Joint inversion of normal mode and body wave data for ...geoweb.princeton.edu/people/tromp/Publications copy/tromp_31.pdf · body wave data to constrain the global average and consider

Joint inversion of normal mode and body wave data for inner

core anisotropy

2. Possible complexities

Miaki Ishii and Adam M. DziewonskiDepartment of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA

Jeroen TrompSeismological Laboratory, California Institute of Technology, Pasadena, California, USA

Goran EkstromDepartment of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts, USA

Received 19 June 2001; revised 10 June 2002; accepted 8 July 2002; published 31 December 2002.

[1] In this study we focus on inner core sensitive body wave data to investigate lateral andradial heterogeneity within the inner core. Normal mode data are used to constrain a globalmodel and to monitor if complexities introduced by body wave data are compatible withmode measurements. In particular, we investigate the possibilities of an isotropic layer nearthe inner core boundary and large-scale variations in anisotropy such as hemisphericdependence proposed in studies based upon differential travel time data. Travel time datafrom distances between 130� and 140� require anisotropy near the inner core boundary.This evidence is supported by differential travel time data based upon diffracted waves,contrasting the previous inferences of isotropy at the surface of the inner core. Ourexperiments also show that variations at a hemispheric scale are not necessary and that thesources of apparent hemispheric differences can be localized. A comparison of differentialand absolute travel time data suggests that differences in inferred inner core anisotropymodels arise mainly from a few anomalous paths. These paths are responsible for the stronganisotropy which is characteristic of models based upon differential data. Assumingconstant anisotropy in the inner core, we investigate the distribution of residual differentialtravel times at the entry and exit points of rays turning within the outer core. The results areconsistent with existing models of structure near the core-mantle boundary. Placing thesource of the difference between differential and absolute travel time data in the lowermostmantle gives a more satisfactory result than attempting to model it with a complex innercore. INDEX TERMS: 7207 Seismology: Core and mantle; 7260 Seismology: Theory and modeling; 7203

Seismology: Body wave propagation; 7255 Seismology: Surface waves and free oscillations; KEYWORDS: inner

core, anisotropy, PKIKP, differential travel times, hemispheric variations

Citation: Ishii, M., A. M. Dziewonski, J. Tromp, and G. Ekstrom, Joint inversion of normal mode and body wave data for inner core

anisotropy, 2, Possible complexities, J. Geophys. Res., 107(B12), 2380, doi:10.1029/2001JB000713, 2002.

1. Introduction

[2] The properties of the Earth’s inner core have beeninvestigated using three different types of data: normal modes[e.g., Woodhouse et al., 1986; Tromp, 1993; Durek andRomanowicz, 1999], absolute travel times of PKIKP (orPKPDF) [e.g., Morelli et al., 1986; Shearer et al., 1988;Su and Dziewonski, 1995], and the differential traveltimes BC�DF (or PKPBC�PKPDF) and AB�DF (orPKPAB�PKPDF) [e.g.,Creager, 1992; Song andHelmberger,1993; Vinnik et al., 1994; McSweeney et al., 1997; Tanakaand Hamaguchi, 1997]. The advantage of the high-quality

differential travel time data is the similarity of the mantle raypath of waves turning in the outer core (BC or AB) and theinner core (DF) (Figure 1). This similarity allows one toassume that differential measurements do not include effectsdue to the source, receiver, or mantle, and hence that thetravel time anomalies are solely due to the path within theinner core. Many models of the inner core have beenproposed using differential travel time data, some of whichcontain structures not seen in models based upon other typesof data, such as an isotropic layer near the inner coreboundary [e.g., Song and Helmberger, 1998], a transitionzone within the inner core [e.g., Song and Helmberger,1998], and hemispherically dependent anisotropy [e.g.,Tanaka and Hamaguchi, 1997; Creager, 1999; Niu andWen, 2001].

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B12, 2380, doi:10.1029/2001JB000713, 2002

Copyright 2002 by the American Geophysical Union.0148-0227/02/2001JB000713$09.00

ESE 21 - 1

[3] In the companion paper (Ishii et al. [2002], hereinafterreferred to as paper 1), we demonstrate that it is relativelyeasy to obtain a simple anisotropic inner core model whichfits all three types of data. Normal mode and mantle-corrected DF data are compatible with one another andgood fits can be achieved using a constant anisotropymodel. Differential travel time data are harder to fit. In thispaper we explore the source of this difficulty by (1)considering in detail paths sampled by differential data;(2) introducing structure within the inner core; and (3)investigating the possible effects of D" heterogeneity. Ourfocus is on large-scale structure, and therefore the existenceof lateral variations [e.g., Su and Dziewonski, 1995], exceptfor hemispheric variations or small-scale structure [e.g.,Creager, 1997; Dziewonski, 2000; Vidale and Earle,2000], is addressed only briefly. We assume that thesymmetry axis of the inner core is aligned with the rotationaxis, and we do not consider differential rotation [e.g.,Shearer and Toy, 1991; Creager, 1992; Song and Richards,1996; Su et al., 1996; Souriau and Poupinet, 2000] in ouranalysis. A detailed discussion of the theory, data, andinversion method used in this paper can be found in paper 1.[4] Using all available data, we investigate if the intro-

duction of an isotropic layer near the inner core boundary(ICB) can improve the fit, especially to differential traveltime data [e.g., Song and Helmberger, 1995; Creager,2000]. We also explore the possibility of hemisphericallydistinct anisotropy, previously proposed on the basis ofbody wave measurements [e.g., Tanaka and Hamaguchi,1997; Creager, 1999; Niu and Wen, 2001]. Normal modesdo not constrain this type of structure, because they are onlysensitive to even-degree anomalies. Focusing on absolutebody wave data, we investigate if large-scale variations,including hemispheric variation, in inner core anisotropycan be observed consistently. We use both normal mode andbody wave data to constrain the global average and considerhemispheric deviations as perturbations from this average.[5] In general, inner core models derived using absolute

and differential travel time data differ most in their level ofanisotropy. Models based upon differential travel times havestrong anisotropy [e.g., Creager, 1992; Song and Helm-berger, 1993], especially near the center of the Earth [e.g.,

Vinnik et al., 1994; Song, 1996; McSweeney et al., 1997],whereas absolute travel times tend to result in models withweaker anisotropy [e.g., Su and Dziewonski, 1995]. Toinvestigate this discrepancy, we compare absolute anddifferential travel time data. Contamination of differentialdata due to mantle structure near the core-mantle boundary(CMB) has also been suggested [e.g., Breger et al., 1999,2000], especially for the AB rays. We follow this suggestionand investigate if the residual differential travel time signalbased upon a constant anisotropy model can be placed in themantle.

