GEOPHYSICAL RESEARCH LETTERS, VOL. 21, NO. 16, PAGES 1671-1674, AUGUST 1, 1994
Anisotropy in the center of the inner core
LevVinnikl,Barbara
Romanowicz
andLudovic
Breger
2
Seismographic
Station,Universityof Californiaat Berkeley, BerkeleyCA 94720-4767
Abstract.
We have assembled a collection
of PKP data from
broadbandrecordsof the Geoscopenetwork. This collectionis
unique because,for the first time, it includespolar paths at
epicentral
distances
between172ø and177ø, for whichPKPDF
samples the central part of the inner core. After Hilbert
transformingthe DF branch,the waveformsof PKPAB and
P KPDF usually become very similar, and we measure
differential travel times with an accuracyof a fraction of a
second.The differential(AB-DF) timesfor equatorialpathsare
closeto thosepredictedby PREM, whereasfor the polar paths,
they are larger by 3 to 6 sec. AbsoluteDF times confirm that
the effect is primarily in the inner core. These observationsare
compatiblewith a model of cylindrical anisotropyin the inner
core with the axis of symmetryaligned with the Earth's spin
axis and an amplitude of 3.5%. They require that the
anisotropy extend to the central part of the inner core,
confirmingextrapolationsmade by Creager(1992) and ruling
out models where anisotropyis confined to the outer 300 km
of the inner core (Tromp, 1993).
recorded on the same seismogramand share approximately
commonpaths in the upper part of the Earth. Shearerand
Toy(1991),Creager(1992) andSongand Helmberger(1993b)
appliedthisto short-period
recordsof DF andBC branches
of
PKP. The main problemof thesestudiesis paucityof records
for polar paths. The difficulty stems from the fact that
seismicityin polarregionsis generallyweak and seismograph
stations are few. The conclusions of the two last studies are
based very substantially on the data for the near-polar
wavepathbetween the South Sandwichislandsin the south
Atlantic and stationCOL in Alaska, althoughother pathsfrom
Song and Helmberger (1993b) include those from Novaya
Zemlya and Alaska to stationsin Antarctica.The epicentral
distances
provided
bythispatharein therange149- 152ø and
correspondto the upper 300 km of the inner core. Both
Creager(1992) and Song and Helmberger(1993b) report that
the path in the inner core near parallel to the Earth rotation
axis is faster than the equatorial one by 1.5 -4 s. The
correspondingfast and slow wave velocitiesin the outer part
of the inner corediffer by 3 - 3.5%.
Although the presenceof anisotropyin the inner core is
Introduction
now reasonablywell established(Tromp 1993), the subject
continues to be a source of debate. The major issues are
Seismicanisotropyin the inner core is a discoveryof the distributionof anisotropywith depth and precise orientation
last decade.The first evidenceof unexplainedcomplexityof of the symmetryaxis (e.g., Su and Dziewonski 1994). Both
the Earthbelow the core-mantleboundarywas documentedby thesequestionsare importantto understandthe origin of inner
measurementsof splitting of eigenfrequencies
of the Earth's core anisotropyand the mechanismby which it is produced.In
normal modes (Masters and Gilbert 1981). The first
this report we present and discuss our measurementsof
indications of a difference between the travel times of P waves
differential travel times of PKP phases at stations of the
propagatingthroughthe inner core in the directionof the spin Geoscope network. Global distribution of these stations
axis of the Earth and other directions were found in the data
provides sub-equatorialand sub-polar paths. The stations,
reported by the International Seismological Center (ISC)
epicentersand surfaceprojectionsof the raypathsare shownin
(Poupinetet al. 1983). Morelli et al. (1986) inferred, from the Figure 1. Compared to other results of application of the
samedata, that the inner core presentscylindricalanisotropy differentialtechniques,our data correspondto largerepicentral
with the axis of symmetryalignedwith the Earth'sspin axis, distancesand include a unique near-polarpath with distances
and a similar explanationwas suggestedfor the anomalous between 172ø and 177ø. This path providesinformationon
splitting of normal modes (Woodhouse et al. 1986). The
anisotropyin the centralpart of the inner core.The arrivalsof
differencebetweenthe fast (along the spin axis) and slow BC branch in the distance range of our study are usually
(equatorial)velocitiesin the outer part of the inner core in missing,and, insteadof BC, we use the AB phasewhich, like
both models is around 3.5%.
