Geophysical Journal InternationalGeophys. J. Int. (2015) 203, 327–333 doi: 10.1093/gji/ggv300

GJI Seismology

Unraveling overtone interferences in Love-wave phase velocitymeasurements by radon transform

Yinhe Luo,1,2,3 Yingjie Yang,3 Kaifeng Zhao,1 Yixian Xu1,2,3 and Jianghai Xia1

1Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, Hubei 430074,China. E-mail: luoyinhe@cug.edu.cn2State Key Laboratory of Geological Processes and Mineral Resources, China University of Geosciences, Wuhan, Hubei 430074, China3ARC Centre of Excellence for Core to Crust Fluid Systems (CCFS)/GEMOC, Department of Earth and Planetary Sciences, Macquarie University, NorthRyde, NSW 2109, Australia

Accepted 2015 July 15. Received 2015 July 14; in original form 2015 March 18

S U M M A R YSurface waves contain fundamental mode and higher modes, which could interfere with eachother. If different modes are not properly separated, the inverted Earth structures using surfacewaves could be biased. In this study, we apply linear radon transform (LRT) to syntheticseismograms and real seismograms from the USArray to demonstrate the effectiveness ofLRT in separating fundamental-mode Love waves from higher modes. Analysis on syntheticseismograms shows that two-station measurements on reconstructed data obtained after modeseparation can completely retrieve the fundamental-mode Love-wave phase velocities. Resultson USArray data show that higher mode contamination effects reach up to ∼10 per cent fortwo-station measurements of Love waves, while two-station measurements on mode-separateddata obtained by LRT are very close to the predicted values from a global dispersion modelof GDM52, demonstrating that the contamination of overtones on fundamental-mode Love-wave phase velocity measurements is effectively mitigated by the LRT method and accuratefundamental-mode Love-wave phase velocities can be measured.

Key words: Surface waves and free oscillations; Seismic tomography; Computationalseismology.

1 I N T RO D U C T I O N

Surface waves propagate along the shallow depth of the Earth withenergy penetrating into the Earth’s crust and mantle, and are par-ticularly useful for imaging crustal and upper mantle structures.Surface waves at different periods are sensitive to the Earth’s struc-tures at different depths with longer period surface waves sensitiveto greater depths, resulting in observed dispersion in surface-wavepropagation. Generally, surface waves, including both Rayleigh andLove waves, contain fundamental mode and higher modes, whichcould interfere with each other. Different modes of surface waveshave completely different sensitivities to the Earth’s structures. Ifthey are not properly separated, the inverted Earth structures usingsurface waves could be biased.

Most surface-wave tomography studies use dispersion curves offundamental mode in imaging because the fundamental modes ofboth Rayleigh and Love waves usually have much stronger en-ergy than higher modes and dominate seismograms. One chal-lenge in surface-wave tomography is to accurately measure thefundamental-mode phase velocities and avoid the contamination byovertones. Because energy of fundamental-mode Rayleigh waves

often dominates seismograms and their group velocity dispersioncurve is completely separated from overtone dispersion curves,fundamental-mode and overtone Rayleigh waves usually tend tobe well separated in vertical- and radial-component seismograms inregional and continental scale studies. However, the situation is dif-ferent for Love waves. The group velocities of fundamental-modeand overtone Love waves are very close to each other (Fig. 1); andfundamental-mode and overtone Love waves severely interfere witheach other, especially for waves propagating through ocean basins(e.g. Thatcher & Brune 1969; Forsyth 1975; Nettles & Dziewonski2011).

Recent studies (e.g. Nettles & Dziewonski 2011; Foster et al.2014b) have shown that, although predicted errors from overtoneinterference in single-station fundament-mode Love-wave phase ve-locity measurements are less than 1 per cent, errors of contaminationare much larger in two-station and array-based measurements: upto ∼10 per cent for two-station measurements and ∼20 per centfor array-based measurements (Foster et al. 2014b). These largeerrors are induced because two-station and array-based measure-ments are obtained from differential measurements of individualsingle-station measurements over short distances and errors caused

C© The Authors 2015. Published by Oxford University Press on behalf of The Royal Astronomical Society. 327

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Figure 1. Love-wave phase and group velocity dispersion curves calculatedfor an oceanic-plate model. The seismic structure of the oceanic-plate modelis constructed by placing an oceanic crustal structure A0 (Mooney et al.1998; Bassin et al. 2000) over the PREM mantle (Dziewonski & Anderson1981). Black lines, red lines, blue lines, yellow lines and grey lines showdispersion curves for fundamental-mode, first overtone, second overtone,third overtone and fourth overtone Love waves, respectively.

by overtone contaminations are expected to be magnified in two-station/array-based phase velocity measurements. The large errorsare present in all array-based methods if the fundamental modes arenot properly separated from higher modes (Foster et al. 2014b).

