Abstract
In the analysis and design of important structures with relatively long life spans, there is a need to generate strong motion data for possible large events. The source of an earthquake is characterized by the spatial distribution of slip on the fault plane. For future events, this is unknown. In this paper, a stochastic earthquake source model is developed to address this issue. Here, 1D and 2D stochastic models for slip distribution developed by Lavallée et al. (2006) are used. The random field associated with the slip distribution is heavy-tailed stable distribution which can be used for large events. Using 236 past rupture models, the spectral scaling parameter and the four stable or Levy’s parameters against empirical relationship for known quantities like magnitude or fault length are developed. The model is validated with data from 411 stations of 1999 Chi-Chi earthquake. The simulated response spectrum showed good agreement to actual data. Further the proposed model is used to generate ground motion for the 1993 Killari Earthquake where strong motion data is not available. The simulated mean peak ground velocity was in turn related to the intensity (MSK) and compared against values in the literature.
Similar content being viewed by others
References
Aki K (1984), “Asperities, Barriers, Characteristic Earthquakes and Strong Motion Prediction,” Journal of Geophysical Research: Solid Earth, 89(B7): 5867–5872.
Andrews DJ (1980), “A Stochastic Fault Model: 1. Static Case,” Journal of Geophysical Research, 85(80): 3867–3877.
Archuleta RJ (1984), “A Faulting Model for the 1979 Imperial Valley Earthquake,” Journal of Geophysical Research: Solid Earth, 89(B6): 4559–4585.
Atkinson GM and Boore DM (2006), “Earthquake ground-motion prediction equations for eastern North America,” Bulletin of the Seismological Society of America, 96(6): 2181–2205.
Baumbach M, Grosser H, Schmidt HG, Paulat A, Rietbrock A, Ramakrishna CV, Rao P, Raju S, Sarkar D and Mohan I (1994), “Study of the foreshocks and aftershocks of the intraplate Latur earthquake of September 30, India,” in H. K. Gupta, editor, Latur earthquake, (Memoir; 35), 33–63. Geological Society of India.
Bayat M, Daneshjoo F and Nisticò N (2017), “The effect of different intensity measures and earthquake directions on the seismic assessment of skewed highway bridges,” Earthquake Engineering and Engineering Vibration, 16(1): 165–179.
Bommer JJ, Abrahamson NA, Strasser FO, Pecker A, Bard PY, Bungum H, Cotton F, Fäh D, Sabetta F, Scherbaum F and Studer J (2004), “The Challenge of Defining Upper Bounds on Earthquake Ground Motions,” Seismological Research Letters, 75(1): 82–95.
Boore DM (2003), “Simulation of Ground Motion Using the Stochastic Method,” Pure and Applied Geophysics, 160(3–4): 635–676.
Boore DM (2009), “Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM,” Bulletin of the Seismological Society of America, 99(6): 3202–3216.
Boore DM and Atkinson GM (1987), “Stochastic Prediction of Ground Motion and Spectral Response Parameters at Hard-Rock Sites in Eastern North America,” Bulletin of the Seismological Society of America, 77(2): 440–467.
Boore DM and Joyner WB (1997), “Site Amplifications for Generic Rock Sites,” Bulletin of the Seismological Society of America, 87(2): 327–341.
Copley A, Avouac J-P, Hollingsworth J, and Leprince S (2011), “The 2001 Mw 7.6 Bhuj Earthquake, Low Fault Friction, and the Crustal Support of Plate Driving Forces in India,” Journal of Geophysical Research: Solid Earth, 116(B08405).
Drenick RF (1970), “Model-Free Design of Aseismic Structure,” Journal of the Engineering Mechanics Division, ASCE, 96: 483–493.
Gahalaut VKKalpna, and Raju PS (2003), “Rupture Mechanism of the 1993 Killari Earthquake, India: Constraints from Aftershocks and Static Stress Change,” Tectonophysics, 369(1–2): 71–78.
Gupta HK, Rastogi BK, Mohan I, Rao CVRK, Sarma SVS, and Rao RUM (1998), “An Investigation into the Latur Earthquake of September 29, 1993 in Southern India,” Tectonophysics, 287(1–4): 299–318.
