The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential t...The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.展开更多
地面磁共振探测(Surface Magnetic Resonance Sounding,SMRS)是近年来发展起来的一种地球物理新方法,这种在地面直接探测地下介质中氢核丰度的技术,不仅可以用于缺水地区的地下水资源勘查与评价,还可以在地下水引起的堤坝渗漏、滑坡、...地面磁共振探测(Surface Magnetic Resonance Sounding,SMRS)是近年来发展起来的一种地球物理新方法,这种在地面直接探测地下介质中氢核丰度的技术,不仅可以用于缺水地区的地下水资源勘查与评价,还可以在地下水引起的堤坝渗漏、滑坡、海水入侵等地质灾害水源的探测预警中发挥独特的作用.本文首次提出了地下磁共振探测方法(Underground Magnetic Resonance Sounding,UMRS),将SMRS方法引入到地下工程领域,实现隧道工程和煤矿开采等地下狭窄空间极端环境的探测.为应用UMRS方法,需要深入研究地下水超前探测理论、准全空间处理与反演方法、旋转多匝小线圈探测模式,强电磁干扰环境自适应噪声压制策略、以及复杂地质环境磁共振与瞬变电磁联合探测关键技术等难题.论文还简要介绍了超导磁探测技术和工程盾构及掘进实时探测等新技术在地下工程生产安全探测预警中的应用前景.展开更多
基金the National Natural Science Foundation of China under Grand No.549974011
文摘The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.
文摘地面磁共振探测(Surface Magnetic Resonance Sounding,SMRS)是近年来发展起来的一种地球物理新方法,这种在地面直接探测地下介质中氢核丰度的技术,不仅可以用于缺水地区的地下水资源勘查与评价,还可以在地下水引起的堤坝渗漏、滑坡、海水入侵等地质灾害水源的探测预警中发挥独特的作用.本文首次提出了地下磁共振探测方法(Underground Magnetic Resonance Sounding,UMRS),将SMRS方法引入到地下工程领域,实现隧道工程和煤矿开采等地下狭窄空间极端环境的探测.为应用UMRS方法,需要深入研究地下水超前探测理论、准全空间处理与反演方法、旋转多匝小线圈探测模式,强电磁干扰环境自适应噪声压制策略、以及复杂地质环境磁共振与瞬变电磁联合探测关键技术等难题.论文还简要介绍了超导磁探测技术和工程盾构及掘进实时探测等新技术在地下工程生产安全探测预警中的应用前景.
