Multiple seismic reflectors in Earth s lowermost mantlesshim5/group/Dan_Shim_-_Research_Site... · 2014. 3. 2. · Multiple seismic reflectors in Earth’s lowermost mantle Xuefeng

Multiple seismic reflectors in Earth’s lowermost mantleXuefeng Shanga,1, Sang-Heon Shimb, Maarten de Hoopc, and Robert van der Hilsta

aDepartment of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139; bSchool of Earth and SpaceExploration, Arizona State University, Tempe, AZ 85287; and cDepartment of Mathematics, Purdue University, West Lafayette, IN 47907

Edited by Barbara A. Romanowicz, University of California, Berkeley, CA, and approved January 10, 2014 (received for review July 4, 2013)

The modern view of Earth’s lowermost mantle considers a D″ re-gion of enhanced (seismologically inferred) heterogeneity boundedby the core–mantle boundary and an interface some 150–300 kmabove it, with the latter often attributed to the postperovskitephase transition (in MgSiO3). Seismic exploration of Earth’s deepinterior suggests, however, that this view needs modification. So-called ScS and SKKS waves, which probe the lowermost mantlefrom above and below, respectively, reveal multiple reflectors be-neath Central America and East Asia, two areas known for subduc-tion of oceanic plates deep into Earth’s mantle. This observation isinconsistent with expectations from a thermal response of a singleisochemical postperovskite transition, but some of the newly ob-served structures can be explained with postperovskite transitionsin differentiated slab materials. Our results imply that the lower-most mantle is more complex than hitherto thought and that inter-faces and compositional heterogeneity occur beyond the D″ regionsensu stricto.

seismic imaging | mineral physics | mantle convection

The lowermost mantle, extending several hundred kilometersabove the ∼2,900-km-deep core–mantle boundary (CMB), is

of considerable interest because it includes the boundary layer ofthermochemical mantle convection across which heat is con-ducted from the core into the mantle. Almost three decades afterthe detection of an interface some 150–300 km above the CMB(1), the base of the mantle is still a challenging target for cross-disciplinary research. Both the seismic discontinuity that marksthe top of the so-called D″ region (1) and the heterogeneitybelow it (2, 3) have been attributed to a perovskite (Pv) topostperovskite (pPv) transition in the dominant mantle silicate (4–8), and this association has inspired estimation of temperaturesabove and heat flux across the CMB (9, 10). The D″ interfaceremains enigmatic, however, and recent high pressure–temperatureexperiments suggest that seismic observations concerning its depthand thickness are inconsistent with those expected for a pPv tran-sition unless the chemical composition of the regions where theyoccur differs significantly from standard bulk composition modelssuch as pyrolite (11–13). The transition thickness could be recon-ciled with nonlinearity in the phase fraction profile (11) or latticepreferred orientation in pPv (14), but the depth is a concern be-cause the pPv transition pressure in pyrolite may be too high for itto occur in the lower mantle (13). Candidate compositions fora seismically detectable pPv transition at mantle pressures includemidoceanic ridge basalt (MORB) and harzburgite components ofsubducted and differentiated oceanic lithosphere. Furthermore,silica may transform from modified stishovite to seifertite in Si-richparts of the lowermost mantle (15). Inspired by these results, wesearch for multiple interfaces in and above the conventional D″region, using seismic waves that sample the lowermost mantle be-neath geographic regions where seismic tomography and platehistories suggest that deep subduction is likely.

Deep Earth Exploration SeismologyFor large-scale seismic exploration of the Earth’s lowermostmantle, we adapted a 3D inverse scattering technique, a gener-alized Radon transform (GRT), from its original use in con-trolled-source hydrocarbon exploration to imaging with ScS andSKKS waves emitted by naturally occurring earthquakes (Fig. 1,

Left; Fig. S1). The GRT can extract subtle signals from largevolumes of waveform data and facilitate the discovery of hithertounknown structures because it does not rely on priori assump-tions about the location or shape of geological targets. Themethod applied here, an improved version of what we used inour previous studies (16, 17), is summarized in the SI Text S1.The ScS and SKKS waveform data are entirely independent, in

that they are associated with different source-receiver combi-nations, they sample the mantle (and core) along different prop-agation paths, they arrive in different time windows, and theyconcern different wave polarizations and, thus, sensitivities toanisotropy. We have shown that despite these differences, theyyield similar images of the first-order structural features found inthe lowermost 400 km of the mantle beneath Central America (16,17), where inferred depth variations of the presumed D″ reflectorcorrelate with tomographic wave speed anomalies (10, 18, 19).We search for impedance contrasts up to 600 km above the

