Northern Luzon Arc: Location and Tectonic Features from Magnetic Data off Eastern Taiwan

A numerical hybrid method was developed to model elastic wave propagation.This algorithm was implemented with both the pseudo-spectrumand the finite-element methods.The pseudo-spectrum is currently a popularnumerical method in earthquake seismology studies due to its high efficiencyand accuracy.On the other hand,its most significant drawback isthe difficulty of implementing a free surface or absorption boundary owingto the nature of its periodic boundary.In addition,since the grid spacemust be defined globally within a model to prevent grid dispersion dependingon the region of strong velocity contrasts,computations may becomevery expensive.However,these drawbacks can be overcome with a hybridof the pseudo-spectrum and the finite-element techniques.With the implementationbased on the finite-element formulation,grid spacing can be determinedaccording to local velocity within a velocity model.In so doing,the coding of the boundary conditions becomes much easier as well.Theadvantages of this proposed hybrid method consist of both reducing theamount of computational time and memory needed and obtaining both accurateand stable results during calculation.Some examples are shown todemonstrate the advantages of the hybrid method.This method can also beeasily expanded to 3-D situations with minor modifications.


INTRODUCTION
The Eurasian and the. Philippine Sea plate. s are active!)' interacting in the Taiwan region ( Figure 1). In the south ot· Taiwan, the lithosphere of the South China Sea subducts eastward beneath the Philippine Sea plate along the Manila Trench and creates the Luzon Arc. In the northeast ()f Tai\\1an, the Philippine Sea plate subducts beneath the Ryukyu Arc and ere . ates the Okinawa Trough backarc basin. So fa r, two principal models have been put forth to explain the t'ormation of Taiwan: the arc-continent collision (Suppe, 1981(Suppe, , 1984Teng, 1990� Lu andHsu, 1992) and the arc-arc collision (Hsu and Sibuet, 1995;Hsu et al., 1996a). Bet\veen these  · -· --· · ....... · '"" . \ ,,�._ -·· :.:: .,,---  Teng ( 1990) Ct)ncluded that the suture is located in weste1�n Tai wan and C()rresponds to the def'c)rn1ation f'ront . Lu and . Hsu ( 199·2 ), on the other hand, proposed that the main suture is along the Lishan Fault and the Laonungchi Fault to the south. Hsu and Sibuet (. 1995) later suggested that the proto-Tai wan was located in a S)'Stem of backarc basins that were )rounger and more active oceanw·ard from the Late Cretaceous t<) Late Miocene (Sibuet and Hsu, 1996)� the Tananao C< . )mplex C()rresponds to a pt)rtion of the t'o1·mer Ryukyu Arc before it collided \Vith the Luzon Arc. Thus, according to Hsu and Sibuet's model, the suture betwee. n the Eurasian and the Philippine Sea plates <.)r mo1�e exactly bet\V·een the t'ormer Ryukyu Arc (Tananao Co1nplex) and the Luzon Arc is located along the Longitudinal Valley. In t'act, both the petrology (Kizaki, 1986) and seismic velocity st14uctt114 es (Cheng et al., 1996) do demonstrate si1nila14ities between the Tananao Complex and the S(luth Ryuk)'U Arc. Furthermore, the direction of the Lishan Fault is continuously in the prolclngati()n of the Okina\\1a Trough axis. Accordingly, the Longitudinal Valley may· well be more st1itable as the suture of the plate. boundary. Howe\1er, the outline ot· the indenter (Luzon Arc) has nclt yet been clea14ly defined.
The n1ost ob\1ious feature from their magnetic interpretation \vas the location of the Lutao Lanhsu Ridge (a portion of the Luzon Arc) ( Figure 2). However, this CC)ttld lead tel the conclt1sion that the northern po1Aticln of the Luzon Arc extends into the coast nea14 Chengkung (Fig   ures I and 2). Since 1991, more magnetic data ha\'e been collected in the eastern and north eastern ot't'shore areas of T'1iwan, which allows to det'ine a more complete location c)f the northern portion of the Luz()n Arc. The tect<)nic featt1res ot' the northern L. uzon Arc are dis cussed later in this paper.

