# Seismic Blind Deconvolution Based on Self-Supervised Machine Learning
## 5 Conclusions  
We present a novel blind deconvolution method based on self-supervised machine learning in this paper. This method eliminates the necessity for generating labeled pairs. Moreover, to overcome the dependence on known wavelets in the existing self-supervised machine learning methods, we leverage a residual neural network and a fully connected  
Figure 20: Three-dimensional field test of iErsk3D data. Amplitude spectra of the original field seismic data, the predicted reflectivity of the SSL-D method [23], and the predicted reflectivity of the proposed SSL-BD method.  
convolutional neural network to invert reflectivity and wavelet simultaneously. To mitigate the ill-posedness of blind deconvolution, we employs two strategies. The first one is estimating an initial zero-phase wavelet by smoothing the spectrum of averaged seismic data. The second one is applying a relative sparsity process on the predicted reflectivity during the joint inversion. Numerical experiments on synthetic data and field data show that the proposed method can obtain reflectivity inversion results with higher resolution than the existing self-supervised machine learning method and eliminates the need for a given wavelet. Our proposed method has potential to be improved by using more advanced neural networks and is promising for generalizing to nonstationary blind deconvolution.  
Conceptualization, X.Y., W.X. and B.W.; methodology, X.Y. and W.X.; formal analysis, X.Y., W.X. and B.W.; investigation, X.Y.; data curation, X.Y., W.X., Z.Y. and B.W.; writing--original draft preparation, X.Y.; writing--review and editing, W.X., X.Y., B.W. and Z.Y., visualization, W.X. and B.W.; supervision, W.X. and B.W.; funding acquisition, B.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the Natural Science Basic Research Program of Shaanxi under Grant 2023-JC-YB-269 and in part by Open Foundation of RIPED (No. 2023-KFKT-25).  
Not applicable.  
The part of the Marmousi2 model comes from [[https://wiki.seg.org/wiki/Dictionary:Marmousi_model/zh](https://wiki.seg.org/wiki/Dictionary:Marmousi_model/zh)]([https://wiki.seg.org/wiki/Dictionary:Marmousi_model/zh](https://wiki.seg.org/wiki/Dictionary:Marmousi_model/zh)) (accessed on 19 August 2023). The iErsk3D field data are obtained from [[https://doi.org/10.5281/zenodo.7233751](https://doi.org/10.5281/zenodo.7233751)]([https://doi.org/10.5281/zenodo.7233751](https://doi.org/10.5281/zenodo.7233751)) (accessed on 14 September 2023). The CNPC field data are unavailable upon request due to restrictions, e.g., privacy and ethical restrictions.  
We thank two anonymous reviewers for their constructive comments on this paper. We also would like to thank [PERSON] et al. for the open-source code of their geophysics-steered self-supervised learning for deconvolution method, and thank [PERSON] et al. for the CNPC field data.  
Author [PERSON] was employed by the company BGP INC. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} SSL-D & self-supervised learning method for deconvolution \\ SSL-BD & self-supervised learning method for blind deconvolution \\ MAE & mean absolute error \\ MSE & mean squared error \\ MARE & mean absolute relative error \\ MSRE & mean square relative error \\ SSIM & structural similarity \\ PSNR & peak signal-to-noise ratio \\ \end{tabular}