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Characteristics of Stress Drop and Energy Budget from Extended Slip-Weakening Model and Scaling Relationships

확장된 slip-weakening 모델의 응력 강하량과 에너지 수지 특성 및 스케일링 관계

  • 최항 ((주)아이맥스트럭처 기술연구소) ;
  • 윤병익 ((주)아이맥스트럭처)
  • Received : 2020.07.08
  • Accepted : 2020.09.23
  • Published : 2020.11.01

Abstract

The extended slip-weakening model was investigated by using a compiled set of source-spectrum-related parameters, i.e. seismic moment Mo, S-wave velocity Vs, corner-frequency fc, and source-controlled high-cut frequency fmax, for 113 shallow crustal earthquakes (focal depth less than 25 km, MW 3.0~7.5) that occurred in Japan from 1987 to 2016. The investigation was focused on the characteristics of stress drop, radiation energy-to-seismic moment ratio, radiation efficiency, and fracture energy release rate, Gc. The scaling relationships of those source parameters were also investigated and compared with those in previous studies, which were based on generally used singular models with the dimensionless numbers corresponding to fc given by Brune and Madariaga. The results showed that the stress drop from the singular model with Madariaga's dimensionless number was equivalent to the breakdown stress drop, as well as Brune's effective stress, rather than to static stress drop as has been usually assumed. The scale dependence of stress drop showed a different tendency in accordance with the size category of the earthquakes, which may be divided into small-moderate earthquakes and moderate-large earthquakes by comparing to Mo = 1017~1018 Nm. The scale dependence was quite similar to that shown by Kanamori and Rivera. The scale dependence was not because of a poor dynamic range of recorded signals or missing data as asserted by Ide and Beroza, but rather it was because of the scale dependent Vr-induced local similarity of spectrum as shown in a previous study by the authors. The energy release rate Gc with respect to breakdown distance Dc from the extended slip-weakening model coincided with that given by Ellsworth and Beroza in a study on the rupture nucleation phase; and the empirical relationship given by Abercrombie and Rice can represent the results from the extended slip-weakening model, the results from laboratory stick-slip experiments by Ohnaka, and the results given by Ellsworth and Beroza simultaneously. Also the energy flux into the breakdown zone was well correlated with the breakdown stress drop, ${\tilde{e}}$ and peak slip velocity of the fault faces. Consequently, the investigation results indicate the appropriateness of the extended slip-weakening model.