BATHYI\t1ETRIC AND MAGNETIC M.Ll\PS
The bathymetric maps ( Figure. s 3 and 7) were made available f1401n the US National Geo physical Data Center (NGOC) and the Institute of Oceanography of National Taiwan Univer sity data banks. Magnetic data \Ve1 · e compiled from cruises of the RN O(:ec111 Re.\·el11�c·/1er I f'rom 1989 to 1994 and t\\1C) cruises ()f. the R/V Professor Gaga14 insky in 1994 ( Figure 4 ). T1·ack ing of the ships through the su14ve . y area were extended out t'rom the eastern coast ()f Taiwan \Vith the track spacing typically 6-8 km. S(lffie tracks along the C()ast and in the north-south trend proved useful for Cf()SS-O\'er correction. Magnetic field measurements were conducted by a proton magnetomete1 · towed 200 m behind the ship. Navigatic)n employed the Global Pc.)sitioning System (OPS) and magnetic restilts were reported as mag11etic anomalies in refer ence to the 1995 International Geomagnetic Reference Field 1nodel (Figu14e 5).
The enl1ance. d analytic signal tec. hnique developed tc) analyze potential field data (Hsu et {ll., l 996b) was used in this stud)'. It demonstrates the following ad\iantages: I) the i11tert'er ence eft.ect between c]()Se anomalies is reduced� · 2) the determined locati()llS ot· maximum a111plitude. s of the analytic signal, corresponding to geological bounda14ies such as fat1lts or cc1ntacts, a1�e independent ()f ambient pa1· ameters such as inclination and declination ot, magne tization; and 3) the determinati<)n of maximum amplitude. s can be automatically achieved by examining ev·ery 9-pl)int grid-cell (Blakely and Simpson, 1986). The. amplitudes of the sec ond-< . )rder analytic signal t·()f the study· area are shown in Figure 6. The details ot· the used clnalytic signal technique is desc1· ibed in Hst1 et al. ( 1996b).
)mpressed and uplifted subducti()O complex (the hatched area in Figure 7). In other words, the Lo11gitudinal Valley is suitable f'o11 the suture along the former l\1anila Trench, as proposed by Hsu and Sibuet ( 1995). The suture can also be extended south\\1ard along the South L. ongi tudinal T11ough in whicl1 a maj(lf magnetic bc)undary is detected (Figure 7). Farther south, the co1npressed subduction C()mplex suft' ers prc)bablj' a right-late11al t��lult, which is consistent with the analy·ses of GPS geodetic dat't (Yu et al., 1995) and 1narine gravity data (Fuh et ct!, 1994). The distribution of earthquake epicenters with magnitudes greater than 4 from 199 1 to 1996 in the Tai \�lan region is sho\�ln in Figure 8. Except for the earthquake distribution around the southernmost Ryuky1u Arc and Okinawa Tr(lugh \vhich are subduction-related, the earth quakes located to the east of the Longitudinal valley are pro11ounced (Figure 8). This directly implies that the Tananao Complex exhibits gre. ater strength than the Luzon ,. .L\rc. In fact, Sibuet ..
. ,, ,,  Hsu (: 1996) and Cheng et al. (l996a·) have demonstrated that the Luzon Arc is probably \veaker than the Tananao Complex. A comparison of' se\ieral magnetic boundaties with earth q uak·e distribution (Fig11re 8) i·e\reals that the proposed boundaries separate the earthquakes into se,,reral distincti\1e provinces surprisingly well. 011e. ot' the detected boundaries may be related to the strike of · an e arthquake belt located in \\'estern Taiwan bec. ause its strike is in the s'tme direction and is p<trallel to the directi()n of· conve. rgence of the Philippine Sea plate rela tive to the Eurasian plate (Figure 8) . It is worth noting that the two northernmost blocks ot' the Luzon Arc closely collide. with the Tananao Complex (Figure 7), �1hich implies a hard arc-arc collision as evidenced by the intensive occurre . nce of earthquakes in that area (Figure 8). A collisional bending eft�ect (Wang, 1988) might in t' act be associated with such a hard collision.
To the. S()Uth of the hard collisil)n area, the collision between the. Tananao Complex and the Luzon Arc is buffered by the cc. 1mp1�essed subdt1ction complex and may correspond to a soft C()] 1 i si on.
Since the Luz()J1 Arc and the Tanana() Comple.x generally exhibit stronger competence with respect to the compressed subduction cornplex in bet\veen (Figure 7), the compressed subduction complex could be regarded as an incompetent stripe. Due to the Je. f' t-lateral motion bet\veen the Luzon Arc and the Tananao Co1nplex, the compressed subduction complex may have been dragged so that the main geological structures of the Coastal Range orient NE-SW.

