High resolution of post-stack seismic data assists in better interpretation of subsurface structures as well as high accuracy of impedance inversion. Therefore, geophysicists consistently strive to acquire higher resolution seismic images in petroleum exploration. Although there have been successful applications of conventional signal processing and machine learning for post-stack seismic resolution enhancement, there is limited reference to the seismic applications of the recent emergence and rapid development of generative artificial intelligence. Hence, we propose to apply diffusion models, among the most popular generative models, to enhance seismic resolution. Specifically, we apply the classic diffusion model—denoising diffusion probabilistic model (DDPM), conditioned on the seismic data in low resolution, to reconstruct corresponding high-resolution images. Herein the entire scheme is referred to as SeisResoDiff. To provide a comprehensive and clear understanding of SeisResoDiff, we introduce the basic theories of diffusion models and detail the optimization objective's derivation with the aid of diagrams and algorithms. For implementation, we first propose a practical workflow to acquire abundant training data based on the generated pseudo-wells. Subsequently, we apply the trained model to both synthetic and field datasets, evaluating the results in three aspects: the appearance of seismic sections and slices in the time domain, frequency spectra, and comparisons with the synthetic data using real well-logging data at the well locations. The results demonstrate not only effective seismic resolution enhancement, but also additional denoising by the diffusion model. Experimental comparisons indicate that training the model on noisy data, which are more realistic, outperforms training on clean data. The proposed scheme demonstrates superiority over some conventional methods in high-resolution reconstruction and denoising ability, yielding more competitive results compared to our previous research.
Alali, A., Alkhalifah, T., 2023. Integrating U-Nets into a multiscale full-waveform inversion for salt body building. IEEE Trans. Geosci. Rem. Sens. 61, 1-11. https://doi.org/10.1109/TGRS.2023.3310886.
Berkhout, A.J., 1977. Least-squares inverse filtering and wavelet deconvolution. Geophysics 42, 1369-1383. https://doi.org/10.1190/1.1440798.
Birnie, C., Alkhalifah, T., 2022. Transfer learning for self-supervised, blind-spot seismic denoising. Front. Earth Sci. 10. https://doi.org/10.3389/feart.2022.1053279.
Brocher, T.M., 2005. Empirical relations between elastic wavespeeds and density in the Earth's crust. Bull. Seismol. Soc. Am. 95, 2081-2092. https://doi.org/10.1785/0120050077.
Cao, S., Sun, Y., Chen, S., 2023. Challenges and solutions to high-resolution data processing for seismic exploration. Coal Geol. Explor. 51, 277-288. https://doi.org/10.12363/issn.1001-1986.22.11.0841.
Cao, S., Yuan, D., 2016. A review of high resolution seismic data processing approaches. Xinjiang Pet. Geol. 37, 112-119. https://doi.org/10.7657/XJPG20160122.
Chai, X., Wang, S., Yuan, S., Zhao, J., Sun, L., Wei, X., 2014. Sparse reflectivity inversion for nonstationary seismic data. Geophysics 79, V93-V105. https://doi.org/10.1190/geo2013-0313.1.
Chen, G., Liu, Y., 2024. Combining unsupervised deep learning and Monte Carlo dropout for seismic data reconstruction and its uncertainty quantification. Geophysics 89, WA53-WA65. https://doi.org/10.1190/geo2022-0632.1.
Chen, G., Liu, Y., Zhang, M., Zhang, H., 2022a. Dropout-based robust self-supervised deep learning for seismic data denoising. Geosci. Rem. Sens. Lett. IEEE 19, 1-5. https://doi.org/10.1109/LGRS.2022.3167999.
Chen, H., Gao, J., Gao, Z., Chen, D., Yang, T., 2021a. A sequential iterative deep learning seismic blind high-resolution inversion. IEEE J. Sel. Top. Appl. Earth Obs. Rem. Sens. 14, 7817-7829. https://doi.org/10.1109/JSTARS.2021.3100502.
Chen, H., Gao, J., Jiang, X., Gao, Z., Zhang, W., 2021b. Optimization-inspired deep learning high-resolution inversion for seismic data. Geophysics 86, R265-R276. https://doi.org/10.1190/geo2020-0034.1.
