عنوان مقاله [English]
A fully Monte Carlo Simulation (MCS) that applies to the across region in each step, allows incorporation spatial correlations in each step conditional on the previous step and each simulation must repeat each several times; therefore, the size of computation is concern. The size of computation can be reduced at each step by developing scenarios. The relatively small set of probabilistic scenarios represents the full set obtained from a MCS.
In order to consider spatial correlation of individual earthquake scenarios as well as when computational demands are of concern, the optimization-based probabilistic scenario (OPS) method are presented. This method is very appropriate approach that could be applied to a region with high seismicity and effect on the regional loss estimation and regional policy decisions. The OPS method can be important: 1- It is easy for users to understand, 2-The spatial correlation of the ground motion is recorded across the region, 3- It also eliminates concerns about the computation size. This method has a simple concept to record the temporal changes of vulnerability model. We use source–magnitude combination to obtain hazard-consistent annual occurrence probabilities.
The OPS method produces a small set of probabilistic seismic scenarios instead of the millions number of scenarios to estimate the seismic hazard and loss estimation of lifelines. This method has a clear framework, includes a step-by-step method for producing earthquake scenarios and ground motion maps. After producing a relatively small set of seismic scenarios, the hazard-consistent annual occurrence probabilities of scenarios are estimated; so that their effect on the across the region approximates that described by given return period maps. For each ground motion map, a set of damage maps are then calculated. Finally, for each damage map, the lifeline system performance is estimated as a function of the system damage. The resulting database of performance levels and associated occurrence probabilities then describe the lifeline risk. Evaluation metrics for computation of the hazard curve errors and spatial correlations errors, introduced by Han and Davidson (2012).
We apply the optimization-based probabilistic scenario method to identify the minimum number of scenarios. These scenarios can be used to loss estimation of Qom lifelines. The city of Qom is situated approximately in central Iran. Hazard curves for nine control points have been provided by PSHA, to generate probabilistic scenarios. These nine control points have been located on the study area boundary and equal distance of 12.5 km from each other.
Using OPS method, open source solvers and time-independent hazard analysis, has been presented a set of probabilistic seismic scenarios for Qom. First, the output of the conventional Monte Carlo simulation for 1 million years includes 1609087 simulated scenarios. Then scenarios have reduced to 55645 scenarios based on the ‘true’ hazard curve. Finally, the reduced set of earthquake scenarios based on optimization includes three scenarios. The scenarios obtained by the PULP_CBC_CMD and Gurobi 8.0 solvers are the same.
Based on the evaluation metrics, the errors are in the appropriate range and there is no unintended bias in the results. The errors are small, 81% of errors in range of ±10%, 91% in range of ±30% and mean hazard curve error is 7.34%. By comparison of the ‘true’ and the reduced set hazard curves in all sites, site 9 has highest average HCEir. For the city of Qom, have been ensured that the difference between the ‘true’ hazard and the reduced set is minimum.
It is now possible to extend the probabilistic scenarios for Qom, thus overcoming limitations of the other hazard-consistent probabilistic scenario approaches. In this paper, the hazard is only measured by the PGA, but other terms (such as PGV, SA…) can be considered for the city of Qom.