ABSTRACT
A novel recursive, self-supervised machine-learning (ML) inversion scheme is developed. It is applied for fast and accurate full-waveform inversion of land seismic data. ML generalization is enhanced by using virtual super gathers (VSGs) of field data for training. These are obtained from midpoint-offset sorting and stacking after applying surface-consistent corrections from the decomposition of the transmitted wavefield. The procedure implements reinforcement learning concepts by adopting an inversion agent to interact with the environment and explore the model space under a data misfit optimization policy. The generated parameter distributions and related forward responses are used as new training samples for supervised learning. The active learning (AL) paradigm is further embedded in the procedure, for which queries on data diversity and uncertainty are used to generate fully informative reduced sets for training. The procedure is recursive. At each cycle, the physics-based inversion is coupled to the ML predictions via penalty terms that promote a long-term data misfit reduction. The resulting self-supervised, AL, physics-driven deep-learning inversion generalizes well with field data. The method is applied to perform full-waveform inversion (FWI) of a complex land seismic data set characterized by transcurrent faulting and related structures. High signal-to-noise VSGs are inverted with a 1.5D Laplace-Fourier FWI scheme. The AL inversion procedure uses a small fraction of data for training while achieving sharper velocity reconstructions and a lower data misfit when compared with previous results. AL FWI is highly generalizable and effective for land seismic velocity model building and for other inversion scenarios.
REFERENCES
- , 2017, Solving ill-posed inverse problems using iterative deep neural networks: Inverse Problems, 33,
124007 , doi:10.1088/1361-6420/aa9581 .INPEEY 0266-5611 - , 2016, 1D elastic full-waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm-Gibbs sampler approach: Geophysical Prospecting, 65,
64–85 , doi:10.1111/1365-2478.12397 .GPPRAR 0016-8025 - , 2020, Robust concurrent detection of salt domes and faults in seismic surveys using an improved U-Net architecture: IEEE Access, 10,
39424–39435 , doi:10.1109/ACCESS.2020.3043973 . - . 2022, Inversion using adaptive physics-based neural network: Application to magnetotelluric inversion: Geophysical Prospecting, 70,
1252–1272 , doi:10.1111/1365-2478.13215 .GPPRAR 0016-8025 - , 2021, A survey of active learning for quantifying vegetation traits from terrestrial earth observation data: Remote Sensing, 13,
287 , doi:10.3390/rs13020287 .RSEND3 - , 2022, Introduction to machine learning: Wolfram.
- , 2013, Pattern recognition with fuzzy objective function algorithms: Springer Science & Business Media.
- , 1966, Hierarchical cluster analysis: Psychological Reports, 18,
851–854 , doi:10.2466/pr0.1966.18.3.851 .PYRTAZ - , 2009, Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion: Geophysics, 74, no. 6,
WCC105–WCC118 , doi:10.1190/1.3215771 .GPYSA7 0016-8033 - , 2011, Convergence rates of efficient global optimization algorithms: Journal of Machine Learning Research, 12,
2879–2904 . - , 2009, Algorithmic strategies for full waveform inversion: 1D experiments: Geophysics, 74, no. 6,
WCC37–WCC46 , doi:10.1190/1.3237116 .GPYSA7 0016-8033 - , 2011, Recovering long wavelength of the velocity model using waveform inversion in the Laplace domain: Application to field data:
81st Annual International Meeting, SEG , Expanded Abstracts,2549–2554 , doi:10.1190/1.3627721 . - , 1992, Surface-consistent deconvolution in the log/Fourier domain: Geophysics, 57,
823–840 , doi:10.1190/1.1443296 .GPYSA7 0016-8033 - , 2022, Accelerating 2D and 3D frequency-domain seismic wave modeling through interpolating frequency-domain wavefields by deep learning: Geophysics, 87, no. 4,
T315–T328 , doi:10.1190/geo2021-0435.1 .GPYSA7 0016-8033 Cdipaolo96 , 2016, Gaussian process regression, https://commons.wikimedia.org/wiki/File:Gaussian_Process_Regression.png, accessed 12 February 2024.- , 2020, Seismic inversion by Newtonian machine learning: Geophysics, 85, no. 4,