CMB beneath two geographical areas that are well sampled byScS or SKKS (Fig. 1, Left) and where subduction has occurred forhundreds of millions of years. The first area is Central America(Fig. 1, Upper Right, and Fig. 2, Right), which has long beena typical locality for studies of deep subduction of the Farallonplate (20–24) and D″ imaging with ScS waves (2, 3, 10, 25, 26).The second is East Asia, which is well sampled by SKKS waves(Fig. 1, Lower Right) and where tomography (20–23) reveals alarge, high-speed anomaly (Fig. 2, Left), presumably produced bydeep subduction of the Izanagi and Pacific plates from the eastand the Tethys and Indo-Australian plates from the south(21, 23). The lowermost mantle beneath East Asia is also sam-pled by ScS, but the available distance and azimuth ranges arenot sufficient for accurate GRT imaging.For Central America, we used (approximately) 130,000 ScS

traces from 1,900 earthquakes [body wave magnitude (mb) > 5.0;

Significance

Deep in the Earth’s interior, the region just above the core–mantle boundary exerts control on mantle convection and heatloss from the core. It has long been thought that the so-calledD″ region is separated from a more uniform mantle above bya single interface, often attributed to a phase transition in Mgperovskite. Systematic deep-mantle exploration with massiveseismic waveforms now yields evidence for multiple reflectorsup to at least 600 km above the core–mantle boundary. Someof the newly discovered interfaces can be explained by post-perovskite transitions in differentiated oceanic slab materials,transported from Earth’s surface through deep subduction andconvection. The lowermost mantle appears more complex thanhitherto thought, and this complexity is not confined to thecanonical D″ region.

Author contributions: M.d.H. and R.v.d.H. designed research; X.S. performed research;M.d.H. contributed new reagents/analytic tools; X.S., S.-H.S., and R.v.d.H. analyzed data;and X.S., S.-H.S., and R.v.d.H. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1312647111/-/DCSupplemental.

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1990–2009] recorded at one or more of a total of 2,700 seis-mographic stations (Fig. 1, Upper Center). For East Asia, we used120,000 SKKS traces from 11,000 events recorded at 1,700 sta-tions (Fig. 1, Lower Center). The range of epicentral distances is0–80° for ScS and 100–180° for SKKS. The data used (∼20% ofall available traces) passed selection criteria on the basis of sig-nal-to-noise and multichannel cross-correlation values. Sourcesignatures are estimated through principal component analysisand removed from the data through Wiener deconvolution (27,28). With GRT, we estimate (from scattered energy) elasticitycontrasts at nodes of a 3D mesh (10 km vertical, 1° lateral spacing);spatial alignment of such contrasts indicates the presence of aninterface. We use a tomographic model (20) to correct for mantleheterogeneity, but the choice of model is not critical for the level ofdetail discussed here. More information about data selection andprocessing is provided in SI Text S2.

Structural Complexity in the Lowermost MantleWe illustrate the main structural features in the lowermostmantle beneath the regions under study by means of 2D (vertical)GRT sections through 3D image volumes. The nearly 1,500-km-long Central America section (Fig. 3A) cuts across the main(tomographically inferred) high-wave speed anomaly (Fig. 2,

Right). This segment parallels section A–A′ in our previous study(10), but it is shorter because detection of weak structures aboveD″ requires more stringent imaging conditions and samplingcriteria than was necessary for the imaging of CMB and D″. Thefirst of the East Asia sections shown here (B–B′; Fig. 3B) also cutsmainly across seismically fast regions, whereas the other section(C–C′; Fig. 3C) samples slow regions as well. In these profiles,black (red) pulses indicate positive (negative) impedance con-trasts with increasing depth; their amplitudes are normalized(with respect to the CMB reflection) and provide only a qualita-tive indicator of the reflector strength. The background colorsdepict the tomographic estimates of local variations in shear wavespeed used to construct the images.Beneath both regions, well-aligned black pulses mark the

