非水平分层区域Helmholtz边值问题的解析解
The Analytical Solution for Helmholtz Boundary Problem in Non Horizontally Stratified Domains
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摘要: 在(x,y,z)直角坐标系中,N个物性参数不同的区域Dj(j=0,1,…,N-1)充斥着整个空间,这些区域间的分界面是非水平的光滑曲面Sj,j+1下面的边值问题称为非水平分层区域Helmholtz边值问题:∇2H(j)+KjH(j)=0(j=0,1,…,N-1)(H(0)-H(1))S0.1=δ(S)(δ(S):广义δ-函数)(H(j)-H(j+1))Sj,j+1=0(j=1,…,N-2)本文给出了此问题的解析解.Abstract: There are N domains Dj(j=0,1,...,N-1) of different physical parameters in the whole space and their interfaces Sj,i+1 are non-horizontally smooth curved surfaces. The following boundary problem is called Hclinholiz boundary problem:∇2H(j)+KjH(j)=0 (j=0,1,…,N-1)(H(0)-H(1))S0.1=δ(S) (δ(S):generalized function)(H(1)-H(i+1))Sj,j+1=0 (j=0,1,…,N-2)The analytical solution of the above problem is given in this paper.
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