BC, travels only in the outer core (Figure 2). Also, our
The variations of absolute travel time data of the core
analysis is performed not for short periods, as in the other
phases are contaminatedby effects of source mislocation, studies,but in the broadbandfrequencyrange.
lateral variationsof structureof the crustand mantle,and by
reading errors. These effects can be minimized by carefully
Method
and results of measurements
reading differential times of various core phasesthat are
1Alsoat:Institute
ofPhysics
oftheEarth,
Moscow,
Russia.
2Nowat:Ecole
Normale
Superieure,
Paris,
France.
Copyright1994 by the AmericanGeophysicalUnion.
The simplest technique of differential travel time
measurements
is to pick arrival timesof the two phasesin the
short-periodrecord.However,very often this simpletechnique
fails, becausetrue first arrivals are not seenclearly enough.An
alternativepossibility is to make measurementsin a broad
frequencyband and correlatewaveformsrather than the first
arrivals.
Paper number 94GL01600
0094-8534/94/94
GL-01600 $03.00
A straightforward
applicationof this approachto AB and
DF is impossiblebecauseDF and AB are forwardand reversed
1671
Vinnik et al: Anisotropyin Ihe Centerof theInnerCore
1672
i
i
i
i
i
i
t
i
i
Figure 1. Geoscopestations, seismic sourcesand surface
projectionsof the raypathsfor the data usedin this study.
Shallow,intermediate
and deepeventsare shownby circles,
trianglesand diamonds,respectively.
branches
of the travel-timecurve,respectively.
The signalon
the reversed branch is the Hilbert transform of that on the
forward branch (Chapman 1978). To get comparable
waveforms on both branches, we Hilbert transform the record
of DF branch.Sometimesusing this technique,the depth Figure 3. Examplesof broadband
DF, AB, andDFh (Hilbert
phases,like pPKPAB and pPKPDF, can alsobe usedfor the transformed DF) records at Geoscope station SEY: adifferentialtraveltime measurements.
Numerousexperiments 12/28/1991; b - 08/24/1992; c - 01/10/1993; d - 03/20/1993
indicatethat uncertaintyof suchmeasurements
is of the order (PKP); e - 03/20/1993 (pPKP); f - 04/05/1993. For the
of a fractionof a second.Examplesof recordsat stationSEY parametersof the events see Table 1.
are shownin Figure3. They canbe regardedasrepresentative
for our dataset as a whole.In very few cases,in spiteof the observed differential time. The residuals thus obtained are
Hilbert transformation, the correlation between DF and AB
shownin Figures4 and5, and,for SEY, theyarealsolistedin
waveformsremainedpoor. Thesecasesare exceptional,and Table I.
originsof the complications
are unclear.In a shorter-period
In Figure 4 we show the residuals as a function of
pass-band the AB and DF waveforms, the latter Hilbertepicentraldistance.There is a systematicdifferencebetween
transformed,often don't match, since both are strongly the dataof SEY (opentriangles)and the otherstationsin the
contaminated
by the effectsof wave scattering.Someof our samedistancerange.The residualsof SEY reach3 - 6 sec.The
canbe approximated
by a regression
line which
analyses
aremadeat distances
beyond175ø. Dueto frequency- otherresiduals
goes through0 at 1550 and whoseslopeis closeto 0.04
dependenteffects of propagationof Pdiff, the AB waveform
could be distorted and an error introduced in the differential
travel-time data. However, the distance where AB could
propagateas the diffractedwave is in the range of a few
degrees,and in the frequencyrange of our analysisthe
waveformdistortionis negligible(Figure3).
The next step is to calculatethe predictedtravel time
difference
betweenthebranches
for everyrecordby usingthe
PREM velocitymodel(Dziewonskiand Anderson1981) and
epicentralparametersof the event reportedby NEIC. For
distances
largerthan 175ø themodeldoesnotpredictan AB
branch,andwe definetheAB traveltimeby extrapolating
data
fromsmallerdistances
with a slowness
of 4.43 sec/deg.
