分数域反褶积Gabor谱图地震信号谱分解

应用Gabor谱图可以将地震信号映射到二维时频域,可提供地震信号的频率随时间的变化规律。然而Gabor谱图的分辨率受到海森堡不确定原理的限制,时频分辨率较低。为此, 本文将分数域自适应的最优窗函数引入Gabor谱图,得到分数域Gabor谱图。为了提高分数域Gabor谱图的时频分辨率,将自适应最优窗函数的Wigner-Ville分布(WVD)作为点扩散函数(PSF),再由分数域Gabor谱图和PSF做反褶积得到分数域反褶积Gabor谱图,同时给出了反褶积分数域Gabor谱图的计算方法和计算复杂度分析。测试信号和实际地震信号的谱分解结果都证明了分数域反褶积Gabor谱图在提高信号时频分辨率方面的优势。

Deconvolution-fractional Gabor spectrogram for seismic signal spectral decomposition

Gabor spectrogram can transform seismic signals into 2D time-frequency domain. However, Gabor spectrogram is suffered from Heisenberg uncertain principle and its resolution is low. In this paper we propose deconvolution-fraction Gabor spectrogram. We first introduce the fractional optimal window function into Gabor spectrogram and develop the fractional Gabor spectrogram. Then we show the deconvolution of image processing technique used in time-frequency analysis for improving time-frequency resolution, and use the Wigner-Ville distribution (WVD) of fractional optimal window as point spread function (PSF) to show more accurately the instantaneous frequency of the signal components. Finally we conduct the deconvolution between fractional Gabor spectrogram and the PSF and obtain the deconvolution-fraction Gabor spectrogram. As the fractional optimal window function is adaptive according the signal, the resolution of deconvolution-fraction Gabor spectrogram is higher. To reduce the computation cost, the PSF is shrunken into a small effective area. Synthetic and real seismic data tests are evaluated to demonstrate the performance of the deconvolution-fraction Gabor spectrogram.