Updated Probabilistic Seismic Hazard Assessment of Pakistan

Probabilistic seismic hazard assessment of Pakistan is carried out to compute hazard in terms of peak ground acceleration (PGA) and spectral acceleration (SA) for 975 and 2475 years return periods. A composite earthquake catalogue consisting of 32,700 events has been compiled having a magnitude range of Mw 4.0-8.2 in this study and used in the analysis to make computations at a rectangular grid of 5 km in the OpenQuake plateform. Ground motion values have been obtained for flat rock reference seismic site conditions with shear wave velocity of 760 m/s. The epistemic uncertainties inherent in ground motion prediction equations and maximum magnitude potential of seismic sources are taken into account through logic tree. Ground motion prediction equations are assigned equal weights in the logic tree while different various weight are assigned to the maximum magnitude potential models. Results of the study are expressed as ground motion contour maps, mean uniform hazard spectra for important cities in Pakistan. PGA ranges from 0.16 to 0.54g for 10 % of probability of exceedance, 0.23 to 0.72g of probability of exceedance 0.32 to 1.02 g for 2 % of probability of exceedance in 50 years. Spectral acceleration at 0.2 s range from 0.67 to 2.19g for 2% chance of exceedance in 50 years, respectively. While spectral acceleration at 1.0 s values range from 0.09 to 0.52g 2% chance of exceedance in 50 years. Comparison of results of this study with other well regarded references of suggest that results of the study are rational and are reliable.

Propagation of epistemic uncertainty in magnitude–frequency relations through PSHA using predictive distributions

The current practice of Probabilistic Seismic Hazard Analysis (PSHA) considers the inclusion of epistemic uncertainties involved in different parts of the analysis via the logic-tree approach. Given the complexity of modern PSHA models, numerous branches are needed, which in some cases leads to concerns regarding performance issues. We introduce the use of a magnitude exceedance rate which, following Bayesian conventions, we call predictive exceedance rate. This rate is the original Gutenberg–Richter relation after having included the effect of the epistemic uncertainty in parameter β. The predictive exceedance rate was first proposed by Campbell but to our best knowledge is seldom used in current PSHA. We show that the predictive exceedance rate is as accurate as the typical logic-tree approach but allows for much faster computations, a very useful property given the complexity of some modern PSHA models.

Modelling earthquake rates and associated uncertainties in the Marmara Region, Turkey

Modelling the seismic potential of active faults and the associated epistemic uncertainty is a fundamental step of probabilistic seismic hazard assessment (PSHA). We use SHERIFS (Seismic Hazard and Earthquake Rate In Fault Systems), an open-source code allowing us to build hazard models including earthquake ruptures involving several faults, to model the seismicity rates on the North Anatolian Fault (NAF) system in the Marmara Region. Through an iterative approach, SHERIFS converts the slip rate on the faults into earthquake rates that follow a magnitude frequency distribution (MFD) defined at the fault system level, allowing us to model complex multi-fault ruptures and off-fault seismicity while exploring the underlying epistemic uncertainties. In a logic tree, we explore uncertainties concerning the locking state of the NAF in the Sea of Marmara, the maximum possible rupture in the system, the shape of the MFD and the ratio of off-fault seismicity. The branches of the logic tree are weighted according to the match between the modelled earthquake rate and the earthquake rates calculated from the local data, earthquake catalogue and palaeoseismicity. In addition, we use the result of the physics-based earthquake simulator RSQSim to inform the logic tree and increase the weight on the hypotheses that are compatible with the result of the simulator. Using both the local data and the simulator to weight the logic tree branches, we are able to reduce the uncertainties affecting the earthquake rates in the Marmara Region. The weighted logic tree of models built in this study will be used in a following article to calculate the probability of collapse of a building in Istanbul.

