral location to a particular distance or a site where we are planning any new construction or any new structure to be constructed. So, the ground motion parameters they vary in terms of magnitude and in terms of distance for a site from the epicentral location. So, that variation that variability of ground motion we need to study because that is most important for our design of any structure at a particular site. How they do vary with respect to magnitude and with respect to the size to source distance. So, in that connection we have mentioned what is known as attenuation relationship that when this predictive parameters, predictive relationship parameters like either peak acceleration, peak velocity, intensity etcetera, how they decrease with increase in the distance. Those are nothing but the attenuation relationship. We have seen what is the peak acceleration attenuation relationship. The pioneering work proposed by Campbell in 1981 for the North California region for North America in the California region with PHA value can be obtained using this attenuation relationship for the magnitude range between 5 to 7.7 and the site to fault source should be within the 50 kilometer distance where this m has to be used as local magnitude scale. If it is within 6, if it is more than 6 then surface magnitude scale has to be used and this r is nothing but the closest distance from the site to the fault structure in the unit of kilometer. Later on Bore et al in 1993 they proposed an advanced or modified attenuation relationship for the same peak horizontal acceleration for the western North America region that is using the earthquake historical records of this region they extended the distance up to 100 kilometer from the epicenter to the source point and magnitude range they have used the same magnitude range and this was their proposed attenuation relationship where various parameters like r, gb, gc coefficients based on the site class. Site class they have classified based on the average shear wave velocity in the top 30 meter from the ground surface based on different values or ranges of values like this given in this table. We have seen what such site class means it is a rocky site this is a hard soil or stiff soil is a soft soil site and various coefficients b 1, b 2, b 3 up to h and their corresponding standard deviation values as proposed by Bore et al. Next we had seen in the previous lecture what is the attenuation relationship for PHA proposed by Toro et al for the mid-continent of North America. So, if somebody wants to use the what is the design acceleration etcetera from this attenuation relationship in California region they should use the Bore et al equation and if somebody is planning to do a design in suppose the Texas region or Denver region which is in the central or mid-continent of North America they should go for the Toro et al expression. So, that is what we have to be very careful where this attenuation relationship has been developed for that is most important. So, this equation where different values here also they have used the moment magnitude like Bore et al and another attenuation relationship proposed only for the subduction zone by Young's et al in 1988 is given by this equation we had seen in the previous lecture. Then the velocity attenuation relationship like peak horizontal velocity P H V can be obtained in the unit of centimeter per second as proposed by Joiner and Bore in 1988 for earthquake magnitude between 5 to 7.7 and various parameters are given over here with their coefficients J 1, J 2, J 3 up to J 7 with the standard deviation value. Then we had seen the attenuation relationship in terms of acceleration horizontal acceleration in unit of centimeter per second square as proposed by Pat Gurdon et al in 1978 using the different types of earthquake shallow earthquake from California, Japan, Nicaragua and India of total 63 records and for subduction zone earthquake using the Japan and South American earthquake of 23 earthquake including total 32 records. So for shallow earthquake they have used media two different types of media rocky strata and steep soil strata whereas for subduction zone earthquake they only got the data from the steep soil region. So that is why they have given different coefficients A, B, E etc. in this equation as proposed in this table and chart. Then we had also discussed this equation of Apthikev and Kopinachev in 1980 as given for the attenuation relationship for the acceleration using the shear wave magnitude scale and they only propose the different five types of faulting. So they only classified for different types of faulting what are the different equations to be used. So these are the relationship proposed for five different categories of faulting like strike slip, strike slip with dip slip, dip slip fault etc. etc. All are detailed here. Total 70 records they had used and these are the values of log of a naught by a e and log of a h by a v a h is horizontal a v is vertical and this is the paper which appeared in 1980 in the seventh world conference proceedings of earthquake engineering. Then we had also discussed about the PML 1982 proposed based on the British earthquake technical report which is reproduced by Ambrace et al. in 1982 the attenuation relationship for acceleration once again in the unit of G using this expression. They used worldwide earthquake data from