Abstract
Earthquake cycle simulations are important for studying earthquake generation processes and physics-based earthquake damage estimations. Earthquake cycle simulation methods typically assume a frictional constitutive relation on a known fault plane in a solid continuum and calculate earthquake evolution as spontaneous fault slip. To carry out such simulations, the boundary integral equation method, based on an elastic half-space, is widely used. In this approach, stress change around the fault plane due to crustal deformation can be computed analytically, but physical properties such as three-dimensional heterogeneous structure and viscoelastic deformation in mantle are generally not taken into account. Here, we incorporate such complex physical properties in the earthquake cycle simulation based on finite element modeling, using state-of-the-art techniques in computational science. We apply the proposed method to a fundamental problem of earthquake cycle generation and obtain results consistent with past studies.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Agata, R., Barbot, S.D., Fujita, K., Hyodo, M., Iinuma, T., Nakata, R., Ichimura, T., Hori, T.: Rapid mantle flow with power-law creep explains deformation after the 2011 tohoku mega-quake, Nature Communications, 10(1), 1385 (2018)
Agata, R., Ichimura, T., Hori, T., Hirahara, K., Hashimoto, C., Hori, M.: An adjoint-based simultaneous estimation method of the asthenosphere’s viscosity and afterslip using a fast and scalable finite-element adjoint solver. Geophys. J. Int. 213(1), 461–474 (2018)
Barbot, S.: Asthenosphere flow modulated by megathrust earthquake cycles. Geophys. Res. Lett. 45(12) (2018)
Dieterich J.H.: Modeling of rock friction: 1. experimental results and constitutive equations. J. Geophys. Res.: Solid Earth 84(B5), 2161–2168 (1979)
Fujita, K., Ichimura, T., Koyama, K., Inoue, H., Hori, M., Maddegedara, L.: Fast and scalable low-order implicit unstructured finite-element solver for earth’s crust deformation problem. In: Proceedings of the Platform for Advanced Scientific Computing Conference, p. 11. ACM (2017)
Hyodo, M., Hori, T.: Re-examination of possible great interplate earthquake scenarios in the Nankai Trough, southwest Japan, based on recent findings and numerical simulations. Tectonophysics 600, 175–186 (2013)
Ichimura, T., Agata, R., Hori, T., Hirahara, K., Hashimoto, C., Hori, M., Fukahata, Y.: An elastic/viscoelastic finite element analysis method for crustal deformation using a 3-D island-scale high-fidelity model. Geophys. J. Int. 206(1), 114–129 (2016)
Ichimura, T., Fujita, K., Tanaka, S., Hori, M., Lalith, M., Shizawa, Y., Kobayashi, H.: Physics-based urban earthquake simulation enhanced by 10.7 BlnDOF x 30 K time-step unstructured FE non-linear seismic wave simulation. In: SC14: International Conference for High Performance Computing, Networking, Storage and Analysis, pp. 15–26 (2014)
Kaneko, Y., Ampuero, J.-P., Lapusta, N.: Spectral-element simulations of long-term fault slip: Effect of low-rigidity layers on earthquake-cycle dynamics. J. Geophys. Res.: Solid Earth 116(B10) (2011)
Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998)
Lambert, V., Barbot, S.: Contribution of viscoelastic flow in earthquake cycles within the lithosphere-asthenosphere system. Geophys. Res. Lett. 43(19), 10,142–10,154 (2016)
Melosh, H.J., Raefsky, A.: A simple and efficient method for introducing faults into finite element computations. Bull. Seismol. Soc. Am. 71(5), 1391–1400 (1981)
Miyazaki, H., Kusano, Y., Shinjou, N., Shoji, F., Yokokawa, M., Watanabe, T.: Overview of the K computer system. Fujitsu Sci. Tech. J. 48(3), 255–265 (2012)
Nakatani, M.: Conceptual and physical clarification of rate and state friction: frictional sliding as a thermally activated rheology. 106, 1 (2001)
Noda, H., Hori, T.: Under what circumstances does a seismogenic patch produce aseismic transients in the later interseismic period? Geophys. Res. Lett. 41(21), 7477–7484 (2014)
Okada, Y.: Internal deformation due to shear and tensile faults in a half-space. Bull. Seismol. Soc. Am. 82(2), 1018–1040 (1992)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C (2nd ed.): The Art of Scientific Computing. Cambridge University Press, New York (1992)
Rice, J.R.: Spatio-temporal complexity of slip on a fault. J. Geophys. Res.: Solid Earth 98(B6), 9885–9907 (1993)
Ruina, A.: Slip instability and state variable friction laws. J. Geophys. Res.: Solid Earth 88(B12), 10359–10370 (1983)
Savage, J.C.: A dislocation model of strain accumulation and release at a subduction zone. J. Geophys. Res.: Solid Earth 88(B6), 4984–4996 (1983)
Winget, J.M., Hughes, T.J.R.: Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies. Comput. Methods Appl. Mech. Eng. 52(1–3), 711–815 (1985)
Acknowledgments
We thank the reviewer for his comments and suggestions that helped us improve the manuscript. This study was supported by JSPS Fellowship (26-8867) and Post K computer project (Priority issue 3: Development of Integrated Simulation Systems for Hazard and Disaster Induced by Earthquake and Tsunami). We obtained the results using the K computer at the RIKEN Center for Computational Science (Proposal number hp160221 and hp170249).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Agata, R., Hori, T., Barbot, S.D., Hyodo, M., Ichimura, T. (2020). Quasi-static Simulation Method of Earthquake Cycles Based on Viscoelastic Finite Element Modeling. In: Itou, H., Hirano, S., Kimura, M., Kovtunenko, V.A., Khludnev, A.M. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications III. CoMFoS 2018. Mathematics for Industry, vol 34. Springer, Singapore. https://doi.org/10.1007/978-981-15-6062-0_11
Download citation
DOI: https://doi.org/10.1007/978-981-15-6062-0_11
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-6061-3
Online ISBN: 978-981-15-6062-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)