Multivariate normality of logarithmic intensity measures (IMs) is conventionally assumed in earthquake engineering applications. This article introduces a vine copula approach as a useful tool for multivariate modeling of IMs. This approach provides a flexible way to decompose a joint distribution into individual marginal distributions and multiple dependences characterized by a cascade of bivariate copulas (pair‐copulas), whereas the conventional multivariate normality can be considered as a special case of the vine copula model. Based on the Next Generation Attenuation‐West1 database and various combinations of ground‐motion prediction equations (GMPEs), the optimal dependence structures among peak ground acceleration, peak ground velocity, and Arias intensity, as well as that for spectral accelerations at four periods, are identified. The joint normality assumption for the two vector sets of logarithmic IMs is examined from the perspective of copula theory. The results illustrate that the normality assumption is generally adequate for bivariate IMs but may not be optimal for multivariate IMs. Using the same set of GMPEs (developed by the same researchers) may improve the joint normality for logarithmic IMs. Furthermore, the impact of dependence structures among IMs on probabilistic seismic slope displacement hazard analysis is explored. The results indicate that using the same Pearson correlation coefficients but different dependence structures for IMs produces different hazard results and this difference is generally enlarged with increasing hazard levels. As hazard difference from different dependence structures is generally not significant, the multivariate normality distribution for logarithmic IMs is judged to be an acceptable assumption in engineering practice. Alternatively, engineers may make a choice between the joint normal distribution and the vine copula tool depending on the specific situation because of the better generality of the latter.

中文翻译：

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基于藤Copula的地面运动强度测度相关模型及其对概率性地震边坡位移危险性分析的影响

通常在地震工程应用中采用对数强度测度（IM）的多元正态性。本文介绍了藤蔓copula方法，作为IM多元建模的有用工具。这种方法提供了一种灵活的方法来将联合分布分解为单个边际分布和以一连串的双变量copula（pair-copulas）为特征的多重依赖关系，而常规的多元正态性可以认为是vine copula模型的特例。基于下一代Attenuation-West1数据库和地面运动预测方程（GMPE）的各种组合，峰值地面加速度，峰值地面速度和Arias强度以及四个周期的频谱加速度之间的最佳依赖关系结构，被识别。从copula理论的角度检查了两个对数IM的向量向量的联合正态性假设。结果表明，正态性假设通常对于双变量IM是足够的，但对于多变量IM可能不是最佳的。使用同一组GMPE（由同一位研究人员开发）可以提高对数IM的关节正常性。此外，还探讨了IM之间的依存结构对概率性地震边坡位移危害分析的影响。结果表明，使用相同的Pearson相关系数，但IM的依赖结构不同，会产生不同的危害结果，并且随着危害水平的提高，这种差异通常会扩大。由于来自不同依赖结构的危害差异通常不大，对数IM的多元正态分布在工程实践中被认为是可以接受的假设。或者，工程师可以根据具体情况在关节正态分布和藤蔓联接工具之间进行选择，因为后者具有更好的通用性。