trans-pacific upper mantle shear velocity structure · [2] seismic velocity structure provides the...

Trans-Pacific upper mantle shear velocity structure

Ying Tan1 and Don V. Helmberger1

Received 10 November 2006; revised 21 March 2007; accepted 25 April 2007; published 1 August 2007.

[1] We use 50 Tonga-Fiji events recorded at the broadband TriNet array, southernCalifornia, to develop a pure path upper mantle shear velocity model across the Pacific. Atthe epicentral distances of 70�–95�, multibounce S waves up to S5 are observed,including their triplicated branches, which become particularly clear after stacking. Sincethese S wave multiples turn at various depths, simultaneously modeling their differentialtraveltimes and waveforms provides strong constraints on the radial velocity structure.We parameterize the velocity model according to a priori information from the previousoceanic models, so that we can take a grid search approach, to fully investigate possibleinterdependencies among the model parameters. We construct synthetics with areflectivity code and study both the SH and SV components. By modeling the wholerecordings from events at different depths, with different mechanisms, we are able toseparate shallow low-velocity zone (LVZ) features from deeper structure. Our preferredmodel (PAC06) contains a fast lid (Vsh = 4.78 km s�1, Vsv = 4.58 km s�1) with athickness of �60 km. The underlying LVZ is prominent with the lowest velocitiesVsh = 4.34 km s�1, and Vsv = 4.22 km s�1 occurring at a depth of �160 km. Thesevelocities are below the estimates of solid-state LVZ, suggesting the presence of partialmelt. The anisotropy (Vsv < Vsh) of PAC06 extends to �300 km depth, which isconstrained by S5 turning at this depth. Besides the 406 km and 651 km discontinuities,PAC06 also has a small (�1%) velocity jump at �516 km. We consider these mainfeatures of PAC06 to be well determined, since PAC06 explains a large data set fromvarious events. Therefore it is ideally suited for comparing with mineralogical models.

Citation: Tan, Y., and D. V. Helmberger (2007), Trans-Pacific upper mantle shear velocity structure, J. Geophys. Res., 112, B08301,

doi:10.1029/2006JB004853.

1. Introduction

[2] Seismic velocity structure provides the most impor-tant constraint on modeling the mineralogical compositionand dynamics of the Earth’s interior. Of particular interest isthe oceanic upper mantle structure, due to its large departurefrom a global average (e.g., PREM by Dziewonski andAnderson [1981]). The origin of the characteristic high-velocity lid, prominent low-velocity zone (LVZ) and thegeneral lack of 220 km discontinuity has warranted a largenumber of investigations from the mineralogical point ofview. The recent work by Stixrude and Lithgow-Bertelloni[2005] suggested a solid-state LVZ, which is the naturalconsequence of a thermal boundary layer and the effects ofpressure and temperature on the elastic wave velocityof subsolidus mantle assemblages. The properties atypicalof the mantle, such as partial melt and bound water, wouldbe permissible, but not required. Their result agrees withFaul and Jackson [2005]. However, the quantitative com-parison of their ‘‘null’’ hypothesis (elasticity, isotropy,absence of partial melt, homogeneity and thermodynamic

equilibrium) with seismological models revealed discrepan-cies in the negative velocity gradient, the absolute velocityvalue in the LVZ, and the high-velocity gradient below theLVZ. To reconcile these discrepancies forced them toexamine variants of the ‘‘null’’ hypothesis and to includethe effects of partial melt, attenuation, and anisotropy.[3] Such mineralogical studies have been matched in

seismology. In particular, the last decade has seen theremarkable progress of seismic tomography, mostly drivenby the advancement of theory and computational power,where global three-dimensional (3-D) models have spannedthe entire depth range of the Earth’s mantle and achievedlateral resolution of less than 1000 km [Romanowicz, 2003].However, many oceanic areas remain unsampled or poorlyresolved in most high-resolution P velocity models. Theother type of long-wavelength S velocity models based onsurface waves generally have good coverage across theoceans, but most of them lack radial resolution. Hence thecurrent generation of global models is not capable ofresolving the hypotheses regarding the layering of theoceanic upper mantle. Instead, ‘‘pure path’’ regional modelscan provide significant information complementary to thetomographic models [Gaherty et al., 1999].[4] Although there is increasing evidence for short length

scale variations in lithospheric thickness across plate bound-aries where subduction has occurred or is occurring [e.g.,

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Melbourne and Helmberger, 2001], structures away fromplate boundaries display much smoother lateral variations ofsmaller scale, where simple corridors appear one-dimensional.Here we will investigate one such strip that runs nearlyacross the central Pacific Ocean connecting the Tonga-Fijisource region to TriNet, southern California (Figure 1).Cross sections from global tomographic models displaylaterally homogeneous features along this corridor [e.g.,Ritsema et al. 1999], where the largest anomalies areassociated with adjustments made to eliminate the 220 kmdiscontinuity in the reference model PREM [Dziewonskiand Anderson, 1981]. The plate history along the corridor isrelatively simple, with most of the seafloor developed bythe spreading of the ancient Pacific-Farallon ridge. Thelithospheric age spans a wide range from approximately125 Ma near the source region to �10 Ma approaching theCalifornia coastal line, where the lithosphere is about 50 kmthick [Melbourne and Helmberger, 2001]. The pure surfacewave studies [e.g., Nishimura and Forsyth, 1989; Ritzwolleret al., 2004; Maggi et al., 2006] indicated progressiveincrease of lithosphere velocity or thickness with increasingplate age, qualitatively mimicking isotherms of theoreticalthermal cooling models. However, these results solely fromsurface wave data can be debated because of their poorvertical resolution. In contrast, Gaherty et al. [1999] sug-gested very little age dependence of the lithosphere thicknesswhen they compared regional models of the old PacificOcean (100–125 Ma) and the younger Philippine Sea (15–50Ma), where the transitions from the high-velocity lid to the

underlying LVZ (the G discontinuity) were mainly deter-mined from ScS reverberation observations [Revenaugh andJordan, 1991b]. They interpreted the G discontinuity mainlyas a compositional boundary rather than a thermal boundary.[5] The whole corridor has been included in an early

