RESEARCH ARTICLE10.1002/2017GC006824

Seafloor age dependence of Rayleigh wave phase velocities inthe Indian OceanKaren E. Godfrey1 , Colleen A. Dalton1, and Jeroen Ritsema2

1Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, Rhode Island, USA,2Department of Earth and Environmental Sciences, University of Michigan, Ann Arbor, Michigan, USA

Abstract Variations in the phase velocity of fundamental-mode Rayleigh waves across the Indian Oceanare determined using two inversion approaches. First, variations in phase velocity as a function of seafloorage are estimated using a pure-path age-dependent inversion method. Second, a two-dimensional parame-terization is used to solve for phase velocity within 1.258 3 1.258 grid cells. Rayleigh wave travel time delayshave been measured between periods of 38 and 200 s. The number of measurements in the study arearanges between 4139 paths at a period of 200 s and 22,272 paths at a period of 40 s. At periods< 100 s, thephase velocity variations are strongly controlled by seafloor age and shown to be consistent with tempera-ture variations predicted by the half-space-cooling model for a mantle potential temperature of 14008C. Theinferred thermal structure beneath the Indian Ocean is most similar to the structure of the Pacific uppermantle, where phase velocities can also be explained by a half-space-cooling model. The thermal structureis not consistent with that of the Atlantic upper mantle, which is best fit by a plate-cooling model andrequires a thin plate. Removing age-dependent phase velocity from the 2-D maps of the Indian Ocean high-lights anomalously high velocities at the Rodriguez Triple Junction and the Australian-Antarctic Discordanceand anomalously low velocities immediately to the west of the Central Indian Ridge.

1. Introduction

Current understanding of the seismic properties of the oceanic upper mantle is based on studies of SS-Sand PP-P travel times [e.g., Kuo et al., 1987; Woodward and Masters, 1991; Vasco et al., 1995; Goes et al., 2013]and surface wave dispersion [e.g., Nishimura and Forsyth, 1989; Gaherty et al., 1996; Forsyth et al., 1998;Ritzwoller et al., 2004; Maggi et al., 2006; Priestley and McKenzie, 2006; Tan and Helmberger, 2007; Weeraratneet al., 2007; Yang et al., 2007; Nettles and Dziewo�nski, 2008; Harmon et al., 2009, 2011; James et al., 2014;Beghein et al., 2014; Burgos et al., 2014; Lin et al., 2016]. In the uppermost mantle, seismic velocity increaseswith the age of the oceanic plate. In vertical profiles of shear wave speed, the minimum velocity and thedepth of the low-velocity zone both increase with the age of the overlying seafloor. The average age-dependent seismic velocities in the Pacific upper mantle can be fit reasonably well by the half-space-cooling model [e.g., Faul and Jackson, 2005; Stixrude and Lithgow-Bertelloni, 2005; Maggi et al., 2006; Jameset al., 2014; Steinberger and Becker, 2017]. However, James et al. [2014] have shown that the phase velocitiesof Rayleigh waves that have propagated across the Atlantic basin can be explained much better by a plate-cooling model than by the half-space-cooling model and require a relatively thin plate (75 km). Further-more, Ma and Dalton [2017] have shown that Rayleigh wave phase velocities in the northern Indian Oceanare best fit by a plate-cooling model with a 125 km thick plate.

Deviations from age-dependent seismic velocity have also been observed. These include a punctuated cool-ing history with reheating events in the Pacific [Ritzwoller et al., 2004], anomalous radial anisotropy in thecentral Pacific [Ekstr€om and Dziewonski, 1998], and asymmetric seismic velocity structure across mid-oceanridges. Lower seismic velocities on the west side of the ridge have been resolved at the East Pacific Rise(EPR) and the Juan de Fuca Ridge [e.g., Forsyth et al., 1998; Scheirer et al., 1998; Bell et al., 2016]. In these loca-tions, the concentration of seamounts is also higher on the western side, suggesting higher temperaturesand more extensive melting to the west of the ridge. Relative to the eastern side, the western side of theEPR is characterized by reduced mantle Bouguer gravity anomalies [Scheirer et al., 1998] and stronger seis-mic anisotropy with fast-direction parallel to the spreading direction [Wolfe and Solomon, 1998]. Toomeyet al. [1998] also observed an asymmetry in P and S wave delays at the EPR, with variations that suggest

Key Points:� Seafloor age-dependent phase

velocities in the Indian Ocean uppermantle are best fit by a half-space-cooling model� Anomalously high velocities are

observed at the Rodriguez TripleJunction and Australian-AntarcticDiscordance� Asymmetric seismic structure is

observed at the Central Indian Ridge

Supporting Information:� Supporting Information S1

Correspondence to:K. E. Godfrey,karen_godfrey@brown.edu

Citation:Godfrey, K. E., C. A. Dalton, andJ. Ritsema (2017), Seafloor agedependence of Rayleigh wave phasevelocities in the Indian Ocean,Geochem. Geophys. Geosyst., 18, 1926–1942, doi:10.1002/2017GC006824.

Received 17 JAN 2017

Accepted 13 APR 2017

Accepted article online 18 APR 2017

Published online 10 MAY 2017

VC 2017. American Geophysical Union.

All Rights Reserved.

GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1926

Geochemistry, Geophysics, Geosystems

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higher partial melt concentrations to the west of the ridge than to the east. Whereas the asymmetry acrossthe EPR has been attributed to the proximity of the EPR to the Pacific Superswell [Conder et al., 2002; Too-mey et al., 2002], Bell et al. [2016] attributed the asymmetry across the Juan de Fuca Ridge to a combinationof asymmetrical forcing and active upwelling provided by the Cobb-Eikelberg hot spot.

