SEISMIC HAZARD ASSESSEMENT USING EXTREME VALUE STATISTICS

Abstract

Seismic Hazard Assessment (SHA) depends on detailed knowledge of physical processes, tectonic set up, comprehensive and qualitative data sets, understanding of internal structure of earth and various mathematical and statistical modelling. The mathematical models of SHA vary with region to region. In the Himalayan arc, a uniform pattern of stress accumulation and its subsequent release has never been observed. The seismicity patterns follow these processes, sporadically as well as spatially, resulting in seismically very active regions as well as seismic gaps, which continuously accumulate stresses over a long period without any release. Generally, in a typical SHA practice, the inadequacy of the dataset used along with the unaccountability for the physical processes are the key reasons for impractical results. Moreover, a sensitive treatment of the prepared earthquake catalogue is another prerequisite for precise estimation of the seismic hazard, which is lengthy and cumbersome. It is thus of paramount importance to use statistical methods that analyse as closely as possible the range of large return period earthquake events in the Himalaya and best describe the seismicity pattern in seismic gap and also required statistical model that well described the seismicity of low seismic region. For this purpose, various earthquake recurrence models have been applied in seismically different regions and then are examined in the light of damaging earthquakes. To capture the realistic behaviour of large return period events the Extreme Value Statistics (EVS) is better alternative. The Extreme Value Distribution (EVD) is based on yearly maximum event, whereas the Generalized Pareto Distribution (GPD) select those events which cross a specified threshold value. The Pareto, Truncated Pareto, and Tapered Pareto are the special cases of the GPD and Gumbel Type I, Type II and Type III are the types of EVD. To perform the EVD and GPD the entire Himalayan region has been divided into five seismogenic source zones (SSZs). Estimated probabilities of earthquakes occurrence using Pareto, Truncated Pareto and Tapered Pareto distribution have also been compared with the Modified Gutenberg-Richter (G-R) and the Characteristics recurrence distribution. Statistical analysis shows that the Tapered Pareto distribution better describes seismicity in all SSZs in comparison to other distributions. The annual probability of earthquake occurrence have been re-examined using two models: Gumbel Type I and Type III distributions and then compared with Modified G-R distribution and found that Gumbel Type I provides highest probability while Modified G-R estimates lowest probability and Gumbel Type III distribution also better defines seismicity in comparison to usual distributions for all SSZs. To look into the effects of such modelling on strong ground motion, the Probabilistic Seismic Hazard Assessment has been ii carried out for the Himalaya. It has been observed that Peak Ground Acceleration (PGA) estimated using Tapered Pareto were relatively higher than the Modified G-R distribution which reveal that the data is incomplete in the range of the large earthquake and not well captured by classical method. Similar trend have been shown by Gumbel Type III i.e. PGA values are relatively higher for Gumbel Type III. Uniform PGA contour maps have been prepared using Tapered Pareto and Gumbel Type III for an exposure time of 50 years for 90% and 98 % confidence level and these contour maps are very close to realistic observations. In low seismicity area where a comprehensively complete catalogue of earthquake events is not available and standard models fail to capture the seismicity, EVD is better alternative for SHA and requires only the annual maximum events and no treatment of earthquake catalogue is prerequisite. To test the applicability of EVD, an attempt has been made for SHA in South India and divided into four SSZs. The Gumbel Type I method has capabilities of reliably deducing the G-R parameters. Parameters of Gumbel Type I have been estimated using two plotting position formulas given by Gumbel (1958) and Bury (1999), respectively. In the present analysis, probabilities of earthquakes occurrences of magnitude Mw ⩾ 4.0 have been estimated and well match with the observed data. Thus, models can be considered as a simplified method to evaluate the SHA at low seismicity area. To understand the seismicity pattern of discordant seismicity of Himalaya, three types of regions have been considered namely: North-West Himalayan, the Garhwal Himalaya and the Nepal. The seismicity parameters have been revisited using Constant Moment release model which is based on strain rate data. Probability of earthquake occurrence with time has compared with Constant Seismicity model assuming Poissonian Distribution. From the comparing the results of above stated two models in North-West region, it has been observed that Constant Moment release model predict the higher occurrence rate of earthquake as compared to Constant Seismicity model, which implies that either the occupied accumulated stress is not being unconfined in the form of earthquakes or the compiled earthquake catalogue is insufficient. Similar trend has been observed for Seismic Gap area but with lesser difference reported from both methods. However, for the Nepal region, the estimated seismicity by the two methods has been found to be relatively less when estimated using Constant Moment Release model which implies that the in Nepal region accumulated strain is releasing in the form of large earthquake occurrence event. To further investigate the effect of these two models in seismic gap, PSHA has been carried out for Uttrakhand Himalaya, which is located in central seismic gap of Himalaya. The annual iii occurrence rates of earthquake have been estimated by Constant Seismicity and Constant Moment release models and Uniform hazard contours for PGA have been obtained for an exposure time of 50 years for 90% and 98 % confidence level. The patterns have been depicted by the PGA contours, which are fairly regular with the major seismotectonic features. In this study, various types of magnitude recurrence models have been applied according to seismotectonic environments. The seismic hazard vis-à-vis the model applicable for a region has been interpreted in terms of the physical process of earthquake occurrence. The fitting of different distribution models for estimating the probability of earthquake occurrence in seismically varying seismic source zones is informative and useful from an engineering point of view, and most certainly from a SHA perspective. The following are the primary outputs of this research work: 1. The application of Constant Seismicity and Constant Moment rate approaches for SHA has revealed discordant patterns of strain release in terms of earthquakes in the Himalaya. In Constant Seismicity model, the occurrence of large earthquake event is not represented well which restrains this model from reflecting the real physical process. The accumulated energy in the region can be released in the form of either a single large earthquake or many small to medium scale earthquakes depending on the tectonic environment of the region. The present study concludes that the Constant Moment Release model is a better alternative to understand the earthquake occurrence in the region where it is necessary to compensate the lowering of 𝑀𝑚𝑎𝑥 by increasing rate of small to moderate earthquakes. 2. In North-West region, the total seismicity rate estimated using Constant Moment release is observed to be 55.67% higher than those obtained by Constant Seismicity model, which reflects that accumulated strain is not released fully by the past earthquakes. This indicates that accumulated strain is compensated either by other tectonic activities like locking or perhaps the earthquake catalogue itself is insufficient and incomplete. 3. The annual occurrence of earthquakes using Constant Moment release rate model is 71% higher than those estimated by Constant Seismicity rate model for all magnitude ranges in Garhwal Himalaya region. If it’s true and Garhwal Himalaya region being in central seismic gap which has experienced relatively lesser seismicity compared to the North-West region, the accumulated energy budget indicates that a major earthquake is ready to strike in the Garhwal Himalaya seismic gap region. 4. In the Nepal region the total seismicity (𝑀𝑚𝑖𝑛) computed using Constant Seismicity model is found to be 78% higher than those estimated using Constant Moment Release model iv which shows that the maximum part of accumulated energy has been released from large earthquake occurrence. 5. The use of EVS has well captured the behaviour of seismicity for larger events whereby Tapered Pareto and Gumbel Type III models were observed to best fitted with the observational data to the lower range of magnitudes as well. 6. It has been proven that for low seismicity regions like South India the methods using Gumbel Type I distribution may be used successfully. Synthetic catalogue can be prepared using relationship of Gumbel parameters to G-R parameters for low seismic area. 7. One of the main conclusions is that the differences in the estimated probabilities using the different distributions has definite bearing on the ultimate results of SHA exercises, and hence it is recommended to use different statistical models that best fit in the seismogenic source zones in an area.