Italy, US, Greece, Pakistan, Yugoslavia, USSR in those days, Nicaragua, India and Atlantic Ocean earthquake. Now let us come to our today's lecture. So today also we will continue further in that attenuation relationship proposed by various researchers across the world and we will also emphasize the attenuation relationship which are valid for India and subcontinent. So for Indian region also we will see that at different locations like northern India in Himalayan region, in northeast India, in the peninsular India different attenuation relationships are proposed and we have to be very careful about using those equations because when we are planning to go for a design required attenuation relationship at a particular site needs to be used. Not that for Indian design we should use the attenuation relationship proposed by Bore et al which is valid for the north west America. We should not use that attenuation relationship for any design of Indian structures. So having said so, let us see what are the other attenuation relationship worldwide developed like Gaul in 1988 proposed the attenuation relationship using the data points of south west western Australia. You can see the paper Gaul 1988 attenuation of strong ground motion in space and time in southwest western Australia. It published again in that proceedings of the ninth world confidence of earthquake engineering in this volume and page number. So log of PGA that is big ground acceleration can be estimated like a 1 times log of r plus a 2 divided by a 3 times m l minus a 4 minus a 5 times log of r minus a 6 times r plus a 7 where this PGA will be in the unit of meter per second square. So we should always consider this unit. These units are very important. You can see at different attenuation relationship we have different units. So a 1 is 5, a 2 is 3, a 3 is 20, a 4 is 6, a 5 is 0.77, a 6 is 0.0045, a 7 is 1.2. As we know these values are obtained based on how many data points they have taken for the prediction or proposing this empirical relation. So now after this 88 onwards suppose if you take some more earthquake data points from that region your these coefficients are going to get changed. So considered earthquakes of magnitudes about 3 and most from the distance below about 20 kilometer that is the range they have used and adds 4 near sources. Near sources means this r value that is from the site to the fault or hypocentral distance within the 5 to 10 kilometers range records from the US, Indian and New Zealand earthquake with magnitude between 6.3 to 6.7 to supplement the high magnitude range. Because in the western Australia you hardly get any large magnitude of earthquake in the historical record. So that is why what they did they used the small earthquake values in and for high earthquake magnitude they have used other country data like New Zealand earthquake they experience higher magnitude of earthquake data, Indian earthquake and US data, 4 near source data within this range that is close to epicentral location. Those data they have combined with their shallow magnitude or low magnitude data and combinedly they have proposed this expression. So we cannot say that this is truly for the western Australia because they have punched here the other earthquake taken from the other regions. Now coming to the pure Indian earthquake acceleration attenuation relationship and velocity attenuation relationship the pioneering work can be mentioned as proposed by the R. P. Singh and his research group from IIT Kanpur in 1996. So in 1996 they proposed the attenuation relations for strong seismic ground motion in Himalayan region. So they considered only the Himalayan region of earthquake till 1996 and this paper was appeared in pure and applied geophysics journal in this volume and issue number and page numbers are given over here. In this equation you remember earlier all the equations were long natural here it is locked to the base 10. So this is the difference A, A is the peak horizontal acceleration in the unit of centimeter per second square this can be calculated using this expression. And another expression they have given for the velocity attenuation relationship. So for the velocity it is a phv peak horizontal velocity in the unit of centimeter per second this is the values coefficients and m and r. So what is r? R is nothing but the hypocentral distance in the unit of kilometer hypocentral distance means from your side to the hypocenter whatever is the distance in the kilometer unit you have to put in this equation. And what is the m? m is the magnitude scale but which scale they have proposed mb mb is that body wave magnitude scale they have proposed that is 5.7 to 7.2 between this range this equation is valid. So this range of earthquake magnitude can be used further to calculate the acceleration and velocity attenuation with respect to distance from a specific source to a particular site of your concern where you are planning to construct your structure. Another attenuation relationship for India specifically it was proposed it is also can be considered as a pioneering word because it is for the peninsular India. Peninsular India means the central Indian portion central and little southern portion of the India. So that generalized predictive attenuation relationship has been proposed for peninsular India by Aayangar and Rahukan from IISC Bangalore. Professor Aayangar