This study is focused on the upper mantle beneath the Indian Ocean. The Indian Ocean comprises threeactive mid-ocean ridge systems and a wide range of spreading rates (Figure 1) and offers an opportunity toinvestigate the formation and evolution of oceanic lithosphere under a range of conditions. The SouthwestIndian Ridge (SWIR) is an ultraslow spreading ridge with a minimum half-spreading rate of 7 mm/yr, theSoutheast Indian Ridge (SEIR) spreads at a half-spreading rate of 28–38 mm/yr, and the Central Indian Ridge(CIR) is characterized by spreading rates in between these two end-members [M€uller et al., 2008]. Further-more, the Wharton Spreading Center southwest of Sumatra has been inactive for 40 Ma [Liu et al., 1983;Krishna et al., 1995].

The Indian Ocean also presents opportunities to explore the origin of deviations from simple dependenceon seafloor age. It includes numerous hot spots [Courtillot et al., 2003] and overlies a portion of the AfricanLarge Low Shear Velocity Province (LLSVP). Burke and Torsvik [2004] argued that the hot spots, such asR�eunion, originate from deep mantle plumes rising from the edges of LLSVPs. The Australian-Antarctic Dis-cordance (AAD) on the SEIR is a region of anomalously deep seafloor with complex bathymetry [Weissel andHayes, 1974]. Numerous previous studies [e.g., Montagner, 1986; Forsyth et al., 1987; Debayle and L�eveque,1997; Ritzwoller et al., 2003] have resolved high seismic velocities in the upper mantle beneath the AAD.Klein et al. [1988] showed that the AAD is the location of a boundary between distinct isotopic compositionsof Pacific and Indian Ocean mid-ocean ridge basalts and suggested that it occurs over a region of downwel-ling in the mantle. Gurnis and M€uller [2003] proposed that this downwelling is related to Mesozoic subduc-tion, with the ancient mantle wedge influencing observed geochemical differences between Indian andPacific upper mantle.

Previous tomographic studies of the upper mantle beneath the Indian Ocean [e.g., Montagner, 1986; Mon-tagner and Jobert, 1988; Debayle and L�eveque, 1997] present good correlation between seismic velocity andsurface tectonics in the shallowest mantle but disagree about the depth extent of this relationship. Mon-tagner [1986] and Montagner and Jobert [1988] found that this correlation disappears around 100 km depthwhereas Debayle and L�eveque [1997] observed that it persists to at least 200 km depth. The shear-velocitymodel of Montagner [1986] contains low-velocity anomalies eastward of the CIR at depths 120–300 kmwhereas the model of Debayle and L�eveque [1997] indicates that low-velocity anomalies extend westward

Figure 1. (a) Seafloor age and (b) half-spreading rate [M€uller et al., 2008] for the Indian Ocean. Black diamonds indicate hot spot locations according to Courtillot et al. [2003] with esti-mate of Amsterdam-St. Paul hot spot location from Johnson et al. [2000]. Labeled hot spots are: 1, Marion, 2, R�eunion, 3, Crozet, 4, Kerguelen, 5, Amsterdam-St.Paul. Abbreviations: AAD,Australian-Antarctic Discordance; CIR, Central Indian Ridge; RTJ, Rodriguez Triple Junction; SB, Somali Basin; SEIR, Southeast Indian Ridge; SMP, Seychelles-Mascarene Plateau; SWIR,Southwest Indian Ridge; WB, Wharton Basin.

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GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1927

from the CIR toward the R�eunion hot spot at depths 88–190 km. The previous studies also found anoma-lously high velocity along the easternmost section of the SWIR at depths larger than 190 km.

Since these studies were published, the available waveform data sets have grown by an order of magnitudeand enable us to resolve the discrepancies between the earlier models and identify additional features ofthe seismic structure of the upper mantle in the Indian Ocean.

2. Data and Methods

We use measurements of fundamental-mode Rayleigh wave travel time delays [Ritsema et al., 2011] to solvefor phase velocity with two approaches. First, we assume that phase velocity varies only as a function of sea-floor age and parameterize velocity variations with five age bins. Second, we investigate deviations fromage-dependence by solving for the 2-D phase velocity variation across the Indian Ocean. We assume thatthe surface waves propagate along minor-arc great-circle paths. While finite-frequency theory describesmore accurately the effects of seismic velocity heterogeneity on surface wave dispersion [e.g., Zhou et al.,2005; Peter et al., 2009], it has been shown that the great-circle ray approximation performs reasonably wellfor travel times accumulated along minor-arc paths [Wang and Dahlen, 1994, 1995; Larson et al., 1998] andthat improvements in the resolution of tomographic images obtained by using finite-frequency theorytrade-off with damping [e.g., Boschi, 2006; Trampert and Spetzler, 2006; Ritsema et al., 2011].

A second assumption inherent to our approach is that azimuthal coverage is sufficiently good that azi-muthal anisotropy can be neglected. Ekstr€om [2011] and Ma et al. [2014] have shown that tradeoffs existbetween isotropic velocity and azimuthal anisotropy, and that ignoring azimuthal anisotropy can introduceartifacts into phase velocity maps. However, if the distribution of azimuths is relatively uniform, isotropicphase velocity maps can be estimated without significant bias. In section 2.5, we demonstrate that, with theexception of the margins of the study area, neglecting azimuthal anisotropy will introduce minimal biasinto the resolution of isotropic Rayleigh wave phase speed.

