 Research Article
 Open Access
 Published:
Stratification of earth’s outermost core inferred from SmKS array data
Progress in Earth and Planetary Sciencevolume 2, Article number: 15 (2015)
Abstract
SmKS arrivals recorded by largescale broadband seismometer arrays are analyzed to investigate the depth profile of P wave speed (V _{ p }) in the outermost core. The V _{ p } structure of the upper 700 km of the outer core has been determined using SmKS waves of FijiTonga events recorded at stations in Europe. According to a recent outer core model (KHOMC), the V _{ p } value is 0.45 % slower at the core mantle boundary (CMB) than produced by the Preliminary Reference Earth Model (PREM), and the slow anomaly gradually diminishes to insignificant values at ∼300 km below the CMB. In this study, after verifying these KHOMC features, we show that the differential travel times measured for SmKS waves that are recorded by other largescale arrays sampling laterally different regions are well matched by KHOMC. We also show that KHOMC precisely fits the observed relative slowness values between S2KS, S3KS, and S4KS (SmKS waves with m= 2, 3, and 4). Based on these observations, we conclude that SmKS predominantly reflect the outer core structure. Then we evaluate biases of secondary importance which may be caused by mantle heterogeneity. The KHOMC V _{ p } profile can be characterized by a significant difference in the radial V _{ p } gradient between the shallower 300 km and the deeper part of the upper 700 km of the core. The shallower part has a V _{ p } gradient of −0.0018 s ^{−1}, which is steeper by 0.0001 s ^{−1} when compared to the deeper core presented by PREM. The steeper V _{ p } gradient anomaly of the uppermost core corresponds to a radial variation in the pressure derivative of the bulk modulus, K ^{′}=d K/d P. The K ^{′} value is 3.7, which is larger by about 0.2 than that of the deeper core. The radial variation in K ^{′} is too large to have a purely thermal origin, according to recent ab initio calculations on liquid iron alloys, and thus requires a thick and compositionally stratified layering at the outermost outer core.
Background
Stratification of the outermost core has been long suspected (e.g., Lay and Young 1990; Buffett and Seagle 2010) and has been recently strongly advocated by Helffrich and Kaneshima (2010) and Kaneshima and Helffrich (2013) (respectively abbreviated as HK2010 and KH2013 hereafter). The present study consolidates the propositions of HK2010 and KH2013 by investigating additional SmKS data obtained for significantly more eventarray pairs and by evaluating possible mantle effects on SmKS travel time and slowness observations. We analyze SmKS arrivals with integer m from 2 to 5 in order to better constrain the V _{ p } profile of the topmost 700 km of the core, anticipating that the results will strengthen the evidence for a compositionally stratified layer. As shown in Fig. 1, the ray paths of S2KS, S3KS, and S4KS propagate quite a long distance through the outermost part of the core. Since each SmKS possesses a distinct depth sensitivity depending both on m and epicentral distance, when used in combination, SmKS waves can form an ideal data set for use in determining the V _{ p } profile of the outermost core. In order to measure differential travel time and slowness differences between two SmKS waves, we used largescale broadband seismometer arrays in Europe, Eastern Asia (including Japan), North and South America, Africa, and Australia.
Prior to HK2010 and KH2013, other studies also investigated the outer core structure by analyzing SmKS data. The proposed models show either slightly or rather strongly slower V _{ p } anomaly relative to the Preliminary Reference Earth Model (PREM) (Dziewonski and Anderson 1981) near the top of the core. For instance, Tanaka (2007) analyzed a composite record section of S2KS, S3KS, and S4KS, which were observed globally, and proposed a model with up to a maximum of 1.2 % slower V _{ p } than PREM in the outermost 90 km of the core. His model (called Tanaka1 hereafter) is similar to that presented in an earlier study by Garnero et al. (1993). Alexandrakis and Eaton (2010) investigated composite globally observed record sections of S2KS to S4KS for the distance range shorter than 140° and showed a permissible range of V _{ p } profiles for the top 200 km of the outer core. The range of permissible models centers around slightly slower V _{ p } values (from ∼0.1 to 0.4 %) than PREM and falls between PREM and the IASP91 velocity model (Kennett and Engdahl 1991). In this study, we also include other global V _{ p } models such as SP6 (Morelli and Dziewonski 2012), AK135 (Kennett et al. 1995), and another model proposed by Tanaka (2007) (called Tanaka3 hereafter) with the models to be compared.
