The Fresnel volume and transmitted waves

作     者：Spetzler, J Snieder, R 

作者机构：Delft Univ Technol Dept Geotechnol NL-2600 GA Delft Netherlands Colorado Sch Mines Dept Geophys Golden CO 80401 USA Colorado Sch Mines Ctr Wave Phenomena Golden CO 80401 USA 

出 版 物：《GEOPHYSICS》 (Geophysics)

年 卷 期：2004年第69卷第3期

页      面：653-663页

核心收录：

学科分类：07[理学] 0708[理学-地球物理学] 

基　　金：European Commission  EC  (NNE5-1999-20211) 

主　　题：.seismic imaging traveltime sensitivity called equation perturbation propagate geometric source and receiver ray theory slowness kernels ected Fresnel ray path transmitted TUTORIAL nite-frequency wave 

摘      要：In seismic imaging experiments, it is common to use a geometric ray theory that is an asymptotic solution of the wave equation in the high-frequency limit. Con- sequently, it is assumed that waves propagate along in- nitely narrow lines through space, called rays, that join the source and receiver. In reality, recorded waves have a nite-frequency content. The band limitation of waves implies that the propagation of waves is extended to a nite volume of space around the geometrical ray path. This volume is called the Fresnel volume. In this tutorial, we introduce the physics of the Fresnel volume and we present a solution of the wave equation that accounts for the band limitation of waves. The nite-frequency wave theory species sensitivity kernels that linearly re- late the traveltime and amplitude of band-limited trans- mitted and reected waves to slowness variations in the ***-frequencysensitiv- ity kernels are closely connected through the concept of constructive interference of waves. The nite-frequency wave theory leads to the counterintuitive result that a pointlike velocity perturbation placed on the geometric ray in three dimensions does not cause a perturbation of the phase of the waveeld. Also, it turns out that Fer- mat s theorem in the context of geometric ray theory is a special case of the nite-frequency wave theory in the limit of innite frequency. Last, we address the miscon- ception that the width of the Fresnel volume limits the resolution in imaging experiments.