In the past two decades, more and more regional arrays aredeployed around the world to image high-resolution regional-scale lithosphere structures, and seismologists are measuringfundamental-model phase velocities from both Rayleigh and Lovewaves using two-station and array-based methods and combiningthem to invert for anisotropy of lithosphere. Several methods havebeen used to reduce the effect of overtone interference (e.g. Cara1973; Forsyth 1975; Herrin & Goforth 1977, 1979; Okal & Jo1987; Montagner & Tanimoto 1991; Stutzmann & Montagner 1993;Trampert & Woodhouse 1995, 1996, 2001, 2003; van Heijst &Woodhouse 1997, 1999; Montagner 2002; Yoshizawa & Kennett2002; Beucler et al. 2003; Lebedev et al. 2005; Beucler & Montag-ner 2006; Visser et al. 2007, 2008); the concepts of these methodshave been well summarized by Foster et al. (2014b). However,to date, few methods are effective in separating fundamental-modeLove waves from higher modes in two-station and array-based mea-

surements due to the overlap of group velocities at intermediate andlong periods (∼20 to ∼100 s).

In this study, we present a method which applies high-resolutionlinear radon transform (LRT) to teleseismic surface waves to sepa-rate fundamental-mode Love waves from higher modes. We analyseboth synthetic seismograms and observed seismograms from theUSArray to demonstrate the effectiveness of our method in mitigat-ing overtone interferences in two-station measurements.

2 M E T H O D

Due to overlapped group velocities of fundamental-mode and over-tone Love waves, one cannot directly inspect and separate the fun-damental mode from overtones in time domain. However, we canrecognize and pick different modes in its period–phase-velocity (p–v) domain because the fundamental mode and overtones of Lovewaves have separated phase velocity dispersion branches (Fig. 1a).It is possible to reduce overtone contamination if we can transformseismograms in time domain to the p–v domain and then isolatedifferent modes in the p–v domain and re-transform them back tothe time domain.

Luo et al. (2008, 2009) has developed a method to imageRayleigh-wave dispersive energy and separate multimode Rayleighwaves from a multichannel record by high-resolution LRT in near-surface applications. In this study, we apply the LRT to intermediate-and long-period Love waves that are used to constrain lithosphericstructures.

The forward LRT maps the radon panel m (in the frequency–slowness (f–s) domain) into the data space d (seismograms in thefrequency–epicentral distance (f–x) domain) under the action of theoperator L = ei2π f px ,

d = Lm (1)

in which p is the slowness (pmin and pmax being the range of slownessvalues investigated), and x is the epicentral distance between sourceand station (xmin and xmax being the epicentral distance range).Casting the radon transform as an inversion problem, m can beobtained by choosing an L1 norm for the model and an L2 normfor the data misfit. So m can be defined by solving the system ofequation (Trad et al. 2002, 2003):(W−T

m LT WTd WdLW−1

m + λI)

Wmm = W−Tm LT WT

d Wdd, (2)

where I denotes the identity matrix, Wd is a matrix of data weights,Wm is a matrix of model weights, and λ is the trade-off parameterthat controls balance between data misfit and model constraints.Small λ will allow minimum data misfit

∥∥Wd(d − LW−1

m Wmm)∥∥2

and large one will allow smoothness model ‖Wmm‖2. Eq. (2) can besolved very efficiently by conjugate gradient (CG) algorithm (e.g.Sacchi & Porsani 1999; Trad et al. 2002, 2003). Although LRT hasbeen widely applied to high-frequency industry seismic data, Wilson& Guitton (2007) have demonstrated that this method can also beapplied to teleseismic data and there are no fundamental differencesbetween low-frequency and high-frequency applications.

