Random noise suppression is of great importance in seismic processing and interpretation, and time–frequency peak filtering (TFPF) is a classic denoising approach. In TFPF, pseudo Wigner–Ville distribution (PWVD) is used to linearise the given signal for an unbiased estimation of the instantaneous frequency. However, window length is a trade-off parameter for preserving valid signals and attenuating random noise. A long window length may cause loss of the desired signal, whereas a short window length may be inadequate to suppress noise. To ensure a good trade-off between signal preservation and noise reduction, empirical mode decomposition (EMD) has been introduced into the TFPF method. Although the EMD-TFPF method can achieve good results, the mode mixing problem in EMD is non-negligible. In this article, we introduce variational mode decomposition (VMD) to overcome the mode mixing problem. VMD decomposes a signal into an ensemble of modes that own their respective centre frequencies. Thus, the modes obtained by VMD contain less noise, which simplifies selection of the window width of TFPF. Therefore, we propose the VMD-based TFPF (VMD-TFPF) method to suppress random noise. Synthetic and field seismic data examples are employed to illustrate the superior performance of the proposed method in attenuating random noise and preserving the desired signal.

中文翻译：

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时频峰值滤波和变分模态分解对地震数据的随机噪声抑制

随机噪声抑制在地震处理和解释中非常重要，时频峰值滤波（TFPF）是一种经典的去噪方法。在 TFPF 中，伪 Wigner-Ville 分布 (PWVD) 用于线性化给定信号，以对瞬时频率进行无偏估计。然而，窗口长度是保留有效信号和衰减随机噪声的权衡参数。长窗口长度可能导致所需信号的丢失，而短窗口长度可能不足以抑制噪声。为了确保信号保留和降噪之间的良好平衡，TFPF 方法中引入了经验模式分解 (EMD)。虽然 EMD-TFPF 方法可以获得很好的结果，但是 EMD 中的模式混合问题是不可忽略的。在本文中，我们引入了变分模式分解（VMD）来克服模式混合问题。VMD 将信号分解为拥有各自中心频率的模式集合。因此，VMD 获得的模式包含较少的噪声，这简化了 TFPF 窗口宽度的选择。因此，我们提出了基于VMD的TFPF（VMD-TFPF）方法来抑制随机噪声。采用合成和现场地震数据示例来说明所提出的方法在衰减随机噪声和保留所需信号方面的优越性能。我们提出了基于 VMD 的 TFPF (VMD-TFPF) 方法来抑制随机噪声。采用合成和现场地震数据示例来说明所提出的方法在衰减随机噪声和保留所需信号方面的优越性能。我们提出了基于 VMD 的 TFPF (VMD-TFPF) 方法来抑制随机噪声。采用合成和现场地震数据示例来说明所提出的方法在衰减随机噪声和保留所需信号方面的优越性能。