DEPTHS OF THE lVIAG:r\ETIC BASEMENT
Based on the assumpti<. )n that the shape of the power-density spectrum of tl1e magnetic anomal)1 produced by a buried uniformly magnetized rectangular prism is in large part con trol1ed by the a\1erage depth of the ensemble, Spector and Grant ( 19 . 70) found that the spec trum decays exponentially �1ith \\'avenumber at a 1-ate of decay prop()rtional t() the average depth of' the ensemble. T)1pical example.s of the application surprisingly indicate that this simple and straightt'c)rward method could pro\1ide ge . ()logicall)' reasonable soluti()JlS (e.g., Smith , 197 4;Blakely, 1988). Garcia-Abdeslern and Ness ( 1994) further modified the above interpretational scheme by prop(1sing that other parameters of the magnetic ensemble (like thickness and horizontal dimension other than depth�) also C()ntribute t() the overall shape ()f the spectrum and should be used in the interpretation. They verified the approach with numeri cal examples and conc.luded that the estimation of the <1verage depth to the sou1-ce may be incor1-ect if < . )nl)' the depth factor is considered , particularly \\1hen the low-wav'enumber part ()f tl1e spectrum is used. They applied the proposed method to magnetic data collected t'rom ot'f sh()re o· t· the Yucatan Peninsul�t, Mexico a11d t' o11nd it s<1tisfacto1-y. Fc)llowing this app1-< . )ach and assuming that the crustal magnetic anornaly· is caused by an ensemble of vertical-sided and unit'or1nly rnagnetized prisms, we selected six regions to esti mate the depths tt) the top ()f. the northern Luzc)n Arc b)' using the pC)\\1er spectrum me. thod of Gai�cia-Abdeslem and Ness ( 1994) (Figure 9). Ectch selected region is 0.5°x().5 <) (containing 5(}x50 grids). For modeling the spectrum, a Gaussia11 (normal) distribution was used to de scribe depth to the source top and a unif'orm dist1-ibuti()n to describe the horizontal dimensions and the thickness function. Figu1-e 10 sho�1s the natural }()garithm t)f' the radially averaged and normalized power spect.rum < . )btained t'rc)m the mc1gnetic anomaly show·n in Figure 5 (in circles) and that from the ite1-atively in\1ersed S()Urce mode] ( _ in solid lines) t'or each l)f' the six regions.
The results of the previous expe1-imental exar11ples show that the. technique has a better control on the solution ot' the depth and its standard dev·iati()n. Only the depth results are indicated in Figure l 0. In general, the t"itting is better in the low-wavenumber part of the spect1-um which is better t'or depth estimation. On av·erage, the n1agnetic basement associated with the Luzon Arc  w·hich produce the signit' icant magnetic anomaly) sho\\1s that it has started subsiding. This is probabl)' associated \:v·ith th. e no14thwestward subduction of' the Philippine Sea plate beneath northeastern Taiwan.  Inverse wavelength (1/km) Fig. 10. Discrepancy bet�'een the natural logarithm of" the radially a\reraged and normalized po�·er spectrum (: circles · ) from the magnetic anoma1y sho\�ln in Figure 5 and that from the iteratively in\1erse. d source model (solid lines) for th€ six regions in Figure 9. The estimated depth to the mag netic source top of each region is indicated.

CONCLlTSIONS
Magnetic data collected between I 989 a11d 1994 in the ot"f"shore area of eastern Taiwan \Vere compiled. The outline of the magnetic sources \\ias de. lineated w·ith the he . Ip of the sec ond-order enhanced analytical signal technique (Hsu et al., 1996b) and the de.pths to the top of the magnetic source were estimated by the power spectrum method ot" Garcia- Abdeslem and Ness (1994). It was found that the magnetic f"eatures corresponding to the existence of the northern Luzon Arc extend to the further east of the Coastal Range. than pr·eviously considered and extend north1W·ard up to 24.18°N and 12 1. 77 {) E. The northern Luzon Arc changes in orientation from NN\\r-SSE to )JNE-SS"\\ 1 at the Taitung Canyon between Lutao and Lanhsu Islands. When the magnetic basement boundaries \\1ere compared with earthquake distribution in east ern Tai \\1an and its ot" t" shore area, the earthquakes could be separated into several distinctive regions lin1ited by the detected magnetic boundaries. The collision at the. northernmost Luzon Arc corresponds to a hard collision betwe. e11 the Luzon and the Tananao Complex� while to the south of 23.5°N, the collisional region corresponds to a soft collision. Most of the Coasta1 Range and the Huatung Ridge could be regarded as a compressed subduction complex (in competent material between the Luzon Arc and the Tananao Complex).
The average depth to the top of the magnetic basement ot"' the northern Luzon Arc is about 2 km. North of 22.7°N the magnetic basement of the Luzon Arc. generally deepens tovv·ards the north, which suggests that the northernmost portion of the Luzon Arc has probably been subsiding.