2-D study from Tonga to Newfoundland [Graves andHelmberger, 1988], where multibounce S waves from asingle event were modeled with a 2-D WKB code andthe emphasis was given to the sharp transition across thePacific–North America boundary. More recently, Gahertyet al. [1996] investigated the older half of the corridorfrom Tonga-Fiji to Hawaii (see Figure 1) with a combineddata set of ScS reverberations and measured frequency-dependent (10–45 mHz) phase delays for body and surfacewaves recorded on the island stations KIP and HON. Herewe use a novel data set of broadband seismograms from thedense TriNet array in southern California. At the epicentraldistances of 70�–95�, multibounce S waves up to S5

sampling over the upper mantle triplication range areobserved, including the guided waves from shallow eventstransversing the LVZ. Simultaneously modeling the move-outs of all these S wave multiples that have their turningpoints at different depths provides strong constraints on theradial velocity structure.[6] Because velocity anomalies associated with a single

leg of a multibounce phase will be mapped into the wholepath, we interpret our model PAC06 as an effective averagealong the corridor as discussed by Zhao and Helmberger[1993]. However, it explains record sections from a large

Figure 1. Source-receiver geometry on a seafloor age map. The source mechanisms are from HarvardCMT solutions and color coded in depth. Blow up is the broadband TriNet array in southern California.The dashed line from Tonga-Fiji to the Hawaiian stations, HON and KIP, indicates the corridor studied byGaherty et al. [1996].

B08301 TAN AND HELMBERGER: PACIFIC UPPER MANTLE SHEAR STRUCTURE

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number of events at different depths, spanning a widedistance range of 70�–95�. Moreover, the good agreementbetween PAC06 and PA5 developed for the older segment[Gaherty et al., 1996], as well as the excellent fits of PAC06to the waveform data from the Hawaiian earthquake sam-pling the younger segment, indicates a relatively simple,uniform structure along the corridor, which proves particu-larly useful for mineralogical investigations.

2. Data

[7] Since early 1999, when the southern California TriNetarray was expanded into a dense broadband network withover 120 stations, hundreds of large events (M > 5.5) thatoccurred in the Tonga-Fiji seismic zone have been recorded.Among them, we selected 50 events (Figure 1), whoseseismic sources are relatively simple, and whose multi-bounce phases are rich. We assumed the event locationsand origin times from Harvard centroid moment tensor(CMT) solutions (see Table 1 for the events discussed here)

[Dziewonski et al., 1981], and the source depths wereadjusted based on the relative timing between direct anddepth phases, if necessary. The exact event locations andorigin times are not critical, since we model differentialtraveltimes between S multiples, and the effects of eventlocation or origin time become second order [Grand andHelmberger, 1984b].[8] Because of the small aperture of TriNet, a single event

provides limited lateral coverage. However, this problem islargely compensated by studying a number of eventsspanning a wide distance range of 70�–95� (Figure 2).Moreover, modeling multiple events of different mecha-nisms, at different depths, provides an effective way toeliminate contaminations of source effects on the velocitystructure. Particularly within the studied distance range,both SSS and S4 become triplicated by the 410 km and660 km discontinuities. A sketch of their triplicationpatterns is displayed in Figure 3. Note that different portionsof the triplication patterns can be observed for SSS and S4

on the same record section.

Table 1. Source Parameters of the Tonga-Fiji Events Used in This Study From Harvard’s CMT Catalog

Event ID

Date Origin Time,UT

Location Depth,km Mw

FM D Correction,kmYear/Month/Day Latitude/Longitude Strike/Dip/Rake

9026350 1997/10/14 0953:32.7 �21.94/�176.15 166 7.7 257/17/�30 �509530269 2000/01/26 1327:1.0 �17.21/�173.51 70 6.2 213/16/�66 –9533473 2000/02/25 0144:5.2 �19.55/174.17 17 7.1 315/74/169 –9563017 2000/09/11 1818:0.3 �15.74/�173.33 125 6.3 331/10/�129 –9564185 2000/09/14 1500:2.3 �15.59/�179.92 15 6.2 154/77/176 –9685024 2000/01/08 1647:30.2 �16.84/�173.81 162 7.2 79/8/�13 –9611653 2001/01/09 1649:37.9 �14.90/167.11 115 7.0 183/44/160 –9648517 2001/04/28 0450:1.9 �18.07/�176.68 367 6.8 106/16/161 –9658105 2001/05/26 1057:31.0 �20.25/�177.65 414 6.3 134/68/�176 –9658317 2001/06/03 0242:9.7 �29.37/�178.23 200 7.1 227/41/138 �409743493 2002/01/03 1017:49.6 �17.84/167.82 20 6.6 359/30/97 –9792597 2002/06/17 2126:33.9 �12.49/166.25 44 6.6 163/38/81 –13980540 2003/07/27 0204:15.6 �21.09/�176.12 216 6.6 294/22/�3 �309927909 2003/07/03 0621:57.3 �21.46/�173.80 16 5.9 192/24/83 �709942373 2003/09/02 1828:10.9 �15.14/�172.92 15 6.4 210/28/171 –14106728 2004/11/17 2109:19.5 �19.87/�178.40 629 6.5 77/8/117 –9982833 2004/02/12 1347:35.9 �19.41/�172.80 12 5.7 213/26/96 �6010100677 2005/05/18 1027:15.0 �15.22/�172.69 12 6.2 144/33/48 –14132656 2005/03/19 1734:45 �21.92/�179.28 610 6.3 97/16/160 –14170576 2005/08/06 0956:19.3 �19.57/�175.35 218 6.6 266/33/�24 –

D correction applies to the events that appear mislocated as discussed in section 3.3. The correction is simply an average distance shift for all the stationsfrom a particular event.

Figure 2. Schematic raypaths of multibounce S waves at epicentral distances of 70�–95� used in thisstudy. Particularly for SSS and SSSS that are triplicated in this distance range, only the early arrivingbranches are shown.


