Accounting for Fault Roughness in Pseudo-Dynamic Ground-Motion Simulations

  • P. Martin MaiEmail author
  • Martin Galis
  • Kiran K. S. Thingbaijam
  • Jagdish C. Vyas
  • Eric M. Dunham
Part of the Pageoph Topical Volumes book series (PTV)


Geological faults comprise large-scale segmentation and small-scale roughness. These multi-scale geometrical complexities determine the dynamics of the earthquake rupture process, and therefore affect the radiated seismic wavefield. In this study, we examine how different parameterizations of fault roughness lead to variability in the rupture evolution and the resulting near-fault ground motions. Rupture incoherence naturally induced by fault roughness generates high-frequency radiation that follows an ω-2 decay in displacement amplitude spectra. Because dynamic rupture simulations are computationally expensive, we test several kinematic source approximations designed to emulate the observed dynamic behavior. When simplifying the rough-fault geometry, we find that perturbations in local moment tensor orientation are important, while perturbations in local source location are not. Thus, a planar fault can be assumed if the local strike, dip, and rake are maintained. We observe that dynamic rake angle variations are anti-correlated with the local dip angles. Testing two parameterizations of dynamically consistent Yoffe-type source-time function, we show that the seismic wavefield of the approximated kinematic ruptures well reproduces the radiated seismic waves of the complete dynamic source process. This finding opens a new avenue for an improved pseudo-dynamic source characterization that captures the effects of fault roughness on earthquake rupture evolution. By including also the correlations between kinematic source parameters, we outline a new pseudo-dynamic rupture modeling approach for broadband ground-motion simulation.


Earthquake rupture dynamics fault-surface roughness physics-based ground-motion simulations near-fault shaking seismic hazard 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



We are grateful to L. Dalguer, Ph. Renault, and Y. Fukushima who organized the initial international IAEA-workshop on Best Practices in Physics-based Fault Rupture Models for Seismic Hazard Assessment of Nuclear Installations (Best-PSHANI), Nov 18-21, 2015, Vienna. The presentations and discussions during this conference inspired us to expand our rough-fault dynamic rupture simulations. Comments and constructive criticism by Guest Editor L. Dalguer and two reviewers greatly helped to focus and clarify this study. Research presented in this paper is supported by King Abdullah University of Science and Technology (KAUST) in Thuwal, Saudi Arabia, Grants BAS/1339-01-01 and URF/1/2160-01-01. Earthquake rupture and ground-motion simulations have been carried out using the KAUST Supercomputing Laboratory (KSL), and we acknowledge the support of the KSL staff.


  1. Akkar, S., Sandıkkaya, M. A., S¸ enyurt, M., Azari, Sisi A., Ay, B. Ö., Traversa, P., et al. (2014). Reference database for seismic ground-motion in Europe (RESORCE). Bulletin of Earthquake Engineering, 12, 311–339.Google Scholar
  2. Ancheta, T. D., Darragh, R. B., Stewart, J. P., Seyhan, E., Silva, W. J., BrianChiou, S.-J., et al. (2014). NGA-West2 database. Earthquake Spectra, 30, 989–1005.Google Scholar
  3. Anderson, J.G. (2012). An overview of the largest amplitudes in recorded ground motions. In Proceedings of the 15th World Conference of Earthquake Engineering (15 WCEE), Lisbon (Portugal), Sept 24–28.Google Scholar
  4. Anderson, J. G., & Brune, J. N. (1999). Probabilistic seismic hazard assessment without the ergodic assumption. Seismological Research Letters, 70, 19–28.Google Scholar
  5. Andrews, D. J. (1976a). Rupture propagation with finite stress in antiplane strain. Journal Geophysical Research, 81, 3575–3582.Google Scholar
  6. Andrews, D. J. (1976b). Rupture velocity of plane strain shear cracks. Journal Geophysical Research, 81(5679), 5687.Google Scholar
  7. Andrews, D. J. (2005). Rupture dynamics with energy loss outside the slip zone. Journal of Geophysical Research, 110, B01307.
