Abstract
The understanding of subsurface information on the Earth is crucial in numerous fields such as economics of oil and gas, geophysical exploration, archaeology and hydro-geophysics, particularly in a context of climate change. The methodology consists in reconstructing the seismic velocity model of the near surface, that contains information about the basement structure, by solving the inverse problem and resolving the related complex nonlinear systems with the data collected from seismic experiments and measurements. In the last few years, many deep neural networks have been proposed to simplify the seismic inversion problem based, for instance, on automatic differentiation of the adjoint operator, or on automatic arrival time picking. However, such approaches require a large amount of labeled training data, which are hardly available in real applications. We present here a deep learning approach for arrival time picking, aimed to deal with unlabeled data. The main building blocks are transfer learning, as well as a semi-supervised learning strategy where the pseudo-labels are greedily computed with robust regression, and classification algorithms. The hybrid method showcases very high scores when evaluating on synthetic data, and its application to a real dataset containing a limited amount of labeled data shows the computational efficiency and very accurate results.
Similar content being viewed by others
References
Adler A, Araya-Polo M, Poggio T (2021) Deep learning for seismic inverse problems: toward the acceleration of geophysical analysis workflows. IEEE Signal Process Mag 38(2):89–119. https://doi.org/10.1109/MSP.2020.3037429
Akazawa T (2004) A technique for automatic detection of onset time of p-and s-phases in strong motion records. In: Proc of the 13th World Conf. on Earthquake Engineering, Vancouver, Canada
Aki K, Richards PG (1980) Quantitative seismology, theory and methods. W. H, Freeman, San Francisco, USA
Araya-Polo M, Jennings J, Adler A, Dahlke T (2018) Deep-learning tomography. Lead Edge 37(1):58–66
Baeten G, Maag JAD, Plessix RE, Klaasen R, Qureshi T, Kleemeyer M, ten Kroode APE, Rujie Z (2013) The use of low frequencies in a full-waveform inversion and impedance inversion land seismic case study. Geophys Prospect 61(4):701–711
Bauer K, Schulze A, Ryberg T, Sobolev SV, Weber M (2003) Classification of lithology from seismic tomography: a case study from the messum igneous complex, namibia. J Geophys Res 108:2152
Bauer K, Moeck I, Norden B, Schulze A, Weber M, Wirth H (2010) Tomographic p wave velocity and vertical velocity gradient structure across the geothermal site groß schönebeck (ne german basin): Relationship to lithology, salt tectonics, and thermal regime. Journal of Geophysical Research: Solid Earth, 115(B8), https://doi.org/10.1029/2009JB006895, https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2009JB006895
Baumann-Wilke M, Bauer K, Schovsbo NH, Stiller M (2012) P-wave traveltime tomography for a seismic characterization of black shales at shallow depth on Bornholm Denmark. Geophysics 77(5):EN53–EN60. https://doi.org/10.1190/geo2011-0326.1
Baydin AG, Pearlmutter BA, Radul AA, Siskind JM (2018) Automatic differentiation in machine learning: a survey. J Mach Learn Res 18:1–43
Bergamo P, Dashwood B, Uhlemann S, Swift R, Chambers JE, Gunn DA, Donohue S (2016) Time-lapse monitoring of fluid-induced geophysical property variations within an unstable earthwork using p-wave refraction. Geophysics 81(4):EN17–EN27. https://doi.org/10.1190/geo2015-0276.1
Bianco MJ, Gerstoft P, Olsen KB, Lin FC (2019) High-resolution seismic tomography of long beach, ca using machine learning. Sci Rep 9(1):1–11
Billette F, Lambare G (1998) Velocity macro-model estimation from seismic reflection data by stereotomography. Geophys J Int 135(2):671–690