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[9] We rotated the original horizontal component (N-Sand E-W) data into radial (SV) and tangential (SH) motions,although we generally found the SV waves on the verticalcomponent to be the most useful for modeling purposes. Anexample of the tangential records from a shallow event(9533473) is displayed as a distance record section in Figure 4,where the various S wave multiples are labeled. The densearray produces coherent seismograms, which warrants asimple stacking procedure and facilitates identification oftriplications or phase interference. At this distance range(�82�–87�), SSS is triplicated due to the 660 km discon-tinuity, resulting in a forward branch (Sef

3 ) turning below thediscontinuity and a shallower backward branch (Scd

3 ). S4

contains more complexity, in that the triplications areinterfering with the shallow guided waves (Love waves).In fact, the apparent interference displayed in Figure 4 ismainly due to the guided waves that are most sensitive toshallow depths, since the amplitude of S4 is much smallerdue to the radiation pattern effect. By examining variousevents of different depths and mechanisms, it becomespossible to separate Love waves from S4 triplications.However, modeling such guided waves at their naturalfrequencies (>10 s) provides powerful constraints on theshallow part of the velocity model. The whole groupbecomes simpler and the so-called ‘‘G phase’’ when filteredto longer periods (>30 s), which is normally used intomographic studies.

3. Waveform modeling

[10] Our modeling effort involves matching the differen-tial traveltimes between multibounce S waves and simulat-ing their waveforms, particularly the waveforms of thehigher-order multiples, S3 and S4, plus shallow guided

waves, which are triplicated or interfering in the uppermantle. Since the different multiples have their own turningdepths, simultaneously modeling their traveltimes providesunique estimates of velocity at various depths. Moreover,finer-scale structures can be inferred by simulating theirsubtle triplication or interference patterns.[11] To model these recordings, we take a ‘‘trial and

error’’ approach which has proven effective in previoussimilar studies [e.g., Grand and Helmberger, 1984b;Melbourne and Helmberger, 2002]. In addition, we param-eterize the velocity model as a composite of a high-velocitylid, a negative gradient zone, a positive gradient zone andthe transition zone, according to a priori information fromprevious oceanic models [e.g., Grand and Helmberger,1984a; Gaherty et al., 1996]. This simple parameterizationenables us to efficiently investigate possible interdependen-cies among the thicknesses, average velocities and gradientsof the layers in a grid search manner, and hence to resolvethe main characteristics of the model.[12] We construct three-component full synthetics with an

isotropic reflectivity code [Zhu and Rivera, 2002], while weuse generalized ray theory [Helmberger, 1983] to helpidentify individual arrivals in cases where ambiguity exists.We model the SH (tangential) and SV (vertical) componentsrespectively, since the higher-order S wave multiples, suchas S3, S4 and S5 are significantly split over the twocomponents. The isotropic nature of the synthetics restrictsour ability to speculate the geometry of anisotropy, althoughthe resolved Vsh > Vsv is consistent with transverse isotropyreported by previous investigators [e.g., Gaherty et al.,1996; Ekstrom and Dziewonski, 1998]. However, theunified methodology for both the SH and SV componentsenables us to address the depth extent of anisotropy and itsrelationship to the upper mantle layering.[13] We started with the attenuation model developed by

Ding and Grand [1993] for the East Pacific Rise (EPR)using multibounce S waves. This model has proved effec-tive in a later study by Melbourne and Helmberger [2002]for EPR events recorded at TriNet. However, we found thatnearly doubled Q values in the upper 200 km of the modelare required to explain the progressive amplitude decay ofthe S multiples (see Table 2). This adjustment is reasonableconsidering that Ding and Grand’s [1993] Q model wasderived from one of the hottest structures on Earth and isprobably near the lower bound.[14] We display the waveform comparison between the

data shown in Figure 4 and the synthetics from our best SHmodel PAC06sh assuming these Q values in Figure 5. Wealign both the data and synthetics on SS to minimize thesource region complexity, since SS has a take off angle closeto those of the higher-order multiples, while the direct Swaveleaves the source at a much steeper angle (see Figure 2). Thewhole record section is nicely reproducedwith the simple 1-Dmodel (Figure 5), particularly the waveforms of the guidedwaves overriding the S4 triplications. There is a slighttendency for the coastal stations to be matched better thanthe inland ones, such as hec, gla, dan, mtp and nee.Moreover, the time lags of the observed ‘‘G + S4’’ wavesrelative to the synthetics are systematically increasing withstation distance (Figure 5c). This ‘‘unmodeled’’ feature isconsistent with the lithospheric thickness change across thePacific–North America boundary reported by Melbourne

Figure 3. Triplication plot of SSS and S4 from PAC06shwith a 10 km deep source. The small triplication patterns onthe ‘‘cd’’ branches are due to the 516 km discontinuity inPAC06. The dashed lines were added to indicate thepositions of diffractions.


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and Helmberger [2001]. Similar sharp transitions are alsoseen in recent tomographic models [e.g., Tanimoto andPrindle Sheldrake 2002]. The major discrepancy of thecomparison in Figure 5 is the time lags of the synthetic Sphases (�5 s) relative to the observations. We attribute thisadvancement of the observed S waves to the fast slabs in thesource region, mainly because the same problem does notexist for the deeper events.[15] In contrast, we display in Figures 6 and 7 the wave-

form fits for the same event 9533473 shown in Figure 5with the preliminary Earth reference model (PREMsh)[Dziewonski and Anderson, 1981] and the path averageof a typical tomographic model S20RTS by Ritsema et al.[1999]. Because S20RTS was developed mainly withRayleigh wave dispersion data, we extrapolated the SHcounterpart of the path averaged S20RTS assuming thesame anisotropy as in the reference model PREM. Thecomparison between PREM, the path average of S20RTSand our preferred model PAC06sh is given in Figure 8.

Table 2. Model PAC06

Depth, km Vsh, km s�1 Vsv, km s�1 Qs

0.2 1.00 1.00 200.2 3.20 3.20 206 3.20 3.20 206 4.78 4.58 16066 4.78 4.58 16066 4.51 4.31 100163 4.34 4.22 100303 4.64 4.64 120406 4.86 4.86 160406 5.02 5.02 180516 5.22 5.22 180516 5.28 5.28 180651 5.54 5.54 180651 6.01 6.01 310736 6.22 6.22 310900 6.33 6.33 310

Figure 4. (left) Velocity record section of the tangential component from a shallow event (9533473).The original records are desampled down to 1 Hz for display purpose. S wave multiples are labeled.(right) Selected records after a simple running stack process, where the record at each station has beenreplaced by the average of the nearest records within 10 km. The number following a station nameindicates how many records have been stacked for the particular station.


