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Observation of Far-Field Mach Waves Generated by the 2001 Kokoxili Supershear Earthquake, M Observation of far-field Mach waves generated by the 2001 Kokoxili supershear earthquake, M. Vallée, E.M. Dunham To cite this version: M. Vallée, E.M. Dunham. Observation of far-field Mach waves generated by the 2001 Kokoxili su- pershear earthquake,. Geophysical Research Letters, American Geophysical Union, 2012, 39 (5), pp.L05311. 10.1029/2011GL050725. hal-01053146 HAL Id: hal-01053146 https://hal.archives-ouvertes.fr/hal-01053146 Submitted on 19 May 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. GEOPHYSICAL RESEARCH LETTERS, VOL. 39, L05311, doi:10.1029/2011GL050725, 2012 Observation of far-field Mach waves generated by the 2001 Kokoxili supershear earthquake M. Vallée1 and Eric M. Dunham2 Received 21 December 2011; revised 13 February 2012; accepted 13 February 2012; published 14 March 2012. [1] Regional surface wave observations offer a powerful Dunham and Archuleta, 2004; Aagaard and Heaton, 2004; tool for determining source properties of large earthquakes, Robinson et al., 2006; Vallée et al., 2008; Walker and especially rupture velocity. Supershear ruptures, being Shearer, 2009]. faster than surface wave phase velocities, create far-field [3] The most distinctive features of supershear ruptures surface wave Mach cones along which waves from all are Mach fronts. These sharp wavefronts occur whenever the sections of the fault arrive simultaneously and, over a source propagates faster than the speed of the waves it sufficiently narrow frequency band, in phase. We present radiates. Supershear ruptures thus produce shear wave Mach the first observation of far-field Mach waves from the fronts [Freund, 1979; Ben-Menahem and Singh, 1987], as major Kokoxili earthquake (Tibet, 2001/11/14, Mw 7.9) and well as surface wave Mach fronts for ruptures in a half-space confirm that ground motion amplitudes are indeed [Dunham and Bhat, 2008]. These Mach fronts are predicted enhanced on the Mach cone. Theory predicts that on the to transport extremely large particle velocities and stress Mach cone, bandpassed surface wave seismograms from a perturbations out to distances comparable to the fault width large supershear rupture will be identical to those from [Bernard and Baumont, 2005; Dunham and Bhat, 2008], much smaller events with similar focal mechanisms, with though this effect has not been substantiated observationally, an amplitude ratio equal to the ratio of the seismic moments possibly due to lack of Mach front coherence [Bizzarri et al., of the two events. Cross-correlation of 15–25 s Love waves 2010; Andrews, 2010]. from the Kokoxili event with those from a much smaller [4] Thus far, almost all theoretical and numerical studies (Mw 5) foreshock indicates a high degree of similarity have focused on the wavefield in the near-source region (i.e., (correlation coefficients ranging from 0.8 to 0.95) in distances within a few source dimensions). In this work we waveforms recorded at stations near the far-field Mach explore properties of Mach waves in the far-field limit. Our cone. This similarity vanishes away from the Mach cone. focus is on surface waves, which carry the largest ground These observations provide further evidence for supershear motion amplitudes outside the near-source region. In par- propagation of the Kokoxili rupture, and demonstrate how ticular, we characterize how waves radiated by different this simple waveform correlation procedure can be used to sections of the fault interfere with each other, and how this identify supershear ruptures. Citation: Vallée, M., and E. M. leads to extreme amplification of surface wave motions at Dunham (2012), Observation of far-field Mach waves generated stations located along the far-field Mach cone. This direc- by the 2001 Kokoxili supershear earthquake, Geophys. Res. Lett., tivity pattern is quite different from that of subshear rup- 39, L05311, doi:10.1029/2011GL050725. tures, which features maximum amplification in the forward direction. 