2. Comparison of Body Wave Data

[6] We use normal mode splitting functions [He andTromp, 1996; Resovsky and Ritzwoller, 1998; Durek andRomanowicz, 1999], ISC DF residuals, and high-qualitydifferential travel time data [Creager, 1992; Vinnik et al.,1994; McSweeney, 1995; Song, 1996; Creager, 1997;McSweeney et al., 1997; Tanaka and Hamaguchi, 1997;Creager, 1999] to investigate the structure of the inner core.Before using these data, we explore the differences betweenmantle-corrected absolute and differential travel time data.For details of data processing, see paper 1. If the mantlecorrection to absolute and differential travel times is appro-priate, these two sets of data should agree well. The fact thatmodels obtained from independent inversions of these twodata sets differ significantly suggest that this is not the case.[7] The BC arrivals are observed in the 145� to 153�

epicentral distance range (Figure 1), and the correspondingBC�DF data are sensitive to inner core structure down toroughly 300 km beneath the ICB. There are 851 BC�DFmeasurements in our data set, spanning the distance from145� to 160�. Data with an epicentral distance greater than�153� involve diffracted BC traveling along the ICB. Wediscard these data when performing inversions but return tothem in section 4, where we consider structure near the ICB.The remaining 512 BC�DF data are binned into twodistance ranges, 145� to 150� and 150� to 153�, andaveraged for each 0.1 increment in cos2 x, where x is theangle between the direction of wave propagation and thesymmetry axis of transverse isotropy. The averaging process

Figure 1. (left) Ray paths for AB, BC, and DF at an epicentral distance range of 150�, and (right) atravel time table for PKP branch using PREM [Dziewonski and Anderson, 1981]. For the travel time tablewe use an earthquake with a source depth of 300 km.

ESE 21 - 2 ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2

reduces the effects of mantle heterogeneity by cancellingout the isotropic signal if the outer core entry and exitpositions of BC or AB cover the globe uniformly. In thispaper we show that differential travel time data coverage isuneven compared to absolute travel time data, and suggestbiased sampling as the reason for difference in inner coremodels derived from these two data sets.[8] We compare BC�DF data in the range from 150� to

153� with DF from the same distance range (Figure 2a). Thetwo sets of data agree well in general, except for 4 points atvalues of cos2 x of 0.45, 0.55, 0.75, and 0.85. The averagesof BC�DF at these points seem to be well constrained byclusters of measurements around values of cos2 x of 0.5 and0.8. However, upon inspection of source-receiver pairs, wefind that the cluster about cos2 x = 0.8 is due to a pathbetween South Sandwich Islands and Alaska. Data from thispath are known to be anomalous [e.g., Su and Dziewonski,1995; Dziewonski and Su, 1998], and the exclusion of thesedata changes both BC�DF and DF values, although thechange in BC�DF data is greater than in DF. The data setsagree better now at cos2 x of 0.75 and 0.85 (Figure 2b). Wealso find that the cluster at about cos2 x = 0.5 is mainly due totwo earthquakes south of Africa recorded at 71 stations inCalifornia. If we remove this cluster (Figure 2c), the agree-ment between DF and BC�DF data is remarkable. Further-more, the constant model of anisotropy obtained in paper 1fits both sets of body wave data. In inversions constrainedonly by, or relying heavily upon, the differential travel times,these anomalous data are up-weighted due to abundantmeasurements, and would produce a model with stronganisotropy. This is evident in Figure 3 of paper 1. The modelof Creager [1992] fits the anomalous data associated withthe paths between South Sandwich Islands to Alaska at theexpense of poorly fitting the data at higher values of cos2 x.Note that the cluster of measurements from the earthquakesouth of Africa were not available to Creager [1992], sincethe earthquake occurred on 29 March 1993.[9] To complement the BC�DF data, which are sensitive

only to shallow structure of the inner core, measurements ofAB�DF data between 145� and 176� (Figure 1, right) areoften included in inner core inversions [e.g., Vinnik et al.,1994; Song and Helmberger, 1995; Song, 1996;McSweeneyet al., 1997;Creager, 1999]. Because the paths of AB and DFdiffer significantly in the mantle (Figure 1, left), contami-nation of AB�DFwith structure in the lowermost mantle hasbeen suggested [e.g., Breger et al., 1999, 2000], but isignored in inner core studies [e.g., Vinnik et al., 1994; Songand Helmberger, 1995; Song, 1996;McSweeney et al., 1997;Creager, 1999]. We will investigate the effect of the mantleon AB�DF and BC�DF in a later section.[10] We group AB�DF data into four distance ranges,

149� to 153�, 153� to 160�, 160� to 165�, and 165� to 180�.Data in each distance range are averaged for every 0.1increment in cos2 x. We compare AB�DF and DF in therange 160� to 165� in Figure 3a. In general, the two types ofdata agree well, which is surprising considering the like-lihood of strong contamination from the mantle. The onlyexception is at cos2 x = 0.75, where the AB�DF averageseems to be well constrained by numerous points betweencos2 x values of 0.7 and 0.8. However, as for BC�DF,examination of these points reveals that they originate, withone exception, from a single earthquake near Bouvet Island

recorded at 35 stations in Alaska. Removal of this earth-quake (Figure 3b) does not improve the compatibility ofAB�DF and DF, but since the average at cos2 x = 0.75 isdetermined by a single datum, it is possible that thisdiscrepancy reflects either another anomalous path or sub-stantial mantle heterogeneity or source mislocation. Verystrong anisotropy near the center of the inner core, inferredin many differential travel time studies [e.g., Vinnik et al.,1994; Song and Helmberger, 1995; Song, 1996;McSweeney

Figure 2. (a) Comparison of mantle-corrected DF data(circles) and BC�DF data (triangles) in the distance range150�–153�. To ease visual comparison, the sign of the DFdata has been reversed, and a baseline shift has been applied(we are interested in the trend in the data as shown inequation (6) of paper 1). The background dots are individualBC�DF measurement, and the solid curve is the predictionbased upon the constant anisotropy model derived in paper1. (b) Same as in Figure 2a, except that the data from thepath between South Sandwich Islands and Alaska have beenremoved. (c) Same as in Figure 2b, except that in addition tothe data from the path between South Sandwich Islands andAlaska, the data from two earthquakes located south ofAfrica and stations in California are removed.