2.1. Data SetOur regional data set of fundamental-mode Rayleigh wave travel time delays is selected from the globaldata set measured by Ritsema et al. [2011]. These frequency-dependent travel time delays, which were mea-sured using the mode-branch stripping technique of van Heijst and Woodhouse [1997], are expressed as per-turbations to synthetic seismograms constructed using the Global CMT solutions [Dziewonski et al., 1981;Ekstr€om et al., 2012] and the PREM model [Dziewonski and Anderson, 1981]. We use travel time delays mea-sured at 16 periods, between 38 and 200 s. The data set includes between 4139 (at period 5 200 s) and22,272 paths (at period 5 40 s) that traverse our study region exclusively (Table 1). The data set includesearthquakes that occurred between 1991 and the start of 2008, with magnitudes that range from 5 to 7.8.Figure 2a shows the locations of the 2029 events and 99 stations that contribute data for period 5 50 s, and

Table 1. Summary of Size of the Data Set and Pure-Path Age-Dependent Phase Velocities in km/s

Period(s) No. of Paths

Pure-Path Age-Dependent Phase Velocity (km/s)

0–4 Myr 4–20 Myr 20–52 Myr 52–110 Myr >110 Myr Continents

38 21,806 3.835 3.895 3.976 4.039 4.074 3.90640 22,272 3.837 3.894 3.974 4.041 4.081 3.92143 21,497 3.836 3.894 3.971 4.045 4.089 3.93547 20,687 3.843 3.893 3.971 4.047 4.098 3.94850 19,793 3.853 3.892 3.974 4.050 4.109 3.95955 18,766 3.870 3.896 3.977 4.053 4.122 3.97260 17,928 3.895 3.906 3.983 4.057 4.130 3.98770 17,134 3.922 3.923 3.996 4.063 4.139 4.00475 16,385 3.954 3.950 4.013 4.076 4.150 4.02590 15,246 3.999 3.987 4.038 4.097 4.168 4.052100 13,854 4.048 4.037 4.074 4.127 4.196 4.088115 12,207 4.112 4.010 4.124 4.172 4.237 4.135130 10,041 4.189 4.181 4.195 4.232 4.292 4.202150 7,969 4.306 4.283 4.287 4.318 4.376 4.291175 5,928 4.424 4.417 4.415 4.434 4.491 4.411200 4,139 4.633 4.590 4.578 4.596 4.649 4.576

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Figure 2b shows the depth sensitivity of Rayleigh wave phase velocity to vertically polarized shear-wavespeed (VSV) for several representative periods.

2.2. Pure-Path Age-Dependent InversionNumerous global models and regional studies of Pacific and Atlantic oceanic lithosphere [e.g., Nishimuraand Forsyth, 1989; Ritzwoller et al., 2004; Maggi et al., 2006; Nettles and Dziewo�nski, 2008; James et al., 2014]indicate that seafloor age has the largest control over phase velocity. We first use the measured travel timedelays to constrain phase velocity as a function of seafloor age and divide the study area into five binsbased on seafloor age: 0–4, 4–20, 20–52, 52–110, and 1101 Myr. A sixth bin captures the areas that havenot been assigned a seafloor age by M€uller et al. [2008], which are primarily continental. We choose theseage bins to simplify the comparison to similar studies of the Pacific [Nishimura and Forsyth, 1989] and Atlan-tic [James et al., 2014]. The distribution of path sampling by area and by path length for each age bin is sum-marized in Table 2.

By a least squares inversion, we solve for perturbations to slowness from the starting model PREM [Dziewon-ski and Anderson, 1981], using

dti xð Þ5X6

j51Xijdpj xð Þ; (1)

where Xij is the length (in km) of the ith path in the jth age bin, dti is the measured travel time delay (in s)for the ith path at angular frequency x, and dpj is the unknown slowness perturbation (in s/km) in the jth

age bin. The sum is over the six age bins. This is a linearinverse problem of the form Gm 5 d, where d containsthe measured travel time delays, m contains theunknown slowness perturbations, and G containsthe matrix of Xij values. We present the results asabsolute phase velocities using the conversionc(x) 5 1/[p0(x)1dp(x)], where p0 is the slowness of thereference model. The uncertainties of the phase veloc-ity values are estimated from bootstrapping tests, inwhich the inversion is repeated 5000 times, each timeusing a different subset of paths randomly selectedfrom the total data set. The number of paths in eachsubset is allowed to vary randomly between 500 and

Table 2. Rayleigh Wave Coverage Within Our Age Binsa

Age Bin % Area % Path Length

0–4 Myr 2.9 3.44–20 Myr 10.6 12.020–52 Myr 19.8 21.652–110 Myr 28.3 31.61101 Myr 9.2 9.0Continental 29.2 22.4

aThe second column shows the area of the IndianOcean (in %) for each age bin. The third column shows theaverage sampling of age bins by path length for a periodof 50 s. For example, on average the 19,793 paths have3.4% of their length in seafloor 0–4 Myr and 12.0% of theirlength in seafloor 4–20 Myr.

0 5 10x 10

−6

0

50

100

150

200

250

300

350

400

Sensitivity to VSV

Dep

th (

km)

40 s50 s100 s150 s200 s

(a) (b)

0˚ 90˚ 180˚−75˚

−60˚

−45˚

−30˚

−15˚

0˚

15˚

30˚

−6000 −5000 −4000 −3000 −2000 −1000 0

Elevation (m)

Figure 2. (a) Seafloor elevation [M€uller et al., 2008] with locations of 2029 events (white stars) and 99 stations (orange squares) that com-prise our 50 s data set. (b) Kernels showing Rayleigh wave sensitivity to vertically polarized shear velocity. They are calculated using ATL2a,which represents average upper mantle velocity in the Atlantic Ocean and is an extension of the seismic study of Gaherty and Dunn[2007].

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GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1929

the total number of paths at each period, foreach inversion. The mean and standard devia-tion of the 5000 inversion results are determinedfor each age bin and period and represent theuncertainties of the phase velocity values. Theminimum and maximum values of standarddeviation for any period and age bin are 0.0019and 0.0231 km/s, respectively. The largest stan-dard deviations are obtained for the 0–4 Myrage bin at the longest periods.

The pure-path age-dependent phase velocities(Figure 3 and Table 1) increase with increasingseafloor age and with increasing period. The phasevelocities of the four youngest age bins merge atperiod 5 70 s for 4–20 Myr, period 5 130 s for20–52 Myr, and period 5 175 s for 52–110 Myr.The phase velocity for the 1101 Myr bin is higherthan the other bins at all periods considered.

