Earthq Si (1)3: 535 539 535 539 Doi: 1.17/s11589-1-75-4 Doppler eet o the rupture proess o the great M W 7.9 Wenhuan earthquake Ge Jin 1,, Youai Tang 1 Shiyong Zhou 1 and Yongshun John Chen 1 1 Institute o Theoretial and Applied Geophysis (ITAG), Shool o Earth and Spae Sienes, Peking University, Beijing 1871, China amont-doherty Earth Observatory, Columbia University in the New York City, Palisades, NY, 1964, USA Abstrat In this study we perormed a lassial spetrum analysis o seismi waveorms reorded at ar ield stations o the great M W 7.9 Wenhuan earthquake to observe the shits o the orner requeny with azimuth due to the Doppler eet. Our results show that this damaging great earthquake had a dominating rupture propagation diretion o 64.. The equivalent radius o the ault rupture surae was estimated to be 33 km, yielding the rupture area o about 3 5 km. Thus the length o the rupture ault surae is about 3 km i the depth (or width) extent is 15 km. The omputer program developed in this study an quikly provide the inormation about the soure o a uture large (damaging) earthquake, whih ould be very useul or prediting atershoks and planning the resue operations. Key words: Doppler eet; rupture proess; Wenhuan earthquake; orner requeny; unidiretional CC number: P315.3 + 3 Doument ode: A 1 Introdution By taking more than seventy thousands lives and making billions o dollars damage, the great M W 7.9 Wenhuan earthquake on May 1, 8 shoked the world not only by seismi waves but also its damaging impat to the Chinese soiety. Sientists hare made great eorts to understand this great earthquake, inluding the tetoni bakground, ault struture and the rupture proess, and et. (Burhiel et al., 8). Although the surae rupture has been learly observed in the ield (Xu et al., 9), arguments about the rupture proess rose between unidiretional and bilateral ater analyzing the teleseismi waveorms (Ji and Hayes 8; Jin et al., 8; iu et al., 8; Zhang et al., 9). In this study, we investigate this problem by using a simple but eetive approah or estimating the rupture diretion, as well as other soure parameters. In the ase o large earthquake, the ault plane usually develops into a long retangle beause the depth extent is limited by the thikness o the brittle seismogeni layer, whih is usually less than km. I the Reeived 7 Otober 1; aepted in revised orm November 1; published 1 Deember 1. Corresponding author. e-mail: jinwar@gmail.om The Seismologial Soiety o China and Springer-Verlag Berlin Heidelberg 1 propagation o rupture is unidiretional, that is, the rupture starts rom one end o the ault rupture plane and propagates to the other end, the spetrum and waveorm o ar ield seismograms reorded at stations at a distane greater than 3 are shited to higher requeny or the stations in the rupture propagation diretion (Shearer, 1999) beause o the Doppler eet, a phenomena disovered by Doppler in 184. For the spetrum o seismi displaement at ar ield, orner requeny is deined by the intersetion o the asymptote o onstant lower requeny omponent and the asymptote o the deaying higher requeny omponent. It is one o the important physial haraters o seismi soure desribed in text books o seismology. The value o orner requeny depends on the geometry o the ault plane, stress drop and magnitude o the earthquake and more importantly, the orner requeny also varies aording to the azimuth rom the soure to the station i the rupture is unidiretional (Shearer, 1999). This phenomenon is related to the at that the propagation speed o rupture on the ault plan is omparable to seismi veloity. As a result, the spetrum o seismi waveorm at ar ield stations shits to a higher requeny in the diretion o rupture propagation and to a lower requeny in the diretion opposite to the rupture
536 propagation. This azimuth dependene ould provide us additional independent inormation on the rupture proess o a large earthquake suh as the great M W 7.9 Wenhuan earthquake. Theory and method In requeny domain the spetrum o a seismogram Y(ω) ould be deined as Y ( ω) = S( ω) H ( ω) I( ω), (1) where S(ω), H(ω) and I(ω) stand or the soure untion, seismi wave propagation eet and the instrument response, respetively (Helmberger, 1983). Ater removing the instrument response I(ω) by deonvolution, we also need to onsider the propagation eet o attenuation and geometrial radiation. For a ar ield seismi body wave, the propagation eet an be simpliied as Rω H ( ω ) = F( R)exp, () Qv where R is the ray distane, Q is a quality ator related to attenuation, v is the seismi wave