离散复镜像理论对近地电偶极子的应用

DISCRETE COMPLEX IMAGE THEORY FOR ELECTRIC DIPOLES ABOVE THE GROUND

对近地电偶极子赫芝矢位中的索末菲积分,仅用 Prony 法,对其被积函数分式部分进行指数函数逼近,可得到近地电偶极子的一串离散镜像,而这类积分就可看作这些镜像在观察点的解。采用此方法大大节省了计算时间,所得结果与沿实轴数值积分结果吻合很好。对索末菲积分在实轴上可能遇到的奇异点,采用分部积分法消去之,避免了给数值积分带来的麻烦。

This paper deals with the evaluation of Sommerfeld integrals that appearin the Hertz vectors of electric dipoles near the ground.The discrete images of an electricdipole above the ground can be abtaind by using Prony's method only,i.e.make case of aseries of expanential functions with different complex coefficients to approximate the frac-tion part in a Sommerfeld type integral.So this kind of integral can be thought as the solu-tion of these discrete images.Utilizing the method can decrease much CPU time.The re-suits agree with the ones of numerical intrgration along real axis.The singular point onthe real axis,can be eliminated using partial integrated method.The touble can be avoid-ed when integrate along real axis.