We compare our estimates of Rayleigh phasevelocity for the Indian Ocean with equivalent

estimates for the Atlantic Ocean [James et al., 2014] in Figure 4a and the Pacific Ocean [Nishimura andForsyth, 1989] in Figure 4b. Figure 4 demonstrates that in all three ocean basins phase velocity increaseswith period and with seafloor age. The phase velocity curves for all three ocean basins are similar for the20–52 and 52–110 Myr age bins. However, there are also notable differences. Compared to the IndianOcean and the Pacific Ocean, the phase velocities of Rayleigh waves through the Atlantic vary less with age.The 52–110 and 1101 Myr curves coincide in the Atlantic but are clearly separated up to periods> 120 s inthe Indian and Pacific. Furthermore, phase velocities for the Pacific are anomalously low for the 0–4 Myr agebin at all periods.

Table 2 shows that on average the 20–52 and 52–110 Myr age bins are best sampled by our data set. Wetest the sensitivity of our results to the distribution of path lengths within each age bin (Table 2) by per-forming an additional inversion in which we use only the 4000 paths that provide the best sampling of the0–4 Myr age bin (supporting information Figure S1). The effects of this data selection on the pure-path age-dependent phase velocities are small and do not alter conclusions drawn from the comparisons to the

50 100 150 2003.8

3.9

4

4.1

4.2

4.3

4.4

4.5

4.6

Period (s)

Pha

se V

eloc

ity (

km/s

)

0−4 Myr4−20 Myr20−52 Myr52−110 Myr110+ Myr

Figure 3. Results of pure-path age-dependent inversion for phasevelocity in the Indian Ocean, with error bars showing two standarddeviations estimated from bootstrapping test.

40 60 80 100 1203.7

3.8

3.9

4

4.1

4.2

4.3

Period (s)

Pha

se V

eloc

ity (

km/s

)

0−4 Myr4−20 Myr20−52 Myr52−110 Myr110+ Myr

40 60 80 100 1203.7

3.8

3.9

4

4.1

4.2

4.3

Period (s)

Pha

se V

eloc

ity (

km/s

)

0−4 Myr4−20 Myr20−52 Myr52−110 Myr110+ Myr

(a) (b)

Figure 4. Comparison of pure-path age-dependent phase velocity in the Indian Ocean with that of (a) the Atlantic [James et al., 2014] and(b) the Pacific [Nishimura and Forsyth, 1989]. Comparison studies are shown as dashed lines. James et al. [2014] used a single 0–20 Myr agebin, which is plotted as the magenta dashed line in Figure 4a, instead of the 0–4 and 4–20 Myr age bins. Solid lines are our results for theIndian Ocean with error bars showing two standard deviations from bootstrapping tests.

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Atlantic and Pacific. Differences between results obtained with the full data set and with the 4000-path sub-set appear to be mostly affected by the decrease in number of total paths used.

Seafloor spreading rates vary strongly in the Indian Ocean (Figure 1b). However, using the pure-pathapproach to estimate the dependence of phase velocity on both spreading rate and seafloor age does notprovide a statistically significant improvement in data fit.

2.3. Inversion for Phase Velocity MapsWe next estimate maps of Rayleigh wave phase velocity at each period by a regularized inversion. The studyarea is parameterized using 9056 grid cells with dimensions of 1.258 3 1.258. We have tested differentparameterizations of the gridded area and the grid cell size, and the main features of the maps and conclu-sions drawn about them are not dependent on these choices. The choice of gridded area represents a com-promise between including as many paths as possible while minimizing contamination from continentallithosphere. We solve for a constant slowness perturbation in each cell. We apply a horizontal smoothnessconstraint to these perturbations by minimizing the model roughness R, defined here as the squared gradi-ent of the slowness perturbation. The horizontal smoothness constraint is implemented as a linear con-straint, Bm 5 c, with damping specified by the coefficient a. The solution to this damped least squaresproblem is:

m5 GT G1a2BT B� �21

GT d1a2BT c� �

(2)

Here G is the matrix of Rayleigh wave path lengths through each grid cell. To account for the variable pathcoverage in our study area (Figure 5), the measurements from well-sampled paths are given less weight in

Figure 5. Path density for Rayleigh waves at periods of 50, 100, 150, and 200 s. The color scale shows the number of great-circle ray paths that travel through each 1.258 3 1.258 gridcell.

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the inversion. In practice, this is implemented by identifying groups of similar event-station paths, definedhere as events located within the same 1.258 3 1.258 grid cell and stations within the same 1.258 3 1.258

grid cell, and weighting the corresponding observations by the inverse of the number of paths in theirgroup. We have performed the inversions for phase-velocity maps with and without the data weightingscheme described above and find that the primary features of the maps are unaffected by this choice, withcorrelation coefficients between pairs of maps of �0.97.

Maps of Rayleigh wave phase velocity are shown in Figure 6. At periods< 100 s, the phase velocities aredominated by age-dependent variations, with low velocities along the three active spreading ridges andhigher velocity in regions of older seafloor akin to the results discussed in section 2.2. The signal of litho-spheric cooling is also visible in the Wharton Basin, with higher velocity on the flanks of and lower velocitycloser to the extinct spreading center. The age dependence of phase velocity at period 5 50 s, extractedfrom Figure 6a, is shown in supporting information Figure S2. The maps also show deviations from age-dependent trends. In particular, for period 5 50 s, the along-ridge variation of phase velocity correlatesroughly with spreading rate (supporting information Figure S3). We observe the highest phase velocityalong the ultraslow SWIR and lowest velocity along the faster spreading SEIR. This may be an artifact of thelimits of our spatial resolution, which is described in section 2.6. The Australian-Antarctic Discordance (AAD)along the SEIR is characterized by elevated wave speed, and anomalously low velocities are associated with

Figure 6. Phase velocity perturbations for Rayleigh waves at periods of 50, 100, 150, and 200 s. Hot spot locations from Courtillot et al. [2003] are shown as diamonds. Geographical loca-tions of features described in the text are identified and labeled in Figure 1.

