Analysis of Rupture Directivity for the 2004 Sumatra Earthquake from the Rayleigh-Wave Phase Velocity

Abstract

The rup ture directivity for the 2004 Su ma tra earth quake is an a lyzed by ex am in ing dif fer ences be tween the phase-de lay times of Ray leigh-waves (in the 140 -160 sec pe riod range) aris ing from the main shock and ref er ence earth quakes. A long source-pro cess time (~463.0 sec) and large rup ture length (~1164.0 km) are de rived from this anal y sis of rup ture directivity. The source-pro cess time for this earth quake is larger than for ei ther the 1960 Chile or 1964 Alaska earth quakes. This might be due to the length of the rup ture that oc curred dur ing earth quake fault ing. The es ti mated rise time for the 2004 Su ma tra earth quake, 92.0 sec, is ap prox i mately 20% of the whole source du ra tion and also larger than those for the 1960 Chile and 1964 Alaska earth quakes. This likely re flects a fun da men tal dif fer ence be tween the fric tional prop er ties of these earth quakes. When the rise time is taken into ac count, an es ti mated rup ture ve loc ity of ap prox i mately 3.1 km sec -1 is ob tained. This value is higher than that found in pre vi ous stud ies car ried out on the ba sis of hydroacoustic data and re gional seis mic net works. In this study, we ob tain ad di tional ev i dence from anal y sis of the sur face-wave phase-de lay time which con firms the ba sic fea tures of the rup tur ing of the 2004 Su ma tra earth quake. The re sults can also provide some constraints for the study of source rupturing for this earthquake. IN TRO DUC TIONOn 26 De cem ber 2004, a large earth quake (M w = 9.0 -9.3) trig gered a de struc tive tsu nami and large rup tur ing between the Sunda and In dia-Aus tra lian plates. The 2004 Suma tra earth quake's (cf. Lay et al. 2005) rup ture length and source-pro cess time were first re ported to be hun dreds of kilometers long with a ~200 -400 sec slip dis tri bu tion inverted from teleseismic P-waves (Yagi 2005;Yamanaka 2005). Re cently, stud ies of high-fre quency en ergy ra di a tion from P-waves, as well as hydroacoustic data have con firmed the rup ture length to be 1100 -1300 km (Guilbert et al.

Rise time and source duration of the 2008 M W 7.9 Wenchuan (China) earthquake as revealed by Rayleigh waves

“…The phase velocity of the Rayleigh wave along the greatcircle path from the earthquake to the station was derived by the single-station method (cf., Hwang and Yu, 2005;Chang et al, 2007;Chang et al, 2010). Hence, the time it takes for the Rayleigh wave to travel from a source to a given station at period T can be written as follows.…”

“…Figure 3 shows the variation in apparent source duration with azimuth, which ful lls the feature of unilateral rupture (cf. Chang, 2009;Chang et al, 2010). Hence, for a unilateral faulting event, T SPT ( ) can be expressed as (e.g., Hwang et al, 2001;Chang, 2009;Chang et al, 2010):…”

“…where C(T ) and t (T ) denote the phase-velocity and the corresponding travel time of a Rayleigh wave at a given period T , respectively; L is the epicentral distance; φ S R (T ) is the station phase after removing the instrumental response; φ 0R (T ) is the initial phase of the source, calculated from a known focal mechanism and the velocity structure of the source area; N is an arbitrary integer for detecting the reasonable phase-velocities in the long-period part (cf., Chang et al, 2007;Chang et al, 2010). Here, the focal mechanism (strike/dip/rake = 231…”

“…Ben-Menahem (1961) rst proposed the nite moving source theory to account for the effect of rupture propagation (i.e., source niteness) on far-eld seismograms, such as the Doppler effect. Source niteness results in a time delay in surface-wave propagation and a number of nodes in the Fourier spectra (Ben-Menahem, 1961;Hwang et al, 2001;Aki and Richards, 2002;Chang et al, 2010). In the study reported here, we have estimated the azimuthdependent phase-delay time of Rayleigh waves (i.e., source duration variation with azimuth) due to source rupture directivity during the 2008 Wenchuan earthquake (cf.…”

“…However, all source models demonstrate that the main energy release is concentrated mostly within 30 km along the dipping-direction from the surface (depth about 20 km). The studies divided the faulting mechanism of the 2008 Wenchuan earthquake into two types: (1) thrusting in the earlier rupture; (2) strike-slip faulting in the later one (e.g., Hwang et al, 2010). Wang et al (2010) calculated co-seismic displacements of the source area from several source rupture models and suggested that the source model of Wang et al (2008) is the best in terms of tting GPS data.…”