Year: 2012
Communications in Computational Physics, Vol. 12 (2012), Iss. 1 : pp. 193–225
Abstract
We develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902–1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.201010.090611a
Communications in Computational Physics, Vol. 12 (2012), Iss. 1 : pp. 193–225
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
-
Effects of three‐dimensional crustal structure and smoothing constraint on earthquake slip inversions: Case study of the Mw6.3 2009 L'Aquila earthquake
Gallovič, František | Imperatori, Walter | Mai, P. MartinJournal of Geophysical Research: Solid Earth, Vol. 120 (2015), Iss. 1 P.428
https://doi.org/10.1002/2014JB011650 [Citations: 56] -
Matrix-free SBP-SAT finite difference methods and the multigrid preconditioner on GPUs
Chen, Alexandre | Erickson, Brittany A. | Kozdon, Jeremy E. | Choi, JeeProceedings of the 38th ACM International Conference on Supercomputing, (2024), P.400
https://doi.org/10.1145/3650200.3656614 [Citations: 0] -
A New Decade in Seismoacoustics (2010–2022)
Dannemann Dugick, Fransiska | Koch, Clinton | Berg, Elizabeth | Arrowsmith, Stephen | Albert, SarahBulletin of the Seismological Society of America, Vol. 113 (2023), Iss. 4 P.1390
https://doi.org/10.1785/0120220157 [Citations: 6] -
Efficient time-domain 3D elastic and viscoelastic full-waveform inversion using a spectral-element method on flexible Cartesian-based mesh
Trinh, Phuong-Thu | Brossier, Romain | Métivier, Ludovic | Tavard, Laure | Virieux, JeanGEOPHYSICS, Vol. 84 (2019), Iss. 1 P.R61
https://doi.org/10.1190/geo2018-0059.1 [Citations: 57] -
The geometry of active shortening in the northwest Himalayas and the implications for seismic hazard
O’Kane, Aisling | Copley, Alex | Mitra, Supriyo | Wimpenny, SamGeophysical Journal International, Vol. 231 (2022), Iss. 3 P.2009
https://doi.org/10.1093/gji/ggac303 [Citations: 6] -
Modeling Three‐Dimensional Wave Propagation in Anelastic Models With Surface Topography by the Optimal Strong Stability Preserving Runge‐Kutta Method
Wang, Nian | Li, Jiahang | Borisov, Dmitry | Gharti, Hom Nath | Shen, Yang | Zhang, Wei | Savage, BrianJournal of Geophysical Research: Solid Earth, Vol. 124 (2019), Iss. 1 P.890
https://doi.org/10.1029/2018JB016175 [Citations: 11] -
A new implementation of convolutional PML for second-order elastic wave equation
Fang, Xiuzheng | Wu, Di | Niu, Fenglin | Yao, GangExploration Geophysics, Vol. 53 (2022), Iss. 5 P.501
https://doi.org/10.1080/08123985.2021.1993441 [Citations: 3] -
Ground-Motion Model for Significant Duration Constrained by Seismological Simulations
Pinilla-Ramos, Camilo | Abrahamson, Norman | Phung, Van-Bang | Kayen, Robert | Castellanos-Nash, PabloBulletin of the Seismological Society of America, Vol. 114 (2024), Iss. 2 P.1015
https://doi.org/10.1785/0120230139 [Citations: 2] -
Joint estimation ofS-wave velocity and damping ratio of the near-surface from active Rayleigh wave surveys processed with a wavefield decomposition approach
Bergamo, Paolo | Maranò, Stefano | Fäh, DonatGeophysical Journal International, Vol. 233 (2023), Iss. 3 P.1560
https://doi.org/10.1093/gji/ggad010 [Citations: 4] -
Broadband (0–4 Hz) Ground Motions for a Magnitude 7.0 Hayward Fault Earthquake With Three‐Dimensional Structure and Topography
Rodgers, Arthur J. | Pitarka, Arben | Petersson, N. Anders | Sjögreen, Björn | McCallen, David B.Geophysical Research Letters, Vol. 45 (2018), Iss. 2 P.739
https://doi.org/10.1002/2017GL076505 [Citations: 50] -
Joint Regional Waveform, First-Motion Polarity, and Surface Displacement Moment Tensor Inversion of the 3 September 2017 North Korean Nuclear Test
Chi-Durán, Rodrigo | Dreger, Douglas S. | Rodgers, Arthur J. | Nayak, AvinashThe Seismic Record, Vol. 1 (2021), Iss. 2 P.107
https://doi.org/10.1785/0320210022 [Citations: 2] -
Ground Motion Modeling in the Eastern Caucasus
Pitarka, Arben | Gok, Rengin | Yetirmishli, Gurban | Ismayilova, Saida | Mellors, RobertPure and Applied Geophysics, Vol. 173 (2016), Iss. 8 P.2791
https://doi.org/10.1007/s00024-016-1311-2 [Citations: 3] -
Regional-Scale 3D Ground-Motion Simulations of Mw 7 Earthquakes on the Hayward Fault, Northern California Resolving Frequencies 0–10 Hz and Including Site-Response Corrections
Rodgers, Arthur J. | Pitarka, Arben | Pankajakshan, Ramesh | Sjögreen, Bjorn | Petersson, N. AndersBulletin of the Seismological Society of America, Vol. 110 (2020), Iss. 6 P.2862
https://doi.org/10.1785/0120200147 [Citations: 41] -
The role of topography and lateral velocity heterogeneities on near-source scattering and ground-motion variability
Imperatori, W. | Mai, P.M.Geophysical Journal International, Vol. 202 (2015), Iss. 3 P.2163
https://doi.org/10.1093/gji/ggv281 [Citations: 53] -
Performance evaluation of the USGS velocity model for the San Francisco Bay Area
Pinilla-Ramos, Camilo | Pitarka, Arben | McCallen M. EERI, David | Nakata, RieEarthquake Spectra, Vol. (2024), Iss.