SmKS waveform data
SmKS data are analyzed for earthquakes that occurred in several different regions and were recorded at largescale broadband stations prior to July 2014 (Table 1). The broadband seismograms in Europe are extracted from the Incorporated Research Institutions for Seismology (IRIS) and the Observatories and Research Facilities for European Seismology (ORFEUS) data management centers. Seismic stations in Japan belong to JArray, Fnet, and the tiltmeter network of Hinet (Obara et al. 2005). Data of the seismic stations in Eastern Asia outside of Japan, the US, and Australia are extracted from the IRIS data management center (DMC). In this study, we loosely define a “largescale array” as a group of 20 or more broadband seismometer stations with aperture lengths exceeding ∼1000 km whose seismograms can be analyzed by standard array processing methods. As we shall show later, travel times of SmKS waves observed at individual stations may be significantly affected by the heterogeneous mantle structure, rather irrespective of the waveform quality. This makes it difficult to investigate a detailed V _{ p } profile of the outer core based on SmKS measurements made for individual traces. However, HK2010 and KH2013 showed that stacking seismograms over an entire largescale array substantially suppresses the mantle effects and thereby enables us to discern the fine structure of the outermost core. In this study, we shall also show that the processing of largescale array data enables us to precisely retrieve differential slowness between two SmKS arrivals, which helps to better constrain the outer core structure. Figure 2 shows an example of observed and computed record sections for a FijiTonga event recorded at the European stations. The synthetic seismograms shown in Fig. 2 2) and a method similar to that of Wang et al. (2008) (HK2010). When SmKS touches an internal caustic and is underside reflected m−1 times at the core mantle boundary (CMB), it suffers from a phase delay by nearly $\frac {m1}{2}\pi $ relative to SKS (Choy 1977). The arrivals of S2KS, S3KS, S4KS, S5KS, and S6KS are clearly visible on this section and are systematically delayed with respect to the theoretical PREM predictions throughout the array.
Methods and results
Array measurements
In this study, we measure differential travel times between two different SmKS waves on stacked waveforms; those between S3KS and S2KS (called d t ^{3−2} hereafter), S4KS and S3KS (called d t ^{4−3}), and S5KS and S3KS (called d t ^{5−3}). Next, the differential time anomalies relative to the ray theoretical predictions based on PREM are computed. Since instrument corrections have negligible effects on the results, stacking and differential time measuring are performed directly on the observed broadband seismograms (HK2010). We also avoid unstable deconvolution of the source time function, which may cause some biases to the d t ^{m−n} (differential travel times between SmKS and SnKS waves) and their anomalies relative to ray theoretical predictions by PREM, which are usually positive. Those biases are mostly less than 0.2 s for the FijiTonga events used in HK2010 and KH2013 but can be larger for other events. Therefore, we evaluate biases by using synthetic seismograms (Fig. 2b). To measure these synthetic seismograms d t ^{m−n}, we use the same array method as the data and compare them with the theoretical ray calculations based on PREM. The difference, which is usually 0.2 to 0.3 s but sometimes could exceed 0.5 s (Table 2), is regarded as the bias. For each event, d t ^{3−2} are measured both by picking peaks and crosscorrelating the stacked waveforms after correcting for the $\frac {\pi }{2}$ phase shift due to the caustic (Choy 1977). Both S2KS and S3KS are used as the alignment phase whenever the S3KS arrival is sufficiently clear, and the agreements between different alignment phases (S2KS or S3KS) and between different methods (peakpicking or cross correlating) are used for evaluating the error of each d t ^{3−2} measurement. The measured differential times are classified into two categories, A (high quality) and B (moderate) (Table 2). When the values obtained by different methods agree with each other, the stacked synthetic and observed seismograms usually agree quite well, and the measurements can be regarded as category A, and have smaller errors.
In addition to the $\frac {\pi }{2}$ phase shift, waveforms of S4KS could be distorted by the interference by S5KS (Eaton and Kendall 2006) or by S3KS when epicentral distances are not large. The S5KS arrivals are not separated completely from S4KS, even when its peak, which is oppositely polarized to S3KS, can be clearly identified. Therefore, d t ^{4−3} and d t ^{5−3} are measured simply by identifying the corresponding peaks. Since alignment on S4KS arrivals is usually unstable, differential times between S4KS and S5KS (called d t ^{5−4}) are calculated by subtracting d t ^{4−3} from d t ^{5−3} with error propagation. Other array measurement details are described in HK2010 and KH2013. We note that, especially for the TongaFiji events (Fig. 2a), the anomalies of d t ^{m−n} relative to PREM are observed more or less uniformly across the entire European array (KH2013). Except for the uniform delays, no systematic trends in the differential times with azimuth from the TongaFiji events, which may be amenable to elaborate modeling, have been identified for the high quality events. This would suggest only minor influences of CMB structure on individual paths.