  8. Aochi, H., & Douglas, J. (2006). Testing the validity of simulated strong ground motion from the dynamic rupture of a fault system, by using empirical equations. Bulletin of Earthquake Engineering, 4, 211–229.Google Scholar
  9. Aochi, H., & Madariaga, R. (2003). The 1999 Izmit, Turkey, earthquake: Nonplanar fault structure, dynamic rupture process and strong ground motion. Bulletin of the Seismological Society of America, 93, 1249–1266.Google Scholar
  10. Aochi, H., & Ulrich, T. (2015). A Probable Earthquake 399 Scenario near Istanbul Determined from Dynamic Simulations. Bulletin of the Seismological Society of America, 105, 1468–1475.
  11. Atkinson, G. M., Assatourians, K., Boore, D. M., Campbell, K., & Motazedian, D. (2009). A guide to differences between stochastic point-source and stochastic finite-fault simulations. Bulletin of the Seismological Society of America, 99, 3192–3201.Google Scholar
  12. Ben-Zion, Y., & Sammis, C. G. (2003). Characterization of fault zones. Pure and Applied Geophysics, 160, 677–715.
  13. Bistacchi, A., Griffith, W. A., Smith, S. A. F., Di Toro, G., Jones, R., & Nielsen, S. (2011). Fault roughness at seismogenic depths from LIDAR and photogrammetric analysis. Pure and Applied Geophysics.
  14. Bizzarri, A. (2012). Rupture speed and slip velocity: What can we learn from simulated earthquakes? Earth and Planetary Science Letters, 317, 196–203.Google Scholar
  15. Bommer, J. J., & Abrahamson, N. A. (2006). Why do modern probabilistic seismic-hazard analyses often lead to increased hazard estimates? Bulletin of the Seismological Society of America, 96, 1967–1977.Google Scholar
  16. Bommer, J. J., Douglas, J., Scherbaum, F., Cotton, F., Bungum, H., & Fa¨h, D. (2010). On the selection of ground-motion prediction equations for seismic hazard analysis. Seismological Research Letters, 81(5), 783–793.Google Scholar
  17. Boore, D. M., & Atkinson, G. M. (2008). Ground-motion prediction equations for the average horizontal component of PGA, PGV, and 5%-damped PSA at spectral periods between 0.01 s and 10.0 s. Earthquake Spectra, 24(1), 99–138.Google Scholar
  18. Boore, D. M., Watson-Lamprey, J., & Abrahamson, N. A. (2006). Orientation independent measures of ground motion. Bulletin of the Seismological Society of America, 96(4A), 1502–1511.
  19. Bora, S. S., Scherbaum, F., Kuehn, N., & Stafford, P. (2014). Fourier spectral-and duration models for the generation of response spectra adjustable to different source-, propagation-, and site conditions. Bulletin of Earthquake Engineering, 12(1), 467–493.Google Scholar
  20. Bozorgnia, Y., et al. (2014). NGA-West2 research project’’. Earthquake Spectra, 30, 973–987 Brune, J. N. (1970). Tectonic stress and the spectra of seismic shear waves from earthquakes. Journal Geophysical Research, 76, 5002.Google Scholar
  21. Campbell, W. K. (2003). Prediction of strong ground motion using the hybrid empirical method and its use in the development of ground-motion (attenuation) relations in Eastern North America. Bulletin of the Seismological Society of America, 93(3), 1012–1033.Google Scholar
  22. Candela, T., Renard, F., Bouchon, M., Brouste, A., Marsan, D., Schmittbuhl, J., et al. (2009). Characterization of fault roughness at various scales: Implications of three-dimensional high resolution topography measurements. Pure and Applied Geophysics, 166, 1817–1851.
