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Extraction of instantaneous frequency from seismic data via the generalized Morse wavelets

机译：通过广义莫尔斯小波从地震数据中提取瞬时频率

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摘要

The instantaneous frequency extracted by the Hilbert transform is susceptible to noise. We propose a robust method to extract instantaneous frequency from seismic data in wavelet domain. A new class of analytic wavelets with some desirable properties, called the generalized Morse wavelets (GMWs), is applied in the proposed method. Based on the proposed discretization scheme, the GMW family can constitute a tight frame and then we can determine the distribution of the effective signal by solving the optimization problem. We use the iterative shrinkage-thresholding (IST) algorithm and fast iterative shrinkage-thresholding algorithm (FISTA) to tackle this l1-norm minimization problem. To improve the convergence rate of the iterative solution, we implement the exponential thresholding scheme with a dynamic stopping criterion. Compared with the conventional instantaneous frequency extraction method based on Hilbert transform, the proposed method is proved to yield higher precision and better anti-noise performance. Experimental results on synthetic signals and real seismic data demonstrate the validity of the method.
机译：希尔伯特变换提取的瞬时频率易受噪声影响。我们提出了一种鲁棒的方法来从小波域的地震数据中提取瞬时频率。所提出的方法应用了一类具有某些理想性质的新型解析小波，称为广义莫尔斯小波（GMWs）。基于提出的离散化方案，GMW系列可以构成一个紧密的框架，然后我们可以通过解决优化问题来确定有效信号的分布。我们使用迭代收缩阈值（IST）算法和快速迭代收缩阈值算法（FISTA）来解决此l1范数最小化问题。为了提高迭代解的收敛速度，我们采用动态停止准则来实现指数阈值方案。与传统的基于希尔伯特变换的瞬时频率提取方法相比，该方法具有更高的精度和更好的抗噪性能。综合信号和真实地震数据的实验结果证明了该方法的有效性。

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