小波包变换及正弦函数模拟消除50 Hz工业干扰

陷波技术是用于消除50 Hz工业干扰的一种有效工具，由于其采用频率切除技术，故在消除50 Hz工业干扰的同时，使50 Hz及其附近的有效信号受到损失，给后续处理带来不利影响。为此，提出采用正弦函数来模拟50 Hz工业干扰，并采用减法运算从数据中减去它，达到消除50 Hz工业干扰又使有效波损失减小到最小的目的。为了使去噪处理仅在有限频带上进行，采用小波包变换分解来得到50 Hz工业干扰所在频带；为使在有限频带内模拟50 Hz工业干扰实现方便，采用了卷积型小波包变换来得到含有50 Hz工业干扰且其小波系数保持了与原始记录相同的样点数。最后给出了理论模型测试结果，并应用实际单炮记录进行了对比处理。

Elimination of 50Hz power interference via wavelet packet transform and sine function simulation

Trapping technique is a useful tool to eliminate 50 Hz power interference. Though trapping can eliminate the power interference of 50 Hz, it is harmful for signals around 50 Hz because frequency muting is used in trapping which is unfavorable for subsequent processing steps. This paper proposed to simulate the 50 Hz power interference with sine function and subtract it from the original records. To ensure the noise elimination is performed on limited frequency band, we used wavelet packet transform to isolate the frequency band of 50 Hz power interference. To facilitate the implement of the algorithm, convolution-type wavelet packet transform was adopted and the number of wavelet coefficients was set to same as the samples of the record. The method was verified on synthetic data and was also demonstrated on shot records.