V _{ p } model for the outermost core
τ−p inversion: effects of starting model
KH2013 built a V _{ p } model of the topmost 700 km of the outer core using differential SmKS travel time anomalies of several FijiTonga events recorded at Europe, d t ^{3−2}, d t ^{4−3}, and d t ^{5−3}, to which a τ−p inversion method had been applied (Garmany et al. 1979; HK2010; KH2013), with PREM as the starting model. The resultant model, KHOMC, has a 0.45 % slower V _{ p } than PREM at the CMB (Fig. 3). The lowerthan PREM V _{ p } values persist down to about 300 km below the CMB. We note here that the τ−p method is a linear inversion that requires a good starting model. Although PREM is known to be a good global model, there may be other reference models as good as PREM. We perform the τ−p inversion using IASP91 as the starting model, as did Alexandrakis and Eaton (2010). By using only the FijiTonga to European stations data, as in the case of KHOMC, we obtained a profile of V _{ p } anomaly relative to IASP91 (called KOCTI). KOCTI has faster V _{ p } values than IASP91 in the shallowest 300 km of the outer core (Fig. 3). KOCTI shows an improved fit to the data compared to IASP91 (Fig. 3), but its overall fit is less suitable than that of KHOMC, with the most significant disagreement for the d t ^{3−2} data of larger distances, as will be shown later in this study. The V _{ p } values of KOCTI for the upper 300 km are only about 0.01 km/s slower than those of KHOMC (the V _{ p } at the CMB is −0.045 km/s relative to PREM, while that of KHOMC is −0.035 km/s). Therefore, it can be seen that the two models agree with each other within the uncertainty range (Fig. 3). We conclude that the V _{ p } at CMB is constrained well by the τ−p inversion to 8.03 ± 0.01 km/s, irrespective of the starting model. The disagreement between KOCTI and KHOMC for the depth range from about 300 km to 700 km from the CMB is larger (by about −0.02 km/s), suggesting a poorer resolution than the shallower core.
Genetic algorithms
In order to check further the effects of the starting model on the result, we perform another V _{ p } inversion using genetic algorithms (e.g., Yamanaka and Ishida 1995) and attempt to find the global minimum of d t ^{m−n} misfit in a fashion that does not explicitly require a starting model. The V _{ p } profile of the outer 700 km of the core is assumed to be continuous and consist of four layers with constant V _{ p } gradients. For each layer, the V _{ p } value at its top and its thickness are determined (see the caption of Fig. 4 for details).
We use the data set consisting of d t ^{3−2}, d t ^{4−3}, and d t ^{5−4} data for four events from FijiTonga to Europe (FEV1, FEV2, FEV3, FEV4) and three events from Argentina to Japan (AEV1, AEV2, AEV3) without correcting for bias (Table 2). The inversion is repeated 40 times with different initial values, and the case with the least misfit, for which the total residual decreases from 0.5 to 0.15 s through the 40 generations, is chosen. As shown in Fig. 4, the obtained model (called “KOCGA” hereafter) is fairly close to KHOMC. The agreement between the model and KHOMC is remarkable especially for the shallower 300 km of modeled depth range. Based on this result, we conclude that the validity of KHOMC is not affected by the choice of the starting model.