The processing flow of LRT includes the following two steps.First, we image dispersive energy by high-resolution LRT. We selectseismograms from a common earthquake and recorded by a num-ber of stations with their propagating great-circle paths all fallingin a small (3◦ in this study) azimuthal bin. According to eq. (1), wetransform the seismograms in time domain to the frequency domainand set the slowness p ranging from 0.2 to 0.4 s km−1 (equivalentphase velocity from 2.5 to 5 km s−1). LRT is performed for each

Unraveling Love wave overtone interferences 329

frequency slice using a weighted preconditioned CG algorithm fol-lowing eq. (2). After that, we obtain the radon panel in the f–sdomain. Linear interpolation is used to transform the radon panelfrom the f–s domain to the p–v domain. At least six stations are re-quired in imaging dispersive energy by LRT (Dal Moro et al. 2003;Luo et al. 2008). Second, we perform mode separation. The energyof fundamental mode is selected manually and the rest energy ismuted in the p–v domain, leaving the radon panel only contain-ing the fundamental mode of surface waves. Then, we apply theforward radon operator to the radon panel that only contains thefundamental-mode surface waves and finally obtain seismogramsonly containing fundamental-mode surface waves.

3 A P P L I C AT I O N T O S Y N T H E T I C DATA

To demonstrate the effectiveness of LRT in separating fundamental-mode Love waves from higher modes, we first apply this methodto synthetic Love waves at 20–150 s periods in which period bandLove waves are most sensitive to crustal and upper mantle structuresand have the severest interferences between the fundamental modeand higher modes.

To generate synthetic Love waves, we choose a model for a typi-cal oceanic plate, similar to the one used by Nettles & Dziewonski(2011), because the fundamental-mode and higher mode Lovewaves propagating across a oceanic plate have overlapped group ve-locities as shown in Fig. 1. The oceanic-plate model is designed asone having a type A0 crust (Mooney et al. 1998; Bassin et al. 2000)underlain by a mantle of the Preliminary Reference Earth Model(PREM; Dziewonski & Anderson 1981). The calculated Love-wavephase and group velocity dispersion curves for this model are shownin Fig. 1. In 25–80 s period range, the fundamental-mode and highermode group velocities overlap with each other, leading to strong-mode interference between fundamental-mode and higher modeLove waves.

We compute synthetic seismograms by normal-mode summation(Gilbert & Dziewonski 1975) for surface waves which are emit-ted by a shallow strike-slip earthquake and propagate through theoceanic-plate model. A Love-wave seismogram can be representedas a sum of N dispersed surface-wave mode branches (n = 0, 1,2, . . . , N). Synthetic seismograms are computed using the programof Modal Summation from the package of Computer Programs inSeismology (Herrmann & Ammon 2004). The selected receivers,from which synthetic seismograms are obtained, are located alonga great-circle path and have the corresponding epicentral distancesranging from 20◦ to 150◦ and a 0.5◦ interval in the direction ofmaximum Love-wave radiation. Two Love-wave synthetic data setsare computed: one with only the fundamental mode and the otherincluding fundamental and the first four higher modes, with theamplitude ratio of 1:0.6:0.3:0.3:0.3 between those five modes. Twoexamples of synthetic seismograms are plotted in Fig. 2(b), and arecord section of all synthesized data is plotted in Fig. 2(c). Clearinterference between those five modes can be noted from the differ-ences of waveforms for these two data sets (Fig. 2b).

We apply the LRT to those synthetic seismograms containing bothfundamental mode and four overtones to obtain dispersive energyin the p–v domain, which is plotted in Fig. 2(a). Clear energy offundamental mode and four overtones are seen in the p–v domainwith the phase velocity dispersion curves well separated from eachother. To isolate the fundamental mode, we manually select thefundamental-mode dispersive energy in a corridor outlined by thered dashed lines in Fig. 2(a) and mute the rest energy (Fig. 2a),

leaving the radon panel only containing the fundamental-mode Lovewaves. We then apply the forward LRT (eq. 1) to the radon panelto reconstruct the fundamental-mode Love waves. Two examples ofthe reconstructed seismograms after model separation are plottedagainst the synthetic seismograms of fundamental Love waves forcomparison in Fig. 2(b). Apparently, the reconstructed seismogramsare almost exactly the same as those fundamental-mode syntheticseismograms, indicating that the LRT works perfectly in separatingthe fundamental mode from higher modes for synthetic data.