veloity and F(R) is the geometrial spreading ator (Zhou and Xu, ). In this study, Q is assumed to be 5 and the travel time o a P phase is onsidered as R/v. In the ω Haskell soure model, the envelope o the soure untion S(ω) an be desribed as ω < τ u( ω ) = < ω <, (3) ωτ / τ τ r ω > ω ( τ rτ / 4) τ r where τ is the duration o the rupture, τ r is the rise time, and M is the earthquake moment. For the real seismograms, usually only one orner requeny an be identiied as the intersetion o ω and ω asymptotes, beause the observed spetrum an be distorted by attenuation and near-surae eets (Shearer, 1999). I the ault rupture surae o a large earthquake is a long retangle (the length to depth ratio is larger than one) and the rupture is unidiretional, the orner requeny beomes azimuth anisotropi beause o the Doppler eet, and this variation as a untion o the azimuth angle an be desribed as ( φ) =, (4) 1 r os( φ ) v φ Earthq Si (1)3: 535 539 where (φ) is the orner requeny at a ar ield station, is the real orner requeny, r v is the ratio o the rupture propagation veloity to the seismi veloity, φ is the azimuth o the station to the epienter and φ is the rupture diretion. As a result, the orner requeny should be higher at the rupture propagation diretion and lower at the opposite diretion. By averaging the orner requeny at dierent azimuths, we ould also estimate the size o the soure (the rupture plane) rom: 1/ r r π =.88 +, 3 9 (5) α v where r is the equivalent radius o the soure, α is the seismi veloity and v is the rupture propagation veloity (Silver, 1983). 3 Data and estimation o orner requeny Seismi data rom global broadband stations (Figure 1) have been downloaded rom IRIS. We only used the data rom stations more than 3 km rom the epienter, and applied a time window 1 s beore and s ater the P arrival o the M W 7.9 Wenhuan earthquake. Beore transorming the seismogram into requeny domain a areul manual seletion is used to ontrol the data quality. The spetrum was then irst three-point smoothed to redue the noise, and only the loal maximum points were used to estimate the envelope o the spetrum. We applied the non-linear least square method to itting the spetrum envelope with three independent parameters: seismi moment, orner requeny and the power o ω in higher requeny. The orner requeny is limited in a reasonable range and the power o ω an vary rom 1 to 3. A visual seletion is also applied here to exluding the unqualiied data. Ater estimating the orner requenies rom dierent azimuths, we try to it the urve desribed in equation (4) to get the real orner requeny, the rupture diretion, and the ratio o rupture veloity to seismi veloity. 4 Results and disussion As shown in Figure, the orner requeny o the main shok o the Wenhuan earthquake is highly azimuth dependant, whih implies that the rupture should
Earthq Si (1)3: 535 539 537 Figure 1 Station distribution (in the middle) and spetrum examples o the M W 7.9 Wenhuan earthquake at our dierent azimuths. The red lines are the square least it result. Only the loal maximum points in the spetrum are plotted. Figure Corner requeny azimuth variation o the main shok o the M W 7.9 Wenhuan earthquake on May 1, 8, obtained by itting the spetrum aording to Equation (4). The dominant rupture diretion is at 64., determined by the highest orner requeny. be unidiretional. Ater using the equation (4) to it the data we ind that the rupture diretion, whih is determined by the highest orner requeny, is at the azimuth o 64.. And the earthquake mehanism given by the Global CMT Projet suggested the ault plane striking at 49, whih agrees with our result with an a dierene o about 15. Besides orner requeny, the phenomenon o Doppler eet an also be observed in the length o a P wavelet (Ni et al., 5). As shown in Figure 3, the longest wavelet appears at the azimuth around 4, orresponding to the opposite diretion o the rupture propagation. We have also applied the same tehnique to two major atershoks o a magnitude o 6. and 5.8, respetively. However, we ould not ind any obvious variation o orner requeny on dierent azimuths