Chen, H., Gao, J., Liu, N., Yang, Y., 2019. Multitrace semiblind nonstationary deconvolution. Geosci. Rem. Sens. Lett. IEEE 16, 1195-1199. https://doi.org/10.1109/LGRS.2019.2893924.
Chen, H., Sacchi, M.D., Lari, H.H., Gao, J., Jiang, X., 2023. Nonstationary seismic reflectivity inversion based on prior-engaged semisupervised deep learning method. Geophysics 88, WA115-WA128. https://doi.org/10.1190/geo2022-0057.1.
Chen, S., Cao, S., Sun, Y., 2022b. Enhancing the resolution of seismic data based on the non-local similarity. Geophys. Prospect. 70, 1116-1128. https://doi.org/10.1111/1365-2478.13202.
Chen, S., Cao, S., Sun, Y., Lin, Y., Gao, J., 2022c. Seismic time-frequency analysis via time-varying filtering based empirical mode decomposition method. J. Appl. Geophys. 204, 104731. https://doi.org/10.1016/j.jappgeo.2022.104731.
Cheng, S., Alkhalifah, T., 2023. Robust data driven discovery of a seismic wave equation. Geophys. J. Int. 236, 537-546. https://doi.org/10.1093/gji/ggad446.
Choi, Y., Jo, Y., Seol, S.J., Byun, J., Kim, Y., 2021. Deep learning spectral enhancement considering features of seismic field data. Geophysics 86, V389-V408. https://doi.org/10.1190/geo2020-0017.1.
Deng, F., Wang, S., Wang, X., Fang, P., 2024. Seismic data reconstruction based on conditional constraint diffusion model. IEEE Geoscience and Remote Sensing Letters 21, 7502305. https://doi.org/10.22541/essoar.168614533.30847426/v1.
Dragomiretskiy, K., Zosso, D., 2014. Variational mode decomposition. IEEE Trans. Signal Process. 62, 531-544. https://doi.org/10.1109/TSP.2013.2288675.
Durall, R., Ghanim, A., Fernandez, M.R., Ettrich, N., Keuper, J., 2023. Deep diffusion models for seismic processing. Comput. Geosci. 177, 105377. https://doi.org/10.1016/j.cageo.2023.105377.
Gao, J.H., Wang, L.L., Zhao, W., 2009. Enhancing resolution of seismic traces based on the changing wavelet model of seismograms. Chin. J. Geophys. 52, 1289-1300. https://doi.org/10.3969/j.issn.0001-5733.2009.05.018.
Gao, Y., Zhang, J., Li, H., Li, G., 2022a. Incorporating structural constraint into the machine learning high-resolution seismic reconstruction. IEEE Trans. Geosci. Rem. Sens. 60, 1-12. https://doi.org/10.1109/TGRS.2022.3157064.
Gao, Y., Zhao, D., Li, T., Li, G., Guo, S., 2023. Deep learning vertical resolution enhancement considering features of seismic data. IEEE Trans. Geosci. Rem. Sens. 61, 1-13. https://doi.org/10.1109/TGRS.2023.3234617.
Gao, Z., Hu, S., Li, C., Chen, H., Jiang, X., Pan, Z., Gao, J., Xu, Z., 2022b. A deep-learning-based generalized convolutional model for seismic data and its application in seismic deconvolution. IEEE Trans. Geosci. Rem. Sens. 60, 1-17. https://doi.org/10.1109/TGRS.2021.3076991.
Gholami, A., Sacchi, M.D., 2012. A fast and automatic sparse deconvolution in the presence of outliers. IEEE Trans. Geosci. Rem. Sens. 50, 4105-4116. https://doi.org/10.1109/TGRS.2012.2189777.
Grady, T.J., Khan, R., Louboutin, M., Yin, Z., Witte, P.A., Chandra, R., Hewett, R.J., Herrmann, F.J., 2023. Model-parallel Fourier neural operators as learned surrogates for large-scale parametric PDEs. Comput. Geosci. 178, 105402. https://doi.org/10.1016/j.cageo.2023.105402.
