二维Wiener滤波器及在物探中应用的一些问题

本文结合二维随机场函数z（x,y）及其统计特征、平稳性和各态遍历性的概念,导出了二维Wiener滤波器的两个波数响应H_opt（u,v）和 _opt（u,v）,并详细地讨论了导出它们的条件。为了正确地应用Wiener滤波技术,我们提供了检验物探观测数据的平稳性和各态遍历性的简单而适用的方法。最后还指出,当应用Wiener滤波的不相关技术时,将在区域异常的谱函数中引入一个非线性畸变因子,这个区域异常是从具有局部干扰的观测数据中提取的。于是,所提取的区域异常必然会产生某种程度的失真。

TWO DIMENSIONAL WIENER FILTER AND SOME PROBLEMS OF APPLICATION IN GEOPHYSICAL PROSPECTING

In this article we have derived two wave-number responses H_opt（u,v） and H_opt（u,v）of Wiener filter and have discussed the conditions deriving them in detail, in association with the concepts of 2-D. stochastic field function z（x,y） and its statistic characters, stationarity and ergodic. In order to apply Wiener filtering technique correctly, we have presented simple and applicable methods detecting the stationarity and the ergodic of the observing data in geophysical prospecting. Finally, we also indicated that, when non-correlation technique of Wiener filtering will be used, a non-linear distortional factor G（u,v） will be introduced in the spectral function of regional anomaly, extracting from observing data with the local disturbance. Thus, the extracting regional anomaly must generate the distortion to a certain extent.