SmKS slowness measurements
In addition to travel time differences, differences in slowness between two SmKS waves provide information on the relative arrival directions of the waves. In HK2010 and KH2013, it was reported that the relative slownesses for the Tonga and Argentina events are close to those predicted by PREM. This observation has been exploited in using the τp inversion. The slowness observations can also give constraints on the degree of largescale heterogeneity in the receiverside mantle, as shall be shown in the “Discussion” section. The differential slowness between two different SmKS waves changes gradually with distance. Therefore, the moveout of a SmSK wave, relative to the reference SmKS wave on a record section, is aligned on a slightly curved line rather than a straight line. Although the curvature is small, when the aperture of an array is as large as 20°, its effect on the differential travel times approaches a second, which could give rise to a small bias of the measured differential slowness between SmKS and SnKS relative to PREM (called “ d p ^{m−n}”). To ensure that d p ^{m−n} is measured accurately, we correct for the curvature by assuming that the moveout around the array center (distance of Δ _{0}) is a quadratic function of epicentral distance when stacking seismograms. Accordingly, the differential slowness between S3KS and S2KS (and similarly between S4KS and S2KS) is expressed as
The curvatures of the moveout curve are fixed to those of the reference model, so that $\frac {d}{d\Delta }dp$ is 0.014 and 0.021 s/ $^{\circ ^{2}}$ for d p ^{3−2} and d p ^{4−2}, respectively, which does not significantly affect the results. We obtain precise slowness measurements of S3KS and S4KS waves with S2KS as the reference wave for eight FijiTonga and Kermadec events observed from Europe, and four Argentina events observed from Japan (Table 3). The d p ^{3−2} and d p ^{4−2} are then compared to the predictions of KHOMC (Table 3).
Figure 5a shows a vespagram example of the cuberoot stack output as a function of slowness and arrival time relative to S2KS, with the small moveout curvature effects corrected. The observed d p ^{3−2} and d p ^{4−2} (red circles) closely agree with theoretical predictions by KHOMC (Table 3), which are shown by red stars in the figure. The RMS residuals computed for the FijiTonga and Argentina events using the outer core models (PREM, IASP91, KOCTI, AK135, SP6, and Tanaka1) show that the least residual is obtained for KHOMC (Fig. 5b). The RMS residual is less than 0.03 s/° for KHOMC (Fig. 5b), and d p ^{3−2} for the majority of the events, which agree with KHOMC within 0.02 s/° (Table 3). The residuals for KHOMC of d p ^{3−2} and d p ^{4−2} are slightly improved in comparison to PREM, while no such d p ^{m−n} improvement is seen for the other models. The small discrepancy of the observed d p ^{3−2} and d p ^{4−2}, with respect to PREM, justifies the usage of PREM as the reference model for stripping the mantle contributions from the observed distance ranges and travel times in the τp inversion that resulted in KHOMC (HK2010; KH2013). While the primary information about the core V _{ p } structure is contained in the differential SmKS travel times, as shown in parameter tests (KH2013), the measured d p ^{3−2} and d p ^{4−2} data not only indicate the validity of our travel time analyses but also further support the validity of KHOMC.
SmKS differential times of other regions
Observations of dt ^{3−2}
KHOMC was built by using the TongaFiji data set that samples rather limited areas of the CMB, mostly beneath western Pacific and Siberia. KH2013 showed that the SmKS differential travel times of the Argentina to Japan data set are consistent with KHOMC, even though they sample entirely different parts of the CMB. In this study, we compile the d t ^{3−2} measurements for additional pairs of event and largescale array that sample a much larger portion of the CMB. We determine the anomalies of d t ^{3−2} for several largescale arrays (Japan, US, Australia, Alaska, Africa, South America, and Southeast Asia; Fig. 6a) using the same processing. The ray paths cover a reasonably large part of the outer core (Fig. 6a).
A striking feature of the result is that the d t ^{3−2} observations based on the largescale array processing are quite well matched by KHOMC (Fig. 6b). On the other hand, the d t ^{3−2} values measured for individual stations (Souriau et al. 2003) show a much larger scatter than the array measurements (Fig. 6b), which suggests that measuring d t ^{3−2} using largescale array data significantly ameliorates the heterogeneous mantle structure effects. Another notable feature is that the array measurements fall approximately in the middle of the range of individual station measurements (Figure six b; Souriau et al. 2003), which also suggests that the array measurement of this study has successfully represented the overall core structure. The total residual of the array measurements is computed for KHOMC and for other outer core V _{ p } models (IASP91, Tanaka1, Tanaka3, ak135, SP6, and PREM), and the least misfit is obtained for KHOMC (Fig. 6c). As mentioned previously, we note that KHOMC definitely gives a better fit than the τp model based on IASP91 (KOCTI) for larger distances. These observations indicate that the mantle effects on d t ^{3−2} are of secondary importance and that the essential features of KHOMC relative to PREM reflect the structure of the core.