Bodet L, Jacob X, Tournat V, Mourgues R, Gusev V (2010) Elasticity profile of an unconsolidated granular medium inferred from guided waves: Toward acoustic monitoring of analogue models. Tectonophysics 496:99–104
Bodet L, Dhemaied A, Martin R, Mourgues R, Rejiba F, Tournat V (2014) Small-scale physical modeling of seismic-wave propagation using unconsolidated granular media. Geophysics 79(6):T323–T339
Bording RP, Gersztenkorn A, Lines LR, Scales JA, Treitel S (1987) Applications of seismic travel-time tomography. Geophys J Int 90(2):285–303
Cao D, Liao W (2015) A computational method for full waveform inversion of crosswell seismic data using automatic differentiation. Comput Phys Commun 188:47–58
Carriere S, Chalikakis K, Danquigny C, Davi H, Mazzilli N, Ollivier C, Emblanch C (2016) The role of porous matrix in water flow regulation within a karst unsaturated zone: an integrated hydrogeophysical approach. Hydrogeol J 24(7):1905–1918. https://doi.org/10.1007/s10040-016-1425-8
Chai C, Maceira M, Santos-Villalobos HJ, Venkatakrishnan SV, Schoenball M, Zhu W, Beroza GC, Thurber C, Team EC (2020) Using a deep neural network and transfer learning to bridge scales for seismic phase picking. Geophys Res Lett 47(16):e2020GL088651
Dai T, Xia J, Ning L, Chaoqiang X, Liu Y, Xing H (2021) Deep learning for extracting dispersion curves. Surv Geophys 42:1–27. https://doi.org/10.1007/s10712-020-09615-3
Dangeard M (2019) Développement d’une approche “ time-lapse ” des méthodes sismiques pour l’hydrogéophysique et la compréhension de la dynamique des hydrosystèmes. Theses, Sorbonne Université, https://tel.archives-ouvertes.fr/tel-02931838
Dangeard M, Bodet L, Pasquet S, Thiesson J, Guérin R, Jougnot D, Longuevergne L (2018) Estimating picking errors in near-surface seismic data to enable their time-lapse interpretation of hydrosystems. Near Surface Geophys 16(6):613–625
Dangeard M, Riviére A, Bodet L, Schneider S, Guérin R, Jougnot D, Maineult A (2021) River corridor model constrained by time-lapse seismic acquisition. Water Resour Res 57(10):e2020WR028911
Drucker H, Burges CJ, Kaufman L, Smola A, Vapnik V et al (1997) Support vector regression machines. Adv Neural Inf Process Syst 9:155–161
Duarte M, Watanabe RN (2021). Notes on scientific computing for biomechanics and motor control. https://doi.org/10.5281/zenodo.4599319
Earp S, Curtis A, Zhang X, Hansteen F (2020) Probabilistic neural network tomography across grane field (north sea) from surface wave dispersion data. Geophys J Int 223(3):1741–1757
Fichtner A, Hp Bunge, Igel H (2006) The adjoint method in seismology: I. theory. Phys Earth Planet Inter 157:86–104. https://doi.org/10.1016/j.pepi.2006.03.016
Fomel S, Luo S, Zhao H (2009) Fast sweeping method for the factored eikonal equation. J Comput Phys 228(17):6440–6455
Hobro JWD, Singh SC, Minshull TA (2003) Three-dimensional tomographic inversion of combined reflection and refraction seismic traveltime data. Geophys J Int 152(1):79–93
Hole JA (1992) Nonlinear high-resolution three-dimensional seismic travel time tomography. J Geophys Res: Solid Earth 97(B5):6553–6562
Huang G, Luo S, Ari T, Li H, Nobes DC (2019) First-arrival tomography with fast sweeping method solving the factored eikonal equation. Explor Geophys 50(2):144–158
Huber PJ (1964) Robust estimation of a location parameter. Ann Math Stat 35(1):73–101. https://doi.org/10.1214/aoms/1177703732
Jones IF (2010) Tutorial: velocity estimation via ray-based tomography. First Break 28(2)
Komatitsch D (1997) Méthodes spectrales et éléments spectraux pour l’équation de l’élastodynamique 2D et 3D en milieu hétérogène (Spectral and spectral-element methods for the 2D and 3D elastodynamics equations in heterogeneous media). PhD thesis, Institut de Physique du Globe, Paris, France, 187 pages