ISHII ET AL.: JOINT INVERSION FOR IC ANISOTROPY, 2 ESE 21 - 3

et al., 1997; Creager, 1999], is the result of trying to fit thelarge AB�DF residuals at large cos2 x.[11] These comparisons demonstrate the biased sampling

of the Earth by the differential travel time data. To quantifythis, Figure 4 shows the coverage of the inner core with theentire set of BC�DF, AB�DF, and DF data in terms ofbottoming point. Most of the inner core is not sampled bythe differential travel time measurements, but it is wellsampled by DF data except for some spots in the SouthAtlantic. Therefore DF data should represent global aniso-tropy better than differential data, and this explains why DFdata are highly compatible with normal mode data (paper1). In addition, at angles where biased data dominate theaverage values, effects due to variations in the mantle areunlikely to have been cancelled. This may explain whyanomalous differential data are poorly fit by a simple model

of the inner core (Figure 3 of paper 1). The origin of theanomalous differential travel times may also be attributed tosmall-scale structure [e.g., Creager, 1997; Dziewonski,2000; Vidale and Earle, 2000] or lateral variations in theinner core [e.g., Su and Dziewonski, 1995].

3. Inversion for Inner Core Models

[12] In this section, we assume that the anomalous differ-ential data originate in the inner core, and investigate if

Figure 3. (a) Comparison of mantle-corrected DF data(circles) and AB�DF data (triangles) in the distance range160�–165�. There are no measurements of AB�DF withcos2 x greater than 0.8 in this distance range. To ease visualcomparison the sign of DF has been reversed, and a baselineshift has been applied. The background dots are individualdifferential AB�DF measurement. (b) Same as in Figure 3a,except that the data from an earthquake near Bouvet Islandrecorded at stations in Alaska are removed.

Figure 4. Plot of all bottoming points for (top) BC�DF,(middle) AB�DF, and (bottom) DF data. This plot is madeusing data from all distances (between 145� and 153� forBC�DF data, between 149� and 180� for AB�DF data, andbetween 120� and 140� and between 150� and 180� for DFdata). Note that DF and combination of two differentialtravel time data sets have been used to derive anisotropicmodel of the whole inner core. In later figures, we show thatcoverage degrades substantially when we start investigatingdepth and lateral dependence of anisotropy.


complex structures, such as an isotropic layer near the ICBand hemispherically dependent anisotropy, can provide amodel that fits both DF and differential travel time data.Although we focus on body wave data, all inversionsinclude normal mode splitting functions. Because a constantmodel of anisotropy fits the data well (paper 1), weassume constant anisotropy in this section, unless otherwiseindicated.

3.1. Isotropic Layer Near the Inner Core Boundary

[13] There have been suggestions that anisotropy in theinner core is weak in the top 50–300 km [e.g., Shearer,1994; Song and Helmberger, 1995; Creager, 2000], or thatthis region is isotropic [Song and Helmberger, 1998]. Toinvestigate if the hypothesis of an isotropic layer is compat-ible with mode and DF data, we perform inversions inwhich an isotropic layer of varying thickness is imposednear the ICB. The fit to the mode data as a function of thethickness of the isotropic layer is shown in Figure 5. The fitimproves marginally as the thickness is increased to about100 km, however the improvement is not statisticallysignificant. A significant drop in variance reduction startsaround 150 km. We conclude that normal mode data areconsistent with an isotropic layer up to about 150 kmthickness, in agreement with Durek and Romanowicz[1999].[14] When the fit to DF travel time data is considered, the

overall variance reduction decreases monotonically withincreasing thickness of the isotropic layer. The most sig-nificant change is observed in the fit to BC�DF data:introduction of an isotropic layer immediately decreasesthe variance reduction and the fit degrades rapidly when thethickness is more than �30 km. The degradation of fitcontradicts previous differential travel time studies, how-ever, it is due to normal mode constraint: modes do notallow strong anisotropy in the interior as required by

differential travel time data. Mantle-corrected DF data atan epicentral distance range less than 153� also exhibit arapid decrease in variance reduction. Therefore data fromrays shallowly penetrating the inner core do not favor theexistence of an isotropic layer. In contrast, the fit to datasuch as AB�DF and DF at large epicentral distances variesonly slightly with the introduction of an isotropic layer andis highly compatible with a layer as thick as �150 km fromthe ICB; however, their sensitivity to shallow structure isless, and the fit is achieved by slightly modifying thestrength of anisotropy in the deeper part. These observationsare robust and they do not depend upon the maximum radialexpansion or the type of basis function used. There are atleast two possible explanations for poor fits to data at smalldistance ranges. The first is that the weak angle-dependenttrend observed in data at these distances is due to inadequatemantle corrections. However, the averaging procedure andcomparison of Figures 5 and 6 of Su and Dziewonski [1995]suggest that this is unlikely for data in the distance range of130�–140�. The second, and our preferred, explanation isthat the inner core is anisotropic near the ICB. Our modelwith 1.8% anisotropy gives good fit to DF data in the 130�–140� range.[15] The data set with the most sensitivity to the shallow

part of the inner core does not support the existence of anisotropic layer near the ICB. Can this observation beintegrated with data from which inferences of isotropiclayer have been made? The concept of an isotropic layerwas introduced based upon Shearer’s [1994] study whichrejected a high (3.5%) level of anisotropy using absolutetravel time data at short distances (132� to 140�). Thisconclusion appears to have been misinterpreted as an argu-ment for an isotropic layer near the ICB [Song andHelmberger, 1998]. Our global anisotropy model achievesa satisfactory fit to Shearer’s data set in this distance range(Figure 6): indeed, a better fit than weak anisotropy modelof Shearer et al. [1988]. None-zero anisotropy near the ICBis not inconsistent with differential travel time data as it mayappear at first. Although isotropy is strongly advocated,differential travel times do not rule out the presence of weak(�1%) anisotropy near the ICB [e.g., Song and Helmberger,1995; Creager, 2000; Garcia and Souriau, 2000]. Thereforeanisotropy at the topmost inner core would explain DF dataat short distances and is consistent with differential traveltime data as long as it is relatively weak. Finally, we presentadditional evidence for finite anisotropy near the ICB usingdiffracted BC�DF data in section 4.

3.2. Large-Scale Variations in Anisotropy

[16] Inner core sensitive normal modes do not seem torequire complicated structure within the inner core (paper1). However, several studies based upon differential traveltime data [e.g., Tanaka and Hamaguchi, 1997; Creager,1999; Niu and Wen, 2001] have suggested that the proper-ties of the inner core have an east-west hemisphericaldependence. The normal mode data are insensitive to thehemispherical difference since such a pattern corresponds tostructure at spherical harmonic degree one. Only body wavedata are sensitive to hemispheric differences; hence wefocus our attention to the travel time data. We investigateif data are consistent with such large-scale structure bydividing the data into subsets based upon their bottoming

Figure 5. Fit to splitting function coefficients of inner coresensitive modes as a function of the thickness of theisotropic layer from the ICB. The variance reduction isobtained from an inversion with an S velocity, P velocity,and density parameterization within the mantle, andassuming constant anisotropy within the inner core belowthe isotropic layer.