Keywords

References

  1. Ohnaka M, Yamashita T. A cohesive zone model for dynamic shear faulting based on experimentally inferred constitutive relation and strong motion source parameters. J. Geophys. Res. 1989 Apr;94(B4):4089-4104. https://doi.org/10.1029/JB094iB04p04089
  2. Papageorgiou A, Aki K. A specific barrier model for the quantitative description of inhomogeneous faulting and the prediction of strong ground motion. I. Description of the model. Bull. Seism. Soc. Am. 1983 Jun;73(3):693-722.
  3. Choi H, Yoon BI. Extended slip-weakening model and inference of rupture velocity. EESK J Earthquake Eng. 2020;24(5):219-232.
  4. Eshelby JD. The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. A.1957;241:376-396.
  5. Keylis-Borok BV. On the estimation of the displacement in an earthquake source and of source dimensions. Ann. Geofisca 1959;12:205-214.
  6. Brune JN. Tectonic stress and spectra of seismic shear waves from earthquakes. J Geophy. Res. 1970 Sep;75(26):4997-5009. https://doi.org/10.1029/JB075i026p04997
  7. Heaton TH. Evidence for and implications of self-healing pulses of slip in earthquake rupture. Phys. Earth Planet. Inter. 1990;64:1-20. https://doi.org/10.1016/0031-9201(90)90002-F
  8. Abercrombie RE, Rice JR. Can observations of earthquake scaling constrain slip weakening?. Geophys. J. Int. 2005;162:406-424. https://doi.org/10.1111/j.1365-246X.2005.02579.x
  9. Aki K. Scaling law of seismic spectrum. J. Geophy. Res. 1967;72:1217-1231. https://doi.org/10.1029/JZ072i004p01217
  10. Causse M, Song SG. Are stress drop and rupture velocity of earthquakes independent? Insight from observed ground motion variability. Geophys. Res. Lett. 2015;42:7383-7389. https://doi.org/10.1002/2015GL064793
  11. Tinti E, Fukuyama E, Piantanesi A, Cocco M. A kinetic source-time function compatible with earthquake dynamics. Bull. Seism. Soc. Am. 2005;95(4):1211-1223. https://doi.org/10.1785/0120040177
  12. Yoffe E. LXXV. The moving Griffith crack. Philosophical Magazine Series 7. 1951;42(330):739-750. https://doi.org/10.1080/14786445108561302
  13. Choi H, Baltay A, Yoon BI. Source properties from the slip-weakening model. Proc. 17WCEE. Paper No. 2603. c2020.
  14. Baltay A, Ide S, Prieto G, Beroza G. Variability in earthquake stress drop and apparent stress. Geophys. Res. Lett. 2011;38(L06303). DOI:10.1029/2011GL046698.
  15. Ida Y. The maximum acceleration of seismic ground motion. Bull. Seism. Soc. Am. 1973 June;63(3):959-968.
  16. Fossum AF, Freund LB. Nonuniformly moving shear crack model of a shallow focus earthquakes mechanism. J. Geophys. Res. 1975;80(23):3343-3347. https://doi.org/10.1029/JB080i023p03343
  17. Kostrov BV. Unsteady propagation of longitudinal shear cracks (English translation). J. Appl. Math. Mech. 1966;30:1241-1248. https://doi.org/10.1016/0021-8928(66)90087-6
  18. Eshelby JD. The elastic field of a crack extending non-uniformly under general anti-plane loading. J. Mech. Phys. Solids. 1969;17:177-199. https://doi.org/10.1016/0022-5096(69)90032-5
  19. Ellsworth WL, Beroza GC. Seismic evidence for an earthquake nucleation phase. Science 1995 May;268:851-855. https://doi.org/10.1126/science.268.5212.851
  20. Udías A, Madariaga R, Buforn E. Source mechanisms of earthquakes: theory and practice. Cambridge Univ. Press. c2014. 302p.
  21. Ohnaka M. A constitutive scaling law and a unified comprehension for frictional slip failure of intact rock, and earthquake rupture. J. Geophys. Res. 2003;108(B2):2080. DOI:10.1029/2000JB000123.
  22. Atkinson C, Eshelby JD. The flow of energy into the tip of a moving crack. Int. J. Fracture. 1968 Mar;4(1):3-8.
  23. Freund LB. The mechanics of dynamic shear crack propagation. J. Geophys. Res. 1979 May;84(B5):2199-2209. https://doi.org/10.1029/JB084iB05p02199
  24. Satoh T, Kawase H, Sato T. Statistical spectra model of earthquakes in the eastern Tohoku District, Japan, based on the surface and borehole records observed in Sendai. Bull. Seism. Soc. Am. 1997;87(2):446-462.
  25. Satoh T, Kobayashi Y, kawano H. Stress drop and fmax estimated from strong motion records observed at deep boreholes in Japan. Proc. 12WCEE. paper No. 0251. c2000.
  26. Satoh T. Radiation pattern and fmax of the Tottori-ken Seibu earthquake and the aftershocks inferred from KiK-net strong motion records. J. Struct. Constr. Eng. AIJ. 2002;556:25-34. (in Japanese with English abstract). https://doi.org/10.3130/aijs.67.25_2
  27. Kawase H, Matsuo H. Separation of source, path, and site effects based on the observed data by K-Net, KiK-net, and JMA strong motion network. J. Earthq. Eng. Japan. 2004;4(1):33-52 (in Japanese with English abstract).
