Abstract
The stress drop (Δσ) is a fundamental parameter used to quantify source physics, and its uncertainty is closely related to seismic hazard. To reveal the relationship between Δσ uncertainty and resultant ground-motion variability, ground motions produced by the 2013 Mw6.6 Lushan earthquake, characterized by various Δσ values, are simulated using the stochastic empirical Green’s function method. First, the variability in spectral amplitudes of simulated ground motions arising from the stochastic rupture process is investigated. Generally, it increases from ~ 0.05 to ~ 0.14 as the period increases up to 2.0 s, irrespective of the Δσ value used. The ground-motion variability due to Δσ uncertainty is then explored. The synthetic spectral amplitude is found to be linearly proportional to Δσb, thus the standard deviation of Δσ (log10 unit) is equal to the standard deviation of the spectral amplitude (log10 unit) multiplied by a factor b. The regressed b values are strongly dependent on the period and generally in the range of 0.7 to 0.6 up to the period of 2.0 s. These results explain how much of the ground-motion variability is caused purely by Δσ uncertainty. Moreover, the standard deviation of the spectral amplitudes is calculated directly from simulations based on random Δσ values following a lognormal distribution. The findings further verify the reliability of the relationship between Δσ uncertainty and ground-motion variability. Assuming that the interevent standard deviation in a ground-motion prediction model is dominated entirely by Δσ uncertainty and the stochastic rupture process, we estimate the standard deviation of log10Δσ (~ 0.2–0.3) for broad regions using various models.
Similar content being viewed by others
References
Abercrombie, R. E. (2015). Investigating uncertainties in empirical Green’s function analysis of earthquake source parameters. Journal of Geophysical Research: Solid Earth. https://doi.org/10.1002/2015JB011984.
Abrahamson, N. A., Silva, W. J., & Kamai, R. (2014). Summary of the ASK14 ground motion relation for active crustal regions. Earthquake Spectra, 30(3), 1025–1055. https://doi.org/10.1193/070913EQS198M.
Allmann, B. P., & Shearer, P. M. (2009). Global variations of stress drop for moderate to large earthquakes. Journal of Geophysical Research, 114, B01310. https://doi.org/10.1029/2008JB005821.
Baltay, A. S., & Hanks, T. C. (2014). Understanding the magnitude dependence of PGA and PGV in NGA-West2 data. Bulletin of the Seismological Society of America, 104(6), 2851–2865. https://doi.org/10.1785/0120130283.
Baltay, A. S., Hanks, T. C., & Beroza, G. C. (2013). Stable stress-drop measurements and their variability: implications for ground-motion prediction. Bulletin of the Seismological Society of America, 103(1), 211–222. https://doi.org/10.1785/0120120161.
Baltay, A., Ide, S., Prieto, G., & Beroza, G. (2011). Variability in earthquake stress drop and apparent stress. Geophysical Research Letters, 38, L06303. https://doi.org/10.1029/2011GL046698.
Beauval, C., Honoré, L., & Courboulex, F. (2009). Ground-motion variability and implementation of a probabilistic-deterministic hazard method. Bulletin of the Seismological Society of America, 99(5), 2992–3002. https://doi.org/10.1785/0120080183.
Bindi, D., Pacor, F., Luzi, L., Puglia, R., Massa, M., Ameri, G., et al. (2011). Ground motion prediction equations derived from the Italian strong motion database. Bulletin of Earthquake Engineering, 9, 1899–1920. https://doi.org/10.1007/s10518-011-9313-z.
Bindi, D., Spallarossa, D., Picozzi, M., Scafidi, D., & Cotto, F. (2018). Impact of magnitude selection on aleatory variability associated with ground-motion prediction equations: part I—local, energy, and moment magnitude calibration and stress-drop variability in central Italy. Bulletin of the Seismological Society of America, 108(3A), 1427–1442. https://doi.org/10.1785/0120170356.
Bjerrum, L. W., Sørensen, M. B., Ottemöller, L., & Atakan, K. (2013). Ground motion simulations for İzmir, Turkey: parameter uncertainty. Journal of Seismology, 17(4), 1223–1252. https://doi.org/10.1007/s10950-013-9389-9.
Boore, D. M. (2003). Simulation of ground motion using stochastic method. Pure and Applied Geophysics, 160, 635–676. https://doi.org/10.1007/PL00012553.