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the Marion, Crozet, and Kerguelen hot spots(Figure 6a), although the shape and extentof these features may be influenced by theresolution (section 2.6) and azimuthal cover-age (section 2.5) of our data set. The lack ofhot spot signature at R�eunion may also beinfluenced by our spatial resolution. Atperiods> 100 s the correlation with seafloorage is weaker. The 150 and 200 s maps con-tain anomalously high velocity beneath theAAD and much of the southwestern oceanincluding the Rodriguez Triple Junction (RTJ)and anomalously low velocity in a broadregion surrounding the St. Paul and Kergue-len hot spots and immediately west of theCIR.

2.4. Variance ReductionThe variance reduction for the pure-pathage-dependent inversion and for the 2-Dmaps at each period is determined by

v %ð Þ51002100 �PN

i51 dtobsi 2dtpred

i

� �2

PNi51 dtobs

i Þ2;

�(3)

where the superscripts obs and pred refer to the observed and predicted travel time delays, respectively, andthe sum is over the N paths at each period. At all periods, the 2-D maps provide higher variance reductionthan the pure-path age-dependent results (Figure 7) as expected given the larger number of free parametersin the map parameterization. The difference in variance reduction grows with increasing period, presumablybecause the sensitivity of Rayleigh waves to shear velocity variations in the lithosphere (and thus to seafloorage) diminishes with increasing period. Furthermore, we use the global data set of Ritsema et al. [2011] todetermine global phase velocity maps expanded in spherical harmonics to degree 20 and not damped. Ourregional 2-D maps reduce the variance of the Indian Ocean travel time data by roughly 10% more than theglobal maps do, demonstrating the value of the higher resolution offered by our 2-D maps.

2.5. Neglecting Azimuthal AnisotropyWe examine the azimuthal coverage by plotting grid cells that contain at least one path in each of eight 458

azimuth bins (supporting information Figure S4a) and those that do not (supporting information FigureS4b). We color-code the plots by the coverage function, cN, in each cell, normalized by the number of pathsthat pass through the cell. The coverage function cN was developed and utilized by Ekstr€om [2006] for auto-mated earthquake detection and is described as:

1cN

5XN

i51

g2i

2pð Þ2(4)

where the sum is over the N number of paths passing through the grid cell. To calculate 1/cN, we first sort allpath azimuths within each grid cell in order from smallest to largest. Next, we compute gi, which is the differ-ence, in radians, between the ordered path azimuths. If the azimuths of all paths in the grid cell are equal,then each gi is equal to zero, or 2p radians, and cN 5 1, and if the azimuths are evenly distributed among theeight bins, then cN 5 N [James et al., 2014]. Supporting information Figure S4 shows that the azimuthal cover-age is good throughout the interior but not along the margins of the study area including at the Australian-Antarctic Discordance. Supporting information Figure S5 shows the azimuthal distribution in four examplegrid cells that are characterized by different values of normalized cN. We conclude that for most of our studyarea neglecting azimuthal anisotropy will introduce minimal bias into the isotropic velocities.

50 100 150 2000

10

20

30

40

50

60

70

80

90

Period (s)

Var

ianc

e R

educ

tion

(%)

Age−Dependent2D mapsGlobal maps

Figure 7. Variance reduction calculated at each period for pure-path age-dependent phase velocity (section 2.2 and Figure 3) and the 2-D phasevelocity maps (section 2.3) for the Indian Ocean calculated in this study.The green curve shows variance reduction calculated for the same dataset using global phase velocity maps that are parameterized with spheri-cal harmonics to degree 20 and determined with the entire global dataset of Ritsema et al. [2011].

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2.6. Resolution of Phase Velocity MapsFigure 8 show results of resolution tests that illustrate how path coverage, parameterization, and regulariza-tion affect model resolution. For these tests, we invert theoretical travel time delays computed for a pre-scribed pattern of slowness perturbations using the same approach, parameterization, and damping asdescribed in section 2.3. We use the same path coverage as our data set for period 5 50 s for these tests.Although path coverage (Figure 5a) changes significantly from the northeast to the southwest of the studyarea, the resolution tests suggest that the geometries of velocity anomalies as small as 6.258 can be esti-mated accurately especially in the interior of our study area where path and azimuthal coverage are good(supporting information Figures S4 and S5). The recovered isolated 6.258 3 6.258 velocity anomalies of26% throughout the Indian Ocean (Figure 8a) are smoother but similar to the input pattern of anomalies.The amplitude of these anomalies decreases with distance from their centers so that we recover half theamplitude at a distance of 200–300 km from the anomaly center. We also test velocity anomalies of 16% atthe Rodriguez Triple Junction (RTJ) and at the Australian-Antarctic Discordance (AAD), where we observehigh phase velocities in our data (Figure 8b). We are able to recover these patterns well, with little lateralsmoothing and difference in amplitude between input and output maps. The RTJ anomaly maintains atleast half its original amplitude to a distance of 700 km from the center of the input anomaly, whereas theAAD anomaly maintains at least half its original amplitude to a distance of 500 km from the center of theinput anomaly. A strictly age-dependent input velocity structure (Figure 8c, left column) is also recoverable,with smearing limited to margins characterized by strong velocity contrasts in the input structure. The dif-ference map (Figure 8c, right column) also shows that the velocities recovered along the ultraslow spread-ing SWIR are slightly higher than prescribed, presumably because it is difficult to isolate the narrow width ofyoung seafloor flanking the ridge. Additionally, the checkerboard test (Figure 8d) shows that we can resolve108 3 108 anomalies, except along the margin of the study area. While these tests explore how our pathcoverage, parameterization, and regularization may limit the resolution of various features in the study area,they ignore modeling artifacts due to the simplified descriptions of wave propagation and the neglect ofazimuthal anisotropy.

3. Constraints on Lithospheric Thermal Structure

Using the pure-path age-dependent Rayleigh wave phase velocities from Figure 3 we can estimate the aver-age lithospheric thermal structure in the Indian Ocean. We consider both the half-space-cooling model(HSCM) and the plate-cooling model (PCM) [e.g., Stein and Stein, 1992] and use a grid-search approach todetermine the values of the mantle potential temperature and plate thickness that are compatible with themeasured phase velocities.

