Chebyshev逼近滤波器在位场分离中的应用

在对经典FIR数字滤波器的设计方法进行研究的基础上,提出了一种可以用于位场分离的基于Chebyshev最佳一致逼近原理的FIR滤波器的设计方法。在理论模型实验中,采用基于Hanning窗的低通滤波器计算出的区域异常最大误差为6.266×10^-6 m/s² ,均方差为2.115×10^-6 m/s² ,最大百分比误差为22.2%,而且计算点在±9 km以外的误差均大于10.1%。而利用最佳一致逼近原理分离出的区域场和局部场与理论异常值拟合得较好,曲线基本重合。分离出的区域异常最大误差为3.101×10^-6 m/s² ,均方差为0.989×10^-6 m/s² ,最大百分比误差仅在边部的几个数据上,为7.76%,其余各点的误差均小于4.1%。实例检验中将该方法用于孙吴—嘉荫剖面布格重力异常场的分离,分离出的区域场中局部场残留少,分离彻底,效果较为理想。

THE APPLICATION OF CHEBYSHEV APPROXIMATION FILTER TO SEPARATING POTENTIAL ANOMALIES

Having investigated the design of classical FIR digital filter, the authors put forward a method of FIR filter design based on Chebyshev best uniform approximation which can be used to separate potential anomalies. In an experiment on the theoretical model, the maximum error of regional anomaly separation by low pass filter of Hanning window is 6.266×10^-6 m/s² , the mean square error is 2.115×10^-6 m/s², and the maximum percentage error is 22.2%. The errors are always higher than 10.1% when the computing points are beyond ±9 km. On the contrary, regional and residual anomalies separated by the best uniform approximation theory fit fairly well with the theoretical anomaly, with the curves in fairly good agreement. The maximum error of regional anomaly separation is 3.101×10^-6 m/s² , the mean square error is 0.989×10^-6 m/s² , and the maximum percentage error is 7.76% for several data on the boundary and is lower than 4.1% for the other points. The method was used to separate Bouguer gravity anomalies along the Sunwu-Jiayin profile with satisfactory results obtained. It is proved that the anomaly separation is quite complete.