points. The eastern and western hemisphere data show cleardifference, but such dichotomy is also observed when theinner core is divided into the northern and southern hemi-spheres. We present a geometrical argument that the appa-rent hemispheric anomalies result from a localized region,and much of data can be explained by our constantanisotropy model.3.2.1. Hemispheric Dependence of Anisotropy[17] Although investigations of hemispheric dependence

of anisotropy concentrated on east-west difference [e.g.,Tanaka and Hamaguchi, 1997; Creager, 1999; Niu andWen, 2001], the division of the inner core into eastern andwestern hemispheres is not the only way in which one canobtain subsets with distinct behavior. We demonstrate thiseffect by separating data according to whether they bottomin the northern or southern hemispheres. A clear differencebetween hemispheres is observed regardless of the defini-tion of hemisphere for DF data (Figures 7a and 7b). Ingeneral, the hemispheric data agree well with one another inthe distance range from 120� to 140�. In addition, there is agood agreement between hemispheres when cos2 x < 0.7over all distance ranges. Because large differences areobserved only at high values of cos2 x, where there areinherently less data, it is possible that the differences are dueto poorer sampling and local structure. For example, biasedsampling of an anomalous region of the inner core or mantleheterogeneity not included in our mantle correction cancreate apparent hemispheric differences.[18] When hemispheric BC�DF data are compared (Fig-

ures 7c and 7d), a smoother variation as a function of cos2 xis observed again for the northern hemisphere than the

western hemisphere. This is partly due to the separationof two clusters into different hemispheres, one associatedwith the south of Africa-California path (cos2 x � 0.5) andanother with the South Sandwich Islands-Alaska path (cos2

x � 0.8), but also because there are only a few measure-ments in the southern hemisphere with small values of cos2

x. Difference between eastern and western hemispheres isnot clear for BC�DF data between 145� and 150�. Divisionof data into northern and southern hemispheres seems toenhance hemispheric differences at this distance range.However, there are only nine measurements above a cos2

x of 0.2 for the southern hemisphere, so little significancecan be attributed to the slightly larger difference betweenthe northern and southern hemispheres. In contrast to DFand BC�DF data, the difference between eastern andwestern or northern and southern hemispheres is notobvious for AB�DF data in general (e.g., Figures 7e and7f ). The difference appears slightly more pronounced forthe north-south division, however, it is difficult to comparethe two subsets as the distribution of data seems to comple-ment one another: where there are many measurements inone hemisphere, there are only a handful of measurementsfor the other. It is, nonetheless, consistent with DF orBC�DF data in that the stronger anisotropy trend can beassociated with the northern or western hemisphere.[19] Inversions using hemispherically divided data sets

produce only marginal improvement in fit including differ-ential travel time data. Hemispheric anisotropy model forthe eastern and the western hemispheres differ considerably,especially for the poorly constrained parameter s. Even ifwe accept the possibility of hemispheric variations for aslowly growing crystal within a homogeneous liquid[Jacobs, 1953], it will be difficult to explain such a largedeviation physically. Although dependence of anisotropywith latitude may be more physically plausible than depend-ence on longitude, inversions for different anisotropy in thenorthern and southern hemispheres do not produce satisfac-tory fits. Because the data trend is smoother with respect tocos2 x than with a east-west division, one might expectbetter fits for the northern and southern data. However, thedivergence of hemispheric data is too rapid at large cos2 xand is inconsistent with the data trend at small values ofcos2 x. In section 3.2.2, we investigate the property of datawith large cos2 x values.3.2.2. Data Distribution and Hemispheric Dependence[20] When we group the data into hemispheres, especially

into the eastern and western hemispheres, the travel timesdiverge rapidly at around cos2 x = 0.7. Such an increase inthe gradient of travel times is inconsistent with a trans-versely anisotropic inner core where travel time dependsquadratically on cos2 x (equation (5) of paper 1). Thereforea difference in the strength of anisotropy is not sufficient toexplain unambiguously the observed change in gradient.Another observation from separating the inner core intohemispheres is that the difference becomes significant whencos2 x is above 0.7. The smallest angle x (hence largest cos2

x) for a ray occurs when it is traveling in the north-southplane perpendicular to the equatorial plane. This geometryis such that the smallest angle x is equal to the latitude of thebottoming point (Figure 8a). The relationship between thelatitude of the bottoming point and the largest cos2 x isplotted in Figure 8b. Clearly, the data with high values of

Figure 6. ISC summary ray residuals for the distancerange 132� to 140� (P. M. Shearer, personal communica-tions, 2001). The residuals are plotted as a function of 90� �x rather than cos2 x to ease comparison with Figure 9 ofShearer [1994]. The standard deviation associated with eachdatum is shown as a vertical bar. Predictions based uponmodels from Shearer et al. [1988], Creager [1992], and theconstant anisotropy model of paper 1 [Ishii et al., 2002] areshown. Note that the strong anisotropy in Creager’s modeloverpredicts residuals at high values of x. Data courtesy ofP. Shearer.


Figure 7. Comparison of data from eastern/western hemispheres and northern/southern hemispheres.(a) and (b) Comparison of DF data in the distance range between 153� and 155�. The inner core isdivided into eastern (solid triangles) and western (shaded circles) hemispheres in Figure 7a, while it isdivided into northern (solid triangles) and southern (shaded circles) hemispheres in Figure 7b. (c) and (d)Same as Figures 7a and 7b except that BC�DF data are compared at the distance range between 150� and153�. The small triangles and circles are individual measurements. Note that there are no data betweencos2 x of 0.2 and 0.4 for the southern hemisphere and between 0.9 and 1.0 for northern hemisphere. (e)and (f ) Same as Figures 7c and 7d except that AB�DF data are compared at the distance range of 153�and 160�. There are no data between cos2 x of 0.6 and 0.7 and between 0.9 and 1.0 for the westernhemisphere, between 0.8 and 0.9 for the eastern hemisphere, between 0.5 and 0.6 for the northernhemisphere, and between 0.8 and 1.0 for the southern hemisphere.