CMB as well as a laterally continuous interface labeled X (fatmagenta lines, Fig. 3). Consistent with previous results (8, 10), Xoccurs some 250–300 km above the CMB beneath CentralAmerica (Fig. 3A); however, beneath East Asia, where such aninterface was detected previously (2, 29), but where our resultsestablish its large-scale structure, it is positioned closer to theCMB. The data also reveal a weaker, unknown interface (here-inafter Y) some 450–500 km above the CMB. Other structures

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Fig. 1. (Left) Generic ray geometry of ScS and SKKS phases, which sample the lowermost mantle from above and below, respectively. Solid lines depict ScSand SKKS reflections at the CMB; dashed lines depict possible paths of scattering at structures above the CMB, which are used to generate the sections shownin Fig. 3. (Upper, Center and Right) Distribution of epicenters (red circles) and stations (blue triangles) that yield the ScS data used in the construction of thecommon image point gathers. The range of epicentral distances is 0–80°. The green rectangle depicts the study region in Central America (5–30°N; 80–105°W).(Inset) Natural logarithm of the number of ScSmidpoints in 2° × 2° geographical bins. (Lower, Center and Right) Same, but for SKKS in East Asia (25–55°N; 65–125°E). The range of epicentral distances for SKKS is 100–180°.

Fig. 2. Tomographically inferred lateral variations (in percentage) in shear wave speed at ∼200 km above the CMB (20). Red boxes indicate regions understudy: East Asia (Left) and Central America (Right). Red arrows in these boxes depict locations of cross sections A–A′ (in Central America) and B–B′ and C–C′(in East Asia), for which the inverse scattering results are shown in Fig. 3.

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exist, but stacking across the sections confirms CMB, X, and Y asthe main interfaces (Fig. 3, Right).Beneath Central America (Fig. 3A), Y is laterally intermittent

but is clearly visible over at least a 1,000-km horizontal distance.The data reveal impedance contrasts between CMB and X, asdescribed before (8, 10), and suggest that one or more wavespeed drops (red pulses, labeled z) occur between X and Y.Locally, z may look like a side lobe of nearby positive pulses, butin many places it clearly appears as a separate signal. The EastAsia section across the fast anomaly (Fig. 3B) is qualitativelysimilar, with a weak, laterally intermittent interface visible some200 km above X. In addition, negative pulses appear here be-tween CMB and X and between X and Y (in particular, around300 km above CMB in the right half of the section). Fig. 3Csuggests that the character of these structures changes whenmoving from (tomographically inferred) high to low wave speedsin the lowermost mantle: interface Y is laterally continuous inthe easternmost, 1,200-km, “fast” part of section C–C′, in-termittent in the center (between 1,000 and 1,500 km horizontaldistance), and absent in the seismically “slow” region furtherwest. In the latter, no coherent scattering is visible above in-terface X, located here ∼200 km above CMB.

Phase Transitions in Differentiated Subducted Lithosphere?Our application of modern imaging techniques to ever-growingdata sets confirms the widespread presence of a positive im-pedance contrast 150–300 km above the CMB beneath Central

America and also establishes its large-scale existence beneath EastAsia. Consistent with previous results, we interpret this horizon Xas the top of the D″ region and associate it with the pPv (Pv→pPv)transition. For reference, we also show (black dashes) the hypo-thetical phase boundary predicted by Sidorin and coworkers (18),who assumed that tomographically inferred wave speed variationshave a thermal origin, that a (pressure-induced) mineralogicalboundary exists (with a positive pressure–temperature depen-dence of 6 MPa/K), and that this boundary can be extrapolatedglobally (18, 19). This prediction is hereafter referred to as the“thermal model.” Along the Central America section (A–A′) andin the western part of Asia section C-C′, interface X coincideswith the hypothetical phase boundary expected from the thermalmodel. In contrast, it does not correlate with thermal predictionsin the high-wave speed parts of the East Asia sections (e.g., B–B′).The large data sets also reveal hitherto unknown structures in

the lowermost mantle. The detection of laterally continuousscatter surfaces above the D″ interface may still be at the edge ofcurrent resolution, but tests with synthetic data demonstrate itcannot be attributed to noise, multiple scattering near sources orreceivers (such as depth phases), reverberations within the D″layer (Fig. S2), or multiples of SKKS (i.e., SKnS, with n > 2) (17).Our first-order observations (both poor correlation between to-mographic wave speed variations and depths to the D″ discon-tinuity and the existence of multiple reflectors) are inconsistentwith a single (pressure-induced, temperature-controlled) phasetransition in magnesium silicate (MgSiO3) Pv in a compositionally