WA185–WA200 , doi:10.1190/geo2019-0434.1 .GPYSA7 0016-8033 - , 2020, Physics-constrained deep learning of geomechanical logs: IEEE Transactions on Geoscience and Remote Sensing, 58,
5932–5943 , doi:10.1109/TGRS.2020.2973171 .IGRSD2 0196-2892 - , 2020a, Deep-learning electromagnetic monitoring coupled to fluid flow simulators: Geophysics, 85, no. 4,
WA1–WA12 , doi:10.1190/geo2019-0428.1 .GPYSA7 0016-8033 - , 2018, Coupling strategies in multi-parameter geophysical joint inversion: Geophysical Journal International, 215,
1171–1184 , doi:10.1093/gji/ggy341 .GJINEA 0956-540X - , 2020b, Transmission-based near-surface deconvolution: Geophysics, 85, no. 2,
V169–V181 , doi:10.1190/geo2019-0443.1 .GPYSA7 0016-8033 - , 2017, Near-surface and anisotropy modeling for efficient land seismic depth imaging in low-relief geology: Interpretation, 5, no. 4,
SR1–SR12 , doi:10.1190/INT-2017-0036.1 . - , 2021c, Near-surface full-waveform inversion in a transmission surface-consistent scheme: Geophysics, 86, no. 2,
U15–U29 , doi:10.1190/geo2020-0474.1 .GPYSA7 0016-8033 - , 2021b, Coupled physics-deep learning inversion: Computers and Geosciences, 157,
104917 , doi:10.1016/j.cageo.2021.104917 .CGEODT 0098-3004 - , 2021a, Physics-driven deep learning inversion with application to transient electromagnetics: Geophysics, 86, no. 3,
E209–E224 , doi:10.1190/geo2020-0760.1 .GPYSA7 0016-8033 - , 2023b, Geophysical inversion via dynamic and adaptive learning Gaussian process with statistical sampling:
84th Annual International Conference and Exhibition, EAGE , Extended Abstracts, doi:10.3997/2214-4609.202310199 . - , 2023a, Machine learning inversion via adaptive learning and statistical sampling: Application to airborne micro-TEM for seismic sand corrections: Geophysics, 88, no. 3,
K51–K68 , doi:10.1190/geo2022-0407.1 .GPYSA7 0016-8033 - , 2013, Active learning: Any value for classification of remotely sensed data? Proceedings of the IEEE, 101,
593–608 , doi:10.1109/JPROC.2012.2231951 .IEEPAD 0018-9219 - , 2021, Bayesian deep learning with Monte Carlo dropout for qualification of semantic segmentation:
IEEE International Geoscience and Remote Sensing Symposium . - , 2022, Combining geophysical inversion with reinforcement learning:
83rd Annual International Conference and Exhibition, EAGE , Extended Abstracts, doi:10.3997/2214-4609.202210229 . - , 2000, Pattern classification, 2nd ed.: A Wiley-Interscience Publication, Wiley Hoboken.
- , 2014, Automatic model construction with Gaussian processes: PhD thesis, University of Cambridge.
- , 2023, DRIP: Deep regularizers for inverse problems: arXiv preprint, doi:
10.48550/arXiv.2304.00015 . - , 1996, A density-based algorithm for discovering clusters in large spatial databases with noise:
2nd International Conference on Knowledge Discovery and Data Mining . - , 2021, Improving uncertainty analysis in well log classification by machine learning with a scaling algorithm: Journal of Petroleum Science and Engineering, 196,
107995 , doi:10.1016/j.petrol.2020.107995 .JPSEE6 0920-4105 - , 1997, Gauss-Newton approximation to Bayesian learning:
Proceedings of the International Joint Conference on Neural Networks . - , 2020, Limitations of physics informed machine learning for nonlinear two-phase transport in porous media: Journal of Machine Learning for Modeling and Computing, 1,
19–37 , doi:10.1615/JMachLearnModelComput.2020033905 . - , 2016, Dropout as a Bayesian approximation: Representing model uncertainty in deep learning:
Proceedings of the 33rd International Conference on Machine Learning ,1050–1059 . - , 2004, Joint two-dimensional DC resistivity and seismic travel time inversion with cross-gradients constraints: Journal of Geophysical Research, 109,
B03311 , doi:10.1029/2003JB002716 .JGREA2 0148-0227 - , 2014, Bayesian optimization with unknown constraints, in N. L. ZhangJ. Tian, eds.,
Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence ,250–259 . - , 2009,
Incremental learning , in S. Z. LiA. Jain, eds., Encyclopedia of biometrics: Springer. - , 2011, A tutorial on Gaussian processes (or why I don’t use SVMs): Machine Learning Summer School.