Gusev AA (2011), “Statistics of the Values of a Normalized Slip in the Points of an Earthquake Fault,” Izvestiya, Physics of the Solid Earth, 47(3) (March 9): 176–185.
Hough SE and Bilham R (2008), “Site Response of the Ganges Basin Inferred from Re-Evaluated Macroseismic Observations from the 1897 Shillong, 1905 Kangra, and 1934 Nepal Earthquakes,” Journal of Earth System Science, 117(2): 773–782.
Hudnut KW, Shen Z, Murray M, McClusky S, King R, Herring T, Hager B, Feng Y, Fang P, Donnellan A, Bock Y (1996), “Co-Seismic Displacements of the 1994 Northridge, California, Earthquake,” Bulletin of the Seismological Society of America, 86(1B): S19–S36.
Iyengar RN, Manohar CS, and Jaiswal OR (1994), “Field Investigation of the 30 September 1993 Earthquake in Maharashtra,” Current Science, 65(5): 368–379.
Jain SK (1998), “Indian Earthquakes: An Overview,” The Indian Concrete Journal, 72(11): 555–562.
Joshi A (2000), “Modelling of Rupture Planes for Peak Ground Accelerations and Its Application to the Isoseismal Map of MMI Scale in Indian Region,” Journal of Seismology, 4(2): 143–160.
Konca AO, Hjorleifsdottir V, Song TA, Avouac J, Helmberger DV, Ji C, Sieh K, Briggs R, and Meltzner A (2007), “Rupture Kinematics of the 2005 Mw 8.6 Nias-Simeulue Earthquake from the Joint Inversion of Seismic and Geodetic Data,” Bulletin of the Seismological Society of America, 97(1A): S307–S322.
Lavallée D (2003), “Stochastic Modeling of Slip Spatial Complexities for the 1979 Imperial Valley, California, Earthquake,” Geophysical Research Letters, 30(5): 1245.
Lavallée D, Liu P and Archuleta R J (2006), “Stochastic Model of Heterogeneity in Earthquake Slip Spatial Distributions,” Geophysical Journal International, 165 (2): 622–640.
Lavallée D, Miyake H, and Koketsu K (2011), “Stochastic Model of a Subduction-Zone Earthquake: Sources and Ground Motions for the 2003 Tokachi-Oki, Japan, Earthquake,” Bulletin of the Seismological Society of America, 101(4): 1807–1821.
Lekshmy PR and Raghukanth STG (2015), “Maximum Possible Ground Motion for Structures,” Journal of Earthquake Engineering, 19(6): 938–955.
Liu P, Archuleta RJ, and Hartzell SH (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) (December 1): 2118–2130.
Liu TJ, Atkinson GM, Hong HP, and Assatourians K (2012), “Intraevent Spatial Correlation Characteristics of Stochastic Finite-Fault Simulations,” Bulletin of Seismological Society of America, 102(4): 1740–1747.
Mai PM and Beroza GC (2000), “Source Scaling Properties from Finite-Fault-Rupture Models,” Bulletin of Seismological Society of America, 90(3): 604–615.
Mai PM and Beroza GC (2002), “A Spatial Random Field Model to Characterize Complexity in Earthquake Slip,” Journal of Geophysical Research: Solid Earth, 107(B11): ESE 10–1–ESE 10–21.
Motazedian D and Atkinson GM (2005), “Stochastic Finite-Fault Modeling Based on a Dynamic Corner Frequency,” Bulletin of the Seismological Society of America, 95(3): 995–1010.
Midzi V, Singh DD, Atakan K and Havskov J (2003) “Local Site Effects in Latur, India: an Empirical Study Based on the Aftershocks of the Killari Earthquake of September 29, 1993,” Engineering Geology, 68(3–4): 251–258.
Olson AH and Apsel RJ (1982), “Finite Faults and Inverse Theory with Applications to the 1979 Imperial Valley Earthquake,” Bulletin of the Seismological Society of America, 72(6A): 1969–2001.
Pant DR and Maharjan M (2016), “On Selection and Scaling of Ground Motions for Analysis of Seismically Isolated Structures,” Earthquake Engineering and Engineering Vibration, 15(4): 633–648.
