Deconvolution-fractional Gabor spectrogram for seismic signal spectral decomposition
Tian Lin1,3, Peng Zhenming1, Zhang Qiheng2
1. School of Optoelectronic Information, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China;
2. Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu, Sichuan 610209, China;
3. Department of Electronics and Information Engineering, Yili Normal University, Yining, Xinjiang 835000, China
Abstract：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.
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