Furthermore, we use a two-station method (e.g. Yao et al. 2006) tomeasure the interstation phase velocities between a pair of stations.For the two-station method to work, we ensure the earthquake andthe station pair are approximately aligned in a same great-circlepath (less than 3◦ in azimuth) to cancel the effects of both thesource and structures outside the station pairs on the traveltimedifference. The interstation phase velocity is obtained by calculatingC(T ) = �D/�t(T ), where C(T) is the phase velocity at period T,�D is interstation distance and �t(T ) is the interstation phasetraveltime difference that is estimated from cross-correlation ofnarrow bandpass filtered waveforms at a central period T. Fig. 2(d)shows the results of the two-station phase velocity measurementsfor the two synthetic data sets and the reconstructed seismogramsobtained after mode separation at 75 s period, plotted as deviationsfrom the theoretical fundamental-mode Love-wave phase velocities(black line in Fig. 1a) as a function of the epicentral distance of thetwo-station midpoint.

The two-station measurements on the synthetic fundamental-mode-only seismograms show very small deviations (<0.02 percent) from the theoretical value. The interference from higher modescould either delay or advance the apparent phase velocity of thefundamental mode, thus introducing oscillating pattern of phasevelocity deviations (Boore 1969). The two-station measurementson the synthetic seismograms that have both fundamental mode andfour higher modes show oscillating deviations. The deviations varyfrom −16.3 per cent to 15.2 per cent for 75 s Love waves, reflect-ing severe overtone interference in measuring fundamental-modeLove-wave phase velocities. The two-station measurements on thereconstructed seismograms after model separation are very closeto the theoretical fundamental-mode phase velocities, indicatingthat overtone interference on fundamental-mode Love waves can beperfectly mitigated after mode separation by high-resolution LRT.

4 A P P L I C AT I O N T O U S A R R AY DATA

Having applied LRT to synthetic data, in this section, we fur-ther demonstrate the effectiveness of this method in separatingfundamental-mode Love waves from higher modes by applying thismethod to real Love waves recorded by USArray.

For demonstration, we select three teleseismic events (Fig. 3a)with surface-wave magnitudes larger than 5.0 and epicentral dis-tances from 35◦ to 65◦ relative to the stations we select from US-Array. We collect the two horizontal components of seismogramsrecorded by USArray and then rotate them to the transverse andradial components. We isolate Love-wave seismograms from thetransverse components using a time window of Love waves definedby group velocities of 3–6 km s−1. At last, the mean, trend andinstrument responses are removed from the seismograms. We usethe same two-station method as used for the synthetic data to mea-sure interstation phase velocities. Because the two-station methodis based on the principle that the two stations and the event mustalign nearly along a common great-circle path, we only select those

330 Y. Luo et al.

Figure 2. (a) Dispersive energy in the p–v domain generated by high-resolution LRT. The two red dashed lines outline energy range of the selected fundamentalmode. (b) Comparison of two examples of seismograms recorded at 60◦ and 80◦ epicentral distances between synthetic data (the black one contains bothfundamental mode and four overtones, and the dashed blue line only contains fundamental-mode Love waves) and reconstructed data after mode separation (inred). (c) Synthetic seismograms containing the fundamental mode and the first four higher modes (an amplitude ratio of 1:0.6:0.6:0.6:0.6) are calculated bynormal-mode summation for a shallow strike-slip earthquake. (d) The differences of measured phase velocities relative to the theoretical ones at 75 s, plottedas a function of the epicentral distance of the two-station midpoint. The red circles, black crosses and blue diamonds represent the velocities measured fromfundamental-mode-only synthetic seismograms, synthetic seismograms containing both the fundamental mode and four overtones, and reconstructed data aftermodel separation, respectively.

station pairs with the differences of their azimuth angles smallerthan 3◦ and their interstation distances ranging from 350 to 750 km.