and his research group his research student Rahukan who is now in IIT Madras faculty in 2004 in their paper they had proposed this attenuation relationship for peninsular India. You can see this is the equation they had proposed natural log they have used y equals to c 1 plus c 2 times m minus 6 plus c 3 times m minus 6 whole square minus ln of r minus c 4 times r plus ln times epsilon. So they have proposed if you see and look at the form of the equation in the similar form of that proposed by Bore et al 1993 right the form of the equation only the coefficients and values will change this c 1 c 2 c 3 depending on the collected historical earthquake in this peninsular region. So where this y m and r refers to y is nothing but peak ground acceleration in the unit of g you are getting m is the moment magnitude of earthquake and r is the hypocentral distance in kilometer unit. Now they have proposed the different coefficient this c 1 c 2 c 3 c 4 and this epsilon c for different region like for Koenner-Warner region they proposed c 1 equals to 1.7615 c 2 as 0.9325 c 3 as minus 0.0706 c 4 as 0.0086 and sigma that is standard deviation of that parameter of ln epsilon is 0.3292. Similarly for western central region like of India they proposed these are the coefficients and for the southern region they proposed this equation. So suppose somebody wants to use the attenuation relationship for further design of any structure in Bangalore region they should use the southern region coefficients if somebody close to the Koenner region wants to do a design they should use this coefficient somebody wants to do a design in the western central region of India they should use this coefficients for obtaining the acceleration attenuation relationship as proposed by Iyengar and Rogukan for Peninsular India region. Coming to some more attenuation relationship for India the following predictive attenuation relationship for peak vertical ground acceleration this is vertical ground acceleration you remember not the horizontal has been proposed for Himalayan region. So this is specific to the Himalayan close to Himalayan region of earthquake of India by Sharma this is professor M. L. Sharma from IIT Roorkee and his research group they developed they initially proposed for the horizontal peak ground acceleration also but which I am referring here in this slide that is for the peak vertical ground acceleration what is the equation they proposed this is the simplest equation they proposed for determining the attenuation relationship of vertical seismic acceleration. In this equation this A is peak ground acceleration vertical in the unit of G then M is moment magnitude of earthquake and this X capital X refers to the hypocentral distance in the unit kilometer. So once you know M value X value at your particular location of your site from your seismic zone map and other information like active fault close to that site you can automatically calculate what will be your attenuated value of the peak ground acceleration peak vertical ground acceleration using this expression for the Himalayan region of India. Suppose somebody wants to construct in Roorkee region some construction they should use this attenuation relationship to obtain the peak vertical ground acceleration which was proposed in 2000. This is the paper which appeared in again the world conference proceedings in 2000 by a professor M L Sharma. So how much database was consisted to derive this attenuation relationship the database consisting of 66 peak ground vertical acceleration from 5 earthquake record by strong motion arrays in India. So only 5 earthquake were used where total 66 data of this peak vertical acceleration were recorded and those were used to develop this equation. So somebody wants to comment on this equation obviously you can mention that from 2000 to this 2013 there is a chance of in a change of this coefficients etcetera when you want to obtain this log of a because between 2000 to 2013 whatever accelerations whatever earthquakes has occurred if they those historical earthquake have experience or have the record of this peak vertical ground acceleration you can use those further for the updation of this equation so which is possible. So that is why as I said earlier this is the continuous process of evaluation of the research in this topic. And another equation Sharma et al had proposed in this paper like vertical to horizontal acceleration ratio how it can be compared and can be estimated based on the hypo central distance. So this is for the horizontal one they proposed this equation which originally was proposed earlier than this 2000. Now let us come to another attenuation relationship of India which is a very recent finding for Kolkata city you can first see this reference of the paper by Shulia and Narayan in 2012 paper deterministic seismic microzonation of Kolkata city in which appeared in the natural hazards journal this is the volume number page number you should go through this paper this is again from IIT Roorkee earthquake engineering department they developed the following predictive attenuation relationship for peak horizontal ground acceleration for Kolkata city it was developed by Abrahamson and Lichester in 1989 based on their model of the equation not based on their data they did not provide this coefficients the coefficients have been proposed by Shulia and Narayanan