For the HSCM, the temperature is calculated as a function of depth z and seafloor age t as

T t; zð Þ5Tad erf z 4jtð Þ212

h i(5)

where j is the thermal diffusivity (j 58 3 1025 m2/s) and Tad is the adiabatic temperature profile, which iscalculated with respect to depth as

Tad zð Þ � T0 11/T gz

cp

� �(6)

Here T0 is the mantle potential temperature, aT is the coefficient of thermal expansion, g is acceleration dueto gravity, and cp is the specific heat at constant pressure. We use aT 5 2.9 3 1025 K21 and cp 5 1350 J kg21

K21, as in Faul and Jackson [2005]. The temperature for the PCM is calculated as

T t; zð Þ5Tadza

1X1n51

2np

exp 2jn2p2t

a2

� �sin

npza

� �" #(7)

where a is the plate thickness. We test values of potential temperature ranging from 12008C to 17008C, inincrements of 508. For the PCM, we test plate thickness values of 75–155 km in increments of 10 km.

Rayleigh waves are sensitive to the vertically polarized shear velocity (VSV). We calculate VSV from the tem-perature profiles using the anelastic parameterization of Jackson and Faul [2010]. We consider grain-size

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GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1934

Figure 8. (left column) Input and (right column) output for resolution tests for (a) various 6.258 3 6.258 26% anomalies, (b) 12.58 3 12.58 16% velocity anomaly at the Rodriguez TripleJunction, and 158 3 8.758 16% velocity anomaly at the Australian-Antarctic Discordance, (c) age-dependent phase velocity structure, and (d) 108 3 108 checkerboard. Right column forFigure 8c shows the difference between the input (left column) and output (not shown) maps (i.e., input minus output), where positive (negative) values indicate higher (lower) velocityin the input map.

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GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1935

values of 1 mm, 1 cm, and 5 cm. We assume that horizontally polarized shear velocity VSH 5 1.04 3 VSV, thatVP/VS 5 1.85, and that all other parameters (i.e., density, bulk and shear attenuation, and the nondimensionalanisotropic parameter g) are fixed to their values in PREM. The oceanic crust is 6 km thick. In the crust, VP

ranges from 6.3 to 6.9 km/s, VS ranges from 3.48 to 3.68 km/s, and density 5 3027 kg/m3. The modelsinclude a 4 km thick layer of water (VP 5 1.5 km/s; density 5 1030 kg/m3) and 300 m thick layer of sediment(VP 5 2.01 km/s, VS 5 0.92 km/s, and density 5 1500 kg/m3). At depths greater than 400 km, the density,elastic, and anelastic parameters from PREM are used. Phase velocity is calculated for the fundamental sphe-roidal modes for each Earth model using the Mineos software package [e.g., Masters et al., 2014].

We compute temperature profiles and their corresponding Earth models for seafloor ages between 5 and155 Myr in increments of 5 Myr. To facilitate comparison with the results of our pure-path age-dependentphase velocity inversion, we use a weighted mean of the predicted phase velocities according to the distri-bution of ages within each of the four age bins (4–20, 20–52, 52–110, and 1101 Myr) used here. We do notanalyze the youngest age bin (0–4 Myr) that includes the active ridges because of its much smaller contri-bution to plate area relative to the other four age bins (Table 2). We calculate misfit between the observedand predicted phase velocity as:

misfit5X4

i51

X16

j51

cpredij 2cobs

ij

� �2(8)

where i indicates each of four age bins used in this comparison and j indicates each of the 16 periods usedin the pure-path age-dependent inversion.

3.1. Best Fitting Thermal ModelsThere is a trade-off between the assumed grain size d and the best fitting mantle potential temperature To.For the HSCM, the best fitting value of To is 14008C at d 5 1 mm, 14508C at d 5 1 cm, and 15008C atd 5 5 cm. While d 5 1 mm provides the lowest overall misfit, there is little difference in minimum misfit forthe various grain-size values. For the PCM, the best fitting values of To are 14008C, 14008C, and 14508C atd 5 1 mm, 1 cm, and 5 cm, respectively. As for the HSCM, d 5 1 mm provides a slightly better fit to theobserved pure-path age-dependent phase velocities. The minimum misfit for the PCM is achieved at platethickness values of 155, 125, and 135 km for grain sizes of d 5 1 mm, 1 cm, and 5 cm, respectively. The factthat the best fitting PCM requires a thick plate and the same To as the HSCM is not surprising, given thatthe thermal structure predicted by the PCM with a thick plate is virtually identical to the HSCM at all but theoldest ages, and is a sign of internal consistency within our analysis.

Figure 9a shows the minimum misfit as a function of mantle potential temperature for both the HSCM andthe best fitting PCM for a grain size of 1 mm. The two models yield a similar misfit, but the HSCM (minimummisfit 5 0.0481) fits the data slightly but significantly better than the PCM (minimum misfit 5 0.0562). Jameset al. [2014] analyzed Rayleigh wave phase velocities in the Atlantic upper mantle and found that the nar-row range of age-dependent phase velocities determined beneath the Atlantic basin requires a thin plate(75 km) and cannot be fit by the HSCM. These authors also showed that while the age-dependent phasevelocities determined by Nishimura and Forsyth [1989] for the Pacific basin are best satisfied by a 95 kmthick plate, they are also reasonably well fit by the HSCM, although at a higher potential temperature(15008C). Auer et al. [2015] have also suggested higher mantle temperatures beneath the Pacific than theAtlantic on the basis of their global shear-velocity model, although their conclusion that wave speeds in thePacific and Atlantic are both broadly consistent with the HSCM differs from our analysis and that of Jameset al. [2014]. Thus, it appears that the average thermal structure of the lithosphere within the Indian Oceanis more similar to the Pacific upper mantle than to the Atlantic, though marked differences between allthree ocean basins exist.