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Fig. 3. Reflectivity profiles superimposed on smooth (tomographically inferred) variations in shear wave speed (20); scale as in Fig. 2. (A) Section A–A′ acrossCentral America: 24.5°N, 96.6°W to 6.5°N, 83°W. (B) Section B–B′ across East Asia: 25°N, 123°E to 55°N, 123°E. (C) Section C–C′ across East Asia: 27°N, 70°E to50°N, 123°E. Black (red) pulses depict positive (negative) impedance contrasts. Magenta lines depict coherent reflectors inferred from data (thick lines depictinterface X; thin lines depict interface Y; black dashes depict the prediction by Sidorin and coworkers (18) from purely thermal considerations. (Right) Stacks(along interface X) showing the main (positive) impedance contrasts CMB, X, and Y, as well as minor negative impedance contrasts located between X and Y(labeled z). In these stacks, the part above 100 km above CMB (the horizontal dashed line) is amplified by a factor of 5. On stacking, laterally coherentreflectors are enhanced and incoherent scattering suppressed, but undulating interfaces may appear broader and weaker than they are at any given location.The question mark (near 900) km in B–B′ indicates complexity in X that is not yet well understood.

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homogeneous mantle. Forward (Pv→pPv) and reverse (pPv→Pv)transitions can produce multiple interfaces in the steep thermalgradient near the CMB (7,8,10), but not several hundreds ofkilometers above it. If X does indeed mark the top of D″, ourresults suggest that interfaces and, by implication, compositionalor phase boundaries exist several hundred kilometers above theD″ region.With hundreds of millions of years of subduction along the

eastern seaboard of Asia and beneath Central America, it ispossible that some of the multiple reflectors are a result of thebuckling of slabs above the CMB (24), as has been suggested tooccur beneath Central America (19, 25). Another explanationinvolving subduction concerns the presence of material that ischemically distinct from a pyrolytic bulk composition. Variationsin mineralogy and iron and aluminum content can influence thepropagation speed of seismic waves (30–32), as well as the pPvtransition depth (11, 13, 33) and detectability (13). Of particularinterest are predictions from experimental mineral physics thatin a heterogeneous mixture of harzburgite, basalt, and bulkmantle, the Pv→pPv transition in the MORB fraction can occurseveral hundreds of kilometers above the transitions in either theharzburgitic component or pyrolite (Fig. 4) (13). The shallowerpPv transition would be weak because MORB contains much lessmagnesium silicate (30%) than harzburgite or pyrolite (60–80%)(34) and because the pPv transition depth interval in MORB isgreater than harzburgite [but still smaller than in pyrolite (13)].Because of complex mineralogy and phase chemistry, uncer-

tainties in absolute pressure in mineral physics data (35), con-troversy about seismic velocities of bulk mantle composition(pyrolite) and (mixtures of) recycled materials (MORB, harz-burgite) (36, 37), and the fact that weaker impedance contrastsare only now beginning to emerge as robust features, one-to-onemapping of phase transitions and seismological boundaries isstill premature. However, combining evidence from mineralphysics and seismic imaging (Fig. 4), we suggest that X marks thepPv transition either in average mantle (if effects from lattice

preferred orientation and element partitioning decrease pPvtransition thickness to within detectable limits) or in the harz-burgitic component of differentiated subducted lithosphere, andthat Y marks the transition in the subducted MORB component.Negative impedance contrasts (z and closer to CMB in Fig. 3)may reflect transformations in silica (34), local existence ofpartial melt (38), or reverse pPv transformations in basalt,harzburgite, or bulk mantle. These are exciting targets of futurejoint research for mineral physics and deep Earth explorationseismology, preferably with both P- and S-type data (39), andmay lead to a further revision of the canonical view of a lower-most mantle with compositional and structural heterogeneityrestricted to the D″ layer.

