强地震动估计中映射法四种映射原则的数学表达

Mathematical Representation for Four Mapping Principles of Mapping Method in Strong Ground Motion Evaluation

运用数学语言对四种映射原则进行阐述,得到四种映射原则对应的数学映射关系;为方便地震动衰减关系转换数值计算设计了计算流程;并以美国西部为参考区,导出了云南地区的基岩水平向地震峰值加速度衰减关系。结果表明本文给出的四种数学映射关系和设计的数值计算流程在转换过程中是可行的,最小扭曲映射原则、最小扭曲可逆映射原则得出的结果在某种程度上要优于IR映射原则、IM映射原则得出的结果。

Four mapping principles are illustrated by means of mathematical language to attain their corresponding mathematical mapping relations.The computing process is designed to facilitate the numerical computation of transformation for ground motion attenuation relation.Taking Western America as the reference area,the horizontal earthquake peak acceleration attenuation relation on bedrock in Yunnan is deduced.The results show that four mathematical mapping relations and the designed numerical computing process are feasible in the course of transformation.Besides,the results of minimal warping mapping principle and minimal warping reversible mapping principle are superior to results of IR mapping principle and IM mapping principle.