using the historical earthquake data of that region. So what they have proposed this is the equation they had proposed log of a equals to minus 0.62 plus 0.177 m minus 0.982 log of r plus e to the power 0.284 m plus 0.132 f minus 0.0132 m plus 0.1 0 0 0 8 e r in this case a is the peak horizontal acceleration in g unit r is the closest distance in the kilometer unit from the site to the zone of energy release that means site to the hypo center or focus of the earthquake m is the earthquake magnitude f is a dummy variable why they have used this dummy variable to take care of different type of fault movement they mentioned that use one this value of f you can use as one when it is a reverse fault or oblique fault otherwise if it is not a reverse or oblique fault in other cases of fault like normal fault etcetera you can use it value of f as 0. So then this parameter vanishes this parameter appears 0.132 comes when it is a reverse or oblique fault and e is again another dummy parameter e r r is already the distance as I said e is again another dummy parameter which comes because of the whether it is a inter plate earthquake or intra plate that is between the plate boundary or within the plate that is what it means. So you have to use the value of e as 1 if it is a inter plate earthquake but if it is a intra plate earthquake then put the value of e as 0 that is what they had proposed. Now let us see other attenuation relationship developed for India you can see in this slide first let us see the reference this is Stacy Martin and Walter Zeliga in 2010 their paper which shows a catalogue of felt intensity data for 570 earthquakes in India during the period 1636 to 2009. So they have taken all 570 recorded data between 1636 to 2009 these are intensity based data remember these are not magnitude scale data this is a different attenuation relationship compared to the other what we have learned so far. So this paper was published in the journal bulletin of seismological society of America B.S.S.A. in short we call this is the volume number of the journal you should go through this paper because this gives you the idea of the intensity because in the olden days it was very difficult to obtain the magnitude because in those days determination of the magnitude scale was not that sophisticated as what we have today. So in those days mostly it is based on the people's feelings or how they felt about a particular earthquake that is why it is mostly on the intensity based data. So that is why the 1636 towards those ages you will get mostly intensity based data and they have used all the intensity based data of the 570 earthquake which are having record actually between this time period to 1636 to 2009. And what they have proposed finally that the predictive attenuation relationship for intensity so using this equation of course you are getting the intensity because they have used the intensity data log of n equals to a plus b times i minus 2. So what is this n? n is the cumulative number of observations per year and it is nothing but the intensity value that is per year how many observed earthquake you can expect for a particular intensity. And i is the value of the intensity and a and b are the coefficients and what are those coefficients they proposed in this table you can see for various cities they have proposed various coefficients and depending on what are the return time in terms of years for the intensity that return times is nothing but this n right is the cumulative number of observations per year which automatically gives you the return period right. So using this expression you can finally get the value of i knowing the value of n a and b from this table. Suppose for Mumbai region you want to find out the intensity you can based on this return period based on whether you want intensity of 6 or intensity of 5 intensity of 6 or intensity of 7 you should use corresponding value of return period like this and corresponding value of coefficients a and b like this. If you want to do the estimation for this intensity based attenuation in Delhi region you should use these values. If you want to use for Bangalore region these values if you want to use Kolkata region these values for Chennai region these values what you can look at here see return time in years you can see over there for Delhi for Kolkata these are pretty low values low values means they have more chances of occurrence so intensity finally what you will get using this equation will be much higher than Mumbai and Bangalore where Mumbai and Bangalore you are having large values of this return time for the intensity clear. So finally you can use these values to obtain a particular intensity at a particular return period of your value at a particular city. Now let us come to another attenuation relationship of India which was proposed by Dunbar et al. Dunbar et al this earthquake loss estimation for India based on macroeconomic indication indicators they proposed this equation of attenuation relationship for peak horizontal ground acceleration a for the south India. So this equation is valid only for the southern India and it has been proposed for peninsular India that is southern part of the peninsular India you can say. So this equation gives you acceleration value m w is in moment magnitude and the relationship between intensity that is intensity of earthquake and the peak