- , 2016, Deep learning: MIT Press.
- , 1995, Migration from topography: Improving the near-surface image: Canadian Journal of Exploration Geophysics, 31,
18–24 . - , 2018, Application of supervised descent method for transient EM data inversion:
88th Annual International Meeting, SEG , Expanded Abstracts,2126–2130 , doi:10.1190/segam2018-2998074.1 . - , 2020, Physics-guided self-supervised learning for low frequency data prediction in FWI:
90th Annual International Meeting, SEG , Expanded Abstracts,875–879 , doi:10.1190/segam2020-3423396.1 . - , 2011, Computational ocean acoustics, 2nd ed.: Springer.
- , 2019, Using a physics-driven deep neural network to solve inverse problems for LWD azimuthal resistivity measurements: Presented at the
60th Annual Logging Symposium, SPWLA . - , 2012, Tutorial: Incorporating near-surface velocity anomalies in pre-stack depth migration models: First Break, 30,
47–58 , doi:10.3997/1365-2397.2011041 . - , 2021, Physics informed machine learning: Nature Reviews Physics, 3,
422–440 , doi:10.1038/s42254-021-00314-5 . - , 2020, Seismic ground-roll noise attenuation using deep learning: Geophysical Prospecting, 68,
2064–2077 , doi:10.1111/1365-2478.12985 .GPPRAR 0016-8025 - , 2023, Efficient 1.5D full waveform inversion in the Laplace-Fourier domain: Inverse Problems, 39,
075012 , doi:10.1088/1361-6420/acda59 .INPEEY 0266-5611 - , 1944, A method for the solution of certain non-linear problems in least-squares: Quarterly of Applied Mathematics, 2,
164–168 , doi:10.1090/qam/10666 .QAMAAY 0033-569X - , 2018, Classifying geological structure elements from seismic images using deep learning:
88th Annual International Meeting, SEG , Expanded Abstracts,4643–4648 , doi:10.1190/segam2018-2998036.1 . - , 2022, Machine learning inversions incorporating geologic information through variational autoencoder and physics-based neural network:
Second International Meeting for Applied Geoscience & Energy, SEG , Expanded Abstracts,2977–2980 , doi:10.1190/image2022-3746882.1 . - , 1989, On the limited memory method for large scale optimization: Mathematical Programming B, 45,
503–528 , doi:10.1007/BF01589116 . - , 2020, Seismic facies classification using supervised convolutional neural networks and semisupervised generative adversarial networks: Geophysics, 85, no. 4,
O47–O58 , doi:10.1190/geo2019-0627.1 .GPYSA7 0016-8033 - , 2013, Elastic full waveform inversion for near surface imaging in CMP domain:
83rd Annual International Meeting, SEG , Expanded Abstracts,1904–1908 , doi:10.1190/segam2013-1066.1 . - , 1992, Bayesian interpolation: Neural Computation, 4,
415–447 , doi:10.1162/neco.1992.4.3.415 .NEUCEB 0899-7667 - , 1963, An algorithm for least-squares estimation of nonlinear parameters: SIAM Journal on Applied Mathematics, 11,
431–441 , doi:10.1137/0111030 .SMJMAP 0036-1399 - , 2002, The learning-curve sampling method applied to model-based clustering: Journal of Machine Learning Research, 2,
397–418 . - , 2020, The geometry of semi-supervised learning: Ph.D. Thesis, Harvard University, Cambridge, Massachusetts.
