数论变换与地震信息滤波

NUMBER THEORY TRANSFORMATION SEISMIC SIGNAL FILTER

褶积滤波是地震资料处理中的常用方法,但由于地震数据的数量一般较大,而褶积滤波因子通常又较长,这就给在时间域进行褶积运算带来一定的困难。快速傅立叶变换(FFT)出现之后,人们就把褶积运算从时间域搬到频率域进行,这就是所谓的“快速褶积滤波”(快速相关亦然)。在这个运算过程中所进行的正向和反向傅立叶变换,实质上是一系列包括三角函数在内的复数运算。由于复数运算比实数运算复杂,又需要存放三角函数的地方,并存在舍入误差等不足。因此,近年来在国外和国内一些部门,针对FFT存在的不足之处,开展了所谓“数论变换”的研究,取得了一定的成效。 本文首先简要地介绍一下“数论变换”,然后用数论变换方法,对地震数据进行快速褶积滤波作初步的探索,最后对结果提出了一些看法。

Convolution filter is a method commonly used in seismic data processing. Because of the vast amount of seismic data and the long convolution filter factors, some difficulties might be brought up as the convolution calculation is carrying out in time domain. Right after the appearence of the Fast Fourier Transformation (FFT) , was the convolution calculation run from time domain to frequency domain. This is the so called"Fast Convolution Filter". The way of doing the calculation is, to speak in concrete terms, to carry out the FFT for the seismic data x(t) and the filter factor h(t) respectively for the purpose of changing them into the seismic frequency spectrum X(f) and the frequency spectrum of filter factor H(f), to multiply X(f) by H(f), then, carrying out the inverse transformation of FFT for the product, the convolution calculation thus accomplished.The Fourier transformation and its inversion are in essence a series of complex number calculation, involving the triangle computations. But owing to the "theorem of scale flexibility", there are still some specified incompleteness in this method, such as the calculation of the complex number is more complicated than that of the real number; there is the need of finding rooms for the store of triangle function! the round-off errors are still in existence and a hard nutto crack--the overflow in fixed point operation. In view of thissituation, a study of "number theory transformation" has been put into practice and some achievements have been obtained both at home and abroad during the last few years. The author's intention is trying to put these achievements into the practice of seismic data processing for the purpose of discovering new oil fields.In the first place, the author made a brief introduction about the "number theory transformation''' and then he made an exploratory examination of the "Fast Convolution Filter" for seismic data by means of the method of "number theory transformation". Some conclusions were drawn at the end of this paper.