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The conditional mean spectrum (CMS) and its generalized forms, like the generalized CMS (GCMS), and the CMS conditioned at the logarithm-average spectral acceleration over a period range (CMS-AvgSa), are anchored on a conditional period (or periods) with a target hazard level. This study evaluated the vector hazard of multiple spectral accelerations (Sa) at different periods for CMS, GCMS, and CMS-AvgSa. By invoking the invariance property of scalar disaggregation and Copula function, we developed the computational methods for three types of multivariate exceedance rate (MER): multivariate simultaneous exceedance rate (MERs), multivariate arbitrary exceedance rate (MERa), and Kendall-function-based MER (MERk). Taking the cities of Xi'an and Kunming (China) as examples, scalar probabilistic seismic-hazard analysis (PSHA), and disaggregation were performed and CMS was built at different conditional periods (T* = 0.05, 0.2, 1.0, and 2.0 s, respectively). The MERk computation results lies between the other two extreme cases (MERa and MERs), which are either too strict or too tolerant compared with the anchored hazard level. It is found that when the earthquake disaggregation characteristics not differ markedly between T* and other periods in CMS, the calculated MERk results would be roughly consistent with the anchored hazard level at Sa(T*). The conclusion holds true when different Sa(T) were considered in the calculation of MERk. On the other hand, the calculated MERa and MERs would be significantly influenced by the choice of Sa(T) and the results are not comparable with the anchored hazard level. We also evaluated the MERk for GCMS and CMS-AvgSa, which were constructed using mean scenario earthquake from vector-valued PSHA and disaggregation. Comparing with the UHS, the MERk of GCMS and CMS-AvgSa are more close to the anchored hazard level within a certain period range. Although no benchmark exists for vector hazard level, the MERk is likely to be a promising approach for measuring the hazard over a vector of intensity measures in target spectrum. [ABSTRACT FROM AUTHOR]

For mainland China, the primary obstacle in conditional spectrum (CS) based ground motion selection work is that the corresponding seismic hazard disaggregation results were not released for the China national standard GB 18306–2015 "Seismic Ground Motion Parameter Zonation Map", which refers to the fifth-generation seismic hazard map. Therefore, this study firstly constructed a probabilistic seismic hazard map for mainland China using the three level seismicity source models as applied to produce the fifth-generation seismic hazard map. The derived peak ground acceleration (PGA) values in our seismic hazard map were basically consistent with the PGA range bins in fifth-generation seismic hazard map for most of the 34 principal cities considered. Then, a three-dimensional disaggregation scheme was performed for PGA and 5%-damped spectral acceleration (Sa) corresponding to mean return periods of 475 and 2475 years. The results clearly identified the potential source areas and corresponding fault zones that dominate the hazard of the target cities regarding different intensity measures. Based on the magnitude-longitude-latitude disaggregation results of three example cities: Xichang, Kunming, and Xi'an, approximate and exact CS were established with/without considering multiple casual earthquakes and possible strike directions of the potential source areas. The mean exact CS lies between the results of approximate CS using long and short axis GMMs. The conditional standard deviation of exact CS is approximately 1.1–1.5 times larger than the approximate CS for the periods away from the conditional period. For three example cities, hazard consistency of the spectral accelerations of the ground motion realizations were validated for matching exact CS and approximate CS. The results suggested that the geometric mean approximate CS without inflation of standard deviation is a practical choice when the target exceedance rate was not too low. Moreover, for the 34 studied cities, we tabulated the uniform hazard curve and disaggregation results for PGA and Sa values (0.2, 0.3, 0.5, 0.7, 1.0, 1.5, and 2.0 s) at mean return period of 475 and 2475 years (https://github.com/JIKUN1990/China-Seismic-Hazard-Deaggregation-34cities). [ABSTRACT FROM AUTHOR]