To investigate the overtone interference, we compare two-stationphase velocity measurements, including two sets of measurementsobtained from Love waves before and after LRT mode separation,respectively, with those phase velocities calculated from the GlobalDispersion Model GDM52 (Ekstrom 2011). The GDM52 is a modelof global dispersion maps for fundamental-mode Rayleigh and Lovewaves in a period range of 25 to 250 s. The data used in constructingthis model are collected from globally distributed seismic stationsand earthquakes. As demonstrated by Foster et al. (2014b), overtonecontaminations on the single-station measurements of fundamental-mode Love waves are typically oscillating in the range of ±1 percent and are averaged out in tomography with measurements fromvarious paths with different epicentral distances, that is, the globalLove-wave dispersion maps of the GDM52 model are almost free ofovertone contaminations. Thus, if the fundamental-mode dispersioncurves of Love waves measured from USArray data are accurate,these measurements should be close to the reference values fromGDM52.

We apply the LRT to the transverse components of seismogramsto separate the fundamental-mode Love waves as we do for thesynthetic seismograms and then measure the interstation phase ve-locities using the two-station method. To visualize the effectivenessof LRT in separating fundamental-mode Love waves from highermodes, as an example, we plot the dispersive energy in the p–vdomain in Fig. 3(e) for Event C as we do for the synthetic datain Fig. 2(a). Clear energy of fundamental mode and overtones isseen in the p–v domain (Fig. 3e) with their phase velocity dis-persion curves separated from each other. Love-wave seismogramsbefore and after mode separation are plotted together in Fig. 3(f)for comparison for two examples from stations TA-F12A and TA-B11A. Large differences of waveform between original waveformand fundamental-mode Love waves are observed, indicating stronginterferences of fundamental mode and higher modes.

Figs 3(b)–(d) show the two-station phase velocity measurementsfor all selected station pairs with and without the mode separa-tion, plotted as deviations from the reference values from GDM52.We only plot the deviations at certain periods (34 s for Event A,Fig. 3b; 30 s for Event B, Fig. 3c; 70 s for Event C, Fig. 3d) where

Unraveling Love wave overtone interferences 331

Figure 3. Two-station phase velocity measurements of original (black cross) and mode-separated (blue diamond) Love waves for three selected teleseismicevents. The selected stations of USArray for two-station measurements are colour coded for the three events and plotted in (a). The two-station measurementsfor event A, B and C are plotted as a function of the epicentral distances of two-station midpoints in (b), (c) and (d), respectively. The measurements are plottedas deviations relative to the interstation phase velocities predicted from GDM52. The interstation distances of these two-station measurements range from 350to 750 km. (e) Dispersive energy of Event C in the p–v domain. The dispersive energy is constructed by high-resolution LRT for Love waves recorded by theTA stations shown as blue in (a). The two red dashed lines outline the energy range of the selected fundamental mode. (f) Comparison of seismograms (filteredin the period band from 25 to 80 s) between original waveforms (in black) and reconstructed fundamental-mode waveforms (in red) for two examples recordedat stations TA-F12A and TA-B11A.

332 Y. Luo et al.

the fundamental-mode Love waves are most severely contaminatedby higher modes. Two-station phase velocity measurements fromthe original Love waves without mode separation scatter around thereference values roughly within ±10 per cent range. The ranges ofdeviations are similar to those two-station measurements shown byFoster et al. (2014b), which is believed to be caused by contamina-tion of higher modes.

Love-wave phase velocity deviations could be also caused byother factors, including off-great-circle propagation (Alsina et al.1993; Foster et al. 2014a) and finite-frequency propagation effects(e.g. de Vos et al. 2013). Foster et al. (2014a) have found that, forthose events we choose in this study, the errors of phase velocitiesat 15–100 s periods caused by the deviations from the off-great-circle propagation fall in the range ±1 per cent, which is consistentwith the results of Alsina et al. (1993) for surface waves travel-ling through oceanic paths into European continents. Regardingfinite-frequency effects, De Vos et al. (2013) have indicated that,for two-station phase velocity measurements, although sensitivityalong the interstation path is dominant, there is still considerablesensitivity far outside the interstation path. Furthermore, they sug-gest that, in order for the two-station method to work, one needsto only choose those station pairs for which there are no stronganomalies at the regions located outside the interstation paths butclose to the station with shorter epicentral distance. In this study,three chosen oceanic events first pass through oceanic plates andthen propagate into the US continent where phase velocity anoma-lies at our interested periods (34 s for Event A; 30 s for Event B;70 s for Event C) are small, about only 5 per cent according to Jin &Gaherty (2015). Thus, we consider that the finite-frequency effectoutside the interstation paths on the phase velocity measurementsshould be much smaller than the observed 10 per cent deviations.Thus, we consider that the large deviations are mainly caused bycontamination by higher modes, which is expected for Love wavespropagating through oceanic plates and testified by the dramaticreduction of deviations after mode separation.