- , 2020, One-dimensional deep learning inversion of electromagnetic induction data using convolutional neural network: Geophysical Journal International, 222,
247–259 , doi:10.1093/gji/ggaa161 .GJINEA 0956-540X - , 2011, A framework for 3-D joint inversion of MT, gravity and seismic refraction data: Geophysical Journal International, 184,
477–493 , doi:10.1111/j.1365-246X.2010.04856.x .GJINEA 0956-540X - , 2018, Fast approximate simulation of seismic waves with deep learning: arXiv preprint, doi:
10.48550/arXiv.1807.06873 . - , 2012, Machine learning: A probabilistic perspective: MIT Press,
Adaptive Computation and Machine Learning Series . - , 2016, A self-taught artificial agent for multi-physics computational model personalization: Medical Image Analysis, 34,
52–64 , doi:10.1016/j.media.2016.04.003 . - , 2012, 3D finite-difference modeling of elastic wave propagation in the Laplace-Fourier domain: Geophysics, 77, no. 4,
T137–T155 , doi:10.1190/geo2011-0238.1 .GPYSA7 0016-8033 - , 2014, Three-dimensional inverse modelling of damped elastic wave propagation in the Fourier domain: Geophysical Journal International, 198,
1599–1617 , doi:10.1093/gji/ggu222 .GJINEA 0956-540X - , 2019, Automatic channel detection using deep learning: Interpretation, 7, no. 3,
SE43–SE50 , doi:10.1190/INT-2018-0202.1 . - , 2022, Physics-constrained deep learning for ground roll attenuation: Geophysics, 87, no. 1,
V15–V27 , doi:10.1190/geo2020-0691.1 .GPYSA7 0016-8033 - , 2020, Missing well log prediction using convolutional long short-term memory network: Geophysics, 85, no. 4,
WA159–WA171 , doi:10.1190/geo2019-0282.1 .GPYSA7 0016-8033 - , 2006, A review of the adjoint-state method for computing the gradient of a functional with geophysical applications: Geophysical Journal International, 167,
495–503 , doi:10.1111/j.1365-246X.2006.02978.x .GJINEA 0956-540X - , 2019, Deep learning electromagnetic inversion with convolutional neural networks: Geophysical Journal International, 218,
817–832 , doi:10.1093/gji/ggz204 .GJINEA 0956-540X - , 2019, Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations: Journal of Computational Physics, 378,
686–707 , doi:10.1016/j.jcp.2018.10.045 .JCTPAH 0021-9991 - , 2019, Bayesian geophysical inversion with trans-dimensional Gaussian process machine learning: Geophysical Journal International, 217,
1706–1726 , doi:10.1093/gji/ggz111 .GJINEA 0956-540X - , 1996, Q-learning combined with spreading: Convergence and results:
Proceedings of the ISRF-IEE International Conference: Intelligent and Cognitive Systems (Neural Networks Symposium) ,32–36 . - , 2019, Seismic data denoising and deblending using deep learning: arXiv preprint, doi:
10.48550/arXiv.1907.01497 . - , 2015, Laplace–Fourier FWI as an alternative model building tool for depth imaging studies: Application to marine carbonates field:
85th Annual International Meeting, SEG , Expanded Abstracts,1054–1058 , doi:10.1190/segam2015-5899569.1 . - , 2018, Analysis of inter-domain coupling constraints for multi-physics joint inversion: Inverse Problems, 34,
124006 , doi:10.1088/1361-6420/aadbc4 .INPEEY 0266-5611 - , 2019, Machine learning and geophysical inversion — A numerical study: The Leading Edge, 38,
512–519 , doi:10.1190/tle38070512.1 . - , 2017, DBSCAN revisited, revisited: Why and how you should (still) use DBSCAN: ACM Transactions on Database Systems, 42,
1–21 , doi:10.1145/3068335 .ATDSD3 0362-5915 - , 2018, A tutorial on Gaussian process regression: Modelling, exploring, and exploiting functions: Journal of Mathematical Psychology, 85,
1–16 , doi:10.1016/j.jmp.2018.03.001 .JMTPAJ 0022-2496 - , 2023, A well in the Wadi — An integrated geophysical and geological solution to unravel complex geology: MEOS-GEO Bahrain.
- , 2009, Active learning literature survey: Computer Sciences Technical Report 1648, University of Wisconsin–Madison, Madison, WI, USA.