  28. Tsurugi M, Kagawa T, Irikura K. Study on high-cut frequency characteristics of ground motions for inland crustal earthquakes in Japan. Proc. 14WCEE. c2008.
  29. Tsurugi M, Kagawa T, Irikura K. Study on high frequency cut-off characteristics of ground motions for intra-slab earthquakes occurred in southwest in Japan. Proc. 15WCEE. c2012.
  30. Satoh T. Short period spectral level, fmax and attenuation of outerrise, intraslab and interplate earthquakes in the Tohoku district. J. Struct. Constr. Eng. AIJ. 2013;689:1227-1236. (in Japanese with English abstract). https://doi.org/10.3130/aijs.78.1227
  31. Tsurugi M, Kagawa T, Irikura K. Spectral decay characteristics fmax and ${\kappa}$ for strong ground motion prediction. Proc. 16WCEE. Paper No. 1232. c2017.
  32. Tsurugi M, Tanaka R, Kagawa T, Irikura K. High-frequency spectral decay characteristics of seismic records of inland crustal earthquakes in Japan: Evaluation of the fmax and ${\kappa}$ models. Bull. Seism. Soc. Am. 2020;110:452-470. DOI:10.1785/0120180342.
  33. Madariaga R. Dynamics of an expanding circular fault. Bull. Seism. Soc. Am. 1976;66(3):639-666.
  34. Koketsu K. Physics of seismic ground motion. Kindaikagaku Co.. c2018. 353p. (in Japanese).
  35. Abercrombie RE. Investigation uncertainties in empirical Green's function analysis of earthquake source parameters. J. Geophys. Res. Solid Earth. 2015;120. DOI:10.1002/2015JB011984.
  36. Kaneko Y, Shearer PM. Seismic source spectra and estimated stress drop derived from cohesive-zone models of circular subshear rupture. Geophys. J. Int. 2014;197:1002-1025. https://doi.org/10.1093/gji/ggu030
  37. Poliakov AN, Dmowska R, Rice JR. Dynamic shear rupture interactions with fault bends and off-axis secondary faulting. J. Geophys. Res. 2002;107(B11):2295. DOI:10.1029/2001JB000572.
  38. Rice JR, Sammis CG, Parsons R. Off-fault secondary failure by a dynamic slip pulse. Bull. Seism. Soc. Am. 2005;95(1):109-134. https://doi.org/10.1785/0120030166
  39. Hirano S, Yamashita T. Modeling of interfacial dynamic slip pulse with slip-weakening friction. Bull. Seism. Soc. Am. 2016;106(4):1628-1636. https://doi.org/10.1785/0120150208
  40. Boore DM. Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra. Bull. Seism. Soc. Am. 1983;76:43-64.
  41. Allmann BP, Shearer PM. Global variation of stress drop for moderate to large earthquakes. J. Geophys. Res. 2009;114(B01310): DOI:10.1029/2008JB005821.
  42. Oth A, Bindi D, Parola S, Di Giacomo D. Earthquake scaling characteristics and the scale-(in)dependence of seismic energy-tomoment ratio: Insights from Kik-net data in Japan. Geophys. Res. Lett. 2010;37(L19304). DOI:10.1029/2010GL044572.
  43. Kanamori H, Rivera L. Static and dynamic scaling relations for earthquakes and their implications for rupture speed and stress drop. Bull. Seism. Soc. Am. 2004;94(1):314-319. https://doi.org/10.1785/0120030159
  44. Abercrombie R. Earthquakes source scaling relationships from -1 to 5 ML using seismograms recorded at 2.5-km depth. J. Geophys. Res. 1995;100(B12):24,015-24,036. https://doi.org/10.1029/95JB02397
  45. Ide S, Beroza GC. Does apparent stress vary with earthquake size?. Geophys. Res. Lett. 2001;28(17):3349-3352. https://doi.org/10.1029/2001GL013106
  46. Beeler NM, Wong TF, Hickman SH. On the expected relationships among apparent stress, static stress drop, effective shear fracture energy, and efficiency. Bull. Seism. Soc. Am. 2003;93(3):1381-1389. https://doi.org/10.1785/0120020162
  47. Venkataraman A, Kanamori H. Observational constraints on the fracture energy of subduction zone earthquakes. J. Geophys. Res. 2004;109(B05302). DOI:10.1029/2003JB002549.
  48. Geller R. Scaling relations for earthquake source parameters and magnitudes. Bull.Seism. Soc. Am. 1976;66(5):1501-1523.
  49. Bizzarri A. On the relationships between fracture energy and physical observables in dynamic earthquake models. J. Geophys. Res. 2010;115(B10307). DOI:10.1029/2009JB007027.
  50. Fineberg J, Marder M. Instability in dynamic fracture. Phys. Rep. 1999;313:1-108. https://doi.org/10.1016/S0370-1573(98)00085-4
  51. Lockner DA. A generalized law for brittle deformation of Westerly granite. J. Geophys. Res. 1988;103(3):5107-5123. https://doi.org/10.1029/97JB03211
  52. Odedra A, Ohnaka M, Mochizuki H, Sammonds P. Temperature and pore pressure effects on the shear strength of granite in the brittle-plastic transition regime. Geophys. Res. Lett. 2001;28(15):3011-3014. https://doi.org/10.1029/2001GL013321