journal article Open Access Sep 14, 2024

Fault geometry invariance and dislocation potential in antiplane crustal deformation: physics-informed simultaneous solutions

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Abstract
AbstractEarthquake-induced crustal deformation provides valuable insights into the mechanisms of tectonic processes. Dislocation models offer a fundamental framework for comprehending such deformation, and two-dimensional antiplane dislocations are used to describe strike-slip faults. Previous earthquake deformation analyses observed that antiplane dislocations due to uniform fault slips are influenced predominantly by fault tips. Here, we state a general principle of fault geometry invariance in antiplane dislocations and exploit its theoretical consequence to define dislocation potentials that enable a streamlined crustal deformation analysis. To demonstrate the benefits of this theory, we present an analytical example and construct a rapid numerical solver for crustal deformation caused by variable fault slip scenarios using physics-informed neural networks, whose mesh-free property is suitable for modeling dislocation potentials. Fault geometry invariance and the dislocation potential may further the analysis of antiplane crustal deformation, particularly for uncertainty quantification and inversion analysis regarding unknown fault geometries in realistic crustal structures.
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References
41
[1]
Agata R, Shiraishi K, Fujie G (2023) Bayesian seismic tomography based on velocity-space stein variation gradient descent for physics-informed neural network. IEEE Trans Geosci Remote Sens 61:1–17. https://doi.org/10.1109/TGRS.2023.3295414 10.1109/tgrs.2023.3295414
[2]
Baker N, Alexander F, Bremer T et al (2019) Workshop report on basic research needs for scientific machine learning: core technologies for artificial intelligence. USDOE Office of Science (SC), Washington, DC. https://doi.org/10.2172/1478744 10.2172/1478744
[3]
Chen Y, de Ridder SA, Rost S, Guo Z, Wu X, Chen Y (2022) Eikonal tomography with physics-informed neural networks: rayleigh wave phase velocity in the northeastern margin of the Tibetan plateau. Geophys Res Lett 49(21):e2022GL099053. https://doi.org/10.1029/2022GL099053 10.1029/2022gl099053
[4]
Dutta R, Jónsson S, Vasyura-Bathke H (2021) Simultaneous Bayesian estimation of non-planar fault geometry and spatially-variable slip. J Geophys Res Solid Earth 126:e2020JB020441. https://doi.org/10.1029/2020JB020441 10.1029/2020jb020441
[5]
Freed A, Bürgmann R (2004) Evidence of power-law flow in the Mojave Desert mantle. Nature 430:548–551. https://doi.org/10.1038/nature02784 10.1038/nature02784
[6]
Fukahata Y, Matsu’ura M (2016) Deformation of island-arc lithosphere due to steady plate subduction. Geophys J Int 204(2):825–840. https://doi.org/10.1093/gji/ggv482 10.1093/gji/ggv482
[7]
Fukushima R, Kano M, Hirahara K (2023) Physics-informed neural networks for fault slip monitoring: simulation, frictional parameter estimation, and prediction on slow slip events in a spring-slider system. J Geophys Res Solid Earth 128(12):e2023JB027384. https://doi.org/10.1029/2023JB027384 10.1029/2023jb027384
[8]
Goldstein H, Poole C, Safko J (2002) Classical mechanics. Addison Wesley, Boston
[9]
Hori T, Agata R, Ichimura T, Fujita K, Yamaguchi T, Iinuma T (2021) High-fidelity elastic green’s functions for subduction zone models consistent with the global standard geodetic reference system. Earth Planets Space 73(1):41. https://doi.org/10.1186/s40623-021-01370-y 10.1186/s40623-021-01370-y
[10]
Karniadakis GE, Kevrekidis IG, Lu L, Perdikaris P, Wang S, Yang L (2021) Physics-informed machine learning. Nat Rev Phys 3:422–440. https://doi.org/10.1038/s42254-021-00314-5 10.1038/s42254-021-00314-5
[11]
Kovachki N, Li Z, Liu B, Azizzadenesheli K, Bhattacharya K, Stuart A, Anandkumar A (2023) Neural operator: learning maps between function spaces with applications to PDEs. J Mach Learn Res 24:1–97
[12]
Kyriakopoulos C, Masterlark T, Stramondo S, Chini M, Bignami C (2013) Coseismic slip distribution for the Mw 9 2011 Tohoku-Oki earthquake derived from 3-D FE modeling. J Geophys Res Solid Earth 118:3837–3847. https://doi.org/10.1002/jgrb.50265 10.1002/jgrb.50265
[13]
Langer L, Gharti HN, Tromp J (2019) Impact of topography and three-dimensional heterogeneity on coseismic deformation. Geophys J Int 217(2):866–878. https://doi.org/10.1093/gji/ggz060 10.1093/gji/ggz060
[14]
Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Lu Lu, Pengzhan Jin, Guofei Pang et al.

