Abstract
Least-squares migration (LSM) is a data-fitting imaging approach seeking the seismic reflectivity image of the most accurate amplitude and optimal resolution. However, the high computational cost of LSM has hindered its broad application. In this study, we combine a convolutional neural network (CNN) with LSM to significantly improve the computational efficiency while retaining the imaging quality. Taking CNN as a “projector,” we treat LSM as the “projection” from the ordinarily migrated images to the least-squares updated images. We conduct this CNN-assisted LSM in the shot gather domain using a Gaussian beam migration and the corresponding LSM. The training data for CNN consist of 10–15% of all shot gathers, with the Gaussian beam migrated shot gathers as the input and the LSM shot gathers as the target. After the training, the processing time for the remaining shot gathers took several minutes for 2D cases. The results from testing with the Sigsbee 2B synthetic dataset and a field marine dataset indicate the CNN-assisted LSM saved 80–90% of the computation time of the full LSM and achieved significantly higher image fidelity than that of the ordinary migration.
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References
Aki K, Richards PG (2002), Quantitative seismology. Lamont-doherty earth observatory of columbia university, Palisades
Aoki N, Schuster GT (2009) Fast least-squares migration with a deblurring filter. Geophysics 74(6):83–93
Bleistein N (1987) On the imaging of reflectors in the earth. Geophysics 52(7):931–942
Červený V, Pšenčík I (2010) Gaussian beams in inhomogeneous anisotropic layered structures. Geophys J Int 180(2):798–812
Červený V, Popov MM, Pšenčík I (1982) Computation of wave fields in inhomogeneous media—Gaussian beam approach. Geophys J Int 70(1):109–128
Claerbout JF, Abma R (1992) Earth soundings analysis: processing versus inversion, Blackwell Scientific Publications, London
Claerbout JF (1985) Imaging the earth's interior. Blackwell scientific publications, Oxford
Dai W, Schuster GT (2013) Plane-wave least-squares reverse-time migration. Geophysics 78(4):S165–S177
Gao K, Huang L, Zheng Y, Lin R, Hu H, Cladohous T (2022) Automatic fault detection on seismic images using a multiscale attention convolutional neural network. Geophysics 87(1):N13–N29
Geng ZC, Zhao ZY, Shi YZ, Wu XM, Fomel S, Sen M (2022) Deep learning for velocity model building with common-image gather volumes. Geophys J Int 228(2):1054–1070. https://doi.org/10.1093/gji/ggab385
Geng ZC, Wu XM, Shi YZ, Fomel S (2020) Deep learning for relative geologic time and seismic horizons. Geophysics 85(4):87–100. https://doi.org/10.1190/Geo2019-0252.1
Gray SH (2005) Gaussian beam migration of common-shot records. Geophysics 70(4):S71–S77
Gray SH, Bleistein N (2009) True-amplitude Gaussian-beam migration. Geophysics 74(2):S11–S23
Guitton A (2004) Amplitude and kinematic corrections of migrated images for nonunitary imaging operators. Geophysics 69(4):1017–1024
Guo R, Yao HM, Li MK, Ng MKP, Jiang LJ, Abubakar A (2021) Joint inversion of audio-magnetotelluric and seismic travel time data with deep learning constraint. IEEE Trans Geosci Remote Sens 59(9):7982–7995. https://doi.org/10.1109/Tgrs.2020.3032743
Hale D (1992) Migration by the Kirchhoff, slant stack, and Gaussian beam methods Rep., Colorado School of Mines, CO (United States). Center for Wave Phenomena, Golden.
Hanitzsch C (1997) Comparison of weight in prestack amplitude-preserving Kirchhoff depth migration. Geophysics 62:1812–1816
He K, Zhang X, Ren S and Sun J (2016), Deep residual learning for image recognition, paper presented at Proceedings of the IEEE conference on computer vision and pattern recognition.