Guo, A.H., Lu, P.F., Wang, D.D., Wu, J.Z., Xiao, C., Peng, H.Y., Jiang, S.H., 2023. Improving the resolution of poststack seismic data based on UNet+GRU deep learning method. Appl. Geophys. 20, 1-10. https://doi.org/10.1007/s11770-023-1038-7.
Hale, D., 1981. An inverse Q-filter. Stanford Exploration Project Report 26, 231-243.
Hamida, A., Alfarraj, M., Al-Shuhail, A.A., Zummo, S.A., 2023. Facies-guided seismic image super-resolution. IEEE Trans. Geosci. Rem. Sens. 61, 1-13. https://doi.org/10.1109/TGRS.2023.3289151.
Hargreaves, N.D., Calvert, A.J., 1991. Inverse Q filtering by fourier transform. Geophysics 56, 519-527. https://doi.org/10.1190/1.1443067.
Harsuko, R., Alkhalifah, T.A., 2022. Storseismic: a new paradigm in deep learning for seismic processing. IEEE Trans. Geosci. Rem. Sens. 60, 1-15. https://doi.org/10.1109/TGRS.2022.3216660.
Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yen, N.C., Tung, C.C., Liu, H.H., 1998. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. Royal Soci. London. Series A: Math. Phys. Eng. Sci. 454, 903-995. https://doi.org/10.1098/rspa.1998.0193.
Jiang, Y., Cao, S., Chen, S., Zheng, D., 2021. A blind nonstationary deconvolution method for multichannel seismic data. Explor. Geophys. 52, 245-257. https://doi.org/10.1080/08123985.2020.1807319.
Kazemi, N., Sacchi, M.D., 2014. Sparse multichannel blind deconvolution. Geophysics 79, V143-V152. https://doi.org/10.1190/geo2013-0465.1.
Kjartansson, E., 1979. Constant Q-wave propagation and attenuation. J. Geophys. Res. Solid Earth 84, 4737-4748. https://doi.org/10.1029/JB084iB09p04737.
Kullback, S., Leibler, R.A., 1951. On information and sufficiency. Ann. Math. Stat. 22, 79-86. https://doi.org/10.1214/aoms/1177729694.
Leinbach, J., 1995. Wiener spiking deconvolution and minimum-phase wavelets: a tutorial. Lead. Edge 14, 189-192. https://doi.org/10.1190/1.1437110.
Levin, S.A., 1989. Surface-consistent deconvolution. Geophysics 54, 1123-1133. https://doi.org/10.1190/1.1442747.
Levy, S., Fullagar, P.K., 1981. Reconstruction of a sparse spike train from a portion of its spectrum and application to high-resolution deconvolution. Geophysics 46, 1235-1243. https://doi.org/10.1190/1.1441261.
Li, G., Liu, Y., Zheng, H., Huang, W., 2015. Absorption decomposition and compensation via a two-step scheme. Geophysics 80, V145-V155. https://doi.org/10.1190/geo2015-0038.1.
Li, H., Li, G.F., Ma, X., Zhang, J.L., Meng, Q.L., Zhang, Z.X., 2021. Multichannel deconvolution with spatial reflection regularization. Appl. Geophys. 18, 85-93.
Li, J., Wu, X., Hu, Z., 2022. Deep learning for simultaneous seismic image super-resolution and denoising. IEEE Trans. Geosci. Rem. Sens. 60, 1-11. https://doi.org/10.1109/TGRS.2021.3057857.
Li, Y., Alkhalifah, T., Huang, J., Li, Z., 2023. Self-supervised pretraining vision transformer with masked autoencoders for building subsurface model. IEEE Trans. Geosci. Rem. Sens. 61, 1-10. https://doi.org/10.1109/TGRS.2023.3308999.
Lin, L., Zhong, Z., Cai, C., Li, C., Zhang, H., 2023. SeisGAN: improving seismic smage resolution and reducing random noise using a generative adversarial network. Math. Geosci. https://doi.org/10.1007/s11004-023-10103-8.
