Abstract
Desert seismic events are disturbed and contaminated by strong random noise, which complicates the subsequent processing, inversion, and interpretation of the data. Thus, noise suppression is an important task. The complex characteristics of random noise in desert seismic records differ completely from those of Gaussian white noise such that they are non-stationary, non-Gaussian, non-linear and low frequency. In addition, desert seismic signals and strong random noise generally share the same frequency bands. Such factors bring great difficulties in the processing and interpretation of desert seismic data. To obtain high-quality data in desert seismic exploration, we have developed an effective denoising method for desert seismic data, which performs energy spectrum analysis in the empirical curvelet transform (ECT) domain. The empirical curvelet coefficients are divided into two different groups according to their energy spectrum distributions. In the first group, which contains fewer effective signals, a large threshold is selected to remove lots of random noise; the second group, with more effective signals, a coherence-enhancing diffusion filter (CEDF) is used to eliminate the noise. Unlike traditional curvelet transforms, ECT not only has the multi-scale, multi-direction, and anisotropy properties of conventional curvelet transform, but also provides adaptability to separate the effective signals from the random noise. We examine synthetic and field desert seismic data. The denoising results demonstrate that the proposed method can be used for preserving effective signals and removing random noise.
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References
Averbuch A., Coifman R.R., Donoho D.L., Elad M. and Israeli M., 2006. Fast and accurate Polar Fourier transform. Appl. Comput. Harmon. Anal., 21, 145–167.
Averbuch A., Coifman R.R., Donoho D.L., Israeli M. and Shkolnisky Y. 2008. A framework for discrete integral transformations — the pseudo polar Fourier transform. SIAM J. Sci. Comput., 30, 764–784.
Bonar D. and Sacchi M., 2012. Denoising seismic data using the nonlocal means algorithm. Geophysics, 77, A5–A8.
Bekara M. and van der Baan M., 2009. Random and coherent noise attenuation by empirical mode decomposition. Geophysics, 74, V89–V98.
Candes E., Demant L., Donoho D. and Ying L., 2006. Fast discrete curvelet transform. Multiscale Model. Simul., 5, 861–899.
Candes E. and Donoho D., 2004. New tight frames of curvelets and optimal representations of objects with piecewise C-2 singularities. Commun. Pure Appl. Math., 57, 219–266.
Deng X.Y., Yang D. and Yang B., 2008. LS-SVR with variant parameters and its practical applications for seismic prospecting data denoising. 2008 IEEE Int. Symp. Ind. Electron., 1–5, 1060–1063.
Donoho D.L., 1995. Denoising by soft thresholding. IEEE Trans. Inform. Theory, 41, 613–627.
Daubechies I., 1992. Ten Lectures on Wavelets. SIAM: Society for Industrial and Applied Mathematics, Philadelphia, PA.
Fehmers G.C. and Höcker C.F.W., 2003. Fast structural interpretation with structure-oriented filtering. Geophysics, 68, 1286–1693.
Fu Y. and Zhang C., 2008. Seismic data denoising based on second wavelet transform. 2008 International Conference on Advanced Computer Theory and Engineering (ICACTE). IEEE Computer Society, Washington, D.C., 186–189, DOI: https://doi.org/10.1109/ICACTE.2008.118.
Gong X., Wang S. and Du L., 2018. Seismic data reconstruction using a sparsity-promoting apex shifted hyperbolic radon-curvelet transform. Stud. Geophys. Geod., 62, 450–165.
Gilles J., Tran G. and Osher S., 2014. 2D empirical transform wavelets, ridgelets and curvelets. SIAM J. Imaging Sci., 7, 157–186.
Herrmann F. and Verschuur E., 2004. Curvelet-domain multiple elimination with sparseness constraints. SEG Technical Program Expanded Abstracts, 12, 1333–1336.
Hennenfent G., Fenelon L. and Herrmann F., 2010. Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach. Geophysics, 75, WB203–WB210.
Jeng Y., Li Y., Chen C. and Chien H., 2009. Adaptive filtering of random noise in near-surface seismic and ground-penetrating radar data. J. Appl. Geophys., 68, 36–46.
Li G. and Li Y., 2016. Random noise of seismic exploration in desert modeling and its applying in noise attenuation. Chinese J. Geophys.-Chinese Ed., 59, 682–692 (in Chinese).
Li G., Li Y. and Yang B., 2017. Seismic exploration random noise on land: modeling and application to noise suppression. IEEE Trans. Geosci. Remote Sensing, 55, 4668–4681.
Naghizadeh M., 2012. Seismic data interpolation and denoising in the frequency-wavenumber domain. Geophysics, 77, V71–V80.
Neelamani R., Baumstein A., Gillard D., Hadidi M. and Soroka W., 2008. Coherent and random noise attenuation using the curvelet transform. The Leading Edge, 27, 240–248.
Ristau J. and Moon W., 2001. Adaptive filtering of random noise in 2-D geophysical data. Geophysics, 66, 342–349.
Tian Y., Li Y., Lin H. and Wu N., 2015. Application of GNMF wavelet spectral unmixing in seismic noise suppression. Chinese J. Geophys.-Chinese Ed., 58, 4568–4575 (in Chinese).
Weickert J. and Scharr H., 2002. A Scheme for coherence-enhancing diffusion filtering with optimized rotation invariance. J. Vis. Commun. Image Represent., 13, 103–118.
Miao X. and Moon W., 1999. Application of wavelet transform in reflection seismic data analysis. Geosci. J., 9, 171–179.
Yuan S. and Wang S., 2013. Edge-preserving noise reduction based on Bayesian inversion with directional difference constraints. J. Geophys. Eng., 10, Art.No. 025001.
Zhong T., Zhang S., Li Y. and Yang B., 2019. Simulation of seismic-prospecting random noise in the desert by a Brownian-motion-based parametric modeling algorithm. C. R. Geosci., 351, 10–16.
Zhong T., Li Y., Wu N., Nie P. and Yang B., 2015. A study on the stationarity and Gaussianity of the background noise in land seismic prospecting. Geophysics, 80, V67–V82.
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We thank for the sponsor of the National Natural Science Foundations of China (grant nos. 41730422). We also thank the authors of TCT and ECT for sharing the codes online. Both of these codes are available at http://www.mathworks.com.
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Li, M., Li, Y., Wu, N. et al. Desert seismic data denoising based on energy spectrum analysis in empirical curvelet domain. Stud Geophys Geod 64, 373–390 (2020). https://doi.org/10.1007/s11200-019-0476-4
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DOI: https://doi.org/10.1007/s11200-019-0476-4