Observations of dt ^{4−3} and dt ^{5−4}
The ray paths for which d t ^{4−3} can be determined by using largescale array data are geographically more restricted around Pacific than in the case of d t ^{3−2} but still sample a reasonably broad portion of the CMB (Fig. 7a). The measured d t ^{4−3} values fall in the middle of individual station measurements (Garnero et al. 1993) and are well consistent with KHOMC (Fig. 7b). Among the V _{ p } models considered (Fig. 7d), the d t ^{4−3} observations are best matched by KOCTI, but the data set (especially for category A) is explained almost equally well by KHOMC; the d t ^{4−3} data set is not useful for discriminating between the two models. The other models (IASP91, Tanaka1, Tanaka3, AK135, and SP6) give significantly poorer fits when compared with KHOMC and KOCTI.
The d t ^{5−4} data set is matched well by some of the models considered, KHOMC, PREM, IASP91, and KOCTI (Fig. 7c), so that it is not crucial to discriminate between the models. Nevertheless, it clearly refutes the class of models that have a strong V _{ p } reduction in a thin layer at the top of the outer core, such as Tanaka1, Tanaka3, and that of Garnero et al. (1993). These models were built without using d t ^{5−4} and were aimed to match mainly d t ^{3−2}, which means that the amount of V _{ p } anomaly relative to PREM across the top several hundred kilometers of the outer core can be well predicted by these models. The mismatch between these models with the observed d t ^{5−4} means that the V _{ p } anomaly relative to PREM needs to be distributed over a broader depth range than those in the models. This also indicates that the V _{ p } gradient near the top of the core is not extremely anomalous compared to PREM (Fig. 3). The inference is further supported by the good match of the observed S6KS waveforms relative to S5KS by KHOMC (KH2013); the V _{ p } gradient near the top of the core is tightly constrained by our data set.
We emphasize again that KHOMC was constructed by using the FijiTonga to Europe data set alone, yet the observations of d t ^{4−3} and d t ^{5−4} for different regions can be matched by the same model quite well. The SmKS data we used, therefore, should primarily reflect the outer core structure.
Anomalous outermost core in terms of V _{ p } gradient
The most important feature of our V _{ p } models (KHOMC and KOCGA) is the presence of marked radial change in the V _{ p } gradient, $V_{p}^{\prime }=dVp/dr$ ; the outermost core of KHOMC and KOCGA is essentially characterized by two distinctive layers with different $V_{p}^{\prime }$ . We parameterize the V _{ p } structure of the outermost 700 km of the core with two layers that have constant $V_{p}^{\prime }$ and compute the misfits of d t ^{3−2}, d t ^{4−3}, and d t ^{5−4} for the FijiTonga and Argentina data sets (KH2013).
The minimum misfit in this modeling is obtained for the V _{ p } value at the CMB near that of KHOMC (−0.35 km/s with respect to PREM). For this case, the obtained $V_{p}^{\prime }$ value of the shallower layer approximately agrees with the mean values of $V_{p}^{\prime }$ of the shallower 300 km for KHOMC and KOCGA (Fig. 8), which indicates that the mean V _{ p } gradient of the shallower layer is well constrained (Fig. 8) by the presence of additional different SmKS waves passing through it. Although the lower layer gradient is rather poorly constrained, the significant difference in the values of $V_{p}^{\prime }$ anomalies relative to PREM between the two layers is robust; the anomaly of $V_{p}^{\prime }$ with respect to PREM ( $dV_{p}^{\prime }$ = d V p/d r _{ profile }  d V p/d r _{ PREM }) is much larger in the shallower part of the depth range considered than below it (Fig. 8). Accordingly, the $V_{p}^{\prime }$ of the shallower 300 km of the outer core is steeper than PREM by about 0.0001 (1/s), while that of the deeper part is closer to that of PREM. The number anomalies of $V_{p}^{\prime }$ (relative to PREM) obtained for the Genetic algorithms (KOCGA) is 0.00012 (1/s) for the upper ∼300 km of the core, while that is −0.00002 (1/s) for the deeper part (300 to 700 km from the CMB).
The V _{ p } gradient and the pressure derivative of bulk modulus (K ^{′}=d K _{ s }/d P) are interrelated, and the principal feature of KHOMC indicates a substantial radial variation in K ^{′} within the uppermost 700 km of the outer core. By using the equation, $V_{p}^{\prime }=g(2V_{p})^{1}(K^{\prime }1)$ , K ^{′} can be computed from V _{ p }. We find that the K ^{′} value of the outermost 300 km of the core is nearly 3.7, which is larger than that of the deeper core by about 0.2 (Butler and Anderson 1978). The estimated anomaly of K ^{′} for the upper 300 to 400 km of the outer core amounts to a nearly 5 % radial anomaly, which is more than an order of magnitude larger than the V _{ p } anomaly itself.