Boore, D. M., Stewart, J. P., Seyhan, E., & Atkinson, G. M. (2014). NGA-West2 equations for predicting PGA, PGV, and 5% damped PSA for shallow crustal earthquakes. Earthquake Spectra, 30(3), 1057–1085. https://doi.org/10.1193/070113EQS184M.
Brune, J. (1970). Tectonic stress and the spectra of seismic shear waves from earthquakes. Journal of Geophysical Research, 75, 4997–5009. https://doi.org/10.1029/JB075i026p04997.
Campbell, K. W., & Bozorgnia, Y. (2014). NGA-West2 ground motion model for the average horizontal components of PGA, PGV, and 5% damped linear acceleration response spectra. Earthquake Spectra, 30(3), 1087–1115. https://doi.org/10.1193/062913EQS175M.
Causse, M., Cotton, F., Cornou, C., & Bard, P.-Y. (2008). Calibrating median and uncertainty estimations for a practical use of empirical Green’s functions technique. Bulletin of the Seismological Society of America, 98(1), 344–353. https://doi.org/10.1785/0120070075.
Causse, M., Dalguer, L. A., & Mai, P. M. (2014). Variability of dynamic source parameters inferred from kinematic models of past earthquakes. Geophysical Journal International, 196, 1754–1769. https://doi.org/10.1093/gji/ggt478.
Causse, M., & Song, S. G. (2015). Are stress drop and rupture velocity of earthquakes independent? Insight from observed ground motion variability. Geophysical Research Letters. https://doi.org/10.1002/2015GL064793.
Chiou, B. S.-J., & Youngs, R. R. (2014). Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra. Earthquake Spectra, 30(3), 1117–1153. https://doi.org/10.1193/072813EQS219M.
Cocco, M., Tinti, E., & Cirella, A. (2016). On the scale dependence of earthquake stress drop. Journal of Seismology, 20, 1151–1170. https://doi.org/10.1007/s10950-016-9594-4.
Cotton, F., Archuleta, R., & Causse, M. (2013). What is sigma of the stress drop? Seismological Research Letters, 84(1), 42–48. https://doi.org/10.1785/0220120087.
Courboulex, F., Converset, J., Balestram, J., & Delouis, B. (2010). Ground-motion simulations of the 2004 M w 6.4 Les Saintes, Guadeloupe, earthquake using ten smaller events. Bulletin of the Seismological Society of America, 100(1), 116–130. https://doi.org/10.1785/0120080372.
Courboulex, F., Vallée, M., Causse, M., & Chounet, A. (2016). Stress-drop variability of shallow earthquakes extracted from a global database of source time functions. Seismological Research Letters, 87(4), 912–918. https://doi.org/10.1785/0220150283.
Dalguer, L. A., Miyake, H., Day, S. M., & Irikura, K. (2008). Surface rupturing and buried dynamic-rupture models calibrated with statistical observations of past earthquakes. Bulletin of the Seismological Society of America, 98(3), 1147–1161. https://doi.org/10.1785/0120070134.
Das, S., & Kostrov, B. V. (1986). Fracture of a single asperity on a finite fault: a model for weak earthquakes? Earthquake Source Mechanism (pp. 91–96). Washington: America Geophysical Union.
Eshelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society, 241(1226), 376–396. https://doi.org/10.1098/rspa.1957.0133.
Hao, J., Ji, C., Wang, W., & Yao, Z. (2013). Rupture history of the 2013 M w6.6 Lushan earthquake constrained with local strong motion and teleseismic body and surface waves. Geophysical Research Letters, 40, 5371–5376. https://doi.org/10.1002/2013GL056876.
Hanks, T. C., & Kanamori, H. (1979). A moment magnitude scale. Journal of Geophysical Research, 84, 2348–2350.
Honoré, L., Courboulex, F., & Souriau, A. (2011). Ground motion simulations of a major historical earthquake (1660) in the French Pyrenees using recent moderate size earthquakes. Geophysical Journal International, 187, 1001–1018. https://doi.org/10.1111/j.1365-246X.2011.05319.x.
