基于正则化理论的时频分析方法及应用

doi:10.11720/wtyht.2023.1369

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Abstract

Time-frequency analysis (TFA) has been widely used in seismic exploration,thus it is crucial to develop a TFA algorithm with high time-frequency resolution.Given the limitations of conventional TFA methods,this study proposed a TFA method based on the regularization theory.The proposed method considers the signal in a short-time window as a superposition of harmonics with different frequencies and takes the TFA problem as an inverse problem.From this perspective,the TFA problem is ill-posed and needs to be solved based on the regularization theory to get a significant time-frequency spectrum.The solution methods under the conditions of L₁ and L₂ norm constraints and the minimum support constraint are commonly used in the regularization theory.This study investigated these solution methods and unified them into the same solution framework.Numerical analysis shows that the TFA method under the condition of the minimum support constraint yielded high time-frequency resolution.This method was systematically applied to the actual data of a specific study area,producing a time-frequency data volume with high time-frequency resolution.Moreover,the planar reservoir distribution was clearly characterized using a single-frequency data volume,demonstrating the promising application prospect of the method.

Key words： time-frequency analysis regularization theory L₁ norm constraint L₂ norm constraint minimium support constraint time-frequency spectrum

Received: 22 July 2022 Published: 11 October 2023

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Jin-Qiang ZHANG. A regularization theory-based method for time-frequency analysis and its applications[J]. Geophysical and Geochemical Exploration, 2023, 47(4): 965-974.

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https://www.wutanyuhuatan.com/EN/10.11720/wtyht.2023.1369 OR https://www.wutanyuhuatan.com/EN/Y2023/V47/I4/965

fig.1a and fig.1b
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Synthetic signal of the two sinuasoidal signals
a—sinuasoidal signal of 20 Hz;b—sinuasoidal signal of 50 Hz;c—summary signal of fig.1a and fig.1b

Comparisons of time-frequency spectrum of different time frequency analysis method
a—time-frequency spectrum of CWT;b—time-frequency spectrum of RL2TFS;c—time-frequency spectrum of RL1TFS;d—time-frequency spectrum of RMSTFS

fig. 3b) obtained by different time-frequency method
">

40 ms Hanning function applied on the ricker wavelet and the correpsonding spectrum
a—40 ms Hanning function and Riker wavelet;b—signal obtained by applying Hanning on ricker wavelet;c—frequency spectrum of the signal (fig. 3b) obtained by different time-frequency method

fig. 4b) obtained by different time-frequency method
">

20 ms Hanning function applied on the ricker wavelet and the correpsonding spectrum
a—20 ms Hanning function and Riker Wavelet;b—signal obtained by applying Hanning on ricker wavelet;c—frequency spectrum of the signal(fig. 4b) obtained by different time-frequency method

Synthetic record of different thikness layers with same recflction coefficient on top and bottom and the corresponding time-frequency spectrum
a—seismic reflection series;b—synthetic record;c—spectrum of CWT;d—spectrum of RMSTFS

Synthetic record of different thikness layers with revese recflction coefficients on top and bottom and the corresponding time-frequency spectrum
a—seismic reflection series;b—synthetic record;c—spectrum of CWT;d—spectrum of RMSTFS

fig. 5a;b—the frequency response curves for reflection paris of fig. 6a
">

The frequency response curves of reflection pairs with different time thickness
a—the frequency response curves for reflection paris of fig. 5a;b—the frequency response curves for reflection paris of fig. 6a

Sections of different frequency spectrum obtained by CWT and RMSTFS
a—section of 10 Hz spectral spectrum of CWT;b—section of 10 Hz spectral spectrum of RMSTFS;c—section of 20 Hz spectral spectrum of CWT;d—section of 20 Hz spectral spectrum of RMSTFS;e—section of 60 Hz spectral spectrum of CWT;f—section of 60 Hz spectral spectrum of RMSTFS

Comparisons of 10 Hz spectrum section obtained by CWT and RMSTFS
a—section of 10 Hz spectral spectrum of CWT(zoomed);b—section of 10 Hz spectral spectrum of RMSTFS(zoomed)

Horizon slices of 10 Hz spectrum by different algorithms
a—Horizon slice of 10 Hz CWT spectrum;b—Horizon slice of 10 Hz RMSTFS spectrum

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