cos2 x come only from rays bottoming near the equatorwhile those with small cos2 x values bottom at all latitudes.[21] We divide our DF data set into four subsets: eastern

polar, eastern equatorial, western polar and western equa-torial regions (Figure 8c). Separating differential traveltime data into quadrants reduces the number of measure-ments so much that it is difficult to study data trend as afunction of cos2 x. Therefore we concentrate on the DF

data. In passing, we note that the two anomalous BC�DFpaths, south of Africa to California and South SandwichIslands to Alaska, both bottom in the western equatorialregion.[22] To ease comparison between the quadrants, we only

show data between cos2 x of 0.0 and 0.7 (Figure 9). Datafrom different quadrants generally agree in their trend (slopeand curvature). Note the good agreement particularly atdistance ranges (150�–153�, 153�–155�, and 155�–160�)where a strong east-west hemispheric difference is observed.Moreover, the data trends from all quadrants agree surpris-ingly well with the prediction from the constant anisotropymodel obtained in paper 1. This suggests that a globalanisotropy model can explain much of the data even if theyare divided into hemispheres or quadrants. The only excep-tion is 175�–180� distance range which is investigated byIshii and Dziewonski [2002]. Comparison of bottominglocations for data with cos2 x above and below 0.7 indicatesthat high values of cos2 x are constrained unavoidably by amuch smaller number of data which bottom in regions wherecoverage by data with smaller values of cos2 x is not verygood (Figure 10a). This is particularly true for the westernhemisphere where large travel time residuals are observed.Because of the relatively small size of the database, cos2 x >0.7 values are affected more by source-receiver pairs withlarge residuals (Figure 10b).[23] The ambiguity of hemispherically dependent aniso-

tropy is demonstrated further when data are binned to makesummary rays depending upon the distance range, the rayangle with respect to the symmetry axis, and the bottomingpoint. One example from 153�–155�, which is the distancerange where hemispheric difference is most prominent, isshown in Figure 11. This approach highlights the unevendistribution of data for all values of cos2 x, indicating thedifficulties of assessing lateral variations in anisotropy.Hemispheric dependence, be it east-west or north-south,can not be clearly identified with such sparse data set. We

Figure 8. (opposite) Geometry of DF in the inner coreand its implications for bottoming latitude. (a) Therelationship between the latitude of the bottoming point ofthe ray (q0) and the smallest value of the ray angle withrespect to the rotation axis (x). At the bottoming point, theray (solid red line) is perpendicular to the unit vector inradius. This implies that x + q = 90�, where q is colatitudeand hence x = q0. (b) Plot of the latitude of ray’s bottomingpoint (y axis) against cos2 x. The solid curve showsmaximum latitude as a function of cos2 x. The dots showwhere individual DF datum between 150� and 153� distancerange plots. Streaks of dots are the results of an earthquakeobserved at various stations and/or a station observing asuite of earthquakes at similar locations. (c) Division of DFdata into eastern polar region (jlatitudej > 30� with 0� �longitude < 180�, indicated by green dots), easternequatorial region (jlatitudej � 30� with 0� � longitude <180�, blue dots), western polar region (jlatitudej > 30� with180� � longitude < 360�, yellow dots), and westernequatorial region (jlatitudej � 30� with 180� � longitude <360�, red dots). Dots on the map are bottoming points of DFdata in the 150� to 153� distance range.


Figure 9. Comparisons of subsets of DF data at various distance ranges. Data with different colorscorrespond to quadrants as shown in Figure 8c. Data with cos2 x > 0.65 are available for the two equatorialregions; however, we truncated the data at 0.65 to ease comparison between quadrants. The black curve isthe prediction based upon constant anisotropy model obtained in paper 1. Note that data from 173�–180�distance range behave differently compared to other distances [Ishii and Dziewonski, 2002].


conclude that the hemispheric difference is only apparent.Most of the data at values of cos2 x � 0.7 are consistentwith the global anisotropy model, suggesting that the hemi-spheric discrepancy is due to a smaller-scale phenomenon.The apparent hemispheric difference is explained easily ifsmall structures are located in the inner core, however,because of the limited number of paths with cos2 x > 0.7and uneven coverage, the possibility of effects from themantle cannot be dismissed.

4. Discussion

[24] We have seen that allowing for complexities, such ashemispheric variations and an isotropic layer near the ICB,does not improve the fit to differential data substantially. Insection 4.1, we return to a simple model of inner coreanisotropy and investigate if the misfit to differential datacan be explained by structure in the lowermost mantle. Thenwe look briefly at differential data that were not used in theinversions: diffracted BC�DF.

4.1. Residual Differential Body Wave Data

[25] Finding a constant anisotropy model that fits bothnormal mode and DF data is very easy and the variancereductions obtained from such a model are high for these

data: 83% and 85%, respectively. In contrast, fitting differ-ential data is more difficult, and variance reductions forthese data are lower although these data should be of higherquality than DF data: 71% for BC�DF and 74% forAB�DF (paper 1). Previous studies [Breger et al., 1999,2000; Tkalcic et al., 2002] have suggested that this may bedue to heterogeneity in the lowermost mantle, where thepaths of BC and DF or AB and DF differ considerably. Forthe rest of this section, we assume constant anisotropy in theinner core based upon paper 1 and investigate if the residualsignal can be associated with structure of the lowermostmantle.[26] Using the constant anisotropy model (paper 1), we

predict the travel time for the differential data. Any devia-tions of a measurement from these predictions are thenplaced at the outer core entry and exit points of the BC orAB ray. The inherent assumption is that the deviationsoriginate in the outer core branch. Therefore we associatepositive residuals with slower velocity and negative resid-uals with faster velocity and calculate the average ofresiduals for each 10� by 10� block. Note that positiveanomalies, if ascribed to the DF part of the differential data,imply faster than average velocity and negative anomaliesindicate slower than average velocity in the inner core. Thisprocedure does not consider the spread of residuals along

Figure 10. (a) Comparison of bottoming point distribution for data with cos2 x smaller and greater than0.7 in the distance range between 150� and 153�. (b) Comparison of eastern (grey curve with triangles)and western (black curve with squares) subsets of data at 150�–153� distance range. When the data fromthe anomalous path between South Sandwich Islands and Alaska are removed from the western data(black dotted curve between 0.65 and 0.95), the difference between the eastern and western hemispheresis smaller.


the ray path of BC or AB. Nevertheless, we still believe thatthe resulting maps give an indication of the importance ofmantle structure near the CMB.[27] Figure 12a shows the hit count and residual map of

BC�DF. The hit count map shows a very biased distribu-tion. Much of the globe is poorly sampled (regions in black)as expected from Figure 4, with few exceptions. Forexample, the high counts under north-western Canada andthe southern Atlantic are due to BC�DF measurements ofearthquakes from the South Sandwich Islands recorded atstations in Alaska. Similarly, the paths from the two earth-quakes south of Africa to numerous stations in Californiaappear as high counts near Antarctica and the southwesternUnited States. The strongest features in the map of BC�DFtravel times without inner core corrections are the three redspots (positive residuals) around the southern Atlantic,Alaska, and the southern Pacific. These are due to measure-ments of anomalies from polar paths. The large-scale andthe strongest feature in this map is a zonal pattern, i.e.,positive anomalies (red to yellow) at high latitudes andnegative (blue to green) anomalies near the equator. The

map view of BC�DF after inner core corrections, incontrast, is highly nonzonal. There are still some strongfeatures, such as a positive (slow if due to BC) anomaly inthe South Pacific and a negative (fast) anomaly betweenSouth America and Antarctica. However, the amplitude ofthese anomalies is much lower compared to a map withoutinner core corrections.[28] Although we have more AB�DF data, Figure 12b

shows that they still come from limited source-receiverpairs; these data cover the globe unevenly, with a biastoward the western hemisphere. This bias implies thatAB�DF data, which are more sensitive to mantle structurethan BC�DF, sample only certain parts of lowermostmantle. Therefore the averaging procedure is insufficientto cancel out the mantle contribution. The zonal pattern inthe uncorrected travel time map (evident in Figure 12a) isnot present for AB�DF, and the pattern looks similar to thecorrected BC�DF map. AB�DF after inner core correc-tions appears virtually identical to the uncorrected map,although inner core corrections reduce the amplitude of theresiduals. AB is a ray that grazes the CMB (Figure 1); a

