Department of Civil Engineering,Indian Institute of Science, Bangalore

Ground Motion Prediction Equation

Ground shaking during an earthquake is responsible for the damages to structures and ground failures within the epicentral region as well as at far distances due to site effects. Seismic hazard analysis estimates these ground shaking in terms of PGA (Peak Ground Acceleration) for a region. Region specific Ground Motion Predictive Equation (GMPE) is an important input in the seismic hazard analysis for macro and micro zonation. Several seismic hazard maps are being produced in India using available attenuation relations with or without checking its degree of fitness or developing representative GMPE for the regions. Himalayas are one of the most active seismic regions in the world and many researchers have highlighted the prospect of big seismic event in the near future. This region is experiencing earthquake from prehistoric times, but GMPE development started only after 1996.

Most suitable GMPE is one which considered region attenuation character, seismotectonic behaviour and capable of predicting seismic future potential of the region. Number GMPEs developed in India is very less when compared to similar seismic region in the rest of world. Most GMPEs developed in India based on regional recordings are applicable to limited distance and magnitude range. The GMPE developed based on synthetic data are by taking attenuation and seismotectonic parameters of other region. First time we have studied attenuation and seismotectonic parameters of Peninsular India and North India using seismic events recoded at region at bedrock stations.

GMPE for PI: A new stochastic GMPE for low and diverse seismicity region, i.e., Peninsular India has been derived for a wide range of magnitude (Mw 4-8) and distance (10-500 km) in our research. Source, path, and site terms have been determined by comparing the recorded and simulated response spectra using derived values from the literature. To capture the non-uniform seismicity of Peninsular India, GMPE has been derived using constant stress and variable stress model. The synthetic data has been regressed using linear mixed-effect model algorithm by determining the functional form that is compatible for magnitude and distance scaling. Further, new GMPEs have been validated using the recorded ground-motion data. The GMPEs functional form given below has been used for deriving the coefficients at different spectral periods considering variable and constant stress drop.

The regression coefficients corresponding to c1, c2, c3, c4, c5, c6 and c7 for different periods considering variable and constant stress drop are given in Table 3 and 4 in our paper Ketan Bajaj and P Anbazhagan (2019). "Regional stochastic ground-motion model for low to moderate seismicity area with variable seismotectonic: application to Peninsular India" Bulletin of Earthquake Engineering Doi: https://doi.org/10.1007/s10518-019-00646-9.

GMPE for North India: New ground motion prediction equation for the active Himalayan region for a wide range of moment magnitude (???? 4-9) and distance (10-750 km) is developed. For simulating the synthetic ground motions; source, path, and site terms are derived using the Fourier amplitude spectrum of the recorded ground motion data in Himalayan Region. Systematic analysis has been carried to Determine the best GMPE functional form for an active region with limited strong motion data: Application to the Himalayan region by Bajaj and Anbazhagan (2018) published in Journal of Seismology, 22(1):161-185. Further synthetic ground motion has been generated using regional seismotectonic parameters and recorded data. Both data are regressed using random-effect maximum likelihood regression algorithm. Best representing GMPE functional form for Himalayan region based on available data is suggested as:

The regression coefficients corresponding to a1, a2, a3, a4, a5, a6, a7 and a8 for different periods are given in Table 4 in our paper Ketan Bajaj and P Anbazhagan (2019). "Regional seismological model parameter estimation and development of GMPE model for the active region of Himalaya" Soil Dynamics and Earthquake Engineering, Published online:https://doi.org/10.1016/j.soildyn.2019.105825. Predicted and recorded response spectra are matching within ±1 standard deviation for the entire period range.

Selection of GMPEs, Ranking and Weights

Seismic hazard analysis provides an estimation of seismic hazard parameters like peak ground acceleration (PGA) or spectral acceleration (SA) for different periods. The extent of ground shaking and the hazard values at a particular region are estimated using ground-motion prediction equations (GMPEs)/attenuation equations. There are several GMPEs applicable for the region to estimate the PGA and SA values. These equations may result in higher or lower PGA and SA values than the region-specific reported values, which are based on the parameters involved in the development of GMPEs. We have given systematic identification of the best GMPEs for various parts of Peninsular India (PI) by performing an "efficacy test," which makes use of the average log likelihood value (LLH). Macroseismic intensity maps of these earthquakes have been digitalized and European Macroseismic Scale (EMS) values at the surface have been synthesized. PGA value determined from each GMPE for known magnitude and hypocentral distances are then converted to EMS values. These calculated EMS values have been used to estimate LLH values which are further used to compute Data Support Index (DSI), rank and weights corresponding to a particular GMPE. Conventionally, LLH values are estimated for the entire distance range and GMPEs are ranked accordingly, but in our study, the LLH is calculated for the distance segments of 0-200 km and 200 km to maximum damaged distance in the region based on Isoseismal maps. If the maximum damaged distance is less than 200 km, a distance segment up to 200 km is adopted. Comparison between the rankings of the GMPEs in segments 0-200 km and 200-maximum damage distance is presented here. Segment-based GMPEs ranking shows different ranks, DSI and weights for each GMPE as compared to ranking considering entire distance. More information can be found in Anbazhagan P, Sreenivas M, Ketan B Sayed SR Moustafa and Nassir S.N. Al-Arifi (2016). "Selection of Ground Motion Prediction Equations for Seismic Hazard Analysis of Peninsular India", Journal of Earthquake Engineering, Vol.20 (5), 699-737; DOI: 10.1080/13632469.2015.1104747.

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