Hill NR (1990) Gaussian beam migration. Geophysics 55(11):1416–1428
Hill NR (2001) Prestack Gaussian-beam depth migration. Geophysics 66(4):1240–1250
Hu JX, Schuster GT, Valasek PA (2001) Poststack migration deconvolution. Geophysics 66(3):939–952
Hu H, Liu YK, Zheng YC, Liu XJ, Lu HY (2016) Least-squares Gaussian beam migration. Geophysics 81(3):S87–S100
Jin S, Madariaga R, Virieux J, Lambaré G (1992) Two-dimensional asymptotic iterative elastic inversion. Geophys J Int 108:575–588
Kaur H, Pham N and Fomel S (2019) Estimating the inverse Hessian for amplitude correction of migrated images using deep learning, paper presented at SEG International exposition and annual meeting, OnePetro.
Kaur H, Pham N, Fomel S (2020) Improving the resolution of migrated images by approximating the inverse Hessian using deep learning. Geophysics 85(4):Wa173–Wa183. https://doi.org/10.1190/Geo2019-0315.1
Kaur H, Sun J, Aharchaou M, Baumstein A, Fomel S (2022) Deep learning framework for true amplitude imaging: effect of conditioners and initial models. Geophys Prospect. https://doi.org/10.1111/1365-2478.13234
Kaur H (2022) Improving accuracy and efficiency of seismic data analysis using deep learning (Doctoreal dissertation).
Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. Adv Neural Inform Process Syst 25:84–90
Kühl H, Sacchi MD (2003) Least-squares wave-equation migration for AVP/AVA inversion. Geophysics 68(1):262–273
LeCun Y, Bengio Y, Hinton G (2015) Deep learning. Nature 521(7553):436–444
Li SC, Liu B, Ren YX, Chen YK, Yang SL, Wang YH, Jiang P (2020) Deep-learning inversion of seismic data. IEEE Trans Geosci Remote Sens 58(3):2135–2149. https://doi.org/10.1109/Tgrs.2019.2953473
Li Y, Wang Y, Wu N (2021) Noise suppression method based on multi-scale dilated convolution network in desert seismic data. Comput Geosci 156:104910
Liu QC, Peter D (2018) One-step data-domain least-squares reverse time migration. Geophysics 83(4):R361–R368
Liu D, Wang W, Wang X, Wang C, Pei J, Chen W (2019) Poststack seismic data denoising based on 3-D convolutional neural network. IEEE Trans Geosci Remote Sens 58(3):1598–1629
Liu Z, Chen Y, Schuster G (2020) Deep convolutional neural network and sparse least-squares migration. Geophysics 85(4):WA241–WA253
McCann MT, Jin KH, Unser M (2017) Convolutional neural networks for inverse problems in imaging A review. IEEE Signal Proc Mag 34(6):85–95. https://doi.org/10.1109/Msp.2017.2739299
Nemeth T, Wu C, Schuster GT (1999) Least-squares migration of incomplete reflection data. Geophysics 64(1):208–221
Popov MM, Semtchenok NM, Popov PM, Verdel AR (2010) Depth migration by the Gaussian beam summation method. Geophysics 75(2):S81–S93
Ronneberger O, Fischer P and Brox T (2015), U-net: convolutional networks for biomedical image segmentation, paper presented at international conference on medical image computing and computer-assisted intervention. Springer, Munich.
