抛物线拉冬变换消除多次波的应用要素分析

Analysis of applied factors for using parabolic Radon transform to remove multiple.

抛物线拉冬变换(PRT)在国外已是消除多次波的最有效方法之一,但国内却很少应用。其中一个重要原因就是对抛物线拉冬变换的物理意义、适用条件、算法和参数的选择等关键问题缺乏足够的认识。本文在模型研究的基础上,通过理论模型试验,分别讨论了时间域拉冬变换的特点和存在的问题、频率域拉冬变换的不同实现方法及其应用效果、拉冬域的假频问题、复系数矩阵方程的求解和白噪系数的选取、拉冬域多次波切除和截断效应、自适应滤波切除等应用要素,获得了一些有指导意义的结论1时间域PRT不宜直接使用;2频率域正变换最小平方法有利于消除多次波;3拉冬域的参数取值要满足采样定理;4求解复系数方程组白噪系数宜取0.1～1;5加一巴特沃兹滤波器式的增益函数可实现自适应滤除多次波。应用本文方法对实际资料进行处理,取得了很好的应用效果。

Parabolic Radon transform is one of the effective methods for removing multiple abroad,but unfortunately is less used at home.One of the important reasons is lack of enough knowledge about the key problems such as physical meaning of parabolic Radon transform,its adaptive conditions,algorithm and selection of parameters etc. On the basis of model study and through theoretical model test,the paper separately discussed the characters and existed problems of Radon transform in time domain,different realizing ways and applied effects of Radon transform in frequency domain,alias of Radon domain,solution of complex coefficient matrix equation and selection of white coefficient,mute and truncation effects of multiple in Radon domain and self adaptive filtering mute etc.,acquired some useful conclusions:①PRT in time domain can't be directly used;②the least square method of forward transform in frequency domain is of benefit to removing multiple;③the parameter values in Radon domain should meet the sampling theorem;④the selected white coefficient of solving complex coefficient equation is in a region of 0.1~1.0;⑤to add a gain function similar to Butterworth filter can realize self adaptive filtering of multiple.Using the method presented in the paper for practical data processing achieved a good applied results.