horizontal ground acceleration were also given by these expressions that is suppose somebody is having intensity scale how to convert it to magnitude scale of m w or m s using this equation for this region of earthquake whatever data they have used and then if you use the intensity based equation the same equation if you put in terms of m w just change to this one right. So on simplification the same equation in terms of intensity will be like this. So what does it mean suppose in southern India you are trying to find out what is the acceleration attenuation attenuated value of acceleration at a particular site you should only know the intensity or you should only know the magnitude then you will get the what is the estimated value of the attenuation relationship. But remember the drawback or limitation of this equation these are based on only the magnitude parameter or the size of the earthquake not based on the distance which is also very important. So that distance criteria is not considered so that is a major drawback or major limitation of using this equation. Now let us come to another attenuation relationship let us look at here. So the following predictive attenuation relationship for pseudo spectral velocity PSV for northeast India has been proposed by Das et al. So this is the paper of Das Gupta and Gupta this is done by IIT Kanpur research group Professor Vinay K Gupta and his student and I. D. Gupta from IMD. So this is the paper new attenuation model for northeast India. So this is as I was mentioning suppose somebody wants to do design in the Guwahati city they should use this kind of attenuation relationship. So region specific attenuation relationship use of that is very essential. You can see for northeast India the pseudo spectral velocity this is the spectral velocity remember it is not the peak value of the velocity it is not the acceleration as also there is a spectral velocity spectral velocity we have seen how it is idealized compared to or based on the single degree of freedom mass spring dashpot model. So where this m value is the earthquake magnitude r value is the epicentral distance h is the focal depth and t is the time period of a single degree of freedom system oscillator this t. And this value of v is equals to 0 and 1 whether it is a horizontal motion or vertical motion. So for horizontal motion it will be 0 for vertical motion it will be 1 then you will get corresponding value of pseudo spectral velocity in horizontal direction and vertical direction. So they used 261 accelerogram recorded data on the stiff soil and rocky site from the 6 earthquake events in this region of northeast India. And these are the various values of those c 1 c 2 c 3 etcetera based on different values of the period these values of the period are typical range of period for a simple harmonic oscillator and within the practical range of our structural periods as I have already mentioned earlier. Now coming to another attenuation relationship for India let us see the following predictive attenuation relationship which is proposed for peak horizontal ground acceleration that is p g a in the horizontal direction for Guwahati city only remember this attenuation relationship first of all it is for peak horizontal ground acceleration and it is only for the Guwahati city that was proposed by Nath et al in 2009. Professor Nath is from IIT Kharagpur Geology Geosciences department. So his research group proposed this attenuation relationship for a particular city based on the collected historical earthquake data of that region. So what is their proposed relationship that natural log of p g a equals to 9.143 plus 0.247 m minus 0.014 times 10 minus m whole cube minus 2.697 natural log of p g a minus 2.697 natural log of r rupture plus 32.9458 e to the power 0.0663 m in this case m they have mentioned it is a earthquake moment magnitude that is m w and r r u p is nothing but the rupture distance rupture distance that is from the side to your focal focus point or the hypocentrum point in kilometer unit and p g a this value what you are getting in terms of g and this is the paper where you will get the details you should go through this paper like Nath et al 2009 ground motion synthesis and seismic scenario in Guwahati city a stochastic approach it was published in the journal seismological research letter we call in short as s r l this is the volume number and this is the page numbers. Now let us see another attenuation relationship which was proposed for peak horizontal ground acceleration for p g a for bhoose region only that is in Gujarat bhoose region after that 2001 bhoose earthquake ayangar and ragukant that professor ayangar from IISC Bangalore and his PhD student those days proposed this equation in 2002 you can see the reference of that paper this ayangar and ragukant 2002 strong ground motion at bhoose city during the touch earthquake it was published in the journal current science this is the volume number this is the page number so how they have proposed they proposed that the p g a that is peak ground acceleration in horizontal direction they mentioned it clearly in the paper in terms of g that can be calculated as 38.82 divided by r to the power 1.12 where this r is the hypocentral distance in the unit of kilometer and remember in this case it is irrespective of magnitude it is they have proposed only the distance based so that