Komatitsch D, Tromp J (1999) Introduction to the spectral-element method for 3-D seismic wave propagation. Geophys J Int 139(3):806–822. https://doi.org/10.1046/j.1365-246x.1999.00967.x
Komatitsch D, Vilotte JP (1998) The spectral-element method: an efficient tool to simulate the seismic response of 2D and 3D geological structures. Bull Seismological Soc Am 88(2):368–392
Komatitsch D, Vilotte JP, Cristini P, Labarta J, Le Goff N, Le Loher P, Liu Q, Martin R, Matzen R, Morency C, Peter D, Tape C, Tromp J, Xie Z (2012) Specfem2d v7.0.0 [software]
Kong Q, Trugman DT, Ross ZE, Bianco MJ, Meade BJ, Gerstoft P (2019) Machine learning in seismology: turning data into insights. Seismol Res Lett 90(1):3–14
Kosloff D, Sherwood J, Koren Z, Machet E, Falkovitz Y (1996) Velocity and interface depth determination by tomography of depth migrated gathers. Geophysics 61(5):1511–1523. https://doi.org/10.1190/1.1444076
Lecomte I, Lubrano-Lavadera P, Anell I, Buckley S, Schmid DW, Heeremans M (2015) Ray-based seismic modeling of geologic models: Understanding and analyzing seismic images efficiently. Interpretation 3:SAC71–SAC89. https://doi.org/10.1190/INT-2015-0061.1
Li S, Liu B, Ren Y, Chen Y, Yang S, Wang Y, 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
Liu Q, Tromp J (2006) Finite-frequency kernels based on adjoint methods 96(6):2383–2397. https://doi.org/10.1785/0120060041
Martin R, Komatitsch D, Gedney SD (2008) A variational formulation of a stabilized unsplit convolutional perfectly matched layer for the isotropic or anisotropic seismic wave equation. Comput Model Eng Sci 37(3):274–304
Mousavi SM, Ellsworth WL, Zhu W, Chuang LY, Beroza GC (2020) Earthquake transformer: an attentive deep-learning model for simultaneous earthquake detection and phase picking. Nat Commun 11(1):1–12
Pasquet S, Bodet L, Dhemaied A, Mouhri A, Vitale Q, Rejiba F, Flipo N, Guérin R (2015) Detecting different water table levels in a shallow aquifer with combined p-, surface and sh-wave surveys: insights from vp/vs or poisson’s ratios. J Appl Geophys 113:38–50
Pasquet S, Bodet L, Longuevergne L, Dhemaied A, Camerlynck C, Rejiba F, Guérin R (2015) 2d characterization of near-surface: surface-wave dispersion inversion versus refraction tomography. Near Surf Geophys 13(4):315–332
Pasquet S, Bodet L, Bergamo P, Guérin R, Martin R, Mourgues R, Tournat V (2016) Small-scale seismic monitoring of varying water levels in granular media. Vadose Zone J. https://doi.org/10.2136/vzj2015.11.0142
Peter D, Komatitsch D, Luo Y, Martin R, Le Goff N, Casarotti E, Le Loher P, Magnoni F, Liu Q, Blitz C, Nissen-Meyer T, Basini P, Tromp J (2011) Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes. Geophys J Int 186(2):721–739. https://doi.org/10.1111/j.1365-246X.2011.05044.x
Plessix RE (2006) A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophys J Int 167(2):495–503
Podvin P, Lecomte I (1991) Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools. Geophys J Int 105(1):271–284
Qian J, Zhang YT, Zhao HK (2007) Fast sweeping methods for eikonal equations on triangular meshes. SIAM J Numer Anal 45:83–107. https://doi.org/10.1137/050627083
Rawlinson N, Sambridge M et al (2003) Seismic traveltime tomography of the crust and lithosphere. Adv Geophys 46:81–199
Richardson A (2018) Seismic full-waveform inversion using deep learning tools and techniques. arXiv preprint arXiv:1801.07232
Ronneberger O, Fischer P, Brox T (2015) U-net: Convolutional networks for biomedical image segmentation. In: International conference on medical image computing and computer-assisted intervention, Springer, pp 234–241
Sen PK (1968) Estimates of the regression coefficient based on kendall’s tau. J Am Stat Assoc 63(324):1379–1389
Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556
Talwani M, Kessinger W (2003) Exploration geophysics. In: Meyers RA (ed) Encyclopedia of Physical Science and Technology (Third Edition), third, edition. Academic Press, New York, pp 709–726
