地震波传播的黎曼几何描述  

Riemann geometric description of seismic wave propagation

作　　者：杨孔庆[1,2] 罗明秋 李幼铭[4] YANG Kongqing;LUO Mingqiu;LI Youming(Lanzhou University,Lanzhou 730000,China;Jimei University,Xiamen 361021,China;Sinopec Houston R&D Center,Houston 77056,China;;Institute of Geology&Geophysics,Chinese academy of Sciences,Beijing 100029,China)

机构地区：[1]兰州大学,甘肃兰州730000 [2]集美大学,福建厦门361021 [3]中石化休斯顿研发中心,休斯顿77056 [4]中科院地质与地球物理研究所,北京100029

出　　处：《石油物探》2018年第5期647-651,共5页Geophysical Prospecting For Petroleum

摘　　要：黎曼流形是对弯曲空间的一种几何描述。地震波在复杂介质中传播的弯曲特性,符合黎曼流形的几何特性。以复杂介质中地震波的走时函数为基础,构造地震波在复杂介质中传播的黎曼几何描述,然后根据黎曼几何中协变的标量场波动方程建立了地震波在复杂介质中传播的标量场波动方程;最后讨论了该几何描述在射线追踪、波场模拟等方面的应用。The Riemannian manifold is a geometric description of curved space.Seismic propagation in complex media with a curved ray-path has similar geometric characters to the Riemannian manifold.In this paper,based on the minimized travel time in wave propagation,we propose a seismic wave propagation formulation with Riemannian geometry.The covariant scalar field equation,which complies with the acoustic wave equation in constant media,is used to describe the wave propagation in complex media with complex curved-space properties.Further,we discuss the application of Riemann geometric description in ray-tracing and seismic simulation.

关 键 词：地震波传播 黎曼流形 黎曼度量 测地线 协变方程 射线方程 

分 类 号：P631[天文地球—地质矿产勘探]