Physics of the Earth and Planetary Interiors, 25 (1981) 297— 356 297 Elsevier Scientific Publishing Company, Amsterdam — Printed in The Netherlands Preliminary reference Earth model * Adam M. Dziewonski’ and Don L. Anderson 2 ‘Department of GeologicalSciences, Harvard University, Cambridge, MA 02138 (U.S.A.) 2 Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125 (U.S.A.) (Received December 3, 1980; accepted for publication December 5, 1980) Dziewonski, A.M. and Anderson, D.L., 1981. Preliminary reference Earth modeL Phys. Earth Planet. Inter., 25: 297—356. A large data set consisting of about 1000 normal mode periods, 500 summary travel time observations, 100 normal mode Q values, mass and moment of inertia have been inverted to obtain the radial distribution of elastic properties, Q values and density in the Earth’s interior. The data set was supplemented with a special study of 12 years of ISC phase data which yielded an additional 1.75 X 106 travel time observations for P and S waves. In order to obtain satisfactory agreement with the entire data set we were required to take into account anelastic dispersion. The introduction of transverse isotropy into the outer 220 km of the mantle was required in order to satisfy the shorter penod fundamental toroidal and spheroidal modet This anisotropy also improved the fit of the larger data set. The horizontal and vertical velocities in the upper mantle differ by 2-4%, both for P and S waves. The mantle below 220 km is not required to be anisotropic. Mantle Rayleigh waves are surprisingly sensitive to compressional velocity in the upper mantle. High S~ velