地震数据分数阶域空间预测滤波方法研究

Study on Spatial Prediction Filtering in Fractional Fourier Domains for Seismic Data

将分数阶傅氏变换引入地震数据空间预测滤波中,研究滤波效果与信号保真的最佳折衷。利用分数阶傅氏变换把信号旋转变换到任意1个角度时"频"平面,运用奇异值分解(SVD)方法求取空间预测滤波算子,实现预测滤波;通过数据相关系数和相对误差能量曲线评价滤波效果。研究结果表明,可以找到1个合适的分数阶域,使得分数阶域空间预测滤波能够在压制噪声和保留信号特征两方面达到最佳折衷,较一般f-x域预测滤波具有更大灵活性。

We generalize the spatial predictive filtering techniques to seismic data by means of the fractional Fourier transform in order to find a balance between signal character preservation and noise removal. The fractional Fourier transform allows transformation to any of a continuous family of spaces intermediate to the time and frequency domains by introducing a fractional parameter, and the SVD technique is used to attain the filter during the course of filtering. The crosscorrelation coefficient curve and relative error energy curve are used as attributes to evaluate the quality of results. The research results of this paper prove that we can find a proper fractional domain in which the spatial prediction filtering can keep a balance between noise removal and signal character conservation. This method is more flexible than the classical one.