Then
the differentialtime for PREM, with the depthof eventand
ellipticity correctiontaken into account,is subtractedfrom the
sec/deg. This means that the differential times for near-
equatorialpathsare closeto thosepredictedby PREM. The
dependence
of thenear-equatorial
residualson distanceis most
likelyexplained
by a slightdeparture
of the"average"
velocity
in D" from that given by PREM. The scatterof the nearequatorialresidualsis within the rangeof +1.5 sec,whichis
larger than at smallerdistances,
as reportedby Songand
Helmberger(1993a). There are two major reasonsfor the
increasedscatter at larger distances.Firstly, differential
slowness
of AB andDF growswith distanceandapproaches
4.1 sec/degwhenthe distanceapproaches
1750. As a resultof
this, a mislocationerrorof up to 0.20 resultsin 0.8 secerror
in differential
time.The othersourceof scatter,asnotedby
SongandHelmberger(1993a),is grazingincidence
of AB in
the lowermost
mantleat largeepicentral
distances.
This layer
is knownto be laterallyheterogeneous,
andtheheterogeneity
shouldaffectAB strongerthanDF.
In Figure5, theresiduals
forthelargest(morethan165ø)
distances
arepresented
asafunction
ofcos
2 •, where
• isthe
anglebetweenthe spin axisof the Earthand the ray in the
inner core. They are comparedwith the theoreticalcurve
calculated
for a distance
of 173ø by usingthemodelof Creager
DF
(1992). To account for the bias of the baseline related to
PREM, as shownby Figure4, we alsoshowthe samecurve
Figure 2. Crosssectionof the earthshowingthe paths dispacedupwardby 0.5 s. The modelis basedon datathat are
sampled
by PKPDFandPKPABin thecore.
sensitiveto the upper300 km, but assumes
thatanisotropy
is
Vinnik et al: Anisotropyin theCenterof the Inner Core
Table
6
•,
sey
ß
ssb
ß
other
1:
date
m/d•
•-•e•
-2
....
ß
ß •'
ß
ß
' ....
160
155
12/28/1991
06/22/1992
08/24/1992
01/10/1993
03/20/1993
ß
ß ß
of
records
at
station
SEY
and
the
corresponding
AB-DF residuals
withrespectto PREM. The
secondresidualgiven for the eventon 03/20/1993 is for
pPKP.
stations
ß
List
1673
• ß ß ß , i , , , , i ....
165
170
175
lat. long.
depth
distance
residual
cos
2•
deg
-56.10
-60.73
-56.62
-59.01
-55.94
deg
-24.61
-21.97
-26.55
-25.88
-27.66
km
10
11
106
33
130
deg
172.98
176.52
173.65
175.97
172.98
180
4.4
3.0
5.0
6.1
5.2
0.74
0.78
0.75
0.77
0.74
4.7
04/05/1993 -59.83 -26.10
distance (deg)
sec
33
176.80
4.5
0.77
Figure 4. AB - DF residualscalculatedwith respectto PREM,
as a functionof epicentraldistance.StationSSB is singledout is smallerby 1 secthan(AB-DF)obs, andthatthe discrepancy
because
it providesdatain a particular
distance
and• range(see is explainedby a velocity near the baseof the mantle which is.
lower thanin PREM. The amountof datain the studyof Song
figure5, andtextfor thedefinitionof •).
and Helmberger(1993a) is larger,but, with a few exceptions,
uniform (independentof depth)throughoutthe inner core.The theyareat distances
lessthan158ø or,practically,
outside
the
curve is shown without ellipticity corrections, because distancerangeof our study.A low velocitynear the baseof the
generallythere is no explicit relation betweenthe corrections mantlethatcanincrease
thedifferential
timeby 1 secat 155ø
andcos2 •. However,
in ourcase
alldataforSEYhave, wouldincrease
it by about2.5 secat 175O. Thenall residuals
practically, the same ellipticity correction.This correction,if
in Figure4 for the near-equatorialpaths would be below the
curve representingthis model. Whatever the origins of the
residualsby -0.3 sec. Figure 5 indicatesthat Creager'smodel disagreementbetween our data and those of Song and
is broadlyconsistentwith our data, includingthe residualsof Helmberger (1993a), they, nevertheless, are of minor
SEY. As exampleof a model with a weaker anisotropyin the importance
for the centralthemeof ourreport.
centralpart of the inner core, we also show the corresponding
The main resultof our studyis a pronounced
increaseof
curve for Tromp's (1993) model, in which the centralpart of differentialtime for the near-polar
pathrepresented
by the data
the inner core is practicallyisotropic.This model doesnot fit of SEY. In agreementwith previousstudies,we assumethat
our observationsfor polar paths.
