Cornell’s, Esteva’s, and classical formulations for seismic hazard analysis are theoretically described and mathematically unified by a suitable treatment of the random ground‐motion variable. Differences and connections among the schemes are discussed, allowing for a better understanding of the underpinning principles of probabilistic seismic hazard analysis. The classical formulation is equivalent to that by Esteva, and they correspond to a general scheme. Although they are mathematically equivalent, the two formulations each has its own particular approach to express the hazard rate, so results may differ. Cornell’s original scheme is a particular case of classical and Esteva’s formulation. It is also shown that intensity exceedance rates for any index of structural performance or at a particular site can be recursively transformed into exceedance rates of other intensity indexes. Formulations are invariant under such a transformation.

中文翻译：

---

概率地震危险性分析不同方法的统一

通过对随机地面运动变量的适当处理，从理论上描述了康奈尔公式，Esteva公式和用于地震危险性分析的经典公式，并在数学上统一了这些公式。讨论了方案之间的差异和联系，以便更好地理解概率地震灾害分析的基本原理。经典公式等效于Esteva的公式，并且它们对应于一般方案。尽管它们在数学上是等效的，但这两种配方各自都有其表达危险率的特定方法，因此结果可能有所不同。康奈尔（Cornell）的原始方案是古典主义和Esteva制定的特殊案例。还表明，对于任何结构性能指标或在特定位置的强度超标率可以递归转换为其他强度指标的超标率。在这种转换下，配方是不变的。