  23. Candela, T., Renard, F., Klinger, Y., Mair, K., Schmittbuhl, J., & Brodsky, E. E. (2012). Roughness of fault surfaces over nine decades of length scales. Journal Geophysical Research, 117, B08409.
  24. Causse, M., Cotton, F., & Mai, P. M. (2010). Constraining the roughness degree of slip heterogeneity. Journal Geophysical Research, 115, B05304.
  25. Causse, M., & Song, S. G. (2015). Are stress drop and rupture velocity of earthquakes independent? Insight from observed ground motion variability. Geophysical Research Letters, 42(18), 7383–7389.Google Scholar
  26. Chiou, B., Darragh, R., Gregor, N., & Silva, W. (2008). NGA project strong-motion database. Earthquake Spectra, 24, 23–44.Google Scholar
  27. Day, S. M. (1982). Three-dimensional simulation of spontaneous rupture: the effect of nonuniform prestress. Bulletin of the Seismological Society of America, 72, 1881–1902.Google Scholar
  28. Delavaud, E., Scherbaum, F., Kuehn, N., & Allen, T. (2012). Testing the global applicability of ground-motion prediction equations for active shallow crustal regions. Bulletin of the Seismological Society of America, 102, 707–721.Google Scholar
  29. Dreger, D., E. Tinti, & A. Cirella. (2007). Slip velocity function parameterization for broadband ground motion simulation, Seismological Society of America 2007 Annual Meeting Waikoloa, Hawaii, 11–13, April 2007.Google Scholar
  30. Dunham, E. M., Belanger, D., Cong, L., & Kozdon, J. E. (2011). Earthquake ruptures with strongly rate-weakening friction and off-fault plasticity, Part 2: Nonplanar faults. Bulletin of the Seismological Society of America, 10, 2308–2322.Google Scholar
  31. Ely, G. P., Day, S. M., & Minster, J.-B. (2008). A support-operator method for visco-elastic wave modeling in 3-D heterogeneous media. Geophysical Journal International, 172, 331–344.Google Scholar
  32. Ely, G. P., Day, S. M., & Minster, J.-B. (2009). A support-operator method for 3-D rupture dynamics. Geophysical Journal International, 177, 1140–1150.Google Scholar
  33. Frankel, A. (1991). High-frequency spectral fall-off of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults. Journal Geophysical Research, 96, 6291–6302.Google Scholar
  34. Gabriel, A. A., Ampuero, J.-P., Dalguer, L. A., & Mai, P. M. (2012). The transition of dynamic rupture modes in elastic media. Journal Geophysical Research, 117(B09311), 2012.
  35. Gabriel, A. A., Ampuero, J. P., Dalguer, L. A., & Mai, P. M. (2013). Source properties of dynamic rupture pulses with offfault plasticity. Journal Geophysical Research, 118, 4117–4126.
  36. Galis, M., Pelties, C., Kristek, J., Moczo, P., Ampuero, J.-P., & Mai, P. M. (2015). On initiation of dynamic rupture propagationwith linear slip-weakening friction. Geophysical Journal International, 200, 888–907.Google Scholar
  37. Gallovicˇ, F., & Brokesˇova´, J. (2004). On strong ground motion synthesis with k-2 slip distributions. Journal of Seismology, 8(2), 211–224.Google Scholar
  38. Graves, R. W., Joran, T. H., Callaghan, S., Deelman, E., Field, E., Juve, G., et al. (2011). CyberShake: A Physics-Based Seismic Hazard Model for Southern California. Pure and Applied Geophysics, 168, 367–381.Google Scholar
  39. Graves, R. W., & Pitarka, A. (2010). Broadband ground-motion simulation using a hybrid approach. Bulletin of the Seismological Society of America, 100(5A), 2095–2123.Google Scholar
  40. Graves, R., & Pitarka, A. (2016). Kinematic ground-motion simulations on rough faults including effects of 3D stochastic velocity perturbations. Bulletin of the Seismological Society of America.
