三维微分方程滤波法及线性噪声压制

3D partial differential equation filtering and linear noise attenuation

（1.同济大学海洋与地球科学学院海洋地质国家重点实验室，上海200092；2.东方地球物理公司采集技术支持部，河北涿州072751）

Reflection Seismic Research Group, School of Ocean & Earth Science, Tongji University, Shanghai 200092, China

对三维面波和其它线性噪声的压制有两个问题需要解决：合适的道集和合适的噪声压制方法。为此，提出了一种时空域Butterworth类三维微分方程滤波方法。该方法的基本原理是：首先在频率波数域中针对具有一定视速度的线性相干噪声设计滤波器；然后把频率波数域中的滤波器变换到时空域，得到偏微分方程形式的时空域滤波方程；用有限差分法求解该方程得到时空域的滤波因子。在求解三维滤波方程时不对三维微分方程进行降维处理，仅对差分方程进行分解，从而获得计算效率很高的滤波因子。数值模拟和实际资料处理结果证明方法是有效的，线性噪声得到了较好的压制，对有效信号的影响很小。

Gathers and filtering method should be appropriately selected in the attenuation of the 3D surface wave and other linear noises. Therefore, a 3D Butterworth filtering method in time-space domain was proposed. Firstly, a wave filter is designed to in the frequency-wave number domain aiming at the linear noises with a specific apparent velocity. Secondly the wave filter is transformed from frequency-wave number domain to time-space domain, and the filtering equations in time-space domain are obtained with partial differential form. Finite difference method is used to solve the equation and obtain the filter factor in time-space domain. Filter factor with high computation efficiency can be obtained through resolving the difference equation without reducing the number of dimension in solving the 3D partial differential equation. Numerical simulation and actual data processing results show the method is effective, noise can be well suppressed and the impact on the effective signals is small.