Nature Machine Intelligence 2021 10.1038/s42256-021-00302-5
[15]
Maruyama T (1964) Statical elastic dislocation in an infinite and semi-infinite medium. Bull Earthq Res Inst 42:289–368
[16]
Masterlark T (2003) Finite element model predictions of static deformation from dislocation sources in a subduction zone: sensitivities to homogeneous, isotropic, Poisson-solid, and half-space assumptions. J Geophys Res 108:2540. https://doi.org/10.1029/2002JB002296 10.1029/2002jb002296
[17]
Triangular dislocation: an analytical, artefact-free solution

Mehdi Nikkhoo, Thomas R. Walter

Geophysical Journal International 2015 10.1093/gji/ggv035
[18]
Ohtani M, Hirahara K (2015) Effect of the Earth’s surface topography on quasi-dynamic earthquake cycles. Geophys J Int 203(1):384–398. https://doi.org/10.1093/gji/ggv187 10.1093/gji/ggv187
[19]
Okada Y (1992) Internal deformation due to shear and tensile faults in a half-space. Bull Seismol Soc Am 82(2):1018–1040. https://doi.org/10.1785/BSSA0820021018 10.1785/bssa0820021018
[20]
Okazaki T, Ito T, Hirahara K, Ueda N (2022) Physics-informed deep learning approach for modeling crustal deformation. Nat Commun 13:7092. https://doi.org/10.1038/s41467-022-34922-1 10.1038/s41467-022-34922-1
[21]
Pan E (2019) Green’s functions for geophysics: a review. Rep Prog Phys 82(10):106801. https://doi.org/10.1088/1361-6633/ab1877 10.1088/1361-6633/ab1877
[22]
Pathak J, Subramanian S, Harrington P et al (2022) FourCastNet: a global data-driven high-resolution weather model using adaptive Fourier neural operators. Preprint at https://doi.org/10.48550/arXiv.2202.11214 10.48550/arxiv.2202.11214
[23]
Pollitz FF (1996) Coseismic deformation from earthquake faulting on a layered spherical earth. Geophys J Int 125(1):1–14. https://doi.org/10.1111/j.1365-246X.1996.tb06530.x 10.1111/j.1365-246x.1996.tb06530.x
[24]
Pollitz FF, Wicks C, Thatcher W (2001) Mantle flow beneath a continental strike-slip fault: postseismic deformation after the 1999 hector mine earthquake. Science 293(5536):1814–1818. https://doi.org/10.1126/science.1061361 10.1126/science.1061361
[25]
Ragon T, Sladen A, Simons M (2018) Accounting for uncertain fault geometry in earthquake source inversions–I. Theory and simplified application. Geophys J Int 214:1174–1190. https://doi.org/10.1093/gji/ggy187 10.1093/gji/ggy187
[26]
Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686–707. https://doi.org/10.1016/j.jcp.2018.10.045 10.1016/j.jcp.2018.10.045
[27]
Rasht-Behesht M, Huber C, Shukla K, Karniadakis GE (2022) Physics-informed neural networks (PINNs) for wave propagation and full waveform inversions. J Geophys Res Solid Earth 127:e2021JB023120. https://doi.org/10.1029/2021JB023120 10.1029/2021jb023120
[28]
Ren P, Rao C, Chen S, Wang J-X, Sun H, Liu Y (2024) SeismicNet: physics-informed neural networks for seismic wave modeling in semi-infinite domain. Comput Phys Commun 295:109010. https://doi.org/10.1016/j.cpc.2023.109010 10.1016/j.cpc.2023.109010
[29]