Idriss, I. M. (2014). An NGA-West3 empirical model for estimating the horizontal spectra values generated by shallow crustal earthquakes. Earthquake Spectra, 30(3), 1155–1177. https://doi.org/10.1193/070613EQS195M.
Irikura, K. (1983). Semi-empirical estimation of strong ground motions during large earthquake. Bulletin of the Disaster Prevention Research Institute, Kyoto University, 33(Part 2), 298.
Kale, Ö., Akkar, S., Ansari, A., & Hamzehloo, H. (2015). A ground-motion predictive model for Iran and Turkey for horizontal PGA, PGV, and 5% damped response spectrum: investigation of possible regional effects. Bulletin of the Seismological Society of America, 105(2A), 963–980. https://doi.org/10.1785/0120140134.
Kanamori, H. (1994). Mechanics of earthquakes. Annual Review of Earth and Planetary Sciences, 22, 207–237.
Kanamori, H., & Anderson, D. L. (1975). Theoretical basis of some empirical relations in seismology. Bulletin of the Seismological Society of America, 65(5), 1073–1095.
Kaneko, Y., & Shearer, P. M. (2014). Seismic source spectra and estimated stress drop derived from cohesive-zone models of circular subshear rupture. Geophysical Journal International, 197, 1002–1015. https://doi.org/10.1093/gji/ggu030.
Kaneko, Y., & Shearer, P. M. (2015). Variability of seismic source spectra, estimated stress drop, and radiated energy, derived from cohesive-zone models of symmetrical and asymmetrical circular and elliptical ruptures. Journal of Geophysical Research: Solid Earth. https://doi.org/10.1002/2014JB011642.
Kohrs-Sansorny, C., Courboulex, F., Bour, M., & Anne, D. (2005). A two-stage method for ground-motion simulation using stochastic summation of small earthquakes. Bulletin of the Seismological Society of America, 95(4), 1387–1400. https://doi.org/10.1785/0120040211.
Lyu, J., Wang, X. S., Su, J. R., Pan, S. L., Li, Z., Yin, L. W., et al. (2013). Hypocenter location and source mechanism of the M s 7.0 Lushan earthquake sequence. Chinese Journal of Geophysics, 56(5), 1753–1763. https://doi.org/10.6038/cjg20130533. (in Chinese).
Madariaga, R. (1976). Dynamics of an expanding circular fault. Bulletin of the Seismological Society of America, 66(3), 639–666.
McGuire, R. K., & Hanks, T. C. (1980). RMS accelerations and spectral amplitudes of strong motion during the San Fernando earthquake. Bulletin of the Seismological Society of America, 70(5), 1907–1920.
Oth, A., Miyake, H., & Bindi, D. (2017). On the relation of earthquake stress drop and ground motion variability. Journal of Geophysical Research: Solid Earth, 122, 5474–5492. https://doi.org/10.1002/2017JB014026.
Pulido, N., Ojeda, A., Atakan, K., & Kubo, T. (2004). Strong ground motion estimation in the Sea of Marmara region (Turkey) based on a scenario earthquake. Tectonophysics, 391, 357–374. https://doi.org/10.1016/j.tecto.2004.07.023.
Salichon, J., Kohrs-Sansorny, C., Bertrand, E., & Courboulex, F. (2010). A M w6.3 earthquake scenario in the city of Nice (southeast France): ground motion simulations. Journal of Seismology, 14(3), 523–541. https://doi.org/10.1007/s10950-009-9180-0.
Sharma, B., Chopra, S., Sutar, A. K., & Bansal, B. K. (2013). Estimation of strong ground motion from a great earthquake M w 8.5 in central seismic gap region, Himalaya (India) using empirical Green’s function technique. Pure and Applied Geophysics, 170(12), 2127–2138. https://doi.org/10.1007/s00024-013-0647-0.
Somerville, P., Irikura, K., Graves, R., Sawada, S., Wald, D., Abrahamson, N., et al. (1999). Characterizing crustal earthquake slip models for the prediction of strong ground motion. Seismological Research Letters, 70(1), 59–70.
Sørensen, M. B., Pulidu, N., & Atakan, K. (2007). Sensitivity of ground-motion simulations to earthquake source parameters: a case study for Istanbul, Turkey. Bulletin of the Seismological Society of America, 97(3), 881–900. https://doi.org/10.1785/0120060044.