- , 2020, A deep learning approach to the inversion of borehole resistivity measurements: Computational Geosciences, 24,
971–994 , doi:10.1007/s10596-019-09859-y . - , 2009, Waveform inversion in the Laplace–Fourier domain: Geophysical Journal International, 177,
1067–1079 , doi:10.1111/j.1365-246X.2009.04102.x .GJINEA 0956-540X - , 2020, ML-descent: An optimization algorithm for full-waveform inversion using machine learning: Geophysics, 85, no. 6,
R477–R492 , doi:10.1190/geo2019-0641.1 .GPYSA7 0016-8033 - , 2022, Deep learning-based shot-domain seismic deblending: Geophysics, 87, no. 3,
V215–V226 , doi:10.1190/geo2020-0865.1 .GPYSA7 0016-8033 - , 2016, Joint inversion of multiple geophysical data using guided fuzzy c-means clustering: Geophysics, 81, no. 3,
ID37–ID57 , doi:10.1190/geo2015-0457.1 .GPYSA7 0016-8033 - , 2018, Magnetization clustering inversion — Part 1: Building an automated numerical optimization algorithm: Geophysics, 83, no. 5,
J61–J73 , doi:10.1190/geo2017-0844.1 .GPYSA7 0016-8033 - , 1999, Handling concept drifts in incremental learning with support vector machines:
Proceedings of ACM International Conference on Knowledge Discovery and Data Mining ,317–321 . - , 1981, Surface-consistent corrections: Geophysics, 46,
17–22 , doi:10.1190/1.1441133 .GPYSA7 0016-8033 - , 1974, Estimation and correction of near surface time anomalies: Geophysics, 39,
441–463 , doi:10.1190/1.1440441 .GPYSA7 0016-8033 - , 2009, The elements of statistical learning: Data mining, inference, and prediction: Springer.
- , 2018, First-break automatic picking with deep semisupervised learning neural network:
88th Annual International Meeting, SEG , Expanded Abstracts,2181–2185 , doi:10.1190/segam2018-2998106.1 . - , 2009, An overview of full-waveform inversion in exploration geophysics: Geophysics, 74, no. 6,
WCC1–WCC26 , doi:10.1190/1.3238367 .GPYSA7 0016-8033 - , 2022, Stochastic inversion of magnetotelluric data using deep reinforcement learning: Geophysics, 87, no. 1,
E49–E61 , doi:10.1190/geo2020-0425.1 .GPYSA7 0016-8033 - , 2021, Physics-constrained seismic impedance inversion based on deep learning: IEEE Geoscience and Remote Sensing Letters, 19,
1–5 , doi:10.1109/LGRS.2021.3072132 . - , 1998, Plio-quaternary movement of the East Arabian block: GeoArabia, 3,
509–540 , doi:10.2113/geoarabia0304509 . - , 1976, Residual static analysis as a general linear inverse problem: Geophysics, 41,
922–938 , doi:10.1190/1.1440672 .GPYSA7 0016-8033 - , 2020, Integrating physics-based modeling with machine learning: A survey: arXiv preprint.
- , 2019b, FaultSeg3D: Using synthetic data sets to train an end-to-end convolutional neural network for 3D seismic fault segmentation: Geophysics, 84, no. 3,
IM35–IM45 , doi:10.1190/geo2018-0646.1 .GPYSA7 0016-8033 - , 2019a, Multitask learning for local seismic image processing: Fault detection, structure-oriented smoothing with edge-preserving, and seismic normal estimation by using a single convolutional neural network: Geophysical Journal International, 219,
2097–2109 , doi:10.1093/gji/ggz418 .GJINEA 0956-540X - , 2020, Removal of multisource noise in airborne electromagnetic data based on deep learning: Geophysics, 85, no. 6,
B207–B222 , doi:10.1190/geo2019-0555.1 .GPYSA7 0016-8033 - , 2018, DeepDetect: A cascaded region-based densely connected network for seismic event detection: IEEE Transactions on Geoscience and Remote Sensing, 57,
62–75 , doi:10.1109/TGRS.2018.2852302 .IGRSD2 0196-2892 - , 2013, Supervised descent method and its application to face alignment:
Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition ,532–539 . - , 2022, Deep learning inversion of gravity data for detection of CO2 plumes in overlying aquifers: Journal of Applied Geophysics, 196,
104507 , doi:10.1016/j.jappgeo.2021.104507 .JAGPEA 0926-9851 - , 2021, Bioinspired scene classification by deep active learning with remote sensing applications: IEEE Transactions on Cybernetics, 52,
5682–5694 , doi:10.1109/TCYB.2020.2981480 . - , 2018, Seismic facies classification using different deep convolutional neural networks:
88th Annual International Meeting, SEG , Expanded Abstracts,2046–2050 , doi:10.1190/segam2018-2997085.1 . - , 2017, Wave-dynamics simulation using deep neural networks, http://cs231n.stanford.edu/reports/2017/pdfs/542.pdf, accessed 12 February 2024.
- , 2022, First break picking with deep learning — Evaluation of network architectures: Geophysical Prospecting, 70,
318–342 , doi:10.1111/1365-2478.13162 .GPPRAR 0016-8025
