基于Adam优化的二维自适应TFPF地震去噪算法

2D-ATFPF Seismic Denoising Algorithm Based on Adam Optimization

在时频峰值滤波(TFPF:Time-Frequency Peak Filtering)算法中,采用固定窗长进行滤波很难在滤除噪声和信号保幅之间取得折衷,无法追踪超出截止频率部分的信号,而且传统TFPF仅沿时间方向滤波,忽略了信号的空间信息。针对上述问题,提出了二维自适应TFPF(2D-ATFPF:Two-Dimensional Adaption TFPF)算法,首先利用一组由不同窗函数决定的TFPF冲激响应构建滤波输出凸集;然后,在凸集下引入一个关于滤波输出的目标函数,该函数基于最小二乘准则并将具有时空相关性的方向导数作为惩罚项;最后,使用可以快速收敛的投影Adam方法优化目标函数,将2D-ATFPF应用于人工合成记录和实际资料。实验结果表明,改进的方法与一维算法相比,能更好地恢复同相轴,信噪比提高约1.3 dB。

It is difficult to get a compromise between amplitude protection and denoising by using fixed window length in TFPF(Time-Frequency Peak Filtering)Algorithm,and the signal beyond the cut-off frequency can not be tracked.Moreover,the traditional TFPF only filters along the time direction,ignoring the spatial information of the signal.To solve these problems,a 2D-ATFPF(Two-Dimensional Adaptive TFPF)algorithm is proposed.Firstly,a set of TFPF impulse responses determined by different window functions are used to construct convex sets of filtering results.Then,an objective function for filtering results is introduced under the convex set,which is based on the least square criterion and takes the directional derivative with spatiotemporal correlation as a penalty term.Finally,the optimization of objective function uses a fast convergent projection Adam method.The application of 2D-ATFPF in synthetic recording and real data show that the new method can restore the event and the the signal-to-noise ratio has increased about 1.3 dB compared to the one-dimensional traditional algorithm.