is a major limitation of this equation because they considered only one scenario earthquake which is the bhoose earthquake or that koth region earthquake so that is why based on that whatever the distance changes based on the change of distance at various locations in Gujarat and that vicinity how the p g a value for a design of any structure will change that is what their problem statement or their goal to obtain that is in the bhoose region suppose if an earthquake similar to of magnitude of bhoose 2001 earthquake occurs how much value of p g a attenuated value of p g a in horizontal direction should be used based on this distance hypocentral distance from the site to the source can be used or can be estimated for design of civil structures. Now, coming to next attenuation relationship for India as proposed by Jain et al in 2000 this research was done by professor SK Jain at IIT Kanpur and his research group in 2000 now he is director at IIT Gandhinagar so their research group proposed the following model for attenuation relationship for India using the database from four regions. So, we will see what are those four regions let us first look at the attenuation relationship. So, this is the attenuation relationship natural log of p g a is equals to b 1 plus b 2 times m plus b 3 times r plus b 4 times natural log of r. So, where this p g a is in g so as I said earlier whatever value you are getting using this equation that will be suppose 0.236 g like that. So, for central Himalayan earthquake he has proposed these values of the coefficients b 1 b 2 b 3 b 4 like this like b 1 is minus 4.135 b 2 is 0.647 b 3 is minus 0.00142 b 4 is minus 0.753 and the sigma value is 0.59 for that whatever earthquake data they have used and for non-subduction earthquakes in northeast India. So, this was for the central Himalayan earthquake means suppose the Uttaranjala or Uttarakhand region that is the central Himalayan region and for the northeast India that is Assam and other places there the values are coefficient they have proposed different coefficients you can see over here. So, the coefficients of other equations not given because they are for a particular earthquake that is for a single earthquake they have used these two are the generalized equation. So, how they have divided the database into four regions so these are the four regions a b c d as you can see they have divided in four regions like central Himalayan earthquake those are thrust type how many record they had 32 SMA records and 117 SRR records from three earthquakes with the magnitude between 5.5 to 7. So, that is the magnitude range they have taken and for that earthquake the focal depths were between 10 to 33 kilometers. So, which are essentially the shallow earthquake as we know and that a hypocentral distance capital R was reported to be between 2 to 322 kilometer that is those earthquake data points which they have used within this range of hypocentral distance the second category or second region they have considered is non-subduction earthquakes in the northeast India in the northeast India the thrust type of earthquake again thrust type fault movement 43 SMA records they have used and no SRR records for that again three earthquake data they have used within the range of values between 5.2 to 5.9 which is a very marginal range I will say. So, focal depth they have used between 33 to 49 kilometer which is again a shallow earthquake and the value of R that is hypocentral distance they have used between 6 to 243 kilometer whereas, category C or region C that subdivided or considered as subduction earthquake in the northeast India for that they had taken 33 SMA records and 104 SRR records from one particular earthquake that is why it is mentioned over here that other region equations are developed based on a single earthquake particular earthquake. So, it cannot be generalized unless you have more number of earthquake you cannot generalize. So, for one particular earthquake of magnitude 7.3 only with focal depth of h equals to 90 kilometer. So, we can say it is something about intermediate earthquake not a pure shallow earthquake and R value that is hypocentral distance was between 39 to 722 kilometer at different recording stations for the same earthquake and the fourth category or fourth region they considered in their study like Bihar Nepal earthquake in Indo gangetic plane where the strike slip type of fault movement had occurred these thrust fault movement this is strike slip type of fault movement here 0 SMA records, but 38 SRR records they used for one particular earthquake again for magnitude of 6.8 and focal depth h was 57 kilometer which is again a shallow earthquake and that hypocentral distance was between 42 to 337 kilometer for different recording stations. So, these are the input data based on which they had proposed this equation. So, when we are planning to use this equation first of all we have to be specific for which region we want to use. So, suppose for central Himalayan region to one if we want to find out the PGA value we should use these coefficients if we want to use for north east India we should use these coefficients and we should remember that these are valid for which range of magnitude range beyond that we should not use this equation for prediction of the peak ground acceleration attenuation relationship. Coming to another attenuation relationship