MethodsWeused a GRT to recover unknown elastic reflectors in the lowermost mantlefrom the scattered ScS and SKKS wave fields (SI Text S1; Fig. S1). In essence,the GRT maps (as in reverse time migration) the scattered seismic wave field(recorded at the surface) back to subsurface contrasts in elasticity. For eachnode of a dense 3D mesh, the GRT exploits data redundancy through theintegration of waveform data over a wide range of scattering angles andazimuths. In theory, point scatterers can be resolved in the Rayleigh dif-fraction limit (which depends on frequency), but in practice, spatial resolu-tion depends on how a subsurface point is illuminated (i.e., the waveslownesses and the range of scattering angles over which data are in-tegrated), which depends on source–receiver distribution. To ensure ro-bustness, we require that target points be sampled from a sufficient rangeof angles (>15°) around the stationary point (specular reflection), whichenables us to resolve structure at lateral scales of 500 km or larger. GRTimaging does not rely on priori assumptions about the location or shape ofgeological targets, which facilitates discovery of hitherto unknown struc-tures. More details of the method and data preprocessing are given in SIText S1 and SI Text S2. For the mineral physics data, the absolute pressure (ordepth) is uncertain by at least ±5 GPa (or ±100 km) (35) and depends on thepressure scale used. We note that the use of the gold pressure scale byTsuchiya (40), originally used in Grocholski and coworkers (13), gives depthsin between those inferred from the gold scales used in Fig. 4B. The relativepressure scale (or difference in pressure or depth) is better constrained

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Fig. 4. (A) Stacks along interface X in sections A–A′, B–B′, and C–C′ (shown in Fig. 3). (B) Depth ranges for pPv transitions in midoceanic ridge basalt (MORB),harzburgite (Harz), and pyrolite (Pyr), after ref. 13, and transitions in silica from modified stishovite to seifertite (Sft), after ref. 15, at ∼2,500 K. Plotted are thelower bounds of the pPv transition thickness. The pressures at the phase boundaries are calculated using a shock wave (gold) scale from ref. 41, a scale bar onthe left of B, or a static compression (gold) scale from ref. 42, on the right. Pressure was converted into depth using preliminary reference Earth model (PREM;43). Absolute pressure (depth) is uncertain by at least ±5 GPa (±100 km), but pressure differences are constrained better (±1 GPa). Given these uncertainties,the depth difference between X and Y agrees remarkably well with the difference in pPv transition depth between MORB and Harz.

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(±1 GPa), and all mineral physics data shown in Fig. 4B are constrained, usingthe same pressure scale (gold). Therefore, depth differences among the phaseboundaries in Fig. 4B are more reliable for comparison with seismic data thanabsolute depths.

ACKNOWLEDGMENTS. We acknowledge the pioneering work by Dr. PingWang (formerly at the Massachusetts Institute of Technology in Cambridge,

now at CGG in Houston) on GRT imaging with SKKS and ScS data. The re-search was conducted by X.S. (under the supervision of R.v.d.H and M.d.H.).S.-H.S. assisted with the interpretation. This research was supported by USNational Science Foundation Grants EAR-0757871 (Cooperative Studies ofThe Earth’s Deep Interior program), DMS-0724778 (Collaboration in Mathe-matical Geosciences program), and EAR-1301813 (to S.-H.S.). All waveformdata used in this study are retrieved from Data Management Center of theIncorporated Research Institutions for Seismology.

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Supporting InformationShang et al. 10.1073/pnas.1312647111SI Text S1Methodology. Inverse scattering in seismology refers to estimatingthe characteristics of a subsurface object from elastic waves thatscatter from it. In the generalized Radon transform (GRT) usedhere, we use the Born approximation (i.e., single scattering) andassume that the scatterers (including interfaces) can be repre-sented as perturbations relative to a smooth background medium(1–3). For this purpose, the medium parameter, for instance,wave speed c(x), can be decomposed into two parts, c(x) = c0(x) +δc(x), where δc(x) is a perturbation relative to a smoothly varyingbackground medium c0(x). Accordingly, the wave field u(x) can bedivided into two parts, u(x) = u0(x) + δu(x), where u0(x) is thedirect wave resulting from propagation in c0(x), and δu(x) is thescattered wave resulting from δc(x). The background smoothmodel can be estimated from reference Earth models and seismictomography. Inverse scattering maps the scattered wave field δu(x) back into images of perturbation of medium properties δc(x).The scattered wave field δu(x) depends on the position of

scattering point y, source xs, and receiver xr (Fig. S1). For a given(y;xs,xr), we define the slowness vector ps(y) for the incident rayfrom source to the scattering point, as well as pr(y) from thereceiver side. These two slowness vectors can define migrationdip νm(y) = pm(y)/jjpm(y)jj, with pm(y) = ps(y) + pr(y), scatteringangle θ, and azimuth ψ (Fig. S1).To do multiscale analysis and avoid artifacts resulting from

caustics (in practice, artifacts might be introduced with in-complete data), the recorded wave field δu(y; xs, xr) can bemapped into angle domain, δu(y; νm, θ, ψ) (3–5), with scatteringangle θ and azimuth ψ. The structural reflectivity at y can beapproximated as