Lin, Y., Chen, S., Zhang, G., Huang, M., Wang, B., 2022. High-resolution time–frequency analysis based on a synchroextracting adaptive S-transform and its application. J. Geophys. Eng. 19, 1124-1133. https://doi.org/10.1093/jge/gxac068.
Liu, D., Niu, W., Wang, X., Sacchi, M.D., Chen, W., Wang, C., 2023a. Improving vertical resolution of vintage seismic data by a weakly supervised method based on cycle generative adversarial network. Geophysics 88, V445-V458. https://doi.org/10.1190/geo2023-0006.1.
Liu, Q., Ma, J., 2024. Generative interpolation via a diffusion probabilistic model. Geophysics 89, V65-V85. https://doi.org/10.1190/geo2023-0182.1.
Liu, S., Birnie, C., Alkhalifah, T., 2023b. Trace-wise coherent noise suppression via a self-supervised blind-trace deep-learning scheme. Geophysics 88, V459-V472. https://doi.org/10.1190/geo2022-0371.1.
Ma, M., Wang, S., Yuan, S., Wang, J., Wen, J., 2017. Multichannel spatially correlated reflectivity inversion using block sparse Bayesian learning. Geophysics 82, V191-V199. https://doi.org/10.1190/geo2016-0366.1.
Margrave, G.F., 1998. Theory of nonstationary linear filtering in the fourier domain with application to time-variant filtering. Geophysics 63, 244-259. https://doi.org/10.1190/1.1444318.
Margrave, G.F., Lamoureux, M.P., Henley, D.C., 2011. Gabor deconvolution: estimating reflectivity by nonstationary deconvolution of seismic data. Geophysics 76, W15-W30. https://doi.org/10.1190/1.3560167.
Min, F., Wang, L., Pan, S., Song, G., 2023. D2UNet: dual decoder U-Net for seismic image super-resolution reconstruction. IEEE Trans. Geosci. Rem. Sens. 61, 1-13. https://doi.org/10.1109/TGRS.2023.3264459.
Oliveira, D.A.B., Ferreira, R.S., Silva, R., Brazil, E.V., 2019. Improving seismic data resolution with deep generative networks. Geosci. Rem. Sens. Lett. IEEE 16, 1929-1933. https://doi.org/10.1109/LGRS.2019.2913593.
Oropeza, V., Sacchi, M., 2011. Simultaneous seismic data denoising and reconstruction via multichannel singular spectrum analysis. Geophysics 76, V25-V32. https://doi.org/10.1190/1.3552706.
Pan, Z., Yu, W., Wang, B., Xie, H., Sheng, V.S., Lei, J., Kwong, S., 2020. Loss functions of generative adversarial networks (GANs): opportunities and challenges. IEEE Transact. Emerg. Topics Computat. Intellig. 4, 500-522. https://doi.org/10.1109/TETCI.2020.2991774.
Peacock, K.L., Treitel, S., 1969. Predictive deconvolution: theory and practice. Geophysics 34, 155-169. https://doi.org/10.1190/1.1440003.
Peng, J., Li, Y., Liao, Z., Wang, X., Yang, X., 2024. Seismic data strong noise attenuation based on diffusion model and principal component analysis. IEEE Trans. Geosci. Rem. Sens. 62, 1-11. https://doi.org/10.1109/TGRS.2024.3355460.
Puryear, C.I., Castagna, J.P., 2008. Layer-thickness determination and stratigraphic interpretation using spectral inversion: theory and application. Geophysics 73, R37-R48. https://doi.org/10.1190/1.2838274.
Robinson, E.A., 1967. Predictive decomposition of time series with application to seismic exploration. Geophysics 32, 418-484. https://doi.org/10.1190/1.1439873.
Sacchi, M.D., 1997. Reweighting strategies in seismic deconvolution. Geophys. J. Int. 129, 651-656. https://doi.org/10.1111/j.1365-246X.1997.tb04500.x.