Schleicher J, Tygel M, Hubral P (1993) 3-D true-amplitude finite-offset migration. Geophysics 58:1112–1126
Schuster GT (1993) Least-squares cross-well migration in SEG technical program expanded abstracts 1993, edited, Society of Exploration Geophysicists. Beijing, pp. 110–113 https://doi.org/10.1190/1.1822308
Shi YZ, Wu XM, Fomel S (2019) SaltSeg: automatic 3D salt segmentation using a deep convolutional neural network. Interpretation-J Sub 7(3):Se113–Se122. https://doi.org/10.1190/Int-2018-0235.1
Shi YZ, Wu XM, Fomel S (2020) Waveform embedding: Automatic horizon picking with unsupervised deep learning. Geophysics 85(4):Wa67–Wa76. https://doi.org/10.1190/Geo2019-0438.1
Tang SH, Ding YS, Zhou HW, Zhou H (2020) Reconstruction of sparsely sampled seismic data via residual U-net. IEEE Geosci Remote Sens Lett 19:3035835. https://doi.org/10.1109/Lgrs.2020.3035835
Tarantola A (1986) A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics 51(10):1893–1903
Wang Y, Wang B, Tu N, Geng J (2020) Seismic trace interpolation for irregularly spatial sampled data using convolutional autoencoder. Geophysics 85(2):V119–V130
Wei Z, Hu H, Zhou H-W, Lau A (2019) Characterizing rock facies using machine learning algorithm based on a convolutional neural network and data padding strategy. Pure Appl Geophys 176(8):3593–3605
Wu H, Zhang B, Li FY, Liu NH (2019a) Semiautomatic first-arrival picking of microseismic events by using the pixel-wise convolutional image segmentation method. Geophysics 84(3):V143–V155. https://doi.org/10.1190/Geo2018-0389.1
Wu H, Zhang B, Lin TF, Cao DP, Lou YH (2019b) Semiautomated seismic horizon interpretation using the encoder-decoder convolutional neural network. Geophysics 84(6):B403–B417. https://doi.org/10.1190/Geo2018-0672.1
Wu H, Zhang B, Lin TF, Li FY, Liu NH (2019c) White noise attenuation of seismic trace by integrating variational mode decomposition with convolutional neural network. Geophysics 84(5):V307–V317. https://doi.org/10.1190/Geo2018-0635.1
Wu XM, Liang LM, Shi YZ, Fomel S (2019) FaultSeg3D: Using synthetic data sets to train an end-to-end convolutional neural network for 3D seismic fault segmentation. Geophysics 84(3):Im35–Im45. https://doi.org/10.1190/Geo2018-0646.1
Xia K, Hilterman F, Hu H (2018) Unsupervised machine learning algorithm for detecting and outlining surface waves on seismic shot gathers. J Appl Geophys 157:73–86
Xu B, Wang N, Chen T and Li M (2015), Empirical evaluation of rectified activations in convolutional network. arXiv preprint arXiv:1505.00853.
Xu P, Wang H, Guo S and Wu C (2020) RTM deblurring with flexible WKBJ PSFs, paper presented at SEG International Exposition and Annual Meeting. Oklahoma, OnePetro.
Yang FS, Ma JW (2019) Deep-learning inversion: A next-generation seismic velocity model building method. Geophysics 84(4):R585-584. https://doi.org/10.1190/Geo2018-0249.1
Yuan P, Wang S, Hu W, Nadukandi P, Botero GO, Wu X, Van Nguyen H, Chen J (2022) Self-supervised learning for efficient antialiasing seismic data interpolation. IEEE Trans Geosci Remote Sens 60:1–19
Zhang Y, Ratcliffe A, Roberts G, Duan L (2014) Amplitude-preserving reverse time migration: from reflectivity to velocity and impedance inversion. Geophysics 79(6):S271–S283
Zhang HR, Yang P, Liu Y, Luo YN, Xu JY (2021a) Deep learning-based low-frequency extrapolation and impedance inversion of seismic data. IEEE Geosci Remote Sens Lett 19:3123955. https://doi.org/10.1109/Lgrs.2021.3123955
Zhang W, Gao JH, Jiang XD, Sun WB (2021b) Consistent least-squares reverse time migration using convolutional neural networks. IEEE Trans Geosci Remote Sens 60:3116455. https://doi.org/10.1109/Tgrs.2021.3116455
Zhong Z, Sun AY, Wu XM (2020) Inversion of time-lapse seismic reservoir monitoring data using cycleGAN: a deep learning-based approach for estimating dynamic reservoir property changes. J Geophys Res Sol Ea 125(3):18408. https://doi.org/10.1029/2019JB018408
Zhou H (2014) Practical seismic data analysis. Cambridge University Press
Zhou H, Zou Z, Li Z (2021) Detecting artifacts in seismic profiles. Rev Geophys Planet Phys Chin 52(1):45–53. https://doi.org/10.19975/j.dqyxx.2020-003
Acknowledgements
Part of this study is supported by NSF Grant (OCE-1832197). We benefit from the discussions with Dr. August Lau and Dr. Alfonso Gonzalez. We appreciate the insightful comments from the three anonymous reviewers.
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Wu, B., Hu, H. & Zhou, HW. Convolutional Neural Network-Assisted Least-Squares Migration. Surv Geophys 44, 1107–1124 (2023). https://doi.org/10.1007/s10712-023-09777-w
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DOI: https://doi.org/10.1007/s10712-023-09777-w