Figure 11. Plot of DF residuals as a function of ray angle and bottoming location. For each plot,average has been removed to enhance lateral variations. Unusually large residuals are due to bins withonly one or two measurements. Using triangular tessellation, the center of each bin is obtained fromdividing the Earth into 362 nearly equal-area triangles as in Figure 1 of Gu et al. [2001]. Radius of eachbin is 10�.


region known to be highly heterogeneous. Hence it is notsurprising that AB�DF data contain strong signals frommantle heterogeneity [Breger et al., 1999, 2000].[29] The inner core corrected residual patterns for BC�DF

(Figure 12a) and AB�DF (Figure 12b) are very similar inregions that are well sampled. This similarity suggests thatthese signals originate in the lowermost mantle. The differ-ence in amplitude likely arises from the path differencebetween BC and AB. AB spends more time in this stronglyheterogeneous layer, hence it is affected more by mantlestructure near the CMB. Some of the features observed inthe residual maps are consistent with P velocity models nearthe CMB, such as the fast anomaly under India and easternAsia, and the slow anomaly in the southern Pacific ocean.The fast, linear anomaly in the northern Pacific is alsoconsistent with some P velocity models [e.g., Vasco andJohnson, 1998; van der Hilst et al., 1998; Boschi andDziewonski, 1999; Karason and van der Hilst, 2001] andsome S velocity models [e.g., Gu et al., 2001]. However,there are features in the residual maps, such as a slowvelocity anomaly under Canada and Alaska, that are notobserved in tomographic models. Most tomographic models

have fast velocity anomalies in this region, with someexceptions, such as the S velocity model of Su and Dzie-wonski [1997], which has close to zero value, and the Pvelocity model of van der Hilst et al. [1998] with a negativevelocity anomaly underneath Alaska. The D00 model ofTkalcic et al. [2002], based upon PcP�P and differentialdata, also shows a negative velocity anomaly under Canada.This anomaly contributes to the large positive BC�DFmeasurements for the path between South Sandwich Islandsto Alaska (Figure 2).[30] The main difference between the maps shown in

Figure 12 and the structure obtained by Tkalcic et al. [2002]is the strength of the anomalies. The residual maps ofBC�DF and AB�DF generally have an amplitude of±1.5 s. If we assume that the signal originates from raypaths with a length of 300 km in the mantle, and the averageP velocity is 13.5 km/s, then a simple conversion givesapproximately ±7% variations for ±1.5 s. Our calculationsdo not consider the geometry and length of the BC or ABray path, so this estimate is likely to be an overestimate.Most recent P velocity models [e.g., Bolton, 1996; Boschiand Dziewonski, 1999] have amplitudes of ±1% and so does

Figure 12. (a) (top) Hit count map for BC�DFmeasurements. Black regions indicate poor sampling andwhite indicate well-sampled regions. This map shows that BC�DF data illuminate only a limited part of themantle. Note that compared to conventional seismic tomography of the mantle or DF measurements fromISC, the number of data is much smaller. The numbers on the scale are the number of rays instead of itslogarithm. (middle) Map view of BC�DF measurements plotted at the entry and exit points of BC. Redregions indicate places with positive travel time anomalies (if attributed to BC, this corresponds to slowerthan average velocity in the mantle), and blue regions indicate negative anomalies (fast velocity). (bottom)Map view of BC�DF measurements after correcting for the inner core signal using a constant model ofanisotropy. The residuals are plotted at the entry and exit points of BC. The scale is the same as the middlepanel. (b) Same as in Figure 12a except for AB�DF measurements.


the D00 model of Tkalcic et al. [2002], although the latterincludes anomalies in excess of ±2.5%. Nonetheless, ampli-tudes as large as ±7% have been observed near the CMBusing diffracted P waves [Sylvander et al., 1997], and thelocations of slow velocity anomalies in the residual maps(Figure 12) correspond well with observations of ultralow-velocity zones (ULVZs), for example, underneath southernPacific and Africa [e.g., Mori and Helmberger, 1995;Garnero and Helmberger, 1996; Vidale and Hedlin, 1998;Garnero et al., 1998].[31] The residual patterns, especially that of AB�DF,

agree remarkably well with the P velocity model within D00

of Tkalcic et al. [2002]. These observations indicate thatmost of the differential anomaly that is not reconciled by aconstant anisotropy model of the inner core results fromheterogeneity deep within the mantle. The strong anisotropyin inner core models derived from differential travel timedata is due to local anomalies or structure near D00. Inparticular, anisotropy near the center of the Earth is con-strained only by a heavily contaminated AB�DF data set,making inferences of increased anisotropy in the deepest partof the inner core questionable. Inverting for inner corestructure using normal mode, absolute, and differential traveltime data allows us to separate mantle and inner core effects.[32] How would such a strongly heterogeneous layer near

the CMB affect DF and normal mode data? The P velocitymodel used to correct DF for mantle structure does notinclude this layer nor does the model derived from themode inversion. Because DF data have better coverage, andsince they are almost vertical when they enter or exit thecore, the effect of the layer near the CMB will be small andis likely to be cancelled out by the averaging procedure.Similarly, deeply-penetrating modes have a broad kernelnear the CMB, and the splitting due to this layer will not besubstantial. Furthermore, the zonal component of the het-erogeneity is relatively small; hence the effect on the zonalpart of the splitting function will be limited. On the otherhand, the nonzonal residual of inner core sensitive modes(Figure 7 of paper 1), may be a result of this stronglyheterogeneous layer. Therefore mantle structure near theCMB must be considered, but it does not significantlyaffect the analysis of inner core anisotropy presented inpaper 1.