IðyÞ=Z

δuðy; νm; θ;ψÞkpmðyÞk3dνmdψdθ; [1]

where δu(x) is integrated over the scattering angle θ and azimuth ψ.In practice, the spatial resolution of GRT depends on how an

image point is illuminated (integration range of Eq. 1). Theimaging result would be biased by uneven source-receiver dis-tribution (e.g., dominant earthquake direction, poor illuminationcoverage). To ensure robustness and mitigate inversion artifacts,we conduct two processing steps. First, all image points are re-quired to be sampled from a sufficient range of angles aroundthe stationary point (i.e., the specular reflection). For each ver-tical profile in Fig. 3 (i.e., the same latitude and longitude withdifferent depths), we check the illumination for an image pointat the core–mantle boundary (CMB). Such a point is included inthe final image only if the data sampling it contain specular re-flections (i.e., migration dip angle is zero) and a wide range ofmigration dip angles (here we use 15°). Second, the contributionsfrom different earthquakes are balanced through simple ray-count normalization. After trace normalization, the ray count isproportional to the incident wave energy. Before summing overthe scattering angle θ in Eq. 1, the ray count is calculated foreach angle bin (3°), and each partial image is normalized by theray count.

SI Text S2Preprocessing of the Data. There are several steps in the selectionand preprocessing of the data. First, for all data, we remove theinstrument response and rotate the data to radial and transversecomponents. We use the transverse component (SH wave) forScS data and the radial component (SV wave) for SKKS data.

Second, all data are band-passed between 10 and 50 s with a4-pole Butterworth filter and then normalized with respect to thereference phase (ScS or SKKS). Third, we discard data on thebasis of a simple quality criterion obtained from multichannelcross-correlation (6). For each earthquake, we organize the datain 10° (epicentral) distance bins, and from each seismic record ina bin, we extract a 50-s time window around the theoretical ScS(or SKKS) arrivals. After energy normalization, we cross corre-late each trace with all others in the bin, which yields a qualita-tive estimate of the average correlation coefficient for eachtrace. Traces with average correlation coefficient lower thana set threshold (we use 0.6) are discarded. Roughly 20% of alldata meet this quality criterion. The trace polarity can be cor-rected according to the sign of average correlation coefficient.After multichannel cross-correlation, traces are aligned withreference phases. Fourth, principle component analysis is ap-plied to estimate the source signature (7), which is then removedfrom the data to enhance image resolution by Wiener decon-volution (8). The so-called water level in Wiener deconvolutionis selected automatically and adaptively based on the noisespectrum of array data. Finally, travel times are corrected forellipticity (9) and for 3D wave speed variations, using a tomo-graphic model for mantle shear wave speed (10).

SI Text S3Tests with Synthetic Data.Because the quality of the GRT imagingoperator depends on the aperture of angles θ and azimuth ψ (SIText S1) and the validity of the single-scattering approximation,tests with synthetic data are necessary to examine the effects ofuneven sampling, noise, interfering main phases (such as depthphases), and multiple scattering (e.g., near-source or receiverscattering and internal reverberations). In all the tests describedhere, we computed synthetic waveforms for the real source-receiver geometry (including focal depths) and focal mechanismobtained from the Global Centroid-Moment-Tensor (CMT) cat-alog. All synthetic seismograms are calculated with the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) method (11), using a radiallystratified wave speed model [ak135 model (12)], on which a 3% Swave velocity jump is superimposed at 250 km above CMB. Be-fore the inversion, all synthetic data are band-pass filtered be-tween 10–50 s. We note that the synthetics merely test numericallywhether the available sampling in migration dip is sufficient. Inother words, the performance of such synthetics (in linearizedinversions) depends mainly on sampling, and not on the strengthof the contrast or the noise level. Indeed, a GRT is stable in L2

and, hence, effectively attenuates additive random noise, allowingthe imaging of weak deterministic reflectors. In concept, this useand limitation as a diagnostic for image quality is similar to the so-called checkerboard test used to verify the effect of sampling onthe ability to recover input patterns in tomography.Fig. S2 shows the effects on the SKKS image gather of random