A procedure to develop a backbone ground-motion model: A case study for its implementation

The backbone modeling in ground-motion characterization (GMC) is a useful methodology to describe the epistemic uncertainty in median ground-motion predictions. The approach uses a backbone ground-motion model (GMM) and populates the GMC logic tree with the scaled and/or adjusted versions of the backbone GMM to capture the epistemic uncertainty in median ground motions. The scaling and/or adjustment should represent the specific features and uncertainties involved in source, path, and site effects at the target site. The identification of the backbone model requires different considerations specific to the nature of the ground-motion hazard problem. In this article, we present a scaled backbone modeling approach that considers the magnitude- and distance-scaling predictors as well as their correlation to address the epistemic uncertainty in median ground-motion predictions. This approach results in a trivariate normal distribution to fully define a range of epistemic uncertainty in a model sample space. The simultaneous consideration of magnitude and distance scaling while defining the epistemic uncertainty and the methodology followed for the simplified representation of trivariate normal distribution in ground-motion logic tree are the two important features in our procedure. We first present the proposed approach that is followed by a case study for Central and Eastern North America (CENA) stable continental region. The case study discusses the underlying assumptions and limitations of the proposed approach.

Conditional probability of distributed surface rupturing during normal-faulting earthquakes

Coseismic surface faulting is a significant source of hazard for critical plants and distributive infrastructure; it may occur either on the principal fault or as distributed rupture on nearby faults. Hazard assessment for distributed faulting is based on empirical relations which, in the case of normal faults, were derived almost 15 years ago using a dataset of US earthquakes. We collected additional case histories worldwide, for a total of 21 earthquakes, and calculated the conditional probability of distributed faulting as a function of distance from the principal fault. We found no clear dependency on the magnitude nor the time of occurrence of the earthquakes, but our data consistently show a higher probability of rupture when compared with the scaling relations currently adopted in engineering practice. We derive updated empirical regressions and show that the results are strongly conditioned by the averaging of earthquakes effectively generating distributed faulting at a given distance and those which did not generate faulting; thus, we introduce a more conservative scenario that can be included in a logic tree approach to consider the full spectrum of potential ruptures. Our results can be applied in the framework of probabilistic assessment of fault displacement hazard.

Simplified methods to estimate mean hazard due to updated ground motion model: Application to nuclear power plants in CEUS

Two methods were developed to estimate updated mean seismic hazard for existing probabilistic seismic hazard analyses (PSHAs) due to a change in the ground motion model (GMM). Both methods were used to estimate updated hazard at nuclear power plant (NPP) sites in the Central and Eastern United States (CEUS) for a change from the Electric Power Research Institute (EPRI) 2013 GMM to the Next Generation Attenuation (NGA)-East GMM. These methods present efficient tools to inform decisions on whether to perform a full PSHA revision or other detailed evaluations, especially when a large number of sites must be analyzed. A Simplified Hazard (SiHaz) method was developed to estimate mean hazard explicitly using a reduced PSHA logic tree that incorporates the updated GMM and potential changes in the site response model. An alternative scaling method was independently developed to be applied directly to current CEUS NPP hazard. Both methods were validated using updated PSHA results at several sites. Estimates at 46 NPP sites using both methods showed good agreement for mean annual frequencies of exceedance between 1E-4 and 1E-5/yr.

A Bayesian Approach to Estimate Weights for GMPE Models in a Logic Tree

In current practice, the seismic hazard curves are generated by combining all possible choices for seismotectonic model (SM), earthquake magnitude recurrence models, and ground motion prediction equation (GMPE) models using logic trees. However, studies have shown that significant uncertainties exist in the evaluation of the seismic hazard, especially in low-to-moderate seismicity regions, such as Central \& Eastern United States and Europe, due to the scarcity of the recorded earthquake data and lack of precise knowledge concerning the earthquake generation and propagation mechanisms. Specifically, these uncertainties lead to conservatisms in the seismic hazard which poses a considerable risk for nuclear facilities. Designing or upgrading facilities with such conservative estimates of seismic hazard results in large capital costs. In standard probabilistic seismic hazard assessment (PSHA) practices, the estimate of branch weights for the GMPE models is based on expert judgment and there is no holistic approach for estimating the weights under uncertainty. In this research, we focus on the GMPE part of the PSHA and we propose a statistical methodology that is based on Bayesian inference, to evaluate the GMPE model weights from a list of GMPE models in the logic tree. In this study, Bayesian model averaging (BMA) approach with Bayesian linear models (BLM) is employed to combine GMPE models and the performance of the BMA model is tested against European Strong-Motion (ESM) database. It is shown that the proposed methodology can calculate the weights at different time periods without any approximations using analytical formulas and it is computationally inexpensive.