Stratification of earth’s outermost core inferred from SmKS array data
 Satoshi Kaneshima^{1}Email author and
 Takanori Matsuzawa^{2}
DOI: 10.1186/s4064501500465
© Kaneshima and Matsuzawa. 2015
Received: 4 January 2015
Accepted: 14 May 2015
Published: 24 June 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.
Keywords
Outermost core Compositional stratification SmKS waves Array processingBackground
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
Event list
Event  Date  Time  Lat. N  Lon. E  h (km)  Mo (dyne cm) 

FEV1  2007/10/05  7:17:52  −25.19  179.46  509  6.8 ×10^{25} 
FEV2  2007/10/16  21: 5:43  −25.77  179.53  509  1.0 ×10^{26} 
FEV3  2008/07/03  3: 2:37  −23.37  −179.78  581  2.8 ×10^{25} 
FEV4  2011/07/29  7:42:24  −23.79  179.75  537.0  1.5 ×10^{26} 
FEV5  2007/05/06  21:11:53  −19.40  −179.35  676  6.1 ×10^{25} 
FEV6  2012/01/24  00:52: 5  −24.977  178.520  580.3  4.2 ×10^{25} 
FEV7  2008/07/19  22:39:53  −17.337  −177.312  391.  5.2 ×10^{25} 
FEV8  2011/08/19  3:54:27  −16.522  −177.004  407.9  2.9 ×10^{25} 
FEV9  2008/10/19  5:10:34  −21.863  −173.819  29.0  2.9 ×10^{26} 
FEV10  2009/03/19  18:17:41  −23.050  −174.660  34.0  3.4 ×10^{27} 
FEV11  2009/11/24  12:47:16  −20.710  −174.040  18.0  1.7 ×10^{26} 
FEV12  2014/07/21  14:54:41  −19.829  −178.464  616.  3.0 ×10^{26} 
FEV13  1998/03/29  19:48:16  −17.552  −179.092  537.5  6.4 ×10^{26} 
KEV1  2013/04/26  6:53:29  −28.68  −178.96  358.8  2.1 ×10^{25} 
KEV2  2011/02/21  10:57:52  −26.142  178.394  558.0  7.9 ×10^{25} 
KEV3  2007/09/25  5:16: 1  −30.965  179.998  417.  2.3 ×10^{25} 
KEV4  2009/08/18  21:20:47  −26.064  −178.391  269.3  3.6 ×10^{25} 
KEV5  2013/08/28  2:54:41  −27.75  179.62  480.3  2.9 ×10^{25} 
KEV6  2014/06/23  19:19:16  −30.118  −177.67  20.  2.6 ×10^{26} 
AEV1  2000/04/23  9:27:23  −28.31  −62.99  609  3.1 ×10^{26} 
AEV2  2005/03/21  12:23:54  −24.98  −63.47  579  2.3 ×10^{26} 
AEV3  2008/09/03  11:25:14  −26.74  −63.22  570  3.3 ×10^{25} 
AEV4  2012/05/28  5: 7:24  −28.06  −63.11  589.3  1.3 ×10^{26} 
AEV5  2011/09/02  13:47:11  −28.420  −63.150  592.8  1.4 ×10^{26} 
AEV6  2014/04/03  1:58:30  −20.311  −70.576  24.1  9.6 ×10^{25} 
NCEV  2014/04/11  20:29:12  11.642  −85.878  135.0  1.0 ×10^{25} 
IEV1  2011/08/30  6:57:42  −6.36  126.76  469.0  2.7 ×10^{26} 
IEV2  2010/03/20  14: 0:50  −3.36  152.24  414  9.2 ×10^{25} 
IEV3  2010/07/23  22: 8:11  6.72  123.41  607.0  1.2 ×10^{27} 
IEV4  2013/06/13  16:47:23  −10.0  107.24  9.0  1.1 ×10^{26} 
IEV5  2011/03/10  17:08:37  −6.87  116.72  510.6  9.7 ×10^{25} 
IEV6  2010/05/31  19:51:45  11.132  93.471  112.  6.4 ×10^{25} 
MEV  2006/02/22  22:19: 8  −21.32  33.58  11  4.2 ×10^{26} 
INEV  2008/05/31  4:37:56  −41.290  80.47  10.  5.1 ×10^{25} 
SEV1  2014/06/29  7:52:56  −55.506  −28.451  16.5  2.4 ×10^{26} 
PEV1  2013/05/14  0:32:26  18.728  145.287  602.3  2.1 ×10^{26} 
Methods and results
Array measurements
Differential travel times are measured on the waveforms which are obtained by linearly stacking the observed broadband seismograms with the relative slowness computed for PREM
Event  Array  Distance  d t ^{3−2} (s)  Bias  d t ^{4−3} (s)  Bias  d t ^{5−3} (s)  Bias  Category 