4.2. Mantle Heterogeneity and Anomalous Paths

[33] There are numerous observations of differentialtravel times for the path between South Sandwich Islandsto Alaska, which have been used to derive global models[e.g., Creager, 1992], laterally varying models [e.g., Cre-ager, 1997], and differential rotation of the inner core [e.g.,Song and Richards, 1996; Su et al., 1996; Creager, 1997].Furthermore, observations of DF from this path led Su andDziewonski [1995] to estimate the tilt of the symmetry axisto be �11�, which was later shown to have been anoverestimate biased by this path [Souriau et al., 1997;Dziewonski, 2000]. In preceding sections, we have shownthat this path is highly anomalous and that the measure-ments do not reflect global anisotropy. Large deviations inBC�DF differential travel time data suggest that theanomaly is mostly within the inner core, although part ofthe anomaly can be explained by an inadequate mantlecorrection.

[34] We address the issue of a possible mantle signal indifferential travel times by comparing the differential traveltime residuals (after correcting for constant anisotropy inthe inner core) with predicted differential travel times froma recent three-dimensional mantle model [Antolik et al.,2002]. The results for BC�DF and AB�DF are shown inFigure 13. In general, the predicted residual due to mantlestructure is much smaller than the observed residuals,consistent with the results of Breger et al. [1999, 2000].It suggests that the amplitude of the P velocity models ofthe lowermost mantle is under-estimated as already docu-mented for S velocity models [e.g., Ritsema et al., 1998;Breger and Romanowicz, 1998]. For BC�DF, there is no

Figure 13. (a) Plot of BC�DF residuals after correctingfor constant anisotropy in the inner core (x axis) andtravel time anomalies predicted by mantle heterogeneitybased upon the recent P velocity model of Antolik et al.[2002] (y axis). The grey dots are for a path between theSouth Sandwich Islands and Alaska, open circles are fora path between south of Africa and California and blackdots are for other paths. (b) Same as in Figure 13a exceptfor the AB�DF residual. The shaded dots are for a pathbetween the South Sandwich Islands and Alaska, andopen circles are for a path between Bouvet Island andCalifornia.


correlation between observed and predicted residuals if theentire data set is considered, but if measurements from thetwo anomalous paths identified in section 4.1 are removed,the data are slightly correlated. The large residuals fromthe anomalous paths from the South Sandwich Islands toAlaska and from south of Africa to California deviate farfrom the main cluster. A similar comparison for AB�DFdata exhibits a stronger correlation between predictionsand observations, indicating that mantle structure is impor-tant for this data set. The South Sandwich Islands toAlaska path does not stand out as particularly anomalous,but Bouvet Island to California produces a cluster awayfrom the origin. Creager [1999] performed a similarexperiment using a mantle model by Karason and vander Hilst [2001] and compared its predictions withBC�DF and AB�DF. He found no significant correlationbetween data and prediction from the mantle model.However, Creager did not correct for inner core aniso-tropy; hence the poor correlation may be due to inner coreeffect obscuring mantle signal or under-estimated mantlestructure near the CMB.[35] Comparison of predictions based upon a three-

dimensional mantle model and residuals after inner coreanisotropy correction confirms the importance of a mantlecorrection and emphasizes the existence of paths withhighly anomalous data, especially the path between SouthSandwich Islands and Alaska. Small-scale variations in theinner core can explain anomalous data, but effects such asdue to slabs [Helffrich and Sacks, 1994] should also beconsidered. Our experiments with mantle models basedupon convection simulations [Pysklywec and Mitrovica,1998] suggest that slabs are capable of producing differ-ential travel time residuals comparable to and sometimeseven larger than residuals due to small-scale heterogeneitynear the CMB. Furthermore, the South Sandwich Islands toAlaska path samples the inner core only in one direction:there are no paths sampling that particular region of theinner core with other azimuths. Therefore it is not clear ifanomalous measurements from this path are associated withanisotropy.

4.3. Diffracted BC��DF Data

[36] Because most BC�DF measurements at distancegreater than �153� use diffracted BC, we have not includedthese data in our inversions. We now investigate if thesedata can be used to constrain inner core structure near theICB. The measurements using diffracted BC are comparedwith BC�DF data at shorter distance ranges in Figure 14.Most of the diffracted BC�DF data (209 measurements outof 339) are within the distance range from 153� to 155�.The residuals are generally smaller (closer to zero) thanBC�DF from 150� to 153�, except when cos2 x = 0.85.Diffracted BC�DF data have a smaller slope and curvatureas a smooth function of cos2 x, indicating that anisotropysensed by this data set is weaker than that from BC�DFwithout diffraction. This is even more evident when theanomalous path from South Sandwich Islands to Alaska isomitted (Figure 14b).[37] The average bottoming depth for data in the dis-

tance range from 150� to 153� is 250 km, and it is 286 kmfor data in the range 153� to 155�. If diffracted BC isinsensitive to the inner core and anisotropy is varying

smoothly, the data from 153� to 155� should have com-patible or larger travel time anomalies than those from150� to 153�. A drastic change in anisotropy in theincremental 36 km may allow smaller anomalies at largerdistance, but our inversions for layered inner core aniso-tropy models position interfaces at other depths (paper 1).If anisotropy is constant, the model of Creager [1992],which fits the BC�DF data well, should give a reasonablefit to data in the 153� to 155� distance range, but itoverpredicts the residuals significantly. This evidencesuggests that the missing signals are due to the diffractedBC ray sampling the uppermost part of the inner core. Theevanescent wave does not penetrate deeply into the innercore, but the accumulation of signal along approximately50 km of the ICB will be significant, and comparable tothe signal observed in the 120� to 130� distance range. Itappears that anisotropy near the ICB is required in order toexplain the diffracted BC�DF data, in addition to the

Figure 14. (a) Comparison of BC�DF data from 150� to153� (triangles) and diffracted BC�DF data from 153� to155� (circles). The shaded dots in the background areindividual measurements of diffracted BC�DF. (b) Same asin Figure 14a, except that the anomalous path from SouthSandwich Islands to Alaska has been removed.


observed trend of DF data between 130� and 140� distancerange.