After LRT is applied to separating the fundamental mode fromovertones, the two-station phase velocity measurements from thereconstructed seismograms are very close to the reference values.The deviations mostly vary in the ±1 per cent ranges (Fig. 3). Themeans of deviations are only 0.60 per cent, 0.74 per cent and 0.72per cent with standard deviations of 0.26 per cent, 0.43 per cent and0.32 per cent for the three chosen events, respectively. These smalldifferences are reasonable and could be caused by the presenceof small-scale phase velocity heterogeneities which are not wellmapped in the GDM52 model based on globally distributed stationsand earthquakes, or the off-great-circle path propagation and finite-frequency effect which are not taken into account in our calculation.

Overall, the strong reduction of deviations of these two-stationmeasurements relative to GDM52 after mode separation againdemonstrates the effectiveness of LRT in separating fundamental-mode Love waves from higher modes.

5 D I S C U S S I O N A N D C O N C LU S I O N S

Love-wave seismograms often contain both fundamental modeand higher modes. Measurements of fundamental-mode Love-wavephase velocities are affected by the presence of overtones. In thesecases, seismograms need to be inspected prior to the analysis anddesired mode of surface waves need to be separated before mea-suring phase velocities. Because group velocities of fundamental-mode Love waves and overtones overlap at certain period ranges,

it is impossible to separate them in time domain. This study hasdemonstrated that by converting time domain seismograms to thep–v domain using radon transformation, we can recognize and pickdifferent modes because phase velocity dispersion curves of differ-ent modes are separated from each other (Fig. 1a). Furthermore,we can isolate the fundamental mode out and then accurately mea-sure fundamental-mode Love-wave phase velocities, mitigating theovertone interference in Love-wave tomography.

It should also be mentioned that properly constructing and sep-arating fundamental-mode surface waves in the radon panel of thep–v domain is the key step in performing mode separation. In con-structing the p–v domain, seismograms collected from a number ofstations for each event must have similar propagation characteris-tics. This requirement is apparently satisfied for a group of stationslocated in a small region and recording teleseismic events. How-ever, in some circumstances where there are very strong horizon-tal and/or vertical velocity variations, phase velocities of differentsurface-wave modes could overlap and interfere with each other inthe p–v domain so that it is difficult to separate fundamental-modesurface waves from seismograms by high-resolution LRT. Eventhough these cases are rare in regional surface-wave tomographyusing teleseismic events, great efforts should be taken to examinedispersion curves of different modes and S-wave velocity structuresto properly carry out mode separation.

In this paper, although we only demonstrate the effectiveness ofLRT in separating fundamental-mode Love waves using two-stationmethod, LRT can also be applied to array-based measurements.The principle of applying LRT to a seismic array is similar to theapplication to the two-station measurements. For example, for alarge seismic array like USArray, we can first divide the large arrayto a series of mini arrays with several hundred kilometre aperture,and then apply LRT to surface waves recorded at each mini array toseparate the fundamental mode because teleseismic surface wavesrecorded in a mini array have similar propagation paths and meetthe requirement for LRT.

A C K N OW L E D G E M E N T S

We thank the editors Jeannot Tramper and Kazunori Yoshizawaand an anonymous reviewer for their constructive comments andsuggestions on this work. All the seismic data used in this studyare obtained from the IRIS Data Management System and specif-ically the IRIS Data Management Center. YL’s work is supportedby the National Science Foundation of China (NSFC, #41374059),Seismic Professional Science Foundation (2014419013) and theSpecial Fund for Basic Scientific Research of Central Colleges,China University of Geosciences (Wuhan) (#CUG090106 and#CUGL100402). YY is supported by Australian Research Coun-cil Discovery grants (DP120102372 and DP120103673) and Fu-ture Fellowship (FT130101220). This is contribution 656 fromthe ARC Centre of Excellence for Core to Crust Fluid Systems(http://www.ccfs.mq.edu.au) and 1027 in the GEMOC Key Centre(http://www.gemoc.mq.edu.au).