as proposed by M L Sharma et al in 2009 again from IIT Roorkee earthquake engineering department this is the equation they have proposed log of A equals to B 1 plus B 2 times M W minus B 3 times log of root over r j B square plus B 4 square plus B 5 times S plus B 6 times H where this r j B is the distance to surface projection of the rupture with damping ratio consideration of 5 percent number of events how many events they considered total 201 58 from India and 143 from Iran. So, we cannot say it is valid only for India it is a punched equation proposed using different earthquake from different regions and all the coefficients etcetera magnitude are given over here. Another researchers another group of researchers Mandel et al in 2009 this is the paper you can see this group of researchers they published ground motion attenuation relation from strong motion records of the 2001 M W 7.7 Bhuj earthquake sequence. So, 2001 to 2003 2006 data they have collected post Bhuj earthquake during and after Bhuj earthquake Gujarat India it has been published in the journal pure and applied geophysics this volume issue number page number you can see this attenuation relationship gives the acceleration again and this r j B in this equation is nothing but distance to the surface projection of the rupture in kilometer unit and M W moment magnitude value is valid between this range and standard deviation is this much. Another attenuation relationship for acceleration this y is p h e horizontal acceleration in centimeter per second square unit as proposed by Gupta in 2010 this I D Gupta in 2010 this is the title of the paper response spectral attenuation relation for in slab earthquakes in Indobarm is subduction zone this is the Indobarma subduction zone they have considered the earthquake which is published in soil dynamics and earthquake engineering journal these are the details of the journal issue this h in this equation this h is the focal depth in the kilometer unit and it has to be limited within 100 kilometer for the deeper events you have to use this equation. Other equation like Ze Liga et al had proposed the in 2010 this is the intensity based intensity based equation once again they considered the earthquake felt attenuation relationship since 1762 1762 to 2009 they have taken but as I said the older earthquake only the intensity scale will be available. So, intensity based again 570 data point 100 instrumented record that is about 570 earthquake data point only 100 were instrumented which are in the recent days. So, this is the proposed intensity based attenuation relationship. So, for different region like entire India how many events for Creighton region for Himalayan region how many events and these are the coefficients a b c d and r is the hypocentral distance in kilometer m w is the moment magnitude can be used. Now, functional form of attenuation relationship as proposed by Bosorgnia et al in 2000 10 this is the ground motion prediction equation ground motion prediction equation which are nothing but an attenuation relationship equation which can be standardized and commonly expressed in this form. We have already seen this several researchers have proposed attenuation relationship or ground motion prediction why another name it is called GMP because in this way you can predict what can be a ground motion at a particular site. So, that is why GMP is a common term which people use in our earthquake engineering problem and these are the various coefficients f magnitude f distance. So, on this various term this attenuation value of whether acceleration or intensity or velocity depends on that is the magnitude term based on different scale of magnitude distance term how far it is from the source to site then style of faulting term that is what type of fault we have seen fault based attenuation relationship earlier. So, this is the fault based attenuation then hanging wall term next one is oblique strike slip all this hanging wall type of term. So, these are various functions and shallow site response term that is whether it is a shallow earthquake type intermediate or deep earthquake type then basin response term that is the sediment or soft basin depth how much. So, based on that this equation can be affected. So, based on all these influence parameter one can estimate what is the proposed value of P g as given by Bozergne et al. So, this is a functional form means this is a generalized form. So, if somebody wants to predict or propose a very good empirical relationship of attenuation relation or GMP the best attenuation relationship will be to use all these terms that is magnitude distance fault hanging fault site basin everything then only we can say it is a complete attenuation relationship or complete GMP or base GMP. Now, let us come to the Fourier amplitude spectra once again like earlier we have seen in the Fourier amplitude spectra two values like corner frequency and the maximum frequency. So, if that f max is assumed as constant for a given geographic region for a given site this f max maximum value is constant say suppose it can be 15 hertz or 20 hertz as reported by western and eastern North America respectively like for western North America it is 15 hertz for eastern part it is 20 hertz that f max value. And this f c then can be calculated using the seismic moment value in this fashion as proposed by Brunei in 1970 and