ESTIMATION OF UNCERTAINTIES IN PROBABILISTIC SEISMIC HAZARD ANALYSES

Abstract

An attempt has been made in the present study to estimate the ground motion and uncertainties which are involved at various steps in Probabilistic Seismic Hazard Assessment (PSHA). PSHA provides a framework in which uncertainties at various steps of seismic hazard assessment can be identified, quantified and combined in a rational manner to provide a more complete picture of the seismic hazard with a quantified range of possibilities in terms of ground motions at the site of interest. These uncertainties have been arising in magnitude scales (measurement and conversion error), earthquake catalog incompleteness (Temporal, Spatial and minimum threshold magnitude), earthquake source modeling, methods of estimations, kinds of earthquake recurrence models and estimation of strong ground motion using different attenuation relationships. While epistemic uncertainty is due to a lack of knowledge about the behavior of the system that is conceptually resolvable, aleatory uncertainty arises because of natural, unpredictable variation in the performance of the system under study. With the objectives to study the behavior of uncertainties the PSHA has been applied to northern Indian region as a case study. The study area lies between latitude 24° - 31.5° N and longitude 74° - 81.5° E with Delhi as its centre for which the geological and tectonic setup was studied and seismicity catalogue was compiled from various sources. After performing the seismotectonic modeling four seismogenic sources namely Himalayan zone (HIM), Delhi-Haridwar Ridge (DHR), Moradabad fault zone (MOR) and Rajasthan Great Boundary Fault (RGBF) zone have been earmarked. in After checking for the completeness, homogenization has been carried out through developing relationships between various magnitude scales for the Northern Indian region around Delhi using orthonormal bivariate regression analysis and a methodology has been recommended to be used for other regions as well. The effects of using different relationships on the catalogue have been demonstrated by considering the relationships recommended in the present study vis-a-vis using empirical linear relationships and the one adopted from other regions. Three catalogues namely CI, C2 and C3 are thus prepared. An endeavor has been made in the present study to estimate seismic hazard parameters namely a & b (Gutenberg- Richter relationship parameters), Minimum magnitude of completeness (Mc). Maximum magnitude (Mmax), activity rate (X) and (3 (equal to 2.303b) using various methodologies with the aim to quantify epistemic uncertainties. These methods (nine in numbers) produced results which were highly variable and the percentage variation was observed to be as high as about 90%. A sensitivity analysis has been carried out between the input to PSHA given in terms of various seismic hazard parameters and the output in terms of strong ground motion (SGM) estimation. To carry out sensitivity analysis PSHA has been applied for Northern Indian region by considering Gutenberg- Richter relationships for size distribution with Poissonian earthquake occurrence. The code CRISIS (version released in 2007) has been used for the purpose (Ordaz et al., 2003). To include the epistemic uncertainty due to the Ground Motion Prediction Equations (GMPEs), three relationships namely, Abrahamson and Silva (1997), Sadigh et al., (1997) and Boore and Atkinson (2008) were considered. Total of 108 combinations (9 methods X 4 sources X 3 GMPEs) were obtained using Logic tree approach. The estimation of the covariance between the seismic hazard parameters and the output in IV terms of ground motion was carried out using 200 samples generated for each of the seismic hazard parameters using Monte Carlo approach. The mean seismic hazard and the uncertainties have been estimated at four sites in Delhi viz., Dwarka, Greenpark, Jwalapuri and Shahadara. At each of the site a distribution of 200 values of PGA and Spectral acceleration (Sa) at 0.1 sec and 1.0 sec were obtained for return periods of 100, 225, 475, 2500 and 10000 years. Their covariance with the predicted strong ground motion (SGM) revealed high variability. The results of the sensitivity analysis were used to select the catalogue C2 for further use and computation of new set of seismic hazard parameters. The seismic hazard parameters were re-evaluated based on more emphasis being given to the physical processes in the region and filtering out of sporadic/intermittent microearthquake records from the catalogue. The variability maps in terms of COV have been used along with the mean SGM in the present case to look into the effect of catalogues, seismic hazard parameters, source modelling and GMPEs. The variation at the input level in terms of both types of source models (i.e., line as well as area) and the three different GMPEs have been used. Equal weights, the most sensitive choice, have been chosen because a scientific preference has not yet been developed for the area. To encompass the whole region from latitude 24° to 31.5° N and longitude 74° to 81.5° Eand for better resolution the strong ground motion (SGM) was estimated at every 15 minute interval. It was observed that the areas showing more variability are located around the boundaries of the source zones (line source model as well as areal source model). COV values in the source zone Himalaya (HIM) and Delhi-Haridwar-Ridge (DHR) were in between 0.45-0.75 and for Moradabad (MOR) and Rajasthan-Great- Boundary (RGB) have been observed in the range of 0.30-0.45. Delhi city shows variability of COV values in between 0.30 to 0.45. It is also noted that COV values for PGA near about Delhi was in between 0.30-0.45 for 100, 225 and 475 years of return period and increases to ranges between 0.45 to 0.60 for 2500 and 10000 years of return periods. The mean SGM generated shows that seismic hazard in the Himalayan region is highest along Northwest- Southeast trending central part of the region, and rapidly decreases to the Southwest and Northeast. To further consider the effect of the variation in the seismic hazard parameters along with the models of source zones and the GMPEs, a set of 100 values of each of the seismic hazard parameters generated using Monte Carlo simulation was added in the analysis to see their effect on COV maps. For the purpose the area in Delhi city was earmarked to estimate the SGM. The SGM was generated for the acceleration spectra with time periods considered as 0.01, 0.1, 0.2, 0.3, 0.5, 0.75, 1.0, 1.5 and 2.0 sec for the return periods of 100, 225, 475, 2500 and 10000 years. One of the conspicuous observations is that the trends of COV maps are governed by the boundaries of the seismogenic sources. While the COV values are governed mostly by line sources in smaller return and time periods, in higher return periods trend of the maps is governed by the boundaries of the areal sources. The central part of Delhi (which is away from the boundaries of the seismogenic sources) has minimum COV values. In the present study the PGA values for 225 and 475 years of return periods have been estimated in the range of 0.06g to 0.1 lg and 0.09g to 0.16g, respectively, with higher values observed to be in the Northwest part of Delhi. The PGA values estimated for Delhi region in the present study falls between 0.18 to 0.3lg corresponding to return period of 2500 years. VI The strong ground motion estimated at the bed rock level along with the uncertainties may be used for the estimation of ground motion at the surface by including the local site effects for seismic microzonation of the area in Delhi.