短垂直阵“简正波分解矩阵”特征值的近似解析表达式

An approximate-analytic expression of the eigenvalues of“mode decomposition matrix”for a short vertical array

在海面和海底反射系数均为－1的理想波导条件下，讨论短垂直阵“简正波分解矩阵”的特性，给出矩阵特征值λn与阵长参数D／H（D为阵长，H为海深）和n之间的近似解析表达式。海面矩阵的λn正比于参数α（即πD／H）的（4n－1）次方，而海中短阵λn正比于α2n－1．理论推导不仅解释了短垂直阵分解声场简正波或匹配场处理效果差的原因，同时指出合理选择短阵深度，将有效提高商正波分解能力和声源定位精度。

The characteristics of 'mode decomposition matrix' for a short vertical array in an ideawaveguide model with the reflective coefficients of both sea-surface and bottom to be equal －1 arediscussed, and the approximate-analytic expression of the eigenvalues λn with the parameters D/H (Dis the length of array, H is the depth of sea water) and n are obtained. The eigenvalues λn. for a seasurface short array is proportional to the (4n-1) power of α(πD/H), while the eigenvalues λn. for asea-middle short array is proportional to α2n－1. The theory derivation we have done in this paper canbe used to explain why the ability of decomposing mode and matched-field processing are poor, and toimprove the quality of mode decomposition and the accuracy of source localization when the depth ofarray is selected reasonably.