改进阈值函数的提升小波在人工震源数据处理中的应用

针对由于软阈值函数存在恒定偏差及硬阈值函数存在不连续，从而导致信号去噪精度较低及出现伪吉布斯现象的问题，提出一种改进的阈值函数，并从数学上证明其连续性、渐进性及偏差性。将本文阈值函数用于加入了高斯白噪声的4种仿真信号中发现，其不仅可提升信号的信噪比，还可弥补由软、硬阈值函数引起的信号失真、震荡等缺点。将本文提出的阈值函数运用于气枪人工震源，可得到与仿真信号一致的结论，同时与带通滤波相比，本文提出的方法能够完整保留信号的相位与幅值信息，证明本文改进的阈值函数在提升气枪人工震源信号的信噪比方面具有一定的可行性。

Application of Lifting Wavelet with Improved Threshold Function in Artificial Seismic Source

In view of the constant deviation of the soft threshold function and the discontinuity of the hard threshold function, which results in low accuracy of signal denoising and pseudo-Gibbs phenomena, we propose an improved threshold function. We further prove its continuity, gradualness and deviation mathematically. When used with the four simulated signals with Gaussian white noise, we find that it not only improves the signal-to-noise ratio of the signal, but also compensates for the signal distortion caused by the soft and hard threshold functions. The threshold function proposed in this paper is applied to the air-gun artificial seismic source, and a conclusion consistent with the simulated signal is obtained. At the same time, compared with band-pass filtering, the method proposed in this paper can completely retain the phase and amplitude information of the signal, which proves that the improved threshold function has certain feasibility in improving the signal-to-noise ratio of the air-gun artificial source signal.