Prediction of Reservoir Induced Seismicity by Analytical Hierarchy Process and Regression Analysis

This study is done to find out the equation for reservoir induced seismicity. The mechanism and histories of reservoir induced seismicity are studied first to find out the factors affecting reservoir induced seismicity. A questionnaire survey is done to get an opinion of an expert on the effect of all the factors affecting reservoir induced seismicity. The results obtained from this questionnaire survey is used to find out the respective weightages of the factors by analytical hierarchy process. In the second part of the study, seismic details of 20 seismic and aseismic dams are found out in a questionnaire survey format. These details along with the weights found out in the first part of the study is used to find out the equation for reservoir induced seismicity by regression analysis. keywords: Reservoir induced seismicity, Analytical hierarchy process, Regression Analysis.

Earthquakes are one of the most devastating among the various natural hazards.In the last few decades, the world has been faced by a number of large earthquakes which has caused significant destruction of human life and property, earthquakes are the major natural disaster in our country too.The Indian subcontinent has suffered much due to earthquakes being one of the most earthquake prone regions of the globe.The damage to human life and property due to large earthquakes are significant, the rapid rate of urbanization and globalization has caused the construction of mega infrastructures to support people which has increased the potential of earthquakes to a greater extent 5,6, .
A particular seismic event or earthquakes refers to the tremors associated with the damage of a rock mass below the surface of earth.The energy released is only a small portion of the energy which is released due to the rupture of the rock mass.A seismic event is caused by excess concentration of stress in discontinuities of rock mass which leads to failure of the rock mass, the excess stress concentration is caused due to stress redistribution.An earthquake or seismic activity is said to be completed when the energy dissipation is complete and the rocks moves from one stress state to another.Seismic activity may vary in intensity and in many events the energy dissipated may not reach the earth surface.But it will reach the earth surface in case of large earthquakes and cause considerable shaking 7,8 .
The impoundment of large reservoirs especially ones with height above 100 m have caused earthquakes which are termed as reservoir induced earthquakes or reservoir triggered earthquakes.The first case of reservoir induced earthquake was that of marathon reservoir, Greece in 1931 7,11 .After that over 100 cases of reservoir induced earthquakes were recorded in which many of them had magnitudes greater than 6 and caused considerable damage 11,3 .

Methodology evaluation of weightage of factors affecting reservoir induced seismicity by Analytical Hierarchy Process
The factors which are likely to affect reservoir induced seismicity are finalised from previous investigation papers and history of reservoir induced seismicity.Even though the factors affecting the RIS is complicated and the exact mechanism is net yet found out, this study focusses on seven factors which have a direct dependence on causing reservoir induced seismicity 3,10,11

Analytical Hierarchy Process
Analytical hierarchy process comes under a multiple criteria decision making approach which was first introduced by saaty in 1977 and 1994..In this process ,the input data are easy to obtain and the solution is found out easily by smooth mathematical properties 1,2 .The analytical hierarchy process is normally used to solve complex mathematical problems.It creates a multilevel hierarchy structure which consists of criteria, objectives, sub criteria and alternatives.The obtained data is solved by formation In our case, an expert opinion is used to create the comparison matrix which correlates the Relative importance of the seven factors affecting reservoir induced seismicity.The right eigen vectors of the matrix gives the weightages of the seven factors affecting reservoir induced seismicity 8,9,10 .The values obtained were checked for consistency and were found to be consistent.

calibration of equation of Reservoir induced seismicity magnitude by regression analysis
The second par t of the study is the calibration of equation for magnitude of reservoir induced seismicity magnitude by regression analysis.This is done by collecting seismic data of seismic and aseismic dams across the nation.It is seen from previous studies and investigations that all the seven factors affecting seismicity can be divided each into four sub factors.These sub factors are incorporated when seismic detail of each dam is found out.All the sub factors are given weightages ranging from 1 to 4 with 1 causing the least chance of reservoir induced seismicity and 4 showing highest probability of causing reservoir induced seismicity.The factors affecting reservoir induced seismicity, their sub factors and their weightages are given in table 3.

Regression Analysis
The seismic details that is the seven factors with the corresponding recorded seismicity is collected from the cases of seismic and aseismic dams around the country.Each of the dam details that is the seven factors affecting reservoir induced seismicity is multiplied by their corresponding weights obtained from part 1 of the study.This weighted details along with the corresponding seismicity value is used for regression analysis to obtain the equation for reservoir induced seismicity.The process of regression analysis is done by Microsoft excel 4,12  The weighted dam details are used and regression analysis is done in Microsoft excel.It is seen that the p value of all factors affecting RIS except W and C are found to be above .15therefore only W and C are used for calibrating the equation.The coefficient of W and C are 2.597 and 4.088 respectively Thus the magnitude of reservoir induced seismicity in any dam is given as M= 0.26 x 2.597 x W + 0.26 x 4.088 x C

ReSULtS AnD DIScUSSIonS
Reser voir induced seismicity is a phenomena whose exact mechanism and factors affecting it has not yet been found out.In this study, an attempt is made to find out the equation for reservoir induced seismicity by use of statistical information and expert opinions.The tools of analytical hierarchy process and regression analysis is used to find out the equation.The first part of the work consists of evaluation of weightage of factors affecting reservoir induced seismicity by an expert opinion followed by analytical hierarchy process.The weightages of the factors are found out as shown below: W=0.26

wa t e r c o n d u c t a n c e ( i n d e p t h o f w a t e
The seismic data is collected in a questionnaire format as shown below Please register your opinion regarding the following geological and geotechnical features of the dam area is a landscape formed from the dissolution of soluble rocks such as limestone, dolomite, and gypsum.It is characterized by underground drainage systems with sinkholes, dolines, and caves.[11]

table 1 .
Please register your opinion regarding the effect of the following factors in causing reservoir induced earthquakes(eg: if a factor has no contribution in causing reservoir induced earthquake mark as no importance & if a factor is an extremely important factor in causing reservoir induced earthquakes mark it as extreme importance)