this changeis causedby wave propagationin the inner core,
not in the outer core. Then the DF travel time at epicentral
applied
tothemodel
data
atcos2 •--0.75,
would
increase
the
Discussion
and
Conclusions
distances
around175ø is 3 - 6 secshorter
for thenear-polar
path than for the equatorialpath. This changeis roughly2
Our conclusionthat PREM providesa reasonable,though
timeslargerthanreportedfor distancesaround150ø for the
not perfect, approximationof the differential times for the
values
ofcos
2 • (Creager
1992;
Song
andHelmberger
near-equatorialpaths is in apparentcontradictionwith the same
conclusion
of Song
andHelmberger
(1993a)
that(AB-DF)prem1993). The length of the DF wavepathin the inner core for
175ø distance
is almost
2 timeslargerthanfor a distance
of
150ø, andthelargereffectin ourdatacanmosteasilybe
6
/•
sey
ß
ssb
explainedby the longer travel time of the wave in the inner
core combined with the nearly uniform magnitude of
ß other
stations
.e
•
....
-2
0
I
,..
.
I ....
I
0.2
....
I ....
0.3
anisotropy.
Our data for SEY couldbe biasedupwardby the
low-velocityanomaliesin D". However,so far as is possible
to concludefrom the mostdetailedglobalmapsof D" that are
unfortunatelyavailablefor the S wavesonly (Suet al. 1993),
all wavepaths
from the SouthSandwichislandsto SEY, except
_
..-
- -*.... :7.:.'...-•,•
0.1
,
I ....
0.4
.
I ....
0.5
i
0.6
....
I
0.7
that for event 06/22/1992,
lie well outside the anomalous
regions.
The other possibility to judge of the effects of the
anomalies in D" is to use the absolute travel times of DF that
....
0.8
are less sensitiveto theseanomalies,thoughmore sensitiveto
someotherdisturbingeffects.In Figure6, we showthesetimes
as a function of epicentral distance, with ellipticity
Figure 5. AB- DF residualsat epicentraldistances
largerthan corrections.The number of data in Figure 6 is less than in
165
ø asafunction
ofcos
2 •. The('-') curve
iscalculated
ata Figure 4, becausein many casesthe absolutetimes of the first
distanceof 172ø for Creager's(1992) uniformanisotropy arrivals are highly uncertain.The differencebetweenthe travel
model.The (.... ) curveis the sameshiftedupwardby 0.5 sec timesfor SEY and for otherstationsin Figure 6 is around3 s
to fit the data better.The solidline is the corresponding
curve which is less than in Figure 4. It shouldbe noted, however,
for Tromp's(1993) model.
that TAM, CAY and MBO, which provide the overwhelming
COS2•
Vinnik et al: Anisotropy
in Ihe Centerof theInnerCore
1674
Dziewonskifor makingtheir manuscriptavailablebeforepublication.
This studywaspartiallysupported
by NSF grantEAR-9204631.
References
ß
ß
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ß
ß
-2
155
•,
sey
ß
ssb
ß
oth•er stations . , ....
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•x
/x
165
170
,
175
Masters, G., and F. Gilbert, Structure of the inner core inferred from
. . .
180
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viewed as fully compatible.
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cylindricalanisotropywith the axis of symmetryalignedwith
the Earth'sspin axis and 3.5% magnitudein the outer part of
the inner core and a similar magnitudein the centralpart. The
amount and quality of data at our disposal, however, are
insufficient to discriminate between this relatively simple
model and some other models with a more complicated
distributionof anisotropywith depthor a differentdirectionof
the symmetryaxis,like that of Su andDziewonski(1994). The
choicebetweenqualitativelydifferentmodelsmay dependupon
the effects in the range of 1 sec that can be observedonly in
polar regions, and it will, unfortunately,be difficult to reach
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digital seismographnetwork.
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L. Vinnik, B. Romanowiczand L. Breger,Seismographic
Station,
Universityof California,BerkeleyCA 94720-4767
Acknowledgments. The authorsthank Lane Johnsonand Lind Gee
for their computercodesand advice, and Wei-Ja Su and Adam
(received:April 4, 1994;accepted:
May 2, 1994)