消减地震勘探随机噪声:导数算子约束下的维纳滤波

Reducing Seismic Random Noise:Derivative Operator Constrainted Wiener Filtering

为使传统的维纳滤波方法在最小均方准则下的解更准确、稳定,采用正则化思想,提出导数算子约束下的最小均方准则;在这种准则下,推导了维纳滤波因子及其频率响应。通过在不同频段取不同的正则化函数值,控制滤波结果。理论及实际地震勘探资料的分析表明:正则化维纳滤波去噪效果比传统维纳滤波好,且对有效波的损失较小,表明了文中所取正则项的可行性及有效性。最后讨论了通过建立正则化函数关系式,方便地提供正则化函数值以及圆滑振幅谱对改进滤波效果的可能性。

To make the solution of the traditional Wiener filtering method with the least mean square criterion more accurate and stable,we proposed a least mean square criterion with regularization idea based on the derivative operator constrains in this paper.Under this criterion,Wiener filter coefficients and its frequency response were derived.The filter result can be controlled by different regularization function values in different frequencies.The analyses of theoretical and practical seismic data show that this method is better than the traditional Wiener filter in the denoising.And the method can reduce the losing of the energy of effective signal.In view of the foregoing it shows that the regular terms is reasonable and effective.Finally,the expression of the regularization function is built;and its purpose is convenient to compute the regularization function value.And the possibility of improved filtering is discussed by smoothing amplitude spectrum.