Savage JC (1983) A dislocation model of strain accumulation and release at a subduction zone. J Geophys Res 88(B6):4984–4996. https://doi.org/10.1029/JB088iB06p04984 10.1029/jb088ib06p04984
[30]
Savage JC, Burford RO (1973) Geodetic determination of relative plate motion in central California. J Geophys Res 78(5):832–845. https://doi.org/10.1029/JB078i005p00832 10.1029/jb078i005p00832
[31]
Segall P (2010) Earthquake and volcano deformation. Princeton University Press, Princeton 10.1515/9781400833856
[32]
Shimizu K, Yagi Y, Okuwaki R, Fukahata Y (2021) Construction of fault geometry by finite-fault inversion of teleseismic data. Geophys J Int 224:1003–1014. https://doi.org/10.1093/gji/ggaa501 10.1093/gji/ggaa501
[33]
Singh SJ, Rani S (1996) 2-D modelling of crustal deformation associated with strike-slip and dip-slip faulting in the Earth. Proc Natl Acad Sci India Sect A 66:187–215
[34]
Smith B, Sandwell D (2004) A three-dimensional semianalytic viscoelastic model for time-dependent analyses of the earthquake cycle. J Geophys Res 109:B12401. https://doi.org/10.1029/2004JB003185 10.1029/2004jb003185
[35]
Smith JD, Azizzadenesheli K, Ross ZE (2020) EikoNet: solving the Eikonal equation with deep neural networks. IEEE Trans Geosci Remote Sens 59(12):10685–10696. https://doi.org/10.1109/TGRS.2020.3039165 10.1109/tgrs.2020.3039165
[36]
Song C, Wang Y (2023) Simulating seismic multifrequency wavefields with the Fourier feature physics-informed neural network. Geophys J Int 232:1503–1514. https://doi.org/10.1093/gji/ggac399 10.1093/gji/ggac399
[37]
Steketee JA (1958) Some geophysical applications of the elasticity theory of dislocations. Can J Phys 36(9):1168–1198. https://doi.org/10.1139/p58-123 10.1139/p58-123
[38]
Sun T, Wang K, Iinuma T, Hino R, He J, Fujimoto H, Kido M, Osada Y, Miura S, Ohta Y, Hu Y (2014) Prevalence of viscoelastic relaxation after the 2011 Tohoku-oki earthquake. Nature 514:84–87. https://doi.org/10.1038/nature13778 10.1038/nature13778
[39]
Sun L, Gao H, Pan S, Wang J-X (2020) Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. Comput Methods Appl Mech Eng 361:112732. https://doi.org/10.1016/j.cma.2019.112732 10.1016/j.cma.2019.112732
[40]
Williams CA, Wallace LM (2015) Effects of material property variations on slip estimates for subduction interface slow-slip events. Geophys Res Lett 42(4):1113–1121. https://doi.org/10.1002/2014GL062505 10.1002/2014gl062505
[41]
Yang Y, Gao AF, Castellanos JC, Ross ZE, Azizzadenesheli K, Clayton RW (2021) Seismic wave propagation and inversion with neural operators. Seism Rec 1(3):126–134. https://doi.org/10.1785/0320210026 10.1785/0320210026
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Published
Sep 14, 2024
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11(1)
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Tomohisa Okazaki, Kazuro Hirahara, Naonori Ueda (2024). Fault geometry invariance and dislocation potential in antiplane crustal deformation: physics-informed simultaneous solutions. Progress in Earth and Planetary Science, 11(1). https://doi.org/10.1186/s40645-024-00654-7