Wang, W. M., Hao, J. L., & Yao, Z. X. (2013a). Preliminary result for rupture process of Apr. 20, 2013, Lushan earthquake, Sichuan, China. Chinese Journal of Geophysics, 56(4), 1412–1417. https://doi.org/10.6038/cjg20130436. (in Chinese).
Wang, Y. S., Li, X. J., & Zhou, Z. H. (2013b). Research on attenuation relationships for horizontal strong ground motions in Sichuan-Yunnan region. Acta Seismologica Sinica, 35(2), 238–249. (in Chinese).
Wang, H. W., Ren, Y. F., & Wen, R. Z. (2018). Source parameters, path attenuation and site effects from strong-motion recordings of the Wenchuan aftershocks (2008–2013) using a non-parametric generalized inversion technique. Geophysical Journal International, 212, 872–890. https://doi.org/10.1093/gji/ggx447.
Wang, H. W., Wen, R. Z., & Ren, Y. F. (2017). Simulating ground-motion directivity using stochastic empirical Green’s function method. Bulletin of the Seismological Society of America, 107(1), 359–371. https://doi.org/10.1785/0120160083.
Wells, D. L., & Coppersmith, K. J. (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.
Wen, R. Z., Wang, H. W., & Ren, Y. F. (2015). Estimation of source parameters and quality factor based on the generalized inversion method in Lushan earthquake. Journal of Harbin Institute of Technology, 47(4), 58–63. https://doi.org/10.11918/j.issn.0367-6234.2015.04.010. (in Chinese).
Wen, R. Z., Xu, P. B., Wang, H. W., & Ren, Y. F. (2018). Single-station standard deviation using strong-motion data from the Sichuan region, China. Bulletin of the Seismological Society of America, 108(4), 2237–2247. https://doi.org/10.1785/0120170276.
Zafarani, H., Vahidifard, H., & Ansari, A. (2012). Sensitivity of ground-motion scenarios to earthquake source parameters in the Tehran metropolitan area, Iran. Soil Dynamics and Earthquake Engineering, 43, 342–354. https://doi.org/10.1016/j.soildyn.2012.07.007.
Zhang, Y., Wang, R., Chen, Y. T., Xu, L., Du, F., Jin, M., et al. (2014). Kinematic rupture model and hypocenter relocation of the 2013 M w 6.6 Lushan earthquake constrained by strong-motion and teleseismic data. Seismological Research Letters, 85(1), 15–22. https://doi.org/10.1785/0220130126.
Zhao, J. X., Zhang, J., Asano, A., Ohno, Y., Oouchi, T., Takahashi, T., et al. (2006). Attenuation relations of strong ground motion in Japan using site classification based on predominant period. Bulletin of the Seismological Society of America, 96(3), 898–913. https://doi.org/10.1785/0120050122.
Acknowledgements
Strong-motion recordings used in this article were collected by the China Strong-Motion Network Center. Due to the current maintenance of its website (http://www.csmnc.net/) (official notice of Institute of Engineering Mechanics, CEA can be obtained at http://www.iem.ac.cn/detail.thml?id=1102), we contacted the email csmnc@iem.ac.cn for data application (last accessed June 2017). Basic information (surface wave magnitude, hypocentral location) on earthquakes was derived from the China Earthquake Network Center at website http://news.ceic.ac.cn/ (last accessed June 2017). The VS30 measurements for some stations were derived from the Next Generation Attenuation (NGA) site database of the Pacific Earthquake Engineering Research Center and are available for download at http://peer.berkeley.edu/nga/ (last accessed June 2017). This work was supported by the National Key R&D Program of China (no. 2017YFC1500801), National Natural Science Foundation of China (nos. 51808514 and 51878632), Natural Science Foundation of Heilongjiang Province (no. E2017065), and Science Foundation of the Institute of Engineering Mechanics, China Earthquake Administration (no. 2018B03). We sincerely appreciate the three anonymous reviewers for their valuable comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wang, H., Ren, Y., Wen, R. et al. Investigating the Contribution of Stress Drop to Ground-Motion Variability by Simulations Using the Stochastic Empirical Green’s Function Method. Pure Appl. Geophys. 176, 4415–4430 (2019). https://doi.org/10.1007/s00024-019-02185-5
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00024-019-02185-5