Discussion
Effects of receiverside mantle
Our previous studies have shown that largescale array analyses adequately extract differential SmKS travel time anomalies representative to the array as a whole (HK2010; KH2013). The receiverside CMB piercing points for the TongaFiji events scatter widely beneath Europe (HK2010; KH2013), making it difficult to envisage a receiverside mantle heterogeneity which causes a systematic anomaly of SmKS differential travel times across the entire array.
Nevertheless, we attempt to conservatively evaluate the effects of mantle heterogeneity on the d t ^{3−2} and d t ^{4−3} measurements, by focusing on the observation of very small residuals of differential slownesses d p ^{3−2} and d p ^{4−2} described above from KHOMC (Fig. 5b). The observations indicate that the relative arrival angles of the different SmKS waves are barely anomalous and the rays of the SmKS waves are not substantially bent with respect to each other. A d p ^{3−2} anomaly of 0.02 s/° or less for the majority of the events (Table 3) corresponds to the anomaly in the separation of S3KS and S2KS piercing points at the CMB of the receiver side by less than 5 km.
We argue that a differential travel time anomaly (d t ^{3−2} and d t ^{4−3}) as large as those observed would need to be accompanied by a large anomaly in the relative direction of ray arrivals at the receivers when the anomaly is caused by the mantle heterogeneity beneath the receiver (Fig. 5c). For a low V _{ s } heterogeneity to cause a d t ^{3−2} anomaly exceeding 1 s across the array, S2KS waves would need to more effectively avoid the heterogeneous body compared to S3KS (e.g., Garnero and Helmberger 1995). This effect on the ray angle deviations was evaluated by ray tracing experiments. The typical dominant period of S2KS and S3KS is nearly 10 s, and d t ^{3−2} values measured for 3 s highpass filtered seismograms of three TongaFiji events (FEV2, FEV3, and FEV4) and two Argentina events (AEV2 and AEV4) agree with those for the original broadband seismograms within 0.3 s. They agree within 0.1 s for two of the Fiji events. This result confirms the utility of conducting theoretical ray estimations on d t ^{3−2} to identify possible mantle heterogeneity effects. Therefore, we will next consider a test case involving an artificially strong and sharpedged 2D low V _{ s } anomaly that extends about 1000 km from the CMB with a V _{ s } anomaly that is a maximum 3 % slower in the receiver side of the lowermost mantle (Fig. 5c). The d t ^{3−2} and d t ^{4−3} anomalies at approximately 150° are 1.8 s and 0.8 s, respectively, which are comparable to the observations. The relative slownesses, d p ^{3−2} and d p ^{4−2}, are 0.10 and 0.14 s/°, respectively, which are nearly five times larger than the observations. Accordingly, the rays of S3KS and S2KS, as well as those of S4KS and S2KS, bend relatively by approximately 25 km at the CMB. The observed minute anomalies in d p ^{3−2} and d p ^{4−2} indicate that the receiverside piercing points are much less significantly bent than is required by this model. The maximum V _{ s } anomaly needs to be as low as 0.6 % in order to match the observed d p ^{3−2} and d p ^{4−2}, which sets the upper bounds on the allowable biases of d t ^{3−2} and d t ^{4−3} due to the receiverside heterogeneity to much less than 0.4 s and 0.2 s, respectively.
Effects of sourceside mantle
A sourceside lower mantle structure that is capable of causing a d t ^{3−2} anomaly of ∼1 s across the entire European array would need to be laterally much larger than 200 km (KH2013). For the sourceside mantle sampled by the FijiTonga data set, the V _{ s } structure in the D ^{′′} of very large scale (≥3000km) beneath the north of Vanuatu seems to have been resolved moderately well by global seismic tomography (e.g., Lekic et al. 2012). Therefore, it would appear worthwhile to check whether V _{ s } heterogeneity of a larger scale in the source side deep mantle accounts for a significant portion of the SmKS differential travel time anomalies.
We focus on five FijiTonga events that are located from 300 to 1000 km laterally separately from each other (Fig. 9a) and for which high quality S2KS, S3KS, and S4KS have been observed (Table 2). The five events sample the CMB regions that are shifted systematically by 200 to 600 km; each event covers a CMB area of ∼1000 km by 300 km (Fig. 9b). Effects of D ^{′′} should be most significant for d t ^{3−2}, since S2KS and S3KS have larger CMB piercing point separations; d t ^{4−3} should be less sensitive to heterogeneity in D ^{′′} as the separations of the CMB entry points between S3KS and S4KS are less than half of d t ^{3−2}.