Saharia, C., Ho, J., Chan, W., Salimans, T., Fleet, D.J., Norouzi, M., 2023. Image super-resolution via iterative refinement. IEEE Trans. Pattern Anal. Mach. Intell. 45, 4713-4726. https://doi.org/10.1109/TPAMI.2022.3204461.
Song, C., Wang, Y., 2022. High-frequency wavefield extrapolation using the Fourier neural operator. J. Geophys. Eng. 19, 269-282. https://doi.org/10.1093/jge/gxac016.
Stockwell, R., Mansinha, L., Lowe, R., 1996. Localization of the complex spectrum: the S transform. IEEE Trans. Signal Process. 44, 998-1001. https://doi.org/10.1109/78.492555.
Sun, H., Demanet, L., 2020. Extrapolated full-waveform inversion with deep learning. Geophysics 85, R275-R288. https://doi.org/10.1190/geo2019-0195.1.
Sun, Q.F., Xu, J.Y., Zhang, H.X., Duan, Y.X., Sun, Y.K., 2022. Random noise suppression and super-resolution reconstruction algorithm of seismic profile based on GAN. J. Pet. Explor. Prod. Technol. 12, 2107-2119. https://doi.org/10.1007/s13202-021-01447-0.
Sun, Y., Liu, Y., Dong, H., Chen, G., Li, X., 2024. Seismic AVO inversion method for viscoelastic media based on a tandem invertible neural network model. IEEE Trans. Geosci. Rem. Sens. 62, 1-18. https://doi.org/10.1109/TGRS.2024.3355481.
Sun, Y.H., Liu, Y., 2022. Model-data-driven P-wave impedance inversion using ResNets and the normalized zero-lag cross-correlation objective function. Petrol. Sci. 19, 2711-2719. https://doi.org/10.1016/j.petsci.2022.09.008.
Taylor, H.L., Banks, S.C., McCoy, J.F., 1979. Deconvolution with the L1 norm. Geophysics 44, 39-52. https://doi.org/10.1190/1.1440921.
Velis, D.R., 2008. Stochastic sparse-spike deconvolution. Geophysics 73, R1-R9. https://doi.org/10.1190/1.2790584.
Wang, F., Huang, X., Alkhalifah, T.A., 2023a. A prior regularized full waveform inversion using generative diffusion models. IEEE Trans. Geosci. Rem. Sens. 61, 1-11. https://doi.org/10.1109/TGRS.2023.3337014.
Wang, L., Gao, J., Zhao, W., Jiang, X., 2013. Enhancing resolution of nonstationary seismic data by molecular-Gabor transform. Geophysics 78, V31-V41. https://doi.org/10.1190/geo2011-0450.1.
Wang, Y., 2002. A stable and efficient approach of inverse Q filtering. Geophysics 67, 657-663. https://doi.org/10.1190/1.1468627.
Wang, Y., 2006. Inverse Q-filter for seismic resolution enhancement. Geophysics 71, V51-V60. https://doi.org/10.1190/1.2192912.
Wang, Y., Xu, J., Zhao, Z., Gao, Y., Zhang, H., 2024. Structurally-constrained unsupervised deep learning for seismic high-resolution reconstruction. IEEE Trans. Geosci. Rem. Sens. 62, 5901115. https://doi.org/10.1109/TGRS.2023.3340888.
Wu, X., Geng, Z., Shi, Y., Pham, N., Fomel, S., Caumon, G., 2020. Building realistic structure models to train convolutional neural networks for seismic structural interpretation. Geophysics 85, WA27-WA39. https://doi.org/10.1190/geo2019-0375.1.
Wu, X., Liang, L., Shi, Y., Fomel, S., 2019. FaultSeg3D: using synthetic data sets to train an end-to-end convolutional neural network for 3D seismic fault segmentation. Geophysics 84, IM35-IM45. https://doi.org/10.1190/geo2018-0646.1.
Xu, L., Gao, Z., Hu, S., Gao, J., Xu, Z., 2022. Simultaneous inversion for reflectivity and Q using nonstationary seismic data with deep-learning-based decoupling. IEEE Trans. Geosci. Rem. Sens. 60, 1-15. https://doi.org/10.1109/TGRS.2022.3226723.
