Abstract
Prediction filtering is one of the most commonly used random noise attenuation methods in the industry; however, it has two drawbacks. First, it assumes that the seismic signals are piecewise stationary and linear. However, the seismic signal exhibits nonstationary due to the complexity of the underground structure. Second, the method predicts noise from seismic data by convolving with a prediction error filter (PEF), which applies inconsistent noise models before and after denoising. Therefore, the assumptions and model inconsistencies weaken conventional prediction filtering’s performance in noise attenuation and signal preservation. In this paper, we propose a nonstationary signal inversion based on shaping regularization for random noise attenuation. The main idea of the method is to use the nonstationary prediction operator (NPO) to describe the complex structure and obtain seismic signals using nonstationary signal inversion instead of convolution. Different from the convolutional predicting filtering, the proposed method uses NPO as the regularization constraint to directly invert the effective signal from the noisy seismic data. The NPO varies in time and space, enabling the inversion system to describe complex (nonstationary and nonlinear) underground geological structures in detail. Processing synthetic and field data results demonstrate that the method effectively suppresses random noise and preserves seismic reflection signals for nonstationary seismic data.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Abma, R., and Claerbout, J., 1995, Lateral prediction for noise attenuation by t-x and f-x techniques: Geophysics, 60(6), 1887–1896.
Alan, R. M., and Panos, G. K., 1990, Efficient tau-p hyperbolic velocity filtering: Geophysics, 55(5), 619–625.
Bednar, J. B., 1983, Applications of median filtering to deconvolution, pulse estimation, and statistical editing of seismic data: Geophysics, 48(12), 1598–1610.
Canales, L., 1984, Random noise reduction: 54th Annual International Meeting, SEG, Expanded Abstracts, 525–527.
Chase, M. K., 1992, Random noise reduction by FXY prediction filtering: Exploration Geophysics, 23, 51–56.
Claerbout, J. F., 1992, Earth soundings analysis: Processing versus inversion: Blackwell Scientific Publications.
Crawley, S., Clapp R., and Claerbout J. F., 1999, Interpolation with smoothly nonstationary prediction-error filters: 69th Annual International Meeting, SEG, Expanded Abstracts, 1154–1157.
Fomel, S., 2007, Shaping regularization in geophysical-estimation problems: Geophysics, 72(2), R29–R36.
Fomel, S., 2009, Adaptive multiple subtraction using regularized nonstationary regression: Geophysics, 74(1), V25–V33.
Gholami, A., 2014, Non, convex compressed sensing with frequency mask for seismic data reconstruction and denoising. Geophysical Prospecting: 62(6), 1389–1405.
Gulunay, N., 1986, FXDECON and complex wiener prediction filter: 56th Annual International Meeting, SEG, Expanded Abstracts, 279–281.
Jones, I. F., and Levy, S., 1987, Signal-to-noise ratio enhancement in multichannel seismic data via the Karhunen-Love transform: Geophysical Prospecting, 35, 12–32.
Liu, G. C., and Chen, X. H., 2013, Noncausal f-x-y regularized nonstationary prediction filtering for random noise attenuation on 3D seismic data: Journal of Applied Geophysics, 93, 60–66.
Liu, G. C., Chen, X. H., Du, J., et al., 2012, Random noise attenuation using f-x regularized nonstationary autoregression: Geophysics, 77(2), V61–V69.
Liu, Y., and Fomel, S., 2010, Trace Interpolation Beyond Aliasing Using Regularized Nonstationary Autoregression: 80th Annual International Meeting, SEG, Expanded Abstracts, 3662–3667.
Liu, Y., Liu, N., and Liu, C., 2014, Adaptive prediction filtering in t-x-y domain for random noise attenuation using regularized nonstationary autoregression: Geophysics, 80(1), V13–V21.
Liu, Z. P., Chen, X. H., and Li, J. Y., 2009, Noncausal spatial prediction filtering based on an ARMA model: Applied Geophysics, 6(2), 122–128.
Neelamani, R., Baumstein, A. I., Gillard, D. G., Hadidi, M. T., and Soroka, W. L., 2008, Coherent and random noise attenuation using the curvelet transform: The Leading Edge, 27(2), 240–248.
Rudin, L. I., Osher, S. and Fatemi, E., 1992, Nonlinear total variation based noise removal algorithms: Physica D, 60(1–4), 259–268.
Sacchi, M., and Kuehl, H., 2001, ARMA formulation of FX prediction error filters and projection filters: Journal of Seismic Exploration, 9, 185–198.
Soubaras, R., 1994, Signal-preserving random noise attenuation by the f-x projection: 64th Annual International Meeting, SEG, Expanded Abstracts, 1576–1579.
Soubaras, R., 2000, 3D projection filtering for noise attenuation and interpolation: 70th Annual International Meeting, SEG, Expanded Abstracts, 2096–2099.
Sun, Y., and Ronen, S., 1996, The pyramid transform and its application to signal/noise separation: Stanford Exploration Project Annual Report, 93, 161–176.
Wang, F., and Chen, S., 2019, Residual learning of deep convolutional neural network for seismic random noise attenuation: IEEE Geoscience and Remote Sensing Letters, 16(8), 1314–1318.
Yu, S., Cai, X., and Su, Y., 1989, Seismic signal enhancement by polynomial fitting: Applied Geophysics, 1, 57–65.
Yuan, S. Y., Wang, S. Y., and Li, G. F., 2012, Random noise reduction using Bayesian inversion: Journal of Geophysics and Engineering, 9, 60–68.
Zhang, R., and Ulrych, T. J., 2003, Phasical wavelet frame denoising: Geophysics, 68(1), 225–231.
Zhao, Y. M., Li, G. F., Wang W., et al., 2017, Inversion-based data-driven time-space domain random noise attenuation method: Applied Geophysics, 14(4), 543–550.
Zhao, Y. X., Li, Y., and Yang, B. J., 2020, Denoising of seismic data in desert environment based on a variational mode decomposition and a convolutional neural network: Geophysical Journal International, 221(2), 1211–1225.
Acknowledgements
This research was financially supported by the CNPC Science Research and Technology Development Project (No. 2019A-3312), the CNPC major promotion project (No. 2018D-0813), the National Natural Science Foundation of China (No. 41874141) and the Project, “New Technology and Software Development for Comprehensive Identification an Evalunation of Cracks” of the Research Institute of Petroleum Exploration & Development-Northwest of CNPC (No. 2015B-3712). We also are grateful to our reviewers, Prof. Li Hui, Wang Yanchun, and Ma Jinfeng, for their feedback that assisted in substantially improving the presentation of this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Yang Wuyang, Ph.D., senior technical expert of CNPC. graduated from Graduate School of the Chinese Academy of Geological Sciences in 2005, currently working in heterogeneous reservoir prediction, fractures modeling, and intelligent geophysical exploration. Email: yangwuyang@petrochina.com.cn
Wang Wei (Communication author), a master’s degree in geological resources and geological engineering from China University of Petroleum (Beijing) in 2018, currently working in the Institute of Geophysics, Northwest Branch of China Petroleum Exploration and Development Research Institute, mainly engaged in intelligent geophysical exploration, signal processing, and software development. Email: wangwei_geophy@petrochina.com.cn
Rights and permissions
About this article
Cite this article
Yang, WY., Wang, W., Li, GF. et al. Nonstationary signal inversion based on shaping regularization for random noise attenuation. Appl. Geophys. 17, 432–442 (2020). https://doi.org/10.1007/s11770-020-0828-4
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11770-020-0828-4