Tarantola A (1984) Inversion of seismic reflection data in the acoustic approximation. Geophysics 49:1259–1266
Tarantola A (1987) Inverse problem theory: methods for data fitting and model parameter estimation. Elsevier Science Publishers, Amsterdam, Netherlands
Tarantola A (1988) Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation 128:365–399
Tarantola A, Valette B (1982) Generalized nonlinear inverse problems solved using the least squares criterion. Rev Geophys Space Phys 20:219–232
Theil H (1950) A rank-invariant method of linear and polynomial regression analysis. Indag Math 12(85):173
Tromp J, Tape C, Liu Q (2005) Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophys J Int 160(1):195–216. https://doi.org/10.1111/j.1365-246X.2004.02453.x
Tromp J, Komatitsch D, Liu Q (2008) Spectral-element and adjoint methods in seismology. Commun Comput Phys 3(1):1–32
Virieux J, Operto S (2009) An overview of full-waveform inversion in exploration geophysics. Geophysics 74(9):WCC127–WCC152
Virieux J, Asnaashari A, Brossier R, Métivier L, Ribodetti A, Zhou W (2017) An introduction to full waveform inversion. In: Encyclopedia of exploration geophysics, Society of Exploration Geophysicists, pp R1–R40
Wang J, Xiao Z, Liu C, Zhao D, Yao Z (2019) Deep learning for picking seismic arrival times. J Geophys Res: Solid Earth 124(7):6612–6624
Xu S, Wang D, Chen F, Zhang Y, Lambare G (2012) Full waveform inversion for reflected seismic data. In: 74th EAGE Conference and exhibition incorporating EUROPEC 2012, European Association of Geoscientists & Engineers, pp cp–293
Yang F, Ma J (2019) Deep-learning inversion: a next-generation seismic velocity model building method. Geophysics 84(4):R583–R599. https://doi.org/10.1190/geo2018-0249.1
Yoo J, Borselen R, Mubarak M, Tsingas C (2019) Automated first break picking method using a random sample consensus (ransac). In: 81st EAGE Conference and Exhibition 2019, European Association of Geoscientists & Engineers, vol 2019, pp 1–5
Yu S, Ma J (2021) Deep learning for geophysics: current and future trends. Rev Geophys 59(3):e20210RG00742
Zelt CA, Barton PJ (1998) Three-dimensional seismic refraction tomography: a comparison of two methods applied to data from the faeroe basin. J Geophys Res: Solid Earth 103(B4):7187–7210
Zheng Y, Zhang Q, Yusifov A, Shi Y (2019) Applications of supervised deep learning for seismic interpretation and inversion. Lead Edge 38(7):526–533. https://doi.org/10.1190/tle38070526.1
Zhu H, Luo Y, Nissen-Meyer T, Morency C, Tromp J (2009) Elastic imaging and time-lapse migration based on adjoint methods. Geophysics 74:WCA167–WCA177
Zhu W, Beroza GC (2018) PhaseNet: a deep-neural-network-based seismic arrival-time picking method. Geophys J Int 216(1):261–273
Zhu W, Xu K, Darve E, Beroza GC (2021) A general approach to seismic inversion with automatic differentiation. Comput Geosci 151:104751
Acknowledgements
Surface seismic data acquisitions used in this study were supported by the equipex CRITEX equipment granted project No ANR-11-EQPX-0011 and performed by Marine Dangeard (now at SNCF-Réseau, DGII/DTR/GC/VA/PGRN, La Plaine Saint-Denis, France) and Ludovic Bodet (UMR 7619 METIS, Sorbonne Université, CNRS, EPHE, France) with the help of K. Chalikakis (UMR EMMAH, Avignon Université, France), whose work we very much want to acknowledge. This work is part of the MADASSY project funded by the RTRA-STAE via the ENV’IA Network (Toulouse/France).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
All authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Huynh, N.N.T., Martin, R., Oberlin, T. et al. Near-Surface Seismic Arrival Time Picking with Transfer and Semi-Supervised Learning. Surv Geophys 44, 1837–1861 (2023). https://doi.org/10.1007/s10712-023-09783-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10712-023-09783-y