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Determination of Euler Parameters of Philippine Sea Plate and the Inferences Vol. 45 No. 2 SCIENCE IN CHINA (Series D) February 2002 Determination of Euler parameters of Philippine Sea plate and the inferences ZANG Shaoxian (臧绍先)1, CHEN Qiyong (陈起永)1*, NING Jieyuan (宁杰远)1, SHEN Zhengkang (沈正康)2 & LIU Yonggang (刘永刚)1 1 Department of Geophysics, Peking University, Beijing 100871, China; 2 Department of Earth Sciences, University of California, Los Angeles, USA Correspondence should be addressed to Zang Shaoxian (email: [email protected]) Received July 20, 2001 Abstract Euler vectors of 12 plates, including Philippine Sea plate (PH), relative to a randomly fixed Pacific plate(PA) were determined by inverting the 1122 data from NUVEL-1 global plate motion model, earthquake slip vectors along Philippine Sea plate boundary, and GPS observed velocities. Euler vectors of Philippine Sea plate relative to adjacent plates are also gained. Our results are well consistent with observed data and can satisfy the geological and geophysical con- straints along the Caroline(CR)-PH and PA-CR boundaries. Deformation of Philippine Sea plate is also discussed by using the plate motion Euler parameters. Keywords: Philippine Sea plate, earthquake slip vectors, intraplate deformation, relative plate motion, plate motion parameters. Euler parameters are the basic parameters describing the plate motion. The Philippine Sea plate, proposed as a distinct plate at the early stage of plate motion theory, plays a special role in the tectonics history of west Pacific and east Eurasia continent. Containing mainly convergent subduction boundaries and lacking of accreting boundary, which is useful to determine relative motion rates, and transform boundary, which can determine relative motion azimuth more accu- rately than earthquake slip vectors, along the boundaries make it very hard to determine Euler vector of Philippine Sea plate. It is a difficulty and also a focus of plate tectonics. Before the availability of accurate Geodesy data, only slip vectors of thrust earthquakes along the subducted boundary of Philippine Sea plate can be used to constrain its motion, but there exist at least three factors that cause uncertainties when using these earthquake slip vectors. First, the back-arc spreading and the deformation of overriding plate, such as the spreading of Mariana Trough and strike slip fault such as Philippine fault within overriding plate, make the azimuth of earthquake slip vectors differ from that predicted by plate motion. Second, Some small colliding zones around the Philippine Sea plate make earthquake focal mechanism more complicated. Fi- nally, it is uncertain whether the north boundary of Philippine Sea plate is adjacent to Eurasia plate or North America plate, or even a distinct Okhotsk plate. These problems must be carefully ana- lyzed before determining the Euler vector of Philippine Sea plate with intraplate earthquake slip * Now at Department of Geological Sciences, Northwestern University, Evanston, IL 60208, USA 134 SCIENCE IN CHINA (Series D) Vol. 45 vectors. Many researchers have discussed or obtained Euler vectors of Philippine Sea plate with earthquake slip vectors[1 6], or discussed the constrain conditions[7]. Seno et al.[8] discussed the deficiencies in previous studies and obtained Euler vector of Philippine Sea plate by using 11 and 16 earthquake slip vectors at Nankai Trough-Ryukyu Trench along the PH-EU boundary and Izu- Bonin Trench along the PH-PA plate boundary respectively, constrained by NUVEL-1[9] EU-PA Euler vector. Seno’s result is now the best, but the data constraining motion of the Philippine Sea plate are still not enough, especially lacking the data of rates. Many new earthquake slip vectors have become available from Harvard CMT catalogue. The foundation of GPS observation network makes the data of rates describe the motion between geological blocks or plates available, which was used to study the deformation of continent[10,11]. It is possible to determine the Euler vector of Philippine Sea plate more accurately now. In this study, we obtain our PH-PA Euler vector with a global inversion by simultaneously inverting these new data, and the 1122 data from NUVEL-1 model. 1 Method of determining the Euler parameters of Philippine Sea plate The Euler parameters of the Philippine Sea plate in NUVEL-1 model were taken from Seno et al.