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Moreover, to correct the crustal effect in PREMsh andS20RTSsh, we have replaced their thick crust (�21 km)with the much thinner one (�6 km) in our modelPAC06sh. As a consequence, the underlying mantle layersin the two models have been thickened to conserve theoverall travel time. The synthetics from PREMsh and

S20RTSsh with their original thick crust are comparedwith data in the auxiliary material (Figures S29–S30).1

As displayed in Figure 6, PREM failed to predict both the

Figure 5. (a) Waveform comparison between the SH data (black) from event 9533473 and thesynthetics with PAC06sh (red). Time axis is relative to the event origin time. (b) Source parameters of theevent from Harvard’s CMT catalog. (c) Time delays (gray circles) of the observed S multiples relative tothe synthetics (tobs � tsyn) measured by waveform cross correlation. Black circles are the residuals afterthe synthetics and data are aligned on SS.

1Auxiliary materials are available in the HTML. doi:10.1029/2006JB004853.


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interference pattern of the guided waves and their travel-times. The tomographic model (S20RTS) containing a well-developed LVZ produces the two interfering branches;however, their traveltimes plus their separations areapparently off. These comparisons suggest strong depen-dence of the guided waves on the shallow part of the model,which we will explore in section 3.1.[16] Although there is some redundancy, the selected

50 events contain extensive sampling of SSS and S4 tripli-cations (Figure 3), plus their interference with the guidedwaves from shallow events. Therefore they provide the moststringent constraint for different depth ranges of the model.For example, as the guided waves traversing the LVZprovides a means of estimating the shallow part of themodel, the triplications of SSS or S4 mainly constrain thetransition zone. In the following, we will give typicalexamples of the events that we use to refine the velocitystructure at different depths, where we will also address

representative sensitivity tests in an attempt to quantify themodel resolution. Our discussion will be restricted to the SH(tangential) component alone, since the adequate SV obser-vations are rather limited.

3.1. Lid and LVZ

[17] The velocity in the shallow part of the model, such asthe lid or the low-velocity zone (LVZ) has the strongesteffect on the differential traveltimes of the multibounce Swaves, since the higher-order multiples systematicallyspend more time traveling at these depths. Moreover, theshallow radial structure largely controls the waveforms ofthe guided waves traversing the LVZ. However, itsinfluence becomes significantly less on the triplicationpatterns of SSS or S4. In particular, it can hardly changethe time separations between the triplicated branches, ex-cept for a small overall shift. This allows us to separate theeffect of the shallow part from that of the underlying

Figure 6. Selected waveform fits for event 9533473 as shown in Figure 5 with the preliminary Earthreference model (PREMsh). Both the data (black) and synthetics (red) are aligned on SS.


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transition zone when modeling the records. The transitionzone, however, mainly controls the triplications.[18] The shallow events (depth < 50 km) are the most

suitable for determining the lid and LVZ structure, sincethey generate the strongest guided waves. Moreover, theirseismograms are relatively simple without obvious depthphases. Figure 9 displays a composite record section of fourshallow events together with overlain synthetics from ourpreferred SH model PAC06sh. The four events have differentsource mechanisms, however, their records are wellexplained with a single model, suggesting the source effectson the velocity structure are largely eliminated. The radialstructure of the lid and LVZ shapes the waveforms of theguided waves. Such influences, however, are rather difficultto quantify or predict, since they generally involve bothtiming and phase changes in the complex waveformpockets. Therefore we have parameterized the model as acomposite of three simple layers (the lid, negative gradient

zone and positive gradient zone) and conducted extensive‘‘grid searches’’ for the basic parameters, such as thickness,average velocity and gradient of each layer. Our preferredmodel PAC06sh produces the best waveform fits to theobservations. The basic characteristics of PAC06sh includea 60 km thick high velocity lid (Vsh = 4.78 km), a prominentLVZ with the lowest velocity of 4.34 km s�1 at a depth of�160 km, and a high gradient (�0.002 s�1) zone underneath.[19] There are some trade-offs among certain model

parameters, of which those between the lid and LVZstructure appear the most severe. Figure 10 displays thesensitivity of the complex ‘‘G + S4’’ waveforms as shown inFigure 9 to the lid and LVZ structure, as well as their trade-offs. We have discarded the traces from the two closerevents in Figure 10 for display purpose, while the results forthe whole record section are given in the auxiliary material(Figures S1–S4). In particular, Figure 10a displays thesensitivity of the ‘‘G + S4’’ waveforms to the lid thickness.

Figure 7. Selected waveform fits for event 9533473 as shown in Figure 5 with the path average of atypical tomographic model S20RTS by Ritsema et al. [1999].


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The lid thickness change in the perturbed models has beenoffset by a velocity adjustment, so that the traveltimes fordeeper phases, such as S, SS, and SSS waves are conserved.However, the interference pattern of the two surface wavebranches are affected significantly, due to their differentialsensitivity to different depths. Particularly, the backwardbranch, that is the most sensitive to the very top of the lid,gets accelerated by the faster velocity there or delayed bythe slower velocity. The similar trend is observed as we fixthe lid thickness, but vary the size of the G discontinuitybetween the lid and LVZ (Figure 10b). Figure 10c displayspossible trade-offs between the lid and LVZ structure bycomparing the waveform fits from PAC06sh to the perturbedmodels, where the lid thickness trades off with the Gdiscontinuity. The models shown, model 1 with a 80 kmthick lid, and model 2 with a 40 km thick lid, are consideredtwo ‘‘end-members’’ outlining the uncertainty of the lid andLVZ structure of PAC06sh, beyond which waveform misfitincreases significantly. These results from the grid searchindicate the robustness of the shadow structure in PAC06sh,although the detailed sharpness of the G discontinuity

cannot be determined since we are dealing with surfacewaves. We present the sensitivity tests for the high gradientzone (HGZ) beneath the LVZ in the auxiliary material(Figure S5), which suggest very little trade-off betweenthe velocities of the HGZ and the shallower part.