Figure 9b compares the HSCM-predicted and pure-path age-dependent phase velocity curves. We notethat the HSCM slightly overestimates phase velocity at short periods. In part, this discrepancy can be attrib-uted to the wide age bins that we use for the pure-path inversion, which make it difficult to directly com-pare observations and predictions. Furthermore, our pure-path age-dependent phase velocities have notbeen corrected for sediment thickness and water depth, both of which can affect the shape of the curves atshorter periods. Beneath young seafloor, where the true water-layer thickness is typically smaller than in thereference model, the effect of the correction is to very slightly reduce phase velocities relative to their

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GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1936

uncorrected values [Ma and Dalton, 2017]. Beneath older seafloor, where the true sediment thickness is typ-ically larger than in the reference model, the effect of the correction is to increase phase velocity, in somecases by 1–2%. Ma and Dalton [2017] showed that correcting observed phase velocities in the northernIndian Ocean for sediment and water thickness results in a larger best fitting plate thickness (125 km versus105 km), mostly as a consequence of the corrections for sediment thickness. Since our preferred model isthe half-space-cooling model, which implies a thick plate, we do not expect corrections for sediment thick-ness to alter our conclusions about thermal structure. However, we note that the discrepancy betweenobserved and predicted phase velocity in the 4–20 Myr age bin (Figure 9b) requires further scrutiny. Allow-ing for regional variations in the magnitude and depth-dependence of radial anisotropy, which is assumedto be 4% from the Moho to 400 km depth throughout the study area, in the predicted phase velocities pro-vides one explanation for the discrepancy.

3.2. Deviations From Age-Dependent Phase VelocityFigure 10 shows Rayleigh wave phase velocity variations with respect to predictions from the HSCM. Theaverage phase velocity perturbation has also been subtracted to highlight the anomalous features. Figure9b shows the level of static offset between our phase velocities and the HSCM predictions at each period.The predominantly small-amplitude and small-scale phase velocity anomalies indicate that the HSCMexplains the basin-wide phase velocity variations well. Bootstrapping tests performed on the pure-pathage-dependent phase velocities discussed in section 2.2 indicate that the uncertainty on phase velocity val-ues is approximately 0.2–0.5%. In Figure 10, we have chosen a color scale that highlights anomalies that dif-fer from the HSCM predictions by >1%, well outside the range that could be attributed to data and modeluncertainty. Notable structures in Figure 10 point to regions where simple cooling models fail. First, at peri-ods between 50 and 200 s anomalously high velocities are associated with the Australian-Antarctic Discor-dance, as observed previously [e.g., Montagner, 1986; Forsyth et al., 1987; Kuo et al., 1996; Debayle andL�eveque, 1997; Ritzwoller et al., 2003]. The AAD is characterized by abrupt changes in magnetic amplitude,geochemistry, and seismicity occurring across the east-bounding transform fault [Marks et al., 1990; Kleinet al., 1988]. Most interpretations of this feature involve anomalously low mantle temperature and convec-tive downwelling [e.g., Weissel and Hayes, 1974; Klein et al., 1988; Gurnis et al., 1998; Whittaker et al., 2010].Figure 10d indicates that phase velocity remains anomalously high to periods> 200 s, suggesting a subli-thospheric origin, but a fully 3-D inversion is needed to constrain the depth dependence of this featureaccurately. Since the azimuthal path coverage of our data set in this area is nonuniform (section 2.5 andsupporting information Figures S4 and S5), which may translate into larger uncertainties on the phasevelocities for the AAD feature, we do not provide any additional interpretation.

1200 1300 1400 1500 1600 17000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Mantle Potential Temperature (deg C)

Mis

fit (

km/s

)2

HSCMPCM−155kmPCM−Minimums

Pla

te T

hick

ness

(km

)

80

90

100

110

120

130

140

150

50 100 150 2003.8

3.9

4

4.1

4.2

4.3

4.4

4.5

4.6

4.7

Period (s)

Pha

se V

eloc

ity (

km/s

)

4−20 Myr20−52 Myr52−110 Myr110+ Myr

(a) (b)

Figure 9. (a) Minimum misfit at each mantle potential temperature between the pure-path age-dependent phase velocities and the pre-dictions of the best fitting half-space-cooling model (HSCM) and plate-cooling model (PCM). Two sets of results are plotted for the PCM:the minimum misfit at each potential temperature, color-coded by the best fitting plate thickness, and the minimum misfit at each poten-tial temperature with plate thickness 5 155 km, in grey. (b) Comparison of pure-path age-dependent phase velocity (solid lines) with pre-dicted phase velocity from HSCM (dashed lines).

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GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1937

Second, there is an asymmetry in seismic velocity across the Central Indian Ridge at longer periods, withlower velocities to the west of the ridge. While we attribute the anomalously low seismic velocities in theSomali Basin to thick sediments and possibly thickened crust [Coffin and Rabinowitz, 1988; Leinweber et al.,2013; Castelino et al., 2015], we expect the region nearer to the ridge where the asymmetry is observed tobe unaffected by this sedimentary basin further to the west. The asymmetry is also far from the R�eunionhot spot, and the strong asymmetry at long periods implies a source other than thickened crust associatedwith, for example, the nearby Seychelles-Mascarene Plateau (SMP). Furthermore, Ma and Dalton [2017] haveshown that the anomalously low velocities west of the CIR at longer periods are distinct from the low veloc-ities at shorter periods that are clearly associated with the SMP. Asymmetric velocity structure across theridge, with lower wave speeds on the western side, has also been observed at the East Pacific Rise [e.g.,Forsyth et al., 1998; The MELT Seismic Team, 1998; Toomey et al., 1998] and at the Juan de Fuca ridge [Bellet al., 2016]. At the EPR, the asymmetry has been attributed to pressure-driven flow in the asthenosphere,where eastward flow from the Pacific Superswell results in greater melt production beneath the westernridge flank [Conder et al., 2002; Toomey et al., 2002]. At the Juan de Fuca ridge, there is not an obvioussource of eastward asthenospheric flow. Instead, Bell et al. [2016] suggested that the seismic asymmetryresults from a combination of asymmetrical forcing and active upwelling. Katz [2010] showed, using numeri-cal experiments, that allowing for an active (buoyant) component of mantle flow in addition to passive flowat mid-ocean ridges can amplify an imposed asymmetry in density and result in a large asymmetry in man-tle upwelling and melting. Bell et al. [2016] proposed that the Cobb-Eickelberg hot spot along the Juan deFuca ridge could be the source of both the asymmetrical forcing (e.g., higher temperature or wetter compo-sition) and the active upwelling. Ma and Dalton [2017] argued that the asymmetric velocity structure across

Figure 10. Phase velocity perturbations at periods of 50, 100, 150, and 200 s with predicted phase velocity from best fitting half-space-cooling model subtracted, with average removed.