then 1971 where this v s is in kilometer per second that is the crustal velocity of the shear wave and m naught is in the unit of dine centimeter and this delta sigma referred to the stress parameter or stress drop in the unit of bar that they mention that use 50 bar and 100 bar for western and eastern North America. So, using this you can find out what is the cut off frequency for Fourier series response spectra of amplitude right. Then another important parameter is the ratio of v max by a max. So, ratio of v max by a max this ratio is the proportional to the magnitude and distance dependency proposed by McGeery in 1978 as shown in the table below that is depending on site condition whether it is rocky site or soil site magnitude dependency will be a function of e to the power 0.4 times m and for soil site it will be e to the power 0.15 times m, m is the magnitude of earthquake and distance dependency will be r to the power 0.12 and r to the power 0.23 based on rocky site or soil site. So, using this suppose for a known earthquake historical earthquake you know the magnitude of earthquake now from that earthquake location point at another particular site where you are interested to estimate what will be my parameters of that v max by a max in future you can estimate very easily. How you will estimate for the older earthquake you should know the value of what is a v max and a max at that particular site whether it is a rock site or soil site based on that that will be known to you that magnitude will be known to you the distance within which you are using that data point should be known to you. Now for different soil site or rock site based on their distance and the design value of earthquake which you want to consider for the design based on that let us look at the slide here it will be simply proportional to this magnitude dependency and the distance dependency. So, using a simple problem which is worked out in Kramer 1996 book you can understand this in a simpler way. Then estimation of other spectral parameters I have mentioned the definition earlier now how to estimate that I am mentioning here this root mean square acceleration can be computed using the equation proposed by Hanks and McGurie in 1981 this is valid for the California earthquake between the range of 4 to 7 and the hypocentral distance between 10 to 100 kilometer then only this proposed empirical relationship is valid that is ARMS can be calculated as 0.199 times root over f max by f c by r this f c is corner frequency you know how to calculate corner frequency for this region because I have already mentioned this in the previous slide f max is the cutoff frequency that is also known for this region western part of America and eastern part of North America it is known r is in kilometer based on what distance you want to find out this rms acceleration can be estimated right. Then then Kawasanze and et al in 1985 use the definition of the duration proposed by these researchers with a database of 83 strong motions from 18 different earthquake and proposed another empirical relation of computing this root mean square acceleration using this equation where r is the distance to the closest point of the rupture on the fault and the database was restricted to m w value more than 5 that is below 5 it should not be used and r that is the hypocentral distance should be within 110 kilometer and rupture depth was less than 30 kilometer and the soil thickness will be greater than the 10 meter based on all these conditions he these researchers proposed the proposed the empirical relation to estimate the root mean square acceleration. Further to estimate the areas intensity empirically campbell and duke in 1974 using the Californian earthquake data between the distance of 15 to 110 kilometer and between the magnitude range of 4.5 to 8.5 scale they proposed using those historical data points this is the empirical relation to estimate the areas intensity I a in the unit of meter per second using this relation 3 1 3 e to the power m s times 0.0 0.33 m s minus 1.47 divided by r to the power 3.79 times s this s is dependent on the type of material in the site local soil type that is for basement rock s can be calculated using this expression for sedimentary rock this expression for alluvial soil within 60 feet of thickness this equation and alluvial soil of thickness more than 60 feet this expression where this r is the distance between the center of energy release and the site of air concern in the unit of kilometer. So, basically the hypocentral distance then Wilson in 1993 analyzed the strong ground motion record from California region once again and developed the attenuation relationship which can be used further to estimate the areas intensity using this equation this equation is proposed by Wilson in 1983 in this equation D is the minimum horizontal distance to the vertical projection of the fault plane and H this H is a correction factor with the default value of 7.5 kilometer and k is a coefficient in this case k is a coefficient of inelastic absorption with default value of 0 and p is the accidents probability that is how much accidents of an earthquake probability you want to use to estimate that areas intensity that was used by Wilson in 1993. So, with this we have come to the end of our module number 4 we will start again in the next lecture with our next module module 5.