3.2. Transition Zone

[20] The transition zone comprising the two major mantlediscontinuities plays the most significant role in shaping thetriplication patterns, since the triplicated branches travelnearly the same paths except in the vicinity of the disconti-nuities. Therefore modeling the separation, the cross overand the relative amplitudes of the triplicated branchesprovides tight constraints on the transition zone [e.g., Grandand Helmberger, 1984b; Melbourne and Helmberger, 1998;Wang et al., 2006]. In this study, we observe the triplicationsof the higher-order multiples SSS and S4 (Figure 3). Amongthem, those of S4 are mainly from intermediate and deepevents, where the shallow guided waves are well sup-pressed. We started with a trial structure for the transitionzone from the tectonic North America model (TNA) [Grandand Helmberger, 1984b] (Figure 11), and used a largenumber of the observed triplications to examine the details.We let the TNA model stand unless modifications wererequired to better explain our observations, since the tran-sition zone structure of TNA is particularly well constrainedwith good sampling of all the triplicated branches due toboth the 410 km and 660 km discontinuities. The resultingtransition zone structure in our preferred model PAC06turned out to be very similar to that of TNA, and the majordifference is that PAC06 has a small velocity jump (DVs �1%) at approximately 516 km. Although we did not observeclear triplications due to such a small discontinuity, it isneeded mainly to explain the timing and amplitudes of thetriplicated ‘‘cd’’ branches (Figure 3), turning within thetransition zone.[21] Our model PAC06 inherited a �406 km discontinu-

ity from TNA. The velocity jump, however, is smaller(�4%), mainly due to the generally larger velocities in theshallower part of the model (see Figure 11), which arerequired to explain the differential traveltimes between the Smultiples and the guided waves. We have conducted varioustests to examine the exact depth, velocity jump and sharp-ness of the discontinuity. However, these fine-scale featurescannot be well resolved with our data set. In particular thesynthetics constructed with the perturbations produce nearlyequal waveform fits to most of the observations. This isbecause our data set does not contain sampling of the410 km triplications as well as those addressed byMelbourne and Helmberger [1998] or Song et al. [2004].[22] However, the radial structure within the transition

zone is well determined, particularly, the average velocitygradient and the �1% velocity jump at approximately�516 km. The constraint is mainly from modeling therelative behavior of the ‘‘cd’’ and ‘‘ef’’ branches. Figure 12gives such an example, where we compare selected SSSwaveform fits with our preferred model PAC06 and theperturbed ones. The data shown were selected from theshallow event collection to avoid complications caused bythe depth phases. As the distance increases, SSScd system-atically moves backward relative to the forward branchSSSef. Although there are small perturbations on the indi-

Figure 8. Comparison of our preferred SH modelPAC06sh with PREM (Vsh > Vsv) and the path average ofthe tomographic model S20RTS by Ritsema et al. [1999].Since S20RTS was developed mainly with Rayleigh wavedata, we have extrapolated its SH counterpart assumingexactly the same anisotropy as in PREM.


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vidual observations, the stability of the triplication patternindicates little significant lateral variation along the path.Our model PAC06 accurately produces both the differentialtimes and relative amplitudes between the triplicatedbranches SSSef and SSScd. The perturbed model ‘‘A’’ witha similar gradient, but no 516 km velocity jump, signifi-cantly overpredicts the amplitudes of the backward branchSSScd. In contrast, the larger 516 km discontinuity in theperturbed model ‘‘B’’ exaggerates the triplication in SSScd,

and causes SSScd to fade away beyond 82�. We alsoincluded two models ‘‘C’’ and ‘‘D’’ with different velocitygradients in Figure 12 to display model sensitivity. As thelarger gradient in model ‘‘C’’ tends to suppress the ‘‘cd’’branch, model ‘‘D’’ with the smaller gradient produces themagnified and advanced SSScd. We have tested the depthresolution of this small discontinuity. Varying its depthmainly changes the position of the triplication on the‘‘cd’’ branch, as well as the travel times near the crossover

Figure 9. Waveform comparison between data (black) and the synthetics (red) from our preferred SHmodel PAC06sh for four shallow events. Both the data and synthetics are aligned on SS. The traces for thetwo thrust events 10100677 and 9743493 have been multiplied by a factor of ‘‘�1’’ for display purposes.


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Figure 10. (a) Waveform fits with our preferred SH model PAC06sh (left) compared to those from theperturbed models with a different lid thickness. The model comparison is displayed to the right wherePAC06 is in black. (b) Waveform fits with our preferred SH model PAC06sh (left) compared to those fromthe perturbed models with a different-sized G discontinuity between the lid and LVZ. (c) Waveform fitswith our preferred SH model PAC06sh (left) compared to those from the perturbed models where the lidthickness trades off with the G discontinuity. In particular, model 1 has a �80 km thick lid, whereasmodel 2 has a thinner lid of �40 km thick.


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point (see Figure 3). Although the depth of approximately516 km provides the best fits to the observations, its uncer-tainty is relatively large. Particularly, a change of ±20 kmproduces little significant increase in waveform misfits.[23] PAC06 contains a slightly shallower 651 km discon-

tinuity and a faster high gradient zone right below thediscontinuity compared to TNA (see Figure 11). Thesefeatures were well determined with our data. Syntheticexperiments showed significant advancement of the ‘‘ef’’branches, particularly of SSS and S4 by the elevated dis-continuity and faster high gradient zone, which however,were required by our observations. A similar issue plus themineralogical implication has been addressed in a recentstudy by Wang et al. [2006].

