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Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation

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Abstract

This paper presents an analytical study of the complete transform of improved Gabor wavelets (IGWs), and discusses its application to the processing and interpretation of seismic signals. The complete Gabor wavelet transform has the following properties. First, unlike the conventional transform, the improved Gabor wavelet transform (IGWT) maps time domain signals to the time-frequency domain instead of the time-scale domain. Second, the IGW’s dominant frequency is fixed, so the transform can perform signal frequency division, where the dominant frequency components of the extracted sub-band signal carry essentially the same information as the corresponding components of the original signal, and the subband signal bandwidth can be regulated effectively by the transform’s resolution factor. Third, a time-frequency filter consisting of an IGWT and its inverse transform can accurately locate target areas in the time-frequency field and perform filtering in a given time-frequency range. The complete IGW transform’s properties are investigated using simulation experiments and test cases, showing positive results for seismic signal processing and interpretation, such as enhancing seismic signal resolution, permitting signal frequency division, and allowing small faults to be identified.

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Correspondence to Zhan-Huai Ji.

Additional information

The research work is supported by the Innovation Fund for Small and Medium Technology-based Enterprise of China (No. 12C26216106562), and Shaanxi Province Education Department Science and Technology Research Plan (No. 11JK0777).

Ji Zhan-Huai, is currently working as a mathematics Lecturer at the School of Science, Xi’an University of Science and Technology, Xi’an, China. He graduated from the Mathematics department of Xianyang Education College, Shaanxi, China, and received the B.E. degree from the Computer Science department at Xi’an University of Science and Technology, Xi’an, China, in 2003. He is now an on-job Ph.D. majoring in Information and Telecommunications Engineering at Northwestern Polytechnical University, Xi’an, China. His main research interests include information and signal processing, seismic signal processing, and computational methods. Email: jizhanhuai88@163.com

Yan Sheng-Gang, is currently working as a Professor and doctoral supervisor at the School of Marine and Technology, Northwestern Polytechnical University, Xi’ an, China. He received the B.E. degree from the Central South University, Hunan, China, in 1988, and the M.S. and Ph.D. degrees from Northwestern Polytechnical University, Xi’an, China, in 1991 and 2008, respectively. His research interests include modern signal processing and its applications, multi-sensor array signal processing, and high-speed signal processing and its applications. Email: yshgang@nwpu.edu.cn

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Ji, ZH., Yan, SG. Properties of an improved Gabor wavelet transform and its applications to seismic signal processing and interpretation. Appl. Geophys. 14, 529–542 (2017). https://doi.org/10.1007/s11770-017-0642-9

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  • DOI: https://doi.org/10.1007/s11770-017-0642-9

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