We find that the d t ^{3−2} anomalies for the five events are nearly uniform and are excellently matched by KHOMC (Fig. 10a), which is also the case for d t ^{4−3} (Fig. 10b). The V _{ s } models produced by global tomography appear to provide moderately reliable images of the deepest ∼200 km of the mantle (essentially corresponding to D ^{′′}) of this region, at least for wavelength features exceeding 2000 km. According to the V _{ s } models for the 2800 km depth of five different tomography studies (Fig. 9c), despite considerable differences in detail, the presence of 1 to 3 % low V _{ s } in the D ^{′′} of the northern half of the study area seems to be commonly resolved. On the other hand, the depth extent of such anomalies are very poorly constrained, and 2500 km depth tomography images show only insignificant anomalies that differ substantially from model to model. Therefore, we only deem the heterogeneity in the D ^{′′} to be significant and evaluate its effects on SmKS travel times, rather than attempting to make corrections on the SmKS travel times for the effects of mantle heterogeneity. Ray theoretical travel times computations show that the tomographyderived structures of D ^{′′} could systematically affect the anomalies of d t ^{3−2} values by 0.3 s on average (Fig. 10a), while the d t ^{4−3} anomalies by 0.2 s (Fig. 10b). These effects may cause small biases to the core models but do not alter them significantly.
If an extreme but currently unresolved heterogeneity that is analogous to LLSVP with a sharp edge exists near the source side CMB entry points of SmKS, it might cause d t ^{3−2} and d t ^{4−3} anomalies of the observed magnitude. As an example of such a scenario, we will next consider a simplified but significantly exaggerated model that has a qualitative resemblance with the tomographic V _{ s } anomalies of the D ^{′′} (Fig. 9c) and evaluate the effects of the extreme lower mantle heterogeneity. The model that we will consider has an axisymmetrical tabularshaped low V _{ s } heterogeneity that has a maximum anomaly of 3.5 % at the CMB and that exponentially decays upward with a scale height of 500 km (Fig. 9c, bottom right). Theoretical d t ^{3−2} and d t ^{4−3} for this model are computed by ray theory (Fig. 10a, b). The values of d t ^{3−2} can be as large as the observed values depending on the epicentral distance. However, there should be a clear trend in d t ^{3−2} with the epicentral distance by about 1 s, which is entirely different from the observed d t ^{3−2} trend. The relative magnitudes of d t ^{3−2} and d t ^{4−3} are also grossly inconsistent with the observation. The heterogeneity model significantly underestimates as a d t ^{4−3} value that is less than half of the observations, mostly because of the smaller separation of the CMB piercing points (Fig. 10a). Although this demonstrates only just one example, the basic feature of V _{ s } structures that potentially cause d t ^{3−2} anomalies as large as the observed values should be more or less the same. S2KS more effectively avoids the low V _{ s } body than S3KS. Simplified mantle heterogeneity models resembling tomography images, no matter how pronounced and sharp they are, have difficulty matching the observed d t ^{3−2} and d t ^{4−3} of the TongaFiji data set. Therefore, we conclude that an unresolved lower mantle heterogeneity is unlikely to be the predominant cause of the observed SmKS anomalies, and estimate its effects on d t ^{3−2} and d t ^{4−3} values based on the current tomography models to be less than 0.3 s and 0.2 s, respectively.
Interpretations in terms of the composition of the core
As suggested by high estimates of liquid iron thermal conductivity, a thermally stratified layer in the neighborhood of 100 km thick might exist in the outermost core (Pozzo et al. 2012). However, a more recent numerical estimate of the electrical conductivity of iron under the Earth’s core conditions has negated the thermal stratification requirement (Zhang et al. 2015). If the stratified layer is nearly 300 km thick, as estimated in this study, the maximum temperature excess over the adiabat at the CMB would be about 300 K. Recent ab initio calculations of liquid and solid iron show that the bulk sound speeds of iron are mostly independent of temperature (Ichikawa et al. 2014; Vocadlo et al. 2009). Therefore, the observed V _{ p } and $V_{p}^{\prime }$ anomalies in the uppermost 300 km of the outer core cannot be of thermal origin and should primarily reflect compositional heterogeneity. Since the effective d K/d P in the layer is larger than the bulk of the core, if the light elements diffuse downward from the CMB (and thus have concentrations decreasing with depth), the addition of the light elements must decrease not only the density of the liquid iron alloy but also its bulk modulus. According to recent ab initio calculations of liquid ironalloy under the core conditions (Badro et al. 2014), these requirements are satisfied. However, the same calculations show that including light elements increases V _{ p }. Thus, it seems that matching the observed V _{ p } value at the CMB cannot be done by simply by adding light elements, even though the effects of nonideal mixing in the iron alloy (which might not be adequately modeled in the simulations) might still play a role in reducing V _{ p } (Helffrich 2012).