[12] and not gained by inversion, possibly because of lacking data describing motion of the Philippine Sea plate, especially the data of rates. So, there are total 12 plates in NUVEL-1 model and Euler parameters of 11 plates relative to Pacific plate are gained by inversion. In this study, we add the Philippine Sea plate to the 12 plates in NUVEL-1 model and gain Euler parameters of 13 plates constrained to consistency with global plate circuit closure. Suppose there exist m plates, we randomly choose the reference frame so that the mth plate is fixed. The 3m-3 independent components of other m-1 plates of a plate motion model then form a model vector M: M = (q 1 ,L ,q m -1 ,f1 ,L f m-1 ,w1 ,L ,w m-1 ) , q i ,f i ,w i are Euler pole’s latitude, longitude, and the rotation rate of ith plate. 0 Suppose there exist N observed data and they form a vector d . s i and di (M ) are the 0 0 standard error and predicted value, respectively, of di , the ith component of d . And, suppose there exist n and N-n observed data of magnitudes and direction, respectively, of relative motion. The total residual error is 2 2 2 N é d 0 - d (M ) ù n éd 0 - d (M ) ù N é d 0 - d (M ) ù c 2 = å ê i i ú = å ê i i ú + å ê i i ú , (1) i=1 ëê s i ûú i=1 ëê s i ûú i=n+1 ëê s i ûú where c 2 achieves a stationary value when its derivatives with respect to the model parameters are zero. And, we suppose that the dispersion between the observed and predicted directions is 0 0 less than 20°, then we replace sin[ di - d i (M )] by di - d i (M ) and get No. 2 DETERMINATION OF EULER PARAMETERS OF PHILIPPINE SEA PLATE 135 N d (M ) ¶d (M ) N d 0 ¶d (M ) i i = i i , j = 1, L , 3m - 3 . (2) å 2 å 2 i =1 s i ¶M j i=1 s i ¶M j Construct a reasonably good starting model M * so that M - M * is small enough and we 2 can replace ¶d i (M ) / ¶M j by ¶d i (M *) / ¶M j . Neglecting terms of (M j - M j *) , finally, we get N 3m-3 1 ¶d ¶d N 1 ¶d i i (M - M *) = i [d 0 - d (M *)] , j = 1, L , 3m - 3 . (3) å å 2 ¶M ¶M k k å 2 ¶M i i i=1 k =1 s i j k i=1 s i j Eq. (3) is a linear equation of M - M * . The matrix expression is AT V -1 AdM = AT V -1dd 0 , (4) where 0 0 ¶d i T 2 dM = M - M *, dd = d - d (M *), Aik = , Aik = Aki, Vik = s i d ik . (5) ¶M k If independent data are as many as model parameters (or more independent data), eq. (4) has the unique solution dM = ( AT V -1 A) -1 AT V -1dd 0 . (6) The new estimate of the model is given by M = dM + M * . This procedure is iterated until convergence is gained. 2 Data and process Data used in this study include: (1) The 1122 data, consisting of spreading rates, transform fault azimuth, and earthquake slip vectors, from NUVEL-1 model. (2) 67 earthquake slip vectors exist along the Philippine Sea plate boundary. In order to make sure that the slip vectors represent the azimuth of interplate motion, we choose them according to three rules. First, the magnitudes of earthquake are big enough. We choose those with a scalar moment scale of 24 or more. Second, epicenters are located in subduction zone and on the top surface of Benioff Zone. Third, the depths of epicenters are between 15 and 60 km, the fault plane solutions are for thrust earthquakes, and the dips of the fault plane are close to the dip of subduc- tion zone. We discard the data in Luzu Trough-Philippine Trend when selecting earthquake slip vectors from Harvard CMT 1977 —1999, because the Philippine Archipelago is a complicated deforma- tion zone with a nearly N-S left-handed strike slip fault passing through it, thus making the rela- tive motion between EU and PH more complicated. Also, we do not use the data in Mariana Trench because of the ~40 mm/a spreading rate at the back-arc of Mariana which changes the coupling status between PH and PA. We finally choose 32 earthquake slip vectors at Nankai Trough-Ryukyu Trench and 35 at Izu-Bonin Trench, including 25 from Seno et al.[8] Table 1-1 shows these earthquake slip vectors and their predicted values of this study. 136 SCIENCE IN CHINA (Series D) Vol. 45 (3) GPS data. Observed velocities of 4 GPS stations located in PH plate relative to EU plate are shown in table 1-2. Data of Guam and Palau stations are not used for inversion. Table 1-1 Data at PH-EU boundary: Nankai Trough-Ryukyu Trench No. 1a) 2 a) 3 a) 4 a) 5 a) 6 a) 7 a) 8 a) 9 10 Lat. (°N) 33.76 33.7 33.13 32.31 32.26 32.24 32.23 32.15 31.84 31.79 Lon. (°E) 137.2 136.05 135.84 131.83 131.78 132.21 131.78 131.98 131.8 131.63 Obs.
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