https://doi.org/10.1177/87552930241270575 [Citations: 0] -
Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method
Petersson, N. Anders | Sjögreen, BjörnJournal of Computational Physics, Vol. 299 (2015), Iss. P.820
https://doi.org/10.1016/j.jcp.2015.07.023 [Citations: 75] -
EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers part I: Computational models and workflow
McCallen, David | Petersson, Anders | Rodgers, Arthur | Pitarka, Arben | Miah, Mamun | Petrone, Floriana | Sjogreen, Bjorn | Abrahamson, Norman | Tang, HoujunEarthquake Spectra, Vol. 37 (2021), Iss. 2 P.707
https://doi.org/10.1177/8755293020970982 [Citations: 57] -
Strain microseismics: Radiation patterns, synthetics, and moment tensor resolvability with distributed acoustic sensing in isotropic media
Vera Rodriguez, Ismael | Wuestefeld, AndreasGEOPHYSICS, Vol. 85 (2020), Iss. 3 P.KS101
https://doi.org/10.1190/geo2019-0373.1 [Citations: 15] -
Regional-scale fault-to-structure earthquake simulations with the EQSIM framework: Workflow maturation and computational performance on GPU-accelerated exascale platforms
McCallen, David | Pitarka, Arben | Tang, Houjun | Pankajakshan, Ramesh | Petersson, N Anders | Miah, Mamun | Huang, JunfeiEarthquake Spectra, Vol. 40 (2024), Iss. 3 P.1615
https://doi.org/10.1177/87552930241246235 [Citations: 1] -
Influence of low-velocity superficial layer on long-period basin-induced surface waves in eastern Osaka basin
Oprsal, Ivo | Sekiguchi, Haruko | Iwata, Tomotaka | Burjanek, JanEarth, Planets and Space, Vol. 75 (2023), Iss. 1
https://doi.org/10.1186/s40623-023-01804-9 [Citations: 0] -
High Order Accurate Finite Difference Modeling of Seismo-Acoustic Wave Propagation in a Moving Atmosphere and a Heterogeneous Earth Model Coupled Across a Realistic Topography
Petersson, N. Anders | Sjögreen, BjörnJournal of Scientific Computing, Vol. 74 (2018), Iss. 1 P.290
https://doi.org/10.1007/s10915-017-0434-7 [Citations: 27] -
Seismic detection and characterization of a man-made karst analog — A feasibility study
Gritto, Roland | Elnaiem, Ali Elobaid | Mohamed, Fateh Alrahman | Sadooni, FadhilGEOPHYSICS, Vol. 86 (2021), Iss. 3 P.WA35
https://doi.org/10.1190/geo2020-0377.1 [Citations: 1] -
Using Dense Array Waveform Correlations to Build a Velocity Model with Stochastic Variability
Pitarka, Arben | Mellors, RobertBulletin of the Seismological Society of America, Vol. 111 (2021), Iss. 4 P.2021
https://doi.org/10.1785/0120200206 [Citations: 6] -
Toward Exascale Earthquake Ground Motion Simulations for Near-Fault Engineering Analysis
Johansen, Hans | Rodgers, Arthur | Petersson, N. Anders | McCallen, David | Sjogreen, Bjorn | Miah, MamunComputing in Science & Engineering, Vol. 19 (2017), Iss. 5 P.27
https://doi.org/10.1109/MCSE.2017.3421558 [Citations: 15] -
The controls on earthquake ground motion in foreland-basin settings: the effects of basin and source geometry
O’Kane, Aisling | Copley, AlexGeophysical Journal International, Vol. 225 (2021), Iss. 1 P.512
https://doi.org/10.1093/gji/ggaa599 [Citations: 5] -
The Effect of Fault Geometry and Minimum Shear Wavespeed on 3D Ground-Motion Simulations for an Mw 6.5 Hayward Fault Scenario Earthquake, San Francisco Bay Area, Northern California
Rodgers, Arthur J. | Pitarka, Arben | McCallen, David B.Bulletin of the Seismological Society of America, Vol. 109 (2019), Iss. 4 P.1265
https://doi.org/10.1785/0120180290 [Citations: 15] -