The estimated thickness of the compositionally stratified layer (∼300 km) cannot be interpreted via a straightforward process. If the stratified layer evolved from the CMB through the diffusion of light elements, the thickness of the layer is essentially determined by the diffusion coefficient of the core liquid. The mass diffusivity of liquid iron under core conditions is thought to be reasonably well constrained (Koci et al. 2007; Pozzo et al. 2012; Helffrich 2014), and the expected thickness is no more than 80 km (Buffett and Seagle 2010; Helffrich and Kaneshima 2013). Helffrich (2014) suggests that the presence of a thick layer is a feature of the Earth’s core that was formed at the time of the putative giant impact.
While the V _{ p } profile of the top 700 km of the core is adequately represented by two layers with nearly constant radial V _{ p } profile gradients, there is certainly room for the profile to be optimized with some physically plausible constraints, such as the diffusion profile of light elements (Helffrich 2014). However, the revelation of detailed features of the V _{ p } profile is somewhat more difficult due to the presence of mantle effects that have secondary importance. Based on the lack of corresponding anomalies in the waveforms, a sharp interface with a large V _{ p } jump at the bottom of the shallower layer near the depth of 300 km is unlikely to exist, but the presence of a weak jump cannot be ruled out. If light elements diffuse from the CMB, and if double diffusion takes place to form the stratified layer, a succession of thin homogeneous layers might occur near the bottom of the stratified layer (e.g., Buffett and Seagle 2010). In such cases, scattering of seismic energy might occur near the bottom of the layer, depending on the contrasts in the elastic properties between the materials enriched and depleted in light elements. A search for such scattering waves might reveal further details about the enigmatic region of deep Earth. On the other hand, the very top of the core is obviously another locality where an anomalous structure is possible. The existence of a thin and anomalously high V _{ p } and low density layer at the top of the core (Helffrich and Kaneshima 2004) is not supported, if the layer thickness exceeds 10 km or so, by a good fit of the waveforms S6KS to KHOMC (KH2013). Nevertheless, a thinner layer might exist.
Conclusions
The differential travels between SmKS measured by analyzing largescale broadband seismometer arrays are shown to predominantly reflect the V _{ p } structure of the outermost outer core. The combination of d t ^{3−2}, d t ^{4−3}, and d t ^{5−4} anomalies restrict permissible V _{ p } models within a narrow range. There is a significant radial change in gradient of V _{ p } at the depth about 300 km below the CMB. The gradient of the shallower layer corresponds to an effective change in d K _{ s }/d P by about 0.2, which is too large to be attributed to thermal effects alone, and requires compositional stratification.
Abbreviations
 LLSVP:

Large low shear velocity province
 HK2010:

Helffrich and Kaneshima (2010)
 KH2013:

Kaneshima and Helffrich (2013).
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Acknowledgements
This study owes a great deal to the management of waveform data by IRIS DMC, the NDIC’s Fnet in Japan, the JArray Data Center, the Taiwan Data Center, and the ORPHEUS Data Center in Europe. Generic Mapping Tools (GMT) (Wessel and Smith 1995) were used for drawing all of the figures. Appreciation is extended to A. Souriau and G. Helffrich for providing individual S3KSS2KS travel time measurement data. Thanks are also extended to George Helffrich who kindly checked our manuscript, and J. Ritsema who generously provided data from his tomography model. T. Tsuchiya is thanked for his enlightening discussions, and the comments and suggestions of Satoru Tanaka and the two anonymous reviewers were very helpful for improving the manuscript.
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Authors’ contributions
SK performed the analyses and wrote the manuscript. TM prepared for the Hinet tiltmeter data. Both authors read and approved the final manuscript.
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Keywords
 Outermost core
 Compositional stratification
 SmKS waves
 Array processing