538 Figure 3 Azimuth variation o a P wavelet length. Waveorms are transormed into energy and staked by azimuth. The azimuth around 4 has the longest wavelet, orresponding to the opposite diretion o the rupture propagation. (Figure 4). This result is reasonable beause that the Earthq Si (1)3: 535 539 ault planes o smaller earthquakes are usually elliptial in shape or with an aspet ratio lose to one, instead o long retangles (aspet ratio o larger than one) where the rupture an propagate unidiretionally as shown in this study. We have demonstrated in this study that to observe the phenomenon o Doppler eet two ritial ondi tions must be satisied. First, the earthquake must be big enough so that the length o the rupture plane is muh larger than the width, (a larger aspet ratio), and the waveorm an be learly reorded by tele-seismi stations. Seond, the rupture must propagate unidiretionally, rom one end o the rupture surae to the other end. The relationship between the geometry o rupture surae and earthquake magnitude an be presented by the ollowing empirial ormula (Wells and Coppersmith 1994), M =.38 + 1.49 log ( ) W 4 1 where is the length o rupture surae, and M W is Figure 4 Corner requeny o two atershoks. (a) is or the earthquake on May 17th, 8 with a magnitude 6. and (b) or an earthquake on May 5th, 8 with a magnitude o 5.8. the moment magnitude o the earthquake. For an earthquake like the Wenhuan earthquake o magnitude 7.9, the rupture length at the surae was reported to be around 3 km. In the ontinent, the average ontinental seismogeni layer thikness is about 15 km. With the aspet ratio o about 15, the Doppler eet an be well observed or the M W 7.9 Wenhuan earthquake as reported here. In the ase o earthquakes with moment magnitude around 6, the length o rupture surae is ~1 km, whih is omparable to the seismogeni layer thikness. Thus an earthquake with a magnitude smaller than 6 dose not to generate observable Doppler eet. Other parameters obtained rom the average o orner requeny and earthquake magnitude (rom USGS) are listed in Table 1. Table 1 Soure parameters o the M W 7.9 Wenhuan earthquake M W 7.9 Corner requeny.59 Equivalent radius /km 33. Rupture Azimuth/ 64. Rupture veloity/km s 1.1 Note: The magnitude is rom USGS and P veloity is assumed to be 6.4. 5 Conlusions Our analysis o the orner requeny variations shows that the great M W 7.9 Wenhuan earthquake had a
Earthq Si (1)3: 535 539 539 dominating rupture propagation diretion along 64.. We also estimated the equivalent radius o the ault rupture surae to be 33 km, yielding the rupture area o about 3 5 km. Thereore we estimate the length o the rupture surae to be about 3 km i the depth (or width) extent o 15 km or the rupture surae is assumed. Tthese results agree well with other studies within a reasonable auray. We also show that an earthquake with a magnitude smaller than 6 does not generate observable Doppler eet. The omputer program developed in this study an quikly provide us the inormation about the soure o a uture large (damaging) earthquake, whih ould be useul or prediting atershoks and planning the resue operations. Reerenes Burhiel B C, Royden H, van der Hilst R D, Hager B H, (8). A geologial and geophysial ontext or the Wenhuan earthquake o 1 May 8, Sihuan, People s Republi o China. GSA Today 18(7): 5. Helmberger D V (1983). Theory and appliation o syntheti seismograms. In: Kanamori H and Boshi E eds. Earthquakes: Observation, Theory and Interpretation. North-Holland, Amsterdam, 174,. Ji C and Hayes G (8). Preliminary result o the May 1, 8 M W 7.9 Eastern Sihuan, China Earthquake. http://earthquake. usgs.gov/earthquakes/eqinthenews/8/us8ryan/inite_a ult.php. Jin G, Tang Y and Chen Y C (8). Spetra analysis o the Wenhuan (M S 8.) great earthquake and its atershoks. AGU Fall Meeting. iu C, Zhang Y, Xu S and Chen Y T (8). A new tehnique or moment tensor inversion with appliations to the 8 Wenhuan M S 8. earthquake sequene. Ata Seismologia Sinia 1(4): 333 343. Ni S, Kanamori H and Helmberger D (5). Energy radiation rom the Sumatra earthquake. Time (s) 33(36):. Shearer P M (1999). Introdution to Seismology. Cambridge University Press, Cambridge, 6 67. Silver P (1983). Retrieval o soure-extent parameters and the interpretation o orner requeny. Bull Seismol So Am 73(6A): 1 499 1 511. Wells D and Coppersmith K J (1994). New empirial relationships among magnitude, rupture length, rupture width, rupture area, and surae displaement. Bull Seismol So Am 84(4): 974 1. Xu X W, Wen X Z, Yu G H, Chen G H, Klinger Y, Hubbard J and Shaw J (9). Coseismi reverse- and oblique-slip surae aulting generated by the 8 M W 7.9 Wenhuan earthquake, China. Geology 37(6): 515. Zhang Y, Feng W P, Xu S, Zhou C H and Chen Y T (9). Spatio-temporal rupture proess o the 8 great Wenhuan earthquake. Siene in China (Series D) 5(): 145 154. Zhou S Y and Xu Z H (). Frature harateristis o the 1997 Jiashi, Xinjiang, China, earthquake swarm inerred rom soure spetra. Ata Seismologia Sinia 13(): 15 135.