  41. Guatteri, M., Mai, P. M., & Beroza, G. C. (2004). A pseudo-dynamic approximation to dynamic rupture models for strong ground motion prediction. Bulletin of the Seismological Society of America, 94(6), 2051–2063.Google Scholar
  42. Gusev, A. A. (2011). Statistics of the values of a normalized slip in the points of an earthquake fault’’. Izvestiya, Physics of the Solid Earth, 47, 176–185.Google Scholar
  43. Hartzell, S., Harmsen, S., & Frankel, A. (2010). Effects of 3D random correlated velocity perturbations on predicted ground motions. Bulletin of the Seismological Society of America, 100(4), 1415–1426.
  44. Hartzell, S. H., & Heaton, T. H. (1983). Inversion of strong ground motion and teleseismic waveform data for the fault rupture history of the 1979 Imperial Valley, California, earthquake. Bulletin of the Seismological Society of America, 73, 1553–1583.Google Scholar
  45. Herrero, A., & Bernard, P. (1994). A kinematic self-similar rupture process for earthquake. Bulletin of the Seismological Society of America, 84, 1216–1228.Google Scholar
  46. Ide, S. (2007). Slip inversion, in Treatise on Geophysics. In H. Kanamori (Ed.), Earthquake Seismology, vol. 4, (pp. 193–224). Amsterdam, The Netherlands: Elsevier. ISBN: 978-0-444-51932-0.Google Scholar
  47. Imperatori, W., & Mai, P. M. (2013). Broadband near-field groundmotion simulations in 3-dimensional scattering media. Geophysical Journal International, 92, 725–744.Google Scholar
  48. Imperatori, W., & Mai, P. M. (2015). The role of topography and lateral velocity heterogeneities on near-source scattering. Geophysical Journal International, 202, 2163–2181.
  49. Kaeser, M., & Gallovic, F. (2008). Effects of complicated 3-D rupture geometries on earthquake ground motion and their implications: a numerical study. Geophysical Journal International, 172, 276–292.
  50. Kluegel, J. U. (2007). Comment on ‘‘Why do modern probabilistic seismic-hazard analyses often lead to increased hazard estimates?’’ by Julian J. Bommer and Norman A. Abrahamson. Bulletin of the Seismological Society of America, 97, 2198–2207.Google Scholar
  51. Kostrov, B. V. (1964). Self-similar problems of propagation of shear cracks. Journal of Applied Mathematics and Mechanics, 28, 1077–1087.Google Scholar
  52. Lavallee, D., Liu, P., & Archuleta, R. J. (2006). Stochastic model of heterogeneity in earthquake slip spatial distributions. Geophysical Journal International, 165, 622–640.Google Scholar
  53. Leonard, M. (2010). Earthquake fault scaling: Self-consistent relating of rupture length, width, average displacement, and moment release. Bulletin of the Seismological Society of America, 100, 1971–1988.Google Scholar
  54. Liu, P., Archuleta, R. A., & Hartzell, S. H. (2006). Prediction of broadband ground-motion time histories: Hybrid low/high-frequency method with correlated random source parameters. Bulletin of the Seismological Society of America, 96(6), 2118–2130.Google Scholar
  55. Mai, P. M. (2009). Ground Motion: Complexity and Scaling in the Near Field of Earthquake Ruptures. In W. H. K. Lee & R. Meyers (Eds.), Encyclopedia of Complexity and Systems Science (pp 4435–4474). Springer.Google Scholar
  56. Mai, P. M., & Beroza, G. C. (2000). Source scaling properties from finite-fault-rupture models. Bulletin of the Seismological Society of America, 90, 604–615.Google Scholar
  57. Mai, P. M., & Beroza, G. C. (2002). A spatial random-field model to characterize complexity in earthquake slip. Journal Geophysical Research.
  58. Mai, P.M., Imperatori, W., & Olsen, K. B. (2010). Hybrid broadband ground-motion simulations: combining long-period deterministic synthetics with high-frequency multiple S-to-S backscattering. Bulletin of the Seismological Society of America, 100, 2124–2142.