Yang, L., Zhang, Z., Song, Y., Hong, S., Xu, R., Zhao, Y., Zhang, W., Cui, B., Yang, M.H., 2023a. Diffusion models: a comprehensive survey of methods and applications. ACM Comput. Surv. 56, 1-39. https://doi.org/10.1145/3626235.
Yang, N.X., Li, G.F., Li, T.H., Zhao, D.F., Gu, W.W., 2024. An improved deep dilated convolutional neural network for seismic facies interpretation. Petrol. Sci. 21, 1569-1583. https://doi.org/10.1016/j.petsci.2023.11.027.
Yang, S., Alkhalifah, T., Ren, Y., Liu, B., Li, Y., Jiang, P., 2023b. Well-log information-assisted high-resolution waveform inversion based on deep learning. Geosci. Rem. Sens. Lett. IEEE 20, 1-5. https://doi.org/10.1109/LGRS.2023.3234211.
Yao, Z., Gao, X., Li, W., 2003. The forward Q method for compensating attenuation and frequency dispersion used in the seismic profile of depth domain. Chin. J. Geophys. 46, 229-233 (in Chinese).
Zeng, D., Xu, Q., Pan, S., Song, G., Min, F., 2023. Seismic image super-resolution reconstruction through deep feature mining network. Appl. Intell. 53, 21875-21890. https://doi.org/10.1007/s10489-023-04660-y.
Zhang, C., Ulrych, T.J., 2007. Seismic absorption compensation: a least squares inverse scheme. Geophysics 72, R109-R114. https://doi.org/10.1190/1.2766467.
Zhang, G.L., Lin, J., Wand, X.M., He, Z.H., Cao, J.X., Zhang, J.J., He, X.L., Lin, K., Xue, Y.J., 2015. A self-adaptive approach for inverse Q-filtering. Chin. J. Geophys. 58, 2525-2535. https://doi.org/10.6038/cjg20150727.
Zhang, H., Alkhalifah, T., Liu, Y., Birnie, C., Di, X., 2023. Improving the generalization of deep neural networks in seismic resolution enhancement. Geosci. Rem. Sens. Lett. IEEE 20, 1-5. https://doi.org/10.1109/LGRS.2022.3229167.
Zhang, H., Chen, T., Liu, Y., Zhang, Y., Liu, J., 2021. Automatic seismic facies interpretation using supervised deep learning. Geophysics 86, IM15-IM33. https://doi.org/10.1190/geo2019-0425.1.
Zhang, H., Yang, P., Liu, Y., Luo, Y., Xu, J., 2022a. Deep learning-based low-frequency extrapolation and impedance inversion of seismic data. Geosci. Rem. Sens. Lett. IEEE 19, 1-5. https://doi.org/10.1109/LGRS.2021.3123955.
Zhang, M., Liu, Y., 2022. 3-D seismic data recovery via neural network-based matrix completion. Geosci. Rem. Sens. Lett. IEEE 19, 1-5. https://doi.org/10.1109/LGRS.2022.3154816.
Zhang, M., Liu, Y., Bai, M., Chen, Y., 2019b. Seismic noise attenuation using unsupervised sparse feature learning. IEEE Trans. Geosci. Rem. Sens. 57, 9709-9723. https://doi.org/10.1109/TGRS.2019.2928715.
Zhang, R., Castagna, J., 2011. Seismic sparse-layer reflectivity inversion using basis pursuit decomposition. Geophysics 76, R147-R158. https://doi.org/10.1190/geo2011-0103.1.
Zhang, S.B., Si, H.J., Wu, X.M., Yan, S.S., 2022b. A comparison of deep learning methods for seismic impedance inversion. Petrol. Sci. 19, 1019-1030. https://doi.org/10.1016/j.petsci.2022.01.013.
Zhou, H.L., Wang, J., Wang, M.C., Shen, M.C., Zhang, X.K., Liang, P., 2014. Amplitude spectrum compensation and phase spectrum correction of seismic data based on the generalized S transform. Appl. Geophys. 11, 468–478+510–511. https://doi.org/10.1007/s11770-014-0456-y.