3.3. Summary: SH Component

[24] In sections 3.1 and 3.2, we concentrated on thederivation of the model, where we showed complete wave-form comparisons only for a small fraction of the studiedevents. Here we summarize the overall fit of the differentialtraveltimes between the S multiples for all the events inFigure 13, where the differences of the differential travel-times, DTSS�S, DTSSS�SS and DTSSSS�SS between the syn-

thetics and data are displayed. To calculate these timingdifferences, we have measured the time lags between thedata and synthetics for S, SS, SSS and S4, respectively, bywaveform cross correlation. In cases for which SSS or S4 istriplicated, the emphasis has been given to the early branch.The alignment of synthetics and data on SS has mostlyeliminated possible origin time problems. Moreover, wehave also applied event mislocation corrections (see Table 1)for the few events that displayed relatively large, systematicdiscrepancies in the differential time measurements. Inparticular, the observed higher-order multiples from theseevents are increasingly faster or slower than the syntheticpredictions, which can be easily explained by the events’mislocation error. The data points in Figure 13 are colorcoded by the depths of the events, and the overlainwaveform comparisons for representative events at differentdepths, with different mechanisms are given in the auxiliarymaterial (Figures S6–S28).[25] The most apparent anomaly in Figure 13 occurs for

DTSS�S, where large negative values ofDTSS�S up to��7 sare observed. This implies that the observed direct S wavesare faster than the model would predict. We attribute theanomaly to the fast slab effects (see the earlier discussion ofFigure 5). Although this warrants further investigation, thereare two main lines of evidence that favor our argument.First, nearly all the problematic events are shallow, sam-pling particular distance ranges. Moreover, many of theseevents are located along the complex New Hebrides sub-duction slab. Secondly, the upper mantle structure is not aneffective modifier on the differential traveltimes between Sand the higher-order multiples. Another noteworthy featurein Figure 13 is the linear trend for DTS4�SS, where DTS4�SS

systematically increases from the westernmost coastal sta-tions to the easternmost inland ones. Such a tendencybecomes particularly obvious when the guided waves areinvolved for the shallow events, due to the sharp transitionfrom fast oceanic lithosphere to thick continental crustacross the Pacific–North America boundary.

3.4. SV Component

[26] The above discussion was restricted to the SH(transverse) component, and here we address the SV waveobservations. We will focus on the vertical component,since it generally produces better signal-to-noise ratios thanthe radial component. The greatest difficulty in modelingthe SV waves is caused by the SV � P wave coupling. Theproblem can be overwhelming, especially when the SV-coupled PL waves are developed, and mainly controlled bythe crustal waveguide for mixed continental-oceanic paths[e.g., Helmberger and Engen, 1974]. Although we widelyobserve the energy leakage of SV waves into P waves in thisstudy, their coupling effect is not significant, which impliesthat the shallow oceanic structure is more uniform. For anexample, we display the record section of the verticalcomponent from a shallow event in Figure 14, where themultibounce SV waves are easily recognized and labeled.Among them, S4 is the strongest due to the constructiveinterference of the triplicated branches at the sampleddistance range (see Figure 3). On the SV records, even S5

can be clearly observed, since the Rayleigh waves are muchslower. As we will address later in this section, these S5

waves that turn near a depth of 300 km provide strong

Figure 11. Comparison of PAC06 with the earlier purepath upper mantle models, TNA, SNA [Grand andHelmberger, 1984b], and ATL [Grand and Helmberger,1984a], developed by modeling similar multibounce S wavedata sets.


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constraint on the depth extent of the observed seismicanisotropy.[27] Many investigators have reported radial anisotropy

(or transverse isotropy) from surface wave studies in theupper mantle beneath the Pacific Ocean [e.g., Ekstrom andDziewonski, 1998]. However, it is not appropriate for us tocontrast the SH and SV observations directly, since themultibounce SH and SV waves contain different phase shiftsfrom the bounce points and the station-side receiver func-

tions. One way to bypass the problem is to compare the SVobservations with the synthetics from our well-constrainedSH model (Figure 14). Since there is some contamination ofSS, we have chosen to align the synthetics and data on S3

instead. The alignment resulted in a large shift of over 20 sfor the synthetics relative to the data, which is not seen forthe SH component. Moreover, the observed higher-ordermultiples S4 and S5 are progressively slower than thesynthetic predictions. In particular, S5 are delayed by over

Figure 12. (a) Selected SSS waveform fits from four shallow events (10100677, 9982833, 9564185,and 9533473 from the bottom to top) with our preferred model PAC06sh and the perturbed models.(b) Model perturbations that are particularly concentrated in the transition zone, where the triplicatedbranch SSScd is the most sensitive. Both the data (black) and synthetics (red) are aligned on SSSef, and thenormalized amplitudes by the maxima on the records are plotted. Note the different behavior of thesynthetic SSS from the perturbed models, in particular, the amplitude contrast between SSSef and SSScd.


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10 s relative to the synthetics. All these discrepanciessuggest that the SV model needs to be slower than the SHcounterpart, especially in the shallow part, such as the lid orLVZ, since the higher-order multiples increasingly spendmore time there.[28] Therefore we have concentrated on the shallow part

in deriving the SV model. Because of the lack of goodtriplication data in the SV observations, the same structurebelow the 406 km discontinuity as in the SH model isassumed. We also retain the characteristic features in the SHmodel, such as the lid thickness and the large ‘‘G’’ discon-

tinuity, in parameterizing the SV model. These features,however, are not well resolved with the SV data. Figure 15displays the waveform fits for the same observations asshown in Figure 14, with our preferred SV model PAC06sv,which accurately reproduces both the waveforms and trav-eltimes of the SV wave multiples. The comparison betweenthe SV and SH model is given in Figure 16c.[29] PAC06sv features slower velocities than the SHmodel

down to a depth of approximately 300 km (Figure 16c).Although there is some trade off between the lid and LVZvelocities for the SV model, the depth extent of anisotropy(Vsv < Vsh) is well determined, and the major constraint isattributed to the S5 turning at a depth of approximately300 km. For an example, we display in Figure 16 thewaveform comparisons with two trial models, where theanisotropy is confined to the top �170 km (model I),essentially in the lid and LVZ, or extends to the 406 kmdiscontinuity (model II). The lid and LVZ velocities havealso been adjusted accordingly, so that the traveltimes ofthe lower-order multiples, such as S, SS, SSS and S4, thatturn below the 406 km discontinuity, are conserved. How-ever, since S5 travels nearly flat at a depth of �300 km(Figure 16d), it is rather sensitive to small velocity perturba-tions there. While the synthetic S5 gets accelerated by thefaster velocities at that depth in model I, it is significantlydelayed by the slower velocities in model II. In fact, suchdiscrepancies between S5 and the lower-order multipleswould be more severe if the lid and LVZ velocities remainedunchanged. Moreover, they cannot be reconciled by perturb-ing the lid or LVZ velocities alone. Our experiments withvarious perturbed models suggest significant anisotropy(DVsh�sv > 1%) extending below 220 km depth.