  59. Mai, P. M., & Thingbaijam, K. K. S. (2014). SRCMOD: An online database of finite-fault rupture models. Seismological Research Letters, 85(6), 1348–1357.Google Scholar
  60. Mena, B., Dalguer, L. A., & Mai, P. M. (2012). Pseudo-dynamic source characterization for strike-slip faulting, including stress heterogeneity and super-shear rupture. Bulletin of the Seismological Society of America, 102(4), 1654–1680.
  61. Mena, B., Mai, P. M., Olsen, K. B., Purvance, M. D., & Brune, J. (2010). Hybrid broadband ground-motion simulation using scattering Green’s functions: application to large-magnitude events. Bulletin of the Seismological Society of America, 100(5A), 2143–2162.
  62. Oglesby, D. D., & Day, S. M. (2002). Stochastic fault stress: Implications for fault dynamics and ground motion. Bulletin of the Seismological Society of America, 92, 3006–3021.Google Scholar
  63. Oglesby, D. D., & Mai, P. M. (2012). Fault Geometry, rupture dynamics, and ground motion from potential earthquakes on the North Anatolian Fault Zone under the Sea of Marmara. Geophysical Journal International.
  64. Oglesby, D. D., Mai, P. M., Atakan, K., & Pucci, S. (2008). Dynamic models of earthquakes on the North Anatolian fault under the Sea of Marmara: The effect of hypocenter location. Geophysical Research Letters, 35, L18302.
  65. Pardo-Iguzquiza, E., & Chica-Olmo, M. (1993). The Fourier integral method: an efficient spectral method for simulation of random fields. Mathematical Geology, 25, 177–217.Google Scholar
  66. Power, M., Chiou, B., Abrahamson, N., Bozorgnia, Y., Shantz, T., & Roblee, C. (2008). An overview of the NGA project. Earthquake Spectra, 24, 3–21.Google Scholar
  67. Power, W. L., & Tullis, T. E. (1991). Euclidean and fractal models for the description of rock surface roughness. Journal Geophysical Research, 96, 415–424.Google Scholar
  68. Renard, F., Voisin, C., Marsan, D., & Schmittbuhl, J. (2006). High resolution 3-D laser scanner measurements of a strike-slip fault quantify its morphological anisotropy at all scales. Geophysical Research Letters, 33, L04305.
  69. Ripperger, J., Ampuero, J. P., Mai, P. M., & Giardini, D. (2007). Earthquake source characteristics from dynamic rupture with constrained stochastic fault stress. Journal Geophysical Research, 112, B04311.
  70. Ripperger, J., & Mai, P. M. (2004). Fast computation of static stress changes on 2D faults from final slip distributions. Geophysical Research Letters, 31(18), L18610.
  71. Ripperger, J., Mai, P. M., & Ampuero, J. P. (2008). Variability of near-field ground-motion from dynamic earthquake rupture simulation. Bulletin of the seismological society of America, 98(3), 1207–1228.Google Scholar
  72. Rodriguez-Marek, A., Cotton, F., Abrahamson, N. A., Akkar, S., Al-Atik, L., Edwards, B., et al. (2013). A model for single-station standard deviation using data from various tectonic regions. Bulletin of the seismological society of America, 103(6), 3149–3163.Google Scholar
  73. Roten, D., Olsen, K. B., Day, S. M., Cui, Y., & Fa¨h, D. (2014). Expected seismic shaking in Los Angeles reduced by San Andreas fault zone plasticity. Geophysical Research Letters, 41(8), 2769–2777.Google Scholar
  74. Ruiz, J. A., Fuentes, M., Riquelme, S., Campos, J., & Cisternas, A. (2015). Numerical simulation of tsunami runup in northern Chile based on non-uniform k-2 slip distributions. Natural Hazards, 79(2), 1177–1198.Google Scholar
  75. Sagy, A., & Brodsky, E. E. (2009). Geometric and rheological asperities in an exposed fault zone. Journal Geophysical Research, 114, B02301.