FEV1  EU  154.0  1.2 ± 0.2  0.1  1.0 ± 0.2  0.2  1.2 ± 0.3  0.2  A 
FEV2  EU  154.0  1.1 ± 0.2  0.2  1.2 ± 0.2  0.2  1.2 ± 0.3  0.3  A 
FEV3  EU  152.5  1.1 ± 0.3  0.1  1.3 ± 0.3  0.3  1.5 ± 0.4  0.2  A 
FEV4  EU  152.  1.6 ± 0.2  0.2  1.3 ± 0.2  0.2  1.2 ± 0.3  0.3  A 
FEV5  EU  147.3  1.5 ± 0.3  0.3  1.3 ± 0.4  0.2  1.6 ± 0.5  0.0  A 
FEV6  EU  153.5  1.6 ± 0.4  0.2  0.9 ± 0.2  0.2  1.1 ± 0.4  0.1  A 
FEV6  US  123.5  0.9 ± 0.3  0.3      B  
FEV7  EU  148.5  1.5 ± 0.4  0.3  1.4 ± 0.3  0.4  1.3 ± 0.4  0.4  B 
FEV8  EU  148.  1.1 ± 0.5  0.3      B  
FEV9  EU  153.  1.2 ± 0.5  −0.1      B  
FEV10  EU  151.9  0.9 ± 0.4  −0.3      B  
FEV11  EU  151.9  1.1 ± 0.4  0.0      B  
FEV12  EU  150.0  1.3 ± 0.2  0.3  1.2 ± 0.2  0.4  1.1 ± 0.3  0.3  A 
FEV13  AF  131.  0.2 ± 0.3  −0.1  0.2 ± 0.2  −0.1    B  
KEV1  EU  155.  1.2 ± 0.2  0.3  1.2 ± 0.3  0.4  1.0 ± 0.4  0.4  A 
KEV2  EU  153.  1.9 ± 0.4  0.2  1.0 ± 0.3  0.2    B  
KEV3  EU  155.  1.4 ± 0.4  0.2      B  
KEV4  EU  155.  1.6 ± 0.5  0.4  1.5 ±   0.4    B  
KEV5  EU  155.5  1.2 ± 0.4  0.3  1.2 ± 0.4  0.2  1.5 ± 0.5  0.1  A 
KEV6  EU  155.  1.4 ± 0.3  0.2  1.5 ± 0.5  0.3    B  
AEV1  JP  162.4  0.5 ± 0.4  0.1  0.9 ± 0.4  0.2    B  
AEV2  HI  157.8  0.9 ± 0.4  −0.1  1.3 ± 0.2  0.2  1.4 ± 0.3  −0.1  A 
AEV3  HI  162.6  0.5 ± 0.5  0.0  0.9 ± 0.4  0.2  0.8 ± 0.5  0.2  B 
AEV4  HI  160.0  0.6 ± 0.3  −0.1  0.6 ± 0.3  0.3  0.5 ± 0.3  0.2  A 
AEV4  AU  124.8  0.7 ± 0.3  0.6      B  
AEV4  AS  167.9  1.0 ± 0.4  0.0      B  
AEV5  JP  163.4  1.0 ± 0.4  0.0      B  
AEV5  AU  124.7  0.6 ± 0.4  0.4      B  
AEV5  AS  167.8  1.0 ± 0.4  0.0  1.4 ± 0.5  0.6    B  
AEV6  JP  153.9  0.6 ± 0.4  −0.1      B  
NCEV  AU  140.1  2.0 ± 0.5  0.7  1.0 ± 0.5  0.3    B  
IEV1  US  130.9  1.3 ± 0.4  0.2      B  
IEV2  EU  122.8  0.9 ± 0.4  0.1      B  
IEV2  US  119.5  0.9 ± 0.4  0.1      B  
IEV3  US  120.9  0.8 ± 0.5  −0.4      B  
IEV4  US  144.  1.0 ± 0.4  0.4  1.0 ± 0.5  0.4  0.9 ± 0.5  0.5  A 
IEV5  US  141.  0.9 ± 0.3  0.1  0.3 ± 0.3  0.0  0.3 ± 0.5  0.2  A 
IEV6  US  133.1  0.4 ± 0.2  0.2  0.1 ± 0.3  −0.2    B  
MEV  US  149.2  1.0 ± 0.5  0.2      B  
INEV  US  168.6  0.2 ± 0.5  −0.3  1.2 ± 0.4  0.5    B  
SEV1  AK  154.1  0.4 ± 0.5  0.1      B  
SEV1  JP  153.8  0.9 ± 0.3  0.2      A  
PEV1  SA  149.5  1.9 ± 0.3  0.5  0.5 ± 0.5  0.6    B 
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
Genetic algorithms
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
Differential slowness (dp ^{32} and dp ^{42},s/°)
Event  Distance Δ _{0}  d p ^{3−2} (s/°)  KHOMC  Residual  d p ^{4−2} (s/°)  KHOMC  Residual 

FEV1  154.0  1.16  1.16  0.0  1.62  1.61  0.01 
FEV2  154.0  1.20  1.16  0.04  1.65  1.61  0.04 
FEV3  152.5  1.15  1.13  0.02  1.60  1.57  0.03 
FEV4  152.0  1.14  1.13  0.01  1.59  1.57  0.02 
FEV6  153.5  1.19  1.18  0.01  1.65  1.65  0.00 
FEV12  150.0  1.12  1.11  0.01  1.56  1.53  0.03 
KEV1  155.0  1.20  1.16  0.04  1.64  1.62  0.02 
AEV2  157.8  1.19  1.21  −0.02  1.70  1.69  0.01 
AEV3  162.6  1.20  1.18  0.02  1.65  1.65  0.00 
AEV4  160.0  1.30  1.23  0.07  1.77  1.73  0.04 
AEV5  167.8  1.30  1.28  0.02  1.80  1.77  0.02 
SmKS differential times of other regions
Observations of dt ^{ 3−2 }
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 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 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.
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).
Declarations
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.
Authors’ Affiliations
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