4. Results and Discussions

[30] In this study, we concentrated on resolving the uppermantle layering by constructing simple models with as fewparameters as possible. In particular, if a linear gradientbetween two depths proved effective in explaining mostobservations, we did not add any other posterior constraints.Our preferred 1-D model, PAC06 (Table 2), however,provides excellent fits to both the waveforms and travel-times of the observed S wave multiples from a largenumber of events at different depths and with differentmechanisms.[31] We interpret PAC06 as an effective path average for

the corridor, since the sampled lithospheric age spans a widerange from approximately 125 Ma near the source region(Tonga-Fiji) to �10 Ma approaching the California coastalline (see Figure 17b). The thinning of lithosphere, or thedecreasing of seismic velocity with the crustal age gettingyounger has been reported from pure surface wave studiesby many researchers [e.g., Nishimura and Forsyth, 1989;Ritzwoller et al., 2004; Maggi et al., 2006]. To address suchlateral variation is out of the scope of this paper. However,we will briefly discuss two pieces of evidence here, whichsuggest little systematic variation along the path.[32] Figure 17a displays the comparison between the

model PAC06 from this study and the model PA5 devel-oped by Gaherty et al. [1996] for the older half of thecorridor from Fiji-Tonga to Hawaii. In their study, Gahertyet al. [1996] mainly utilized relatively long period (>25 s)

Figure 13. Differences of the S wave multiples’ differ-ential times, particularly DTSS�S, DTSSS�SS, andDTSSSS�SS,between the data and synthetics. A positive value impliesthat the separation between the multiples on the data issmaller than that on the synthetics, whereas a negative valuesuggests the opposite. The data points from different eventsare color coded by the events’ depths.


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body and surface waves plus the ScS reverberations [e.g.,Revenaugh and Jordan 1991b] for determining the dis-continuities. Although PA5 samples relatively old oceaniclithosphere (100–125 Ma), while our studied path covers awider range from 125 Ma to �10 Ma at the receiver side,the two models display remarkable agreement (Figure 17a)despite small detailed differences. Moreover, PA5 does areasonably good job of explaining our data as presented inthe auxiliary material (Figure S31). On the other hand,Figure 17c compares the synthetic prediction of PAC06sh

to the data from the recent Hawaii earthquake. The showncomparison for the coastal station VES is typical for the overa hundred stations of TriNet. This data set from the Hawaiievent samples the younger half of the path, however, thewaveforms and the separations between S and ‘‘G + SS’’ arenicely reproduced from PAC06. In particular, the separationsbetween S and ‘‘G + SS’’ are rather sensitive to the velocitiesin the lid or LVZ. For example, a decrease of lid velocity byless than 4% from our experiments would have narrowed theseparation between S and ‘‘G + SS’’ by over 15 s. In

Figure 14. Selected waveform fits for the vertical component of a shallow event 9792597 (see Table 1)with our preferred SH model PAC06sh.The data are shown in black with synthetics in red. We chose toalign the synthetics and data on ‘‘S3’’ since there is some contamination on ‘‘SS.’’ S wave multiples up toS5 that can be easily recognized are labeled. Note that the synthetics have been shifted by �20 s for suchan alignment. However, that is about the amount the observed direct S waves are advanced. Moreover,the higher-order multiples S4 and S5 are delayed on the data relative to the synthetics.


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summary, these comparisons between PAC06 and the halfpath model (PA5) or observations suggest very little system-atic lateral variation in the lid or LVZ, and the whole pathappears uniform.[33] Another supporting evidence comes from our study

of multiScS waves. For about 1/3 of our studied events, thatare intermediate depth and thrust, the multibounce ScSwaves are rich and strong. Figure 18 displays an example,where we include the multiScS waves in the waveformcomparison for an intermediate-depth event (9648517). Asit might be expected from lower mantle studies [e.g.,

Garnero and Helmberger, 1993; Ritsema et al., 1997;Breger et al., 2001], these multibounce ScS waves (ScSnand sScSn) are consistently delayed by over 5 s relative toPAC06. However, if we align the synthetics and data on aparticular multiple ScSn, we obtain remarkable fits for theirfirst-order reverberations, e.g., S660�S, S660+S from themantle discontinuities as discussed by Revenaugh andJordan [1989]. Note that these ‘‘precursors’’ (ScSnSd�S) or‘‘peglegs’’ (ScSnSd+S) each comprise a family of n or n + 1rays that travel different paths, but have the same traveltime,amplitude, and phase, assuming a 1-D model. Consequently,

Figure 15. Selected waveform fits for the vertical component of the same event as shown in Figure 14with our preferred SV model PAC06sv. The data are shown in black with synthetics in red. We aligned thesynthetics and data on ‘‘S3,’’ which resulted in an average shift of �2 s for the synthetics relative to thedata. Note the nice fits for all the labeled S wave multiples. Particularly, the poorly fit phases followingdirect S are the shear coupled PL waves.


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the strength of these precursors or peglegs relative to theirparent phases (ScSn’s) gets stronger for the higher-order‘‘n’’, due to the increasing redundancy, which is exactlywhat we observe in the data (Figure 18b). Similar results areobtained for the other studied events, although they sampledifferent portions along the path. Presently we do not knowhow much lateral variation is needed to decrease theredundancy in these multiScS reverberations, and suchefforts will be addressed in the future study.[34] The derived anisotropy in PAC06 represents an

effective average over detailed variability along the path.We are not able to resolve the geometry of anisotropy, or itstrue amount, due to the isotropic nature of the synthetics aswell as the limited azimuthal sampling. However, theanisotropy of Vsh > Vsv and its magnitude in PAC06 areconsistent with transverse isotropy reported by previousinvestigators [e.g., Gaherty et al., 1996; Ekstrom andDziewonski, 1998]. The accuracy and uniqueness of map-

ping the actual anisotropy to transverse isotropy using datafrom a single corridor have been discussed in detail byGaherty et al. [1996]. PAC06 contains anisotropy down to adepth of �300 km, beyond the lid and LVZ, which isconsistent with the results from previous studies [e.g.,Nishimura and Forsyth, 1989; Ekstrom and Dziewonski,1998]. The anisotropy of Vsh > Vsv in the lid can beattributed to the lattice preferred orientation (LPO) in olivinewhen the lid was formed [e.g., Nicolas and Christensen1987], since the studied path is consistently oblique to theancient spreading direction. The anisotropy in and below theLVZ could be caused by the preferred orientation of melt-filled pockets [e.g., Schlue and Knopoff 1977] or shearing inthe asthenosphere due to mantle flow or plate motions [e.g.,Zhang and Karato, 1995; Montagner and Tanimoto, 1991].[35] Figure 11 compares PAC06 to the earlier pure path

models developed with similar multibounce S wave data,particularly, TNA, SNA for the North America shield