noise (100% noise level), depth phases, and multiple reverber-ations. Even when the signal cannot be identified in most in-dividual traces, the reflector at 250 km above CMB is clearlyrecovered after stacking over the scattering angle (Fig. S2A). Thedepth phase can produce small waveform distortion (Fig. S2B);however, it does not produce significant artifacts in the image.The reverberation in the crust and D″ layer can also be a po-tential source of artifacts because such phases could interferewith the coda wave of SKKS. Applying the GRT to the syntheticdata with such signals shows they do not, in general, contaminatethe image profile (Fig. S2 C and D). Moreover, such multiples

Shang et al. www.pnas.org/cgi/content/short/1312647111 1 of 2

would generate structures that are (within uncertainty of thebackground wave speed) parallel to the main interfaces, which isnot generally the case in the results presented here.SKKS multiples SKnS (n > 2), which reverberate within the

liquid outer core, arrive later and could interfere with the re-

flections from lowermost mantle interfaces in time domain. Inangle gathers, their slownesses differ from those of SKKS (andSKSdSKS), and therefore they can be distinguished by a clearresidual move out and suppressed by parabolic Radon trans-forms (5).

1. Miller D, Oristaglio M, Beylkin G (1987) A new slant on seismic imaging: Migrationand integral geometry. Geophysics 52:943–964.

2. Beylkin G (1990) Linearized inverse scattering problems in acoustics and elasticity.Wave Motion 12:15–52.

3. De Hoop M, Bleistein N (1997) Generalized Radon transform inversions for reflectivityin anisotropic elastic media. Inverse Probl 13:669–690.

4. Wang P, de Hoop M, van der Hilst RD, Ma P, Tenorio L (2006) Imaging of structure atand near the core mantle boundary using a generalized radon transform: 1.Construction of image gathers. J Geophys Res 111:B12304, 10.1029/2005JB004241.

5. Wang P, de Hoop M, van der Hilst RD (2008) Imaging the lowermost mantle (D″) andthe core-mantle boundary with SKKS coda waves. Geophys J Int 175:103–115.

6. VanDecar J, Crosson R (1990) Determination of teleseismic relative phase arrival timesusing multi-channel cross-correlation and least squares. Bull Seismol Soc Am 80:150–159.

7. Rondenay S, Bostock MG, Fischer KM (2013) Multichannel inversion of scatteredteleseismic body waves: practical considerations and applicability. Seismic Earth: ArrayAnalysis of Broadband Seismograms, eds Levander A, Nolet G (American GeophysicalUnion, Washington DC), pp 187–203.

8. Chen C-W, Miller D, Djikpesse H, Haldorsen H, Rondenay S (2010) Array-conditioneddeconvolution of multiple-component teleseismic recordings. Geophys J Int 182:967–976.

9. Kennett B, Gudmundsson O (1996) Ellipticity corrections for seismic phases. Geophys JInt 127:40–48.

10. Grand SP (2002) Mantle shear-wave tomography and the fate of subducted slabs.Philos Trans A Math Phys Eng Sci 360(1800):2475–2491.

11. Chapman C (1978) A new method for computing synthetic seismograms. Geophys J RAstron Soc 54:481–518.

12. Kennett B, Engdahl E, Buland R (1995) Constraints on seismic velocities in the Earthfrom traveltimes. Geophys J Int 122:108–124.

Fig. S1. Illustration of ray path geometry considered in the generalized Radon transform of ScS (blue paths) and SKKS (red paths) phases for subsurface imagepoint y. Slowness vectors at y are given by p. The slowness of the incident ray direction (from source xs to y) is ps; pr denotes the scattered path (from receiver xr

to y), and pm = ps + pr defines the migration dip direction (which controls the radial resolution). Scattering angle and azimuth are given by θ and ψ, re-spectively. CMB and ICB denote core-mantle boundary and inner-core boundary, respectively.

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Fig. S2. Effects on the SKKS GRT image gathers of the presence of (A) white noise (100% additive noise), (B) depth phases, (C) multiple reverberations in thecrust, and (D) multiple reverberations between D″ discontinuity and CMB. In the tests, a 3% shear wave velocity jump at 250 km above CMB is superimposed ona layered model (ak135) (12).

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