5. Conclusions

[38] In paper 1 we found that normal mode and mantle-corrected DF data are highly compatible, but BC�DF andAB�DF differential travel time data differ slightly. Com-parison of DF and BC�DF or AB�DF data shows that thismay be due to biased sampling. The absolute and differ-ential travel time measurements disagree strongly wheneverthere is a cluster of differential data from a particularsource-receiver pair. These clusters of data seem to driveinferences of very strong anisotropy in the inner core basedupon differential measurements. In addition, differentialdata sample a limited part of the mantle and the innercore, whereas DF data have better coverage and henceaverage isotropic mantle structure more effectively. Thisglobal sampling by DF explains why the normal modedata, which are global by definition, are more consistentwith DF data than with differential travel time data.Because of this agreement between normal mode and DFdata, the source of anomalous measurements of BC�DF orAB�DF must be heterogeneity within the inner core [e.g.,Creager, 1997; Dziewonski, 2000; Vidale and Earle, 2000]or to lateral variations within the mantle [Breger et al.,1999, 2000; Tkalcic et al., 2002] which are small enoughthat they do not substantially affect average structure of theinner core.[39] Our preferred model of constant anisotropy (paper

1) contradicts the hypothesis that the inner core is isotropicnear the ICB [e.g., Song and Helmberger, 1998; Ouzounisand Creager, 2001; Song and Xu, 2002]. We investigatewhether our data set supports an isotropic layer near theICB, and show that normal mode data can accommodate anisotropic layer of less than 150 km thickness. However,data from body waves penetrating shallowly in the innercore cannot be well fit by a model with an isotropic layer.In addition, a comparison of BC�DF data in the distanceranges 150�–153� and 153�–155� (using diffracted BC)suggests that the topmost inner core is anisotropic. Argu-ments for an isotropic layer are mainly based upon differ-ential travel time data [e.g., Song and Helmberger, 1998;Creager, 1999], however, a weak level of anisotropy canbe accommodated by this data set [e.g., Song and Helm-berger, 1995; Creager, 2000; Garcia and Souriau, 2000].Recent studies based upon waveform modeling proposeinner core models with a �250 km thick isotropic layerabove a highly anisotropic (�8%) interior [Ouzounis andCreager, 2001; Song and Xu, 2002]. Normal mode obser-vations would not be consistent with this model since theisotropic layer is too thick to fit modes which are onlysensitive to the shallow part of the inner core, and theinterior is too strongly anisotropic for modes with deepersensitivity. In addition, �8% anisotropy overpredicts DFresidual at distances above 150�. In the future, the dif-fracted BC�DF data may be used to constrain anisotropicstructure near the ICB. In the meantime, one should becautious when using diffracted data for modeling inner coreanisotropy: assuming insensitivity to inner core structuremay lead to anisotropic models which are more compli-cated than necessary.

[40] We also considered the possibility of a large-scaledependence of anisotropy, relying in this effort upon bodywave data. Hemispherically averaged data show a distinctbehavior between the eastern and western hemispheres, butthe number of measurements used for each hemisphere differgreatly, and it is not clear how much of the hemisphericdiscrepancy originates from biased sampling. The inversionresults show an unreasonably large difference betweenhemispheres, and overall improvements in fit are onlymarginal. Furthermore, the division of the inner core intoeastern and western hemispheres is somewhat artificial: adifference in data can also be obtained if the inner core isdivided into northern and southern hemispheres. On theother hand, the data from two hemispheres are similar atsmall values of cos2 x and diverge almost discontinuously atlarge values of cos2 x regardless of hemispheric division.Using a geometrical argument, we divide the inner core intoquadrants and show that data with large cos2 x originate fromrays bottoming near the equator, hence localizing the sourceof apparent hemispheric difference to a much smaller region.Moreover, the simple model of anisotropy obtained in paper1 is equally valid for all quadrants when data with cos2 x <0.7 are considered, suggesting that the inner core anisotropyis laterally homogeneous at large scales.[41] Because these complexities fail to improve the fit to

differential data while maintaining a good fit to normal modeand absolute travel time data, we investigate if the unmodeledpart of differential data can be placed in the mantle. A simpleprocedure of assigning the residual signal of differential data(i.e., after correction using a constant model of inner coreanisotropy) to exit and entry points produces similar maps forBC�DF and AB�DF. In addition, these maps are highlycompatible with a recent study of P velocity structure near theCMB [Tkalcic et al., 2002]. However, the required level oflateral heterogeneity is very high, approximately ±7% overthe bottommost 300 km in the mantle. Although this could bean overestimate, it is consistent with the amplitude ofvariations observed using diffracted P waves [Sylvander etal., 1997] and may be related to observations that have beeninterpreted as evidence for ULVZs [e.g., Garnero et al.,1998]. Regions where the ULVZs are observed correspondsto regions where we observe very slow velocity anomaliesand the ULVZs are not observed where very fast velocityanomalies exist in our residual maps. Good agreement ofresidual distributions between BC�DF and AB�DF, inaddition to models of P velocity near the CMB, suggests thatmuch of the residual differential data originates in the mantlein agreement with Breger et al. [1999].[42] There are residuals that cannot be entirely explained

by large-wavelength mantle structure near the CMB. Thelargest of such anomalies involves observations from pathbetween the South Sandwich Islands and Alaska. Themeasurements from this path remain anomalous after cor-rection due to constant anisotropy in the inner core and areso large that mantle structure alone cannot explain theanomalous values unless there is an enhanced slab effect.The observations suggest that there may be small-scalevariations in the inner core, although the origin of suchstructure within a body that developed under essentiallyhomogeneous conditions is unclear.[43] This study highlights the advantage of combining

different types of data which are sensitive to inner core


structure. In particular, normal mode data with less biasedsampling of the inner core provide an invaluable constrainton anisotropy at a global scale and should not be ignored insuch studies. In addition, our attempt to derive a modelwhich simultaneously satisfies normal mode, absolute traveltime, and differential travel time data has allowed us toseparate a mantle signature and regional structure fromglobal anisotropy of the inner core. We can explain mostdata with a constant inner core anisotropy model andcomplex structure near the CMB, but there are some signals,such as residual degree 2 order 2 splitting function (Figure 7of paper 1), and the apparent difference of body wave databetween the eastern and western hemisphere, that remainunexplained.

[44] Acknowledgments. The authors would like to thank K. C.Creager for making the differential travel time data readily available, P.Shearer for ISC summary ray data used in Figure 6, W.-J. Su for processingthe ISC data and for programs to analyze them, Y. Gu for travel timeprograms, M. Antolik for means to calculate travel times in 3D mantlestructure, and J. X. Mitrovica for suggestions that improved the manuscript.We also thank B. Kennett, C. Matyska, and B. Romanowicz for a con-structive review. Some figures were generated using the GMT [Wessel andSmith, 1991] and Geomap (provided by W.-J. Su) software. This researchwas supported in part by grant EAR02-30625 from the National ScienceFoundation. M.I. was also supported by a Julie Payette Research Scholarshipfrom the Natural Sciences and Engineering Research Council of Canada.

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��A. M. Dziewonski, G. Ekstrom, and M. Ishii, Department of Earth and

Planetary Sciences, Harvard University, 20 Oxford Street, Cambridge, MA02138, USA. ([email protected]; [email protected]; [email protected])J. Tromp, Seismological Laboratory, California Institute of Technology,

Mail Code 252-21, Pasadena, CA 91125, USA. ( [email protected])


Joint inversion of normal mode and body wave data for ...geoweb.princeton.edu/people/tromp/Publications copy/tromp_31.pdf · body wave data to constrain the global average and consider

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