Figure 16. Waveform fits for the same event as shown in Figure 15 with two perturbed SV models:(a) model I and (b) model II. Note the traveltimes of the lower-order multiples up to S4, that turn below the406 km discontinuity are conserved, however the synthetic S5 is advanced with perturbed model I, whileslowed by model II. (c) Comparison of the perturbed models with PAC06. (d) Raypaths of the first legs ofS4 and S5. The two dashed lines indicate the 406 km and 651 km discontinuities. Note that the raypath ofS5

is nearly at a depth of ~300 km; hence it is rather sensitive to small velocity perturbations there.


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[Grand and Helmberger, 1984b] and ATL featuring the oldAtlantic (�70–150 Ma) [Grand and Helmberger, 1984a].Except for SNA, the other three models all contain a well-developed LVZ. Moreover, the high gradient zone (HGZ)beneath the LVZs appear unique for the oceanic paths, incontrast with the continental model SNA. The steep gradientin the HGZ is intriguing, since it cannot be easily explainedwith a subadiabatic thermal gradient or decreasing partialmelt with depth. One way to match the fast velocity increasebelow the LVZ is to progressively increase the grain size byabout one order of magnitude from approximately milli-meters to approximately centimeters [Faul and Jackson,2005]. A possible explanation for such increase in grain sizewith depth is a change in deformation mechanism, such asthe transition from dislocation to diffusion creep suggestedby Karato and Wu [1993]. A depth-dependent increase inthe amount of pyroxenite could also produce an enhancedvelocity gradient in the HGZ, though a plausible dynamicalpicture is absent [e.g., Stixrude and Lithgow-Bertelloni,2005]. It is noteworthy in Figure 11 that the velocity

minimum in the LVZ migrates upward below the ridges(TNA) and downward beneath the old oceans (ATL). Thevalue also tends to increase with age. Similar features havebeen observed in a number of surface wave studies [e.g.,Nishimura and Forsyth, 1989; Zhang and Lay, 1999]. Thismight suggest that possible flows in the LVZ are notconfined within a certain depth range.[36] Compared to the other models, PAC06 contains a

velocity jump at �516 km (Figure 11). This is in goodagreement with global stacks of SS precursors [Shearer,1990, 1993] or ScS reverberations [Revenaugh and Jordan,1991a]. The small velocity jump at the discontinuity isconsistent with the b � g transition in (Mg, Fe)2SiO4 of themineralogical models [e.g., Rigden et al., 1991].

5. Conclusion

[37] In this study, we developed a pure path shear velocitymodel PAC06 along the corridor from Tonga-Fiji toCalifornia. The model contains a fast lid (Vsh = 4.78 km s�1,Vsv = 4.58 km s�1) �60 km thick. The underlying low-

Figure 17. (a) Comparison of PA5 developed by Gaherty et al. [1996] for the corridor from Tonga-Fijito Hawaii with our preferred model PAC06. (b) Comparison of the source receiver geometry for PAC06,PA5, and the recent Hawaii event (star). (c) Selected transverse component waveform fits with PAC06shat the station VES for the Hawaii event 12261875 (25 October 2006, 1707:49.200 UT). The sourceparameters are from Harvard’s CMT solutions. The data are shown in black with synthetics in red.


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velocity zone (LVZ) is prominent with the lowest velocitiesVsh = 4.34 km s�1, and Vsv = 4.22 km s�1. The anisotropy(Vsv < Vsh) of PAC06 extends to a depth of �300 km.Besides the 406 km and 651 km discontinuities, PAC06 alsohas a small (�1%) velocity jump at �516 km. We consider

these main features of PAC06 to be well determined, sincePAC06 explains a large data set from various events.Therefore it is ideally suited for comparing with mineral-ogical models.

Figure 18. (a) Extended waveform comparison for an intermediate-depth (�367 km) event (9648517)at three stations. See Figure S22 of the auxiliary material for the comparison of the whole record sectionof the multibounce S waves. The data are shown in black, while the synthetics from PAC06 in red.Labeled are the multibounce S waves as well as the multibounce ScS waves. The data and synthetics arealigned on SS. Note that the observed multiScS waves are apparently delayed. (b) Waveform comparisonof the multibounce ScS waves (ScS2, ScS3, and ScS4), where the data and synthetic traces are the stackedrecords from the whole record section. Both the data and synthetics are aligned on ScS3 and the time axisis relative to the event’s origin time. The windowed data and synthetics are aligned up on each individualScS multiple ScSn in the right, where their amplitudes are plotted as normalized. The first-orderreflections of the ScS multiples, such as the precursors, S660�S, S410�S, sS660�S and the peglegs,S660+S, sS410+S, and sS660+S are easily recognized and labeled.


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[38] Acknowledgments. The authors would like to thank JamesGaherty and an anonymous reviewer for their constructive comments andsuggestions, which have helped to improve the manuscript. We also thankLupei Zhu for using his FK code. This work is supported by NationalScience Foundation under the contracts EAR-0636012 and EAR-0456433.Caltech Seismological Laboratory contribution 9168.

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��D. V. Helmberger and Y. Tan, Seismological Laboratory 252-21, Division

of Geological Planetary Sciences, California Institute of Technology,Pasadena, CA 91125, USA. ([email protected])


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trans-pacific upper mantle shear velocity structure · [2] seismic velocity structure provides the...

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