1. Introduction [5] We next prove that at stations along the far-field Mach cone, narrowband seismograms from a large supershear [2] The speed at which an earthquake rupture propagates earthquake will be identical to those from a small earthquake influences the amplitude and character of the radiated of similar focal mechanism (except for an overall amplitude wavefield. Rupture velocities less than the shear wave speed difference equal to the ratio of seismic moments). We test b are typically inferred by source inversions and seismic our theoretical predictions using regional Love wave records imaging studies. In fact, b is the limiting velocity in certain from the Kokoxili earthquake, and confirm that maximum geometries, including along-strike propagation of megathrust directivity effects indeed occur at stations located along the ruptures in subduction zones. However, under mode II far-field Mach cone. loading conditions, in which slip occurs parallel to the rup- b ture propagation direction, rupture velocities in excess of 2. Far-Field Surface Waves From Supershear become possible [Burridge, 1973; Andrews, 1976; Xia et al., Ruptures 2004]. Seismic studies suggest supershear rupture velocities in several major strike-slip earthquakes (Izmit, Turkey, 1999; [6] In this section we discuss the relationship between far- Kokoxili, Tibet, 2001; Denali, Alaska, 2002) [Bouchon et al., field surface waves from a large supershear earthquake and a 2001; Bouchon and Vallée, 2003; Ellsworth et al., 2004; small earthquake located in the vicinity of the large one. Both earthquakes have identical focal mechanisms corresponding to horizontal slip on vertically dipping faults. 1 Geoazur, University of Nice Sophia-Antipolis, IRD, OCA, Valbonne, [7] First consider the small earthquake with seismic France. 2 moment m . At sufficiently low frequencies, seismic wave- Department of Geophysics and Institute for Computational and 0 Applied Mathematics, Stanford University, Stanford, California, USA. lengths are larger than the source dimension and the earth- quake can be described with the point source moment density Copyright 2012 by the American Geophysical Union. m0d(x)H(t), where d(⋅) and H(⋅) are the delta function and 0094-8276/12/2011GL050725 L05311 1of5 L05311 VALLÉE AND DUNHAM: OBSERVATION OF SEISMIC MACH WAVES L05311 unit step function, respectively. Within the approximation of [11] The Mach angle fM(w) is the value of f for which a layered medium (i.e., neglecting lateral heterogeneity in X(f, w) = 0. Thus from (3) we see that on the Mach cone material properties), the far-field displacement spectrum (and only on it), the displacement spectrum of the large corresponding to fundamental mode surface waves can be earthquake is identical to that of the small earthquake: written in the form [Aki and Richards, 2002] ^ U iðr0; fM ðwÞ; wÞ¼ðM0=m0Þu^iðr0; fM ðwÞ; wÞ; ð6Þ ^ ikr0 u^iðr0; f; wÞ¼m0Fiðr0; f; wÞe ; ð1Þ a result that holds even forR spatially variable slip in the ≡ m L D where r0 =|x| and f are the distance and azimuthal angle large event since M0 W 0 u(x)dx. While a similar between the source (at the origin) and the station, and w is the result holds for all f at frequencies less than b/L ^ f w natural frequency. The excitation function F iðr0; f; wÞ and (because |X( , )| 1), we emphasize that (6) applies at wavenumber k = k(w) are specific to the fundamental surface frequencies less than b/W. For large strike-slip earth- wave eigenmode, with the former also depending on the focal quakes, this includes periods greater than about 5 s mechanism of the earthquake. (considering W equal to 15 km and a shear wave speed [8] Now consider a much larger earthquake, in the vicinity of 3 km/s), rather than just those greater than 100 s. of the small one, involving unilateral rupture propagation at [12] Since surface wave phase velocities c(w) are slightly b constant rupture velocity vr. The seismic moment M0 is less than the shear wave speed , then the surface wave released over width W and length L (0 ≤ x ≤ L). At fre- Mach cone will exist for supershear earthquakes (for which b quencies less than b/W, seismic wavelengths are larger vr > ). Since the Mach angle (5) depends on frequency, than W and the source can be described in terms of the observational confirmation of our theory is facilitated by w w depth-averaged slip Du(x). The far-field surface wave dis- working with a limited frequency band centered on = 0 placement spectrum, in the far-field limit [Aki and Richards, over which the average surface wave phase velocity is 2002], is c ≈ cðw0Þ. The corresponding Mach angle is fM ≈ fM ðw0Þ. For bandpassed signals recorded at stations along the Mach Z L ^ ^ ikr0 iwx=vrÀikxcosf cone, we can inverse Fourier transform (6) to obtain the U iðr0; f; wÞ¼mWFiðr0; f; wÞe DuðxÞe dx; ð2Þ 0 remarkable result where m is the shear modulus. We have introduced the phase Uiðr0; fM ; tÞ ≈ ðM0=m0Þuiðr0; fM ; tÞ: ð7Þ w À f factors ei x/vr and e ikxcos to account for variations in sur- face wave arrival times due to both the rupture time and At these stations, the bandpassed seismogram from the large source-receiver distance, respectively, for points along the event is predicted to match that of the small event, up to an length of the fault. overall normalization factor that is the ratio of the moments [9] Using (1) to eliminate the excitation function, we of the two events.
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