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GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1938

the CIR at periods of 50 and 100 s originates in the mantle and could be produced by pressure-driven flow inthe asthenosphere, which could originate from the hot spots located on the margins of the African LLSVP.

Third, the Rodriguez Triple Junction in the center of our study area is characterized by anomalously highvelocity at all periods. The elevated along-axis wave speeds are visible in the raw phase velocity maps (Fig-ure 6) and become more apparent when the predicted signature due to the HSCM is removed (Figure 10).High shear velocities at the RTJ around 200 km depth have also been observed by Montagner [1986], andhigher velocities at the RTJ than elsewhere along the Indian Ocean ridges are present in global maps of Ray-leigh wave phase speed [e.g., Ekstr€om, 2011]. The question is then whether the high Rayleigh wave speedsreflect anomalous isotropic or radially anisotropic elastic structure in the mantle. Georgen and Lin [2002]used numerical models to simulate mantle flow beneath the RTJ. The model predicted increased rates ofupwelling near the triple junction, and the changes in upwelling rate were found to be largest along theslowest spreading ridge (SWIR). The enhanced upwelling would produce greater alignment of olivine crys-tals in the vertical direction and therefore higher vertically polarized shear-wave speed (VSV), to which Ray-leigh wave phase velocity is most sensitive. We would also expect a corresponding reduction in horizontallypolarized shear-wave velocity (VSH) so that isotropic velocity remains constant. Global maps suggest a slightreduction in along-axis Love wave phase velocity at the RTJ [Ekstr€om, 2011], and global long-wavelengthradially anisotropic shear velocities exhibit lower along-axis VSH/VSV near the RTJ [Kustowski et al., 2008].Both of these observations are suggestive of an anisotropic origin for the anomalous phase velocities at theRTJ. On the other hand, seafloor elevation from which predictions of a half-space-cooling model have beenremoved contains depressed seafloor in the vicinity of the RTJ (Figure 11). This correspondence of anoma-lously high wave speed and deep seafloor suggests that both elastic properties and mantle density and/orcrustal thickness are affected, which may hint at a thermal origin for the observation. For example, reducedtemperatures would lead to greater mantle density, less melting and therefore thinner crust, and higher iso-tropic shear velocity. Determining whether the RTJ anomaly has an isotropic or anisotropic origin willrequire jointly inverting measurements of Rayleigh and Love wave travel time with a sufficiently fine param-eterization that allows small-scale variations in this area to be imaged.

4. Conclusions

We present pure-path age-dependent Rayleigh wave phase velocities and regional Rayleigh wave phasevelocity maps for the Indian Ocean in the period range 38–200 s. The first-order control on phase velocity inthe Indian Ocean upper mantle is seafloor age. Our pure-path age-dependent phase velocities are best

(a) (b)

0˚ 30˚ 60˚ 90˚ 120˚ 150˚

−60˚

−45˚

−30˚

−15˚

0˚

15˚

30˚

−1000 −500 0 500 1000 1500 2000

Res Basement (m)

Figure 11. (a) 100 s phase velocity perturbations from which the HSCM predicted velocities have been subtracted, and the average removed. (b) Residual basement: difference betweenobserved basement depth corrected for sediment loading and predicted basement depth from the half-space-cooling model of Crosby et al. [2006]. Negative values show basementdeeper than would be predicted from half-space-cooling alone. Black indicates residual basement <–1000 m, while white indicates residual basement >2000 m.

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GODFREY ET AL. PHASE VELOCITIES IN THE INDIAN OCEAN 1939

described by allowing the plate thermal structure to evolve according to a half-space-cooling model. Thisresult shows closer similarity of Indian Ocean phase velocities to those in the Pacific, which can be reason-ably well fit by a half-space-cooling model, than to those in the Atlantic, which require a thin plate.

Our 2-D phase velocity maps contain high velocities near the Rodriguez Triple Junction. Numerical modelsof mantle flow at triple junctions suggest that upwelling rates should increase with proximity to the triplejunction [Georgen and Lin, 2002]. The vertical alignment of olivine a-axes that would likely accompany thisflow pattern would increase vertically polarized shear velocity and thus Rayleigh wave phase velocity, pro-viding one possible explanation for our observation. We also note, however, that the seafloor is depressedin the same general area surrounding the triple junction, a correspondence that could point to a thermalorigin for both the seismic and bathymetric observations. Joint analysis of Rayleigh and Love wave phasevelocities must determine whether the anomalous velocities have an isotropic or anisotropic origin.

Asymmetric structure across the Central Indian Ridge, with lower velocities to the west in the period range50–200 s, may be attributed to eastward mantle wind within the asthenosphere.

Our maps resolve high velocities at the Australian-Antarctic Discordance, which have been noted by numer-ous earlier studies, in addition to deviations from age-dependent structure near various hot spots at shortperiods. We note that while our high velocities at the AAD are consistent with earlier results, our maps maybe influenced by poor azimuthal ray path coverage in this area.

Our frequency-dependent Rayleigh wave phase velocity maps are useful for identifying the seismic characteris-tics of this region. A fully 3-D shear velocity model is needed to constrain these seismic structures in depth.

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