Coupling of regional geophysics and local soil-structure models in the EQSIM fault-to-structure earthquake simulation framework
McCallen, David | Tang, Houjun | Wu, Suiwen | Eckert, Eric | Huang, Junfei | Petersson, N AndersThe International Journal of High Performance Computing Applications, Vol. 36 (2022), Iss. 1 P.78
https://doi.org/10.1177/10943420211019118 [Citations: 6] -
EQSIM—A multidisciplinary framework for fault-to-structure earthquake simulations on exascale computers, part II: Regional simulations of building response
McCallen, David | Petrone, Floriana | Miah, Mamun | Pitarka, Arben | Rodgers, Arthur | Abrahamson, NormanEarthquake Spectra, Vol. 37 (2021), Iss. 2 P.736
https://doi.org/10.1177/8755293020970980 [Citations: 31] -
Joint Inversion of Regional Waveform, First-Motion Polarity, and Synthetic Aperture Radar Surface Displacement for the Fourth and Sixth North Korean Declared Nuclear Explosions
Chi-Durán, Rodrigo | Dreger, Douglas S. | Rodgers, Arthur J.Bulletin of the Seismological Society of America, Vol. 114 (2024), Iss. 5 P.2409
https://doi.org/10.1785/0120230237 [Citations: 0] -
Evaluation and Updates for the USGS San Francisco Bay Region 3D Seismic Velocity Model in the East and North Bay Portions
Hirakawa, Evan | Aagaard, BradBulletin of the Seismological Society of America, Vol. 112 (2022), Iss. 4 P.2070
https://doi.org/10.1785/0120210256 [Citations: 5] -
A discrete representation of a heterogeneous viscoelastic medium for the finite-difference modelling of seismic wave propagation
Kristek, Jozef | Moczo, Peter | Chaljub, Emmanuel | Kristekova, MiriamGeophysical Journal International, Vol. 217 (2019), Iss. 3 P.2021
https://doi.org/10.1093/gji/ggz132 [Citations: 14] -
Broadband (0–5 Hz) Fully Deterministic 3D Ground‐Motion Simulations of a Magnitude 7.0 Hayward Fault Earthquake: Comparison with Empirical Ground‐Motion Models and 3D Path and Site Effects from Source Normalized Intensities
Rodgers, Arthur J. | Anders Petersson, N. | Pitarka, Arben | McCallen, David B. | Sjogreen, Bjorn | Abrahamson, NormanSeismological Research Letters, Vol. 90 (2019), Iss. 3 P.1268
https://doi.org/10.1785/0220180261 [Citations: 61] -
Modeling the Seismic Response of Unstable Rock Mass With Deep Compliant Fractures
Burjánek, Jan | Kleinbrod, Ulrike | Fäh, DonatJournal of Geophysical Research: Solid Earth, Vol. 124 (2019), Iss. 12 P.13039
https://doi.org/10.1029/2019JB018607 [Citations: 20] -
The Impact of the Three-Dimensional Structure of a Subduction Zone on Time-dependent Crustal Deformation Measured by HR-GNSS
Fadugba, Oluwaseun | Sahakian, Valerie | Melgar, Diego | Rodgers, Arthur | Shimony, RoeySeismica, Vol. 3 (2024), Iss. 1
https://doi.org/10.26443/seismica.v3i1.887 [Citations: 0] -
Exploring Basin Amplification within the Reno Metropolitan Area in Northern Nevada Using a Magnitude 6.3 ShakeOut Scenario
Eckert, Eric | Scalise, Michelle | Louie, John N. | Smith, Kenneth D.Bulletin of the Seismological Society of America, Vol. 112 (2022), Iss. 1 P.457
https://doi.org/10.1785/0120200309 [Citations: 3] -
Highly accurate stability-preserving optimization of the Zener viscoelastic model, with application to wave propagation in the presence of strong attenuation
Blanc, Émilie | Komatitsch, Dimitri | Chaljub, Emmanuel | Lombard, Bruno | Xie, ZhinanGeophysical Journal International, Vol. 205 (2016), Iss. 1 P.414
https://doi.org/10.1093/gji/ggw024 [Citations: 61]