余弦变换和Fourier变换在位场数据处理与转换中的对比研究  

Study of contrast in processing and transformation of field data based on cosine transform and Fourier transform

作　　者：罗新刚 王万银[1] 

机构地区：[1]长安大学重磁方法技术研究所长安大学地质工程与测绘学院长安大学西部矿产资源与地质工程教育部重点实验室,西安710054

出　　处：《地球物理学进展》2017年第3期1197-1207,共11页Progress in Geophysics

基　　金：中央高校基本科研业务费专项资金(2014G3262010;310826163301)资助

摘　　要：余弦变换是一种实数域变换方法,Fourier变换是一种复数域变换方法.而位场数据是实数,因此对于余弦变换来讲可以直接使用;但对Fourier变换需要将实数转化为复数才可以使用,这样就降低了效率.本文通过整理余弦变换和Fourier变换的定义、性质、快速算法的计算量以及在位场数据处理和转换上的频率响应,对余弦变换和Fourier变换进行对比研究.通过对比表明,余弦变换的性质、频率响应均比Fourier变换复杂;余弦变换快速算法的计算量比复数域Fourier变换的计算量少一倍,但与实数域Fourier变换的计算量相当.理论模型测试和实际资料处理结果表明,余弦变换和Fourier变换在位场数据处理和转换方面的计算精度相当,且计算量也基本相同.因此,Fourier变换用于位场数据处理和转换时比余弦变换更具有优势.The Cosine transform is a transformation method in real domain,and the Fourier transform is a complex field transformation method. So the potential field data,which is a real number,can be used directly in Cosine transform. However,it needs to convert potential data into complex domain in Fourier transform,which will lower the calculation efficiency. In this paper,we have compared the Cosine transform with the Fourier transform by definition,properties,the computational time of the fast algorithm and the frequency response in potential field data processing and transformation. The result of comparison exhibits that Cosine transform is more complicated than Fourier transform in properties and frequency response,and takes half of time of the complex domain Fourier transform,but almost the same with the real domain Fourier transform. The results of theoretical model test and practical data processing shows that the calculation accuracy of potential field data processing and transformation based on Cosine transform equals to that based on the Fourier transform as well as in computational time.Therefore,Fourier transform takes more advantage than Cosine transform in the field data processing and transformation.

关 键 词：余弦变换 FOURIER变换 位场数据处理和转换 频率响应 计算精度 计算量 

分 类 号：P631[天文地球—地质矿产勘探]