Parvez IA, Vaccari F and Panza G F (2003), “A Deterministic Seismic Hazard Map of India and Adjacent Areas,” Geophysical Journal International, 155 (2): 489–508.
PEER-NGA Database (2012), Pacific Earthquake Engineering Research Center: NGA Database, https://doi.org/peer.berkeley.edu/nga/.
Raghu Kanth STG and Iyengar RN (2007), “Estimation of Seismic Spectral Acceleration in Peninsular India,” Journal of Earth System Science, 116(3): 1–16.
Raghu Kanth STG and Iyengar RN (2008), “Strong Motion Compatible Source Geometry,” Journal of Geophysical Research, 113(B4) (April 29): B04309.
Raghukanth STG (2008), “Source mechanism model for ground motion simulation,” Applied Mathematical Modeling, 32: 1417–143.
Raghu Kanth STG and Sangeetha S (2016), “A stochastic Model for Earthquake Slip Distribution of Large Events,” Geomatics, Natural Hazards and Risk, 7(2): 493–521.
Roumelioti Z and Beresnev I (2003), “Stochastic Finite-Fault Modeling of Ground Motions from the 1999 Chi-Chi, Taiwan, earthquake: Application to Rock and Soil Sites with Implications for Nonlinear Site Response,” Bulletin of the Seismological Society of America, 93(4): 1691–1702.
Schmedes J, Archuleta RJ and Lavallée D (2013), “A Kinematic Rupture Model Generator Incorporating Spatial Interdependency of Earthquake Source Parameters,” Geophysical Journal International, 192(3) (March 1): 1116–1131.
Seeber L, Ekström G, Jain S K, Murty C V R, Chandak N and Armbruster J G (1996), “The 1993 Killari Earthquake in Central India: A New Fault in Mesozoic Basalt Flows?” Journal of Geophysical Research: Solid Earth, 101(B4): 8543–8560.
Shao G, Li X, Ji C and Maeda T(2011), “Focal Mechanism and Slip History of 2011 Mw 9.1 offthe Pacific Coast of Tohoku Earthquake, Constrained with Teleseismic Body and Surface Waves,” Earth Planets Space, 63(7): 559–564.
Singh S K, Ordaz M, Dattatrayam R S and Gupta H K (1999), “A Spectral Analysis of the 21 May 1997, Jabalpur, India, earthquake (Mw=5.8) and Estimation of Ground Motion from Future Earthquakes in the Indian Shield Region,” Bulletin of the Seismological Society of America, 89(6): 1620–1630.
Somerville P, Irikura K, Graves R, Sawada S, Wald D, Abrahamson Y, Iwasaki N, Kagawa T, Smith N and Kowada A (1999), “Characterizing Crustal Earthquake Slip Models for the Prediction of Strong Ground Motion,” Seismological Research Letters, 70(1): 59–80.
SRCMOD (2015), Finite-Source Rupture Model Database compiled by P.M. Mai, https://doi.org/equake-rc.info/SRCMOD/.
STABLE toolbox in MATLAB® (2013), https://doi.org/in.mathworks.com/matlabcentral/fileexchange/37514-stbl--alpha-stable-distributions-for-matlab.
Steidl J H, Archuleta R J and Hartzell S H (1991), “Rupture History of the 1989 Loma Prieta, California, Earthquake,” Bulletin of the Seismological Society of America, 81(5): 1573–1602.
Takewaki I (2013), Critical Excitation Methods in Earthquake Engineering, Second Ed., Elsevier Science, Oxford, UK.
UCSB (2015), Big Earthquakes Database compiled by C. Ji, University of California San Barbara, California, https://doi.org/www.geol.ucsb.edu/faculty/ji/big_earthquakes/home.html.
Wells DL and Coppersmith KJ (1994), “New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement,” Bulletin of the Seismological Society of America, 84(4): 974–1002.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lekshmy, P.R., Raghukanth, S.T.G. Stochastic earthquake source model for ground motion simulation. Earthq. Eng. Eng. Vib. 18, 1–34 (2019). https://doi.org/10.1007/s11803-019-0487-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11803-019-0487-8