  76. Sagy, A., Brodsky, E. E., & Axen, G. J. (2007). Evolution of faultsurface roughness with slip. Geology, 35(3), 283–286.
  77. Schmedes, J., Archuleta, R. J., & Lavallée, D. (2010). Correlation of earthquake source parameters inferred from dynamic rupture simulations. Journal Geophysical Research, 115, B03304.
  78. Schmedes, J., Archuleta, R. J., & Lavallée, D. (2013). A kinematic rupture model generator incorporating spatial interdependency of earthquake source parameters. Geophysical Journal International,192, 1116–1131.
  79. Shi, Z., & Day, S. M. (2013). Rupture dynamics and ground motion from 3-D rough-fault simulations. Journal Geophysical Research, 118(3), 1122–1141.
  80. Song, S. G., & Dalguer, L. A. (2013). Importance of 1-point statistics in earthquake source modelling for ground motion simulation. Geophysical Journal International, 192, 1255–1270.Google Scholar
  81. Song, S.-G., Dalguer, L. A., & Mai, P. M. (2013). Pseudo-dynamic source modeling with 1-point and 2-point statistics of earthquake source parameters. Geophysical Journal International, 196(3), 1770–1786.
  82. Song, S. G., & Somerville, P. (2010). Physics-based earthquake source characterization and modeling with geostatistics. Bulletin of the Seismological Society of America, 100(2), 482–496.Google Scholar
  83. Spudich, P., & Xu, L. (2003). Software package COMPSYN: Programs for earthquake ground motion calculation using complete 1-D Green’s functions, in International Handbook of Earthquake & Engineering Seismology. In W. H. K. Lee, H. Kanamori, P. Jennings, & C. Kisslinger (Eds.), International Geophysics Series (Vol. 81). Amsterdam: Academic Press.Google Scholar
  84. Stewart, J. P., Douglas, J., Javanbarg, M., Bozorgnia, Y., Abrahamson, N. A., Boore, D. M., et al. (2015). Selection of ground motion prediction equations for the Global Earthquake Model. Earthquake Spectra, 31, 19–45.Google Scholar
  85. Strasser, F. O., Abrahamson, N. A., & Bommer, J. J. (2009). Sigma: Issues, insights, and challenges. Seismological Research Letters, 80, 40–56.Google Scholar
  86. Thingbaijam, K. K. S., & Mai, P. M. (2016). Evidence for truncated exponential probability distribution of earthquake slip. Bulletin of the Seismological Society of America.
  87. Tinti, E., Fukuyama, E., Piatanesi, A., & Cocco, M. (2005). A kinematic source-time function compatible with earthquake dynamics. Bulletin of the Seismological Society of America, 95, 1211–1223.Google Scholar
  88. Trugman, D. T., & Dunham, E. M. (2014). A 2D pseudo-dynamic rupture model generator for earthquakes on geometrically complex faults. Bulletin of the Seismological Society of America, 104(1), 95–112.
  89. Vyas, J. M., Galis, M., & Mai, P. M. (2016). Distance and azimuthal dependence of ground-motion variability. Bulletin of the Seismological Society of America.
  90. Wang, Z., & Zhou, M. (2007). Comment on ‘‘Why do modern probabilistic seismic-hazard analyses often lead to increased hazard estimates?’’ by Julian J. Bommer and Norman A. Abrahamson. Bulletin of the Seismological Society of America, 97, 2212–2221.Google Scholar
  91. Yoffe, E. (1951). The moving Griffith crack. Philosophical Magazine, 42, 739–750.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Division of Physical Science and EngineeringKing Abdullah University of Science and TechnologyThuwalKingdom of Saudi Arabia
  2. 2.Department of GeophysicsStanford UniversityStanfordUSA

Personalised recommendations