R E F E R E N C E S

Alsina, D., Snieder, R. & Maupin, V., 1993. A test of the great circle ap-proximation in the analysis of surface waves, Geophys. Res. Lett., 20(10),915–918.

Bassin, C., Laske, G. & Masters, G., 2000. The current limits of resolutionfor surface wave tomography in North America, EOS, Trans. Am. geophys.Un., 81, Fall Meet. Suppl., F897.

Unraveling Love wave overtone interferences 333

Beucler, E. & Montagner, J.-P., 2006. Computation of large anisotropicseismic heterogeneities, Geophys. J. Int., 165, 447–468.

Beucler, E., Stutzmann, E. & Montagner, J.-P., 2003. Surface wave higher-mode phase velocity measurements using a roller-coaster-type algorithm,Geophys. J. Int., 155(1), 289–307.

Boore, D., 1969. Effect of higher mode contamination on measured Lovewave phase velocities, J. geophys. Res., 74(27), 6612–6616.

Cara, M., 1973. Filtering of dispersed wave trains, Geophys. J. R. astr. Soc.,33, 65–80.

Dal Moro, G., Pipan, M., Forte, E. & Finetti, I., 2003. Determination ofRayleigh wave dispersion curves for near surface applications in uncon-solidated sediments, in Technical Program with Biographies, SEG, 73rdAnnual Meeting, Dallas, TX, pp. 1247–1250.

de Vos, D., Paulssen, H. & Fichtner, A., 2013. Finite-frequency sensitiv-ity kernels for two-station surface wave measurements, Geophys. J. Int.,194(2), 1042–1049.

Dziewonski, A. & Anderson, D., 1981. Preliminary reference Earth model(PREM), Phys. Earth planet. Inter., 25, 289–325.

Ekstrom, G., 2011. A global model of Love and Rayleigh surface wavedispersion and anisotropy, 25–250 s, Geophys. J. Int., 187, 1668–1686.

Forsyth, D., 1975. A new method for the analysis of multi-mode surface wavedispersion: application to Love-wave propagation in the East Pacific, Bull.seism. Soc. Am., 65, 323–342.

Foster, A., Ekstrom, G. & Nettles, M., 2014a. Surface-wave phase velocitiesof the western United States from a two-station method, Geophys. J. Int.,196(2), 1189–1206.

Foster, N., Nettles, M. & Ekstrom, G., 2014b. Overtone interference inarray-based Love-wave phase measurements, Bull. seism. Soc. Am., 104,2266–2277.

Gilbert, F. & Dziewonski, A.M., 1975. Application of normal-mode theoryto retrieval of structural parameters and source mechanisms from seismicspectra, Phil. Trans. R. Soc. Lond., A, 278, 187–269.

Herrin, E. & Goforth, T., 1977. Phase-matched filters: application to thestudy of Rayleigh waves, Bull. seism. Soc. Am., 67, 1259–1275.

Herrin, E. & Goforth, T., 1979. Phase-matched filters: application to thestudy of Love waves, Bull. seism. Soc. Am., 69(1), 27–44.

Herrmann, R.B. & Ammon, C.J., 2004. Surface Waves, Receiver Func-tions and Crustal Structure, in Computer Programs in Seismology, Ver-sion 3.30 [electronic], Saint Louis Univ., St. Louis, MO. Available at:http://www.eas.slu.edu/People/RBHerrmann/CPS330.html, last accessed10 October 2014.

Jin, G. & Gaherty, J.B., 2015. Surface wave phase-velocity tomographybased on multichannel cross-correlation, Geophys. J. Int., 201(3), 1383–1398.

Lebedev, S., Nolet, G., Meier, T. & van der Hilst, R.D., 2005. Automatedmultimode inversion of surface and S waveforms, Geophys. J. Int., 162,951–964.

Luo, Y., Xia, J., Miller, R.D., Xu, Y., Liu, J. & Liu, Q., 2008. Rayleigh-wavedispersive energy imaging by high-resolution linear Radon transform,Pure appl. Geophys., 165, 903–922.

Luo, Y., Xia, J., Miller, R.D., Xu, Y., Liu, J. & Liu, Q., 2009. Rayleigh-wavemode separation by high-resolution linear Radon transform, Geophys. J.Int., 179(1), 254–264.

Montagner, J.-P., 2002. Upper mantle low anisotropy channels below thePacific Plate, Earth planet. Sci. Lett., 202, 263–274.

Montagner, J.-P. & Tanimoto, T., 1991. Global upper mantle tomography ofseismic velocities and anisotropies, J. geophys. Res., 96(B12), 20 337–20 351.

Mooney, W.D., Laske, G. & Masters, G., 1998. CRUST 5.1: a global crustalmodel at 5◦ × 5◦, J. geophys. Res., 103, 727–747.

Nettles, M. & Dziewonski, A.M., 2011. Effect of higher-mode interferenceon measurements and models of fundamental-mode surface-wave disper-sion, Bull. seism. Soc. Am., 101(5), 2270–2280.

Okal, E.A. & Jo, B.-G., 1987. Stacking investigations of the dispersionof higher order mantle Rayleigh waves and normal modes, Phys. Earthplanet. Inter., 47, 188–204.

Sacchi, M. & Porsani, M., 1999. Fast high resolution parabolic RT, in69th Annual International Meeting, Society of Exploration Geophysicists,Expanded Abstracts, Houston, TX, pp. 1477–1480.

Stutzmann, E. & Montagner, J.-P., 1993. An inverse technique for retrievinghigher mode phase velocity and mantle structure, Geophys. J. Int., 113,669–683.

Thatcher, W. & Brune, J.N., 1969. Higher mode interference and observedanomalous apparent Love wave phase velocities, J. geophys. Res., 74(27),6603–6611.

Trad, D., Ulrych, T. & Sacchi, M., 2002. Accurate interpolation with high-resolution time-variant radon transforms, Geophysics, 67(2), 644–656.

Trad, D., Ulrych, T. & Sacchi, M., 2003. Latest views of the sparse Radontransform, Geophysics, 68, 386–399.

Trampert, J. & Woodhouse, J.H., 1995. Global phase velocity maps of Loveand Rayleigh waves between 40 and 150 seconds, Geophys. J. Int., 122,675–690.

Trampert, J. & Woodhouse, J.H., 1996. High resolution global phase velocitydistributions, Geophys. Res. Lett., 23(23), 21–24.

Trampert, J. & Woodhouse, J.H., 2001. Assessment of global phase velocitymodels, Geophys. J. Int., 144, 165–174.

Trampert, J. & Woodhouse, J.H., 2003. Global anisotropic phase velocitymaps for fundamental mode surface waves between 40 and 150 s, Geo-phys. J. Int., 154, 154–165.

van Heijst, H.J. & Woodhouse, J.H., 1997. Measuring surface-wave overtonephase velocities using a mode branch stripping technique, Geophys. J. Int.,131, 209–230.

van Heijst, H.J. & Woodhouse, J., 1999. Global high-resolution phase ve-locity distributions of overtone and fundamental-mode surface wavesdetermined by mode branch stripping, Geophys. J. Int., 137, 601–620.

Visser, K., Lebedev, S., Trampert, J. & Kennett, B.L.N., 2007. GlobalLove wave overtone measurements, Geophys. Res. Lett., 34, L03302,doi:10.1029/2006GL028671.

Visser, K., Trampert, J., Lebedev, S. & Kennett, B.L.N., 2008. Probabilityof radial anisotropy in the deep mantle, Earth planet. Sci. Lett., 270,241–250.

Wilson, C. & Guitton, A., 2007. Teleseismic wavefield interpolation andsignal extraction using high-resolution linear radon transforms, Geophys.J. Int., 168, 171–181.

Yao, H., van der Hilst, R.D. & de Hoop, M.V., 2006. Surface-wave ar-ray tomography in SE Tibet from ambient seismic noise and twostationanalysis – I. Phase velocity maps, Geophys. J. Int., 166(2), 732–744.

Yoshizawa, K. & Kennett, B., 2002. Non-linear waveform inversion forsurface waves with a neighbourhood algorithm–application to multimodedispersion measurements, Geophys. J. Int., 149, 118–133.