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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 filtering is a common method in seismic data processing. However, since the amount of seismic data is generally large and the convolution filter factors are usually longer, it is difficult to perform convolution in the time domain. After the appearance of Fast Fourier Transform (FFT), people move the convolution operation from the time domain to the frequency domain, which is called “fast convolutional filtering” (fast correlation is also true). The forward and inverse Fourier transforms made during this operation are essentially a series of complex operations, including trigonometric functions. As the complex operations than the real number of complex operations, but also need to store trigonometric functions, and the existence of rounding error and other deficiencies. Therefore, in recent years, some foreign and domestic departments have carried out the so-called “number theory transformation” research on the shortcomings of the FFT, and achieved some results. In this paper, we first briefly introduce the “number theory transformation”, and then use the number theory transformation method, the seismic data for rapid convolution filtering as a preliminary exploration, and finally some results are put forward.