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Phase estimation in bispectral domain based on conformal mapping and applications in seismic wavelet estimation

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Applied Geophysics 2011年第1期8卷 36-47,95页

作者： Yu Yong-Cai Wang Shang-Xu Yuan San-Yi Qi Peng-Fei State Key Laboratory of Petroleum Resource and Prospecting CNPC Key Laboratory of Geophysical Exploration China University of Petroleum Beijing 0 China China University of Geosciences （Beijing） Beijing 100083 China.

Seismic wavelet estimation is an important part of seismic data processing and interpretation, whose preciseness is directly related to the results of deconvolution and inversion. wavelet estimation based on higher-order spectra is an important new method. However, the higher-order spectra often have phase wrapping problems, which lead to wavelet phase spectrum deviations and thereby affect mixed-phase wavelet estimation. To solve this problem, we propose a new phase spectral method based on conformal mapping in the bispectral domain. The method avoids the phase wrapping problems by narrowing the scope of the Fourier phase spectrum to eliminate the bispectral phase wrapping influence in the original phase spectral estimation. The method constitutes least-squares wavelet phase spectrum estimation based on conformal mapping which is applied to mixed-phase wavelet estimation with the least-squares wavelet amplitude spectrum estimation. Theoretical model and actual seismic data verify the validity of this method. We also extend the idea of conformal mapping in the bispectral wavelet phase spectrum estimation to trispectral wavelet phase spectrum estimation.

关键词： conformal mapping higher-order spectra phase wrapping wavelet estimation

Asymptotic Properties of wavelet Estimators in Partially Linear Errors-in-variables Models with Long-memory Errors

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Acta Mathematicae Applicatae Sinica 2018年第1期34卷 77-96页

作者： Hong-chang HU Heng-jian CUI Kai-can LI School of Mathematics and Statistics Hubei Normal University Huangshi 435002 China School of Mathematical science Capital Normal University Beijing 100048 China

While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.

关键词： partially linear errors-in-variables model nonlinear long dependent time series wavelet estimation asymptotic representation asymptotic distribution weak convergence rates

Multi-well wavelet-synchronized inversion based on particle swarm optimization

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Applied Geophysics 2024年第4期21卷 728-739,879,880页

作者： Yuan Huan Yuan San-Yi Su Qin Wang Hong-Qiu Zeng Hua-Hui Yue Shi-Jun College of Geophysics China University of Petroleum(Beijing)Beijing 102249China Research Institute of Petroleum Exploration and Development-Northwest PetrochinaLanzhou730020China.

wavelet estimation is an important part of high-resolution seismic data ***,itis diffi cult to preserve the lateral continuity of geological structures and eff ectively recover weak geologicalbodies using conventional deterministic wavelet inversion methods,which are based on the joint inversionof wells with seismic *** this study,starting from a single well,on the basis of the theory of single-welland multi-trace convolution,we propose a steady-state seismic wavelet extraction method for synchronizedinversion using spatial multi-well and multi-well-side seismic *** proposed method uses a spatiallyvariable weighting function and wavelet invariant constraint conditions with particle swarm optimization toextract the optimal spatial seismic wavelet from multi-well and multi-well-side seismic data to improve thespatial adaptability of the extracted wavelet and inversion *** simulated data demonstrate that thewavelet extracted using the proposed method is very stable and *** at a low signal-to-noise ratio,the proposed method can extract satisfactory seismic wavelets that refl ect lateral changes in structures andweak eff ective geological *** processing results for the fi eld data show that the deconvolution resultsimprove the vertical resolution and distinguish between weak oil and water thin layers and that the horizontaldistribution characteristics are consistent with the log response characteristics.

关键词： particle swarm optimization synchronized inversion wavelet estimation spatial adaptability weak eff ective signal

Supersmooth density estimations over L^p risk by wavelets

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Science China Mathematics 2017年第10期60卷 1901-1922页

作者： LI Rui LIU YouMing Department of Applied Mathematics Beijing University of Technology College of Science Tianjin University of Technology

This paper studies wavelet estimations for supersmooth density functions with additive noises. We first show lower bounds of Lprisk(1 p < ∞) with both moderately and severely ill-posed noises. Then a Shannon wavelet ... 详细信息

This paper studies wavelet estimations for supersmooth density functions with additive noises. We first show lower bounds of Lprisk(1 p wavelet estimator provides optimal or nearly-optimal estimations over Lprisks for p 2, and a nearly-optimal result for 1 estimation with moderately ill-posed noise by using the Meyer wavelet. Finally, the practical estimators are considered. Our results are motivated by the work of Pensky and Vidakovic(1999), Butucea and Tsybakov(2008), Comte et al.(2006), Lacour(2006) and Lounici and Nickl(2011).

关键词： wavelet estimation supersmooth density additive noise optimality