Abstract
Unilateral rupture propagation along earthquake faults results in asymmetric radiation in and opposite to the direction of rupture travel, known as forward and backward directivity. Correct simulation of fault directivity pulses in ground velocity has engineering significance. Forward velocity pulses are typically recognized as short bursts of energy with large amplitude, compared to elongated and much weaker backward wave trains. A classic model of such behavior is the line source in the far field, undergoing rupture propagation with constant speed. In reality, earthquake ruptures can be reasonably expected to travel in a variable, often irregular, manner. Simulation of the distinctions introduced by the variable rupture velocity into the characteristic features of directivity should not only involve the line source but also finite sources in the near field. The differences with the case of constant rupture velocity are threefold. First, sharp amplitude contrast between the velocity pulses in the forward and reverse directions is substantially subdued by the variable fracture speed. Second, complex ruptures result in the longer duration of radiation in both directions. Third, unlike the relatively simple radiation pulses in the scenario of constant velocity, complexity in the rupture travel time creates multiple pulses of both forward and reverse directivity. Randomization of rupture velocity nearly erases the differences in the spectral content of radiation in the forward and backward directions. Well known features of fault directivity appear to be artifacts of the constant-velocity assumption and the resulting orderly interference. The complexity that randomization introduces into the directivity pulses is gradually reduced with lesser randomness. Since irregularity in the rupture travel time should be viewed as the norm rather than an exception, correct simulation of fault directivity must involve variable velocity of rupture propagation.
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References
Aagaard, B. T., & Heaton, T. H. (2004). Near-source ground motions from simulations of sustained intersonic and supersonic fault ruptures. Bulletin of the Seismological Society of America, 94, 2064–2078.
Aki, K., & Richards, P. G. (1980). Quantitative seismology. W. H Freeman and Company.
Anderson, T. L. (2005). Fracture mechanics (3rd ed.). Taylor and Francis.
Beresnev, I. A. (2001). What we can and cannot learn about earthquake sources from the spectra of seismic waves. Bulletin of the Seismological Society of America, 91, 397–400.
Beresnev, I. A. (2003). Uncertainties in finite-fault slip inversions: To what extent to believe? (A critical review). Bulletin of the Seismological Society of America, 93, 2445–2458.
Beresnev, I. (2013). Reflections on frequency dependence in earthquake-source inversions. Natural Hazards, 66, 1287–1291.
Beresnev, I. A. (2017a). Factors controlling high-frequency radiation from extended ruptures. Journal of Seismology, 21, 1277–1284.
Beresnev, I. A. (2017b). Simulation of near-fault high-frequency ground motions from the representation theorem. Pure and Applied Geophysics, 174, 4021–4034.
Beresnev, I. A. (2021). The strongest possible earthquake ground motion. Journal of Earthquake Engineering. https://doi.org/10.1080/13632469.2019.1691681
Beresnev, I. A., & Atkinson, G. M. (1997). Modeling finite-fault radiation from the ωn spectrum. Bulletin of the Seismological Society of America, 93, 67–84.
Beresnev, I. A., & Atkinson, G. M. (2002). Source parameters of earthquakes in eastern and western North America based on finite-fault modeling. Bulletin of the Seismological Society of America, 92, 695–710.
Beresnev, I. A., & Roxby, K. (2021). The effects of variable and constant rupture velocity on the generation of high-frequency radiation from earthquakes. Pure and Applied Geophysics, 178, 1157–1164.
Boore, D. M., & Joyner, W. B. (1978). The influence of rupture incoherence on seismic directivity. Bulletin of the Seismological Society of America, 68, 283–300.
Bray, J. D., & Rodriguez-Marek, A. (2004). Characterization of forward-directivity ground motions in the near-fault region. Soil Dynamics and Earthquake Engineering, 24, 815–828.
Burridge, R. (1973). Admissible speeds for plane-strain self-similar shear cracks with friction but lacking cohesion. Geophysical Journal of the Royal Astronomical Society, 35, 439–455.
Graves, R. W., Aagaard, B. T., Hudnut, K. W., Star, L. M., Steward, J. P., & Jordan, T. H. (2008). Broadband simulations for Mw 7.8 southern San Andreas earthquakes: Ground motion sensitivity to rupture speed. Geophysical Research Letters, 35, L22302.
Graves, R. W., & Pitarka, A. (2010). Broadband ground-motion simulation using a hybrid approach. Bulletin of the Seismological Society of America, 100, 2095–2123.
Infantino, M., Mazzieri, I., Özcebe, A. G., Paolucci, R., & Stupazzini, M. (2020). 3D physics-based numerical simulations of ground motion in Istanbul from earthquakes along the Marmara segment of the North Anatolian fault. Bulletin of the Seismological Society of America, 110, 2559–2576.
Kaneko, Y., & Shearer, P. M. (2014). 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, 120, 1053–1079.
Marder, M., & Fineberg, J. (1996). How things break. Physics Today, September, pp 24–29.
Mavroeidis, G. P., & Papageorgiou, A. S. (2003). A mathematical representation of near-fault ground motions. Bulletin of the Seismological Society of America, 93, 1099–1131.
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.
Somerville, P., Irikura, K., Graves, R., Sawada, S., Wald, D., Abrahamson, N., Iwasaki, Y., Kagawa, T., Smith, N., & Kowada, A. (1999). Characterizing crustal earthquake slip models for the prediction of strong ground motion. Seismological Research Letters, 70, 59–80.
Somerville, P. G., Smith, N. F., Graves, R. W., & Abrahamson, N. A. (1997). Modification of empirical strong ground motion attenuation relations to include the amplitude and duration effects of rupture directivity. Seismological Research Letters, 68, 199–222.
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, 974–1002.
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Beresnev, I.A. The Effects of Variable Velocity of Rupture Propagation on Fault’s Directivity Pulses. Pure Appl. Geophys. 178, 3427–3439 (2021). https://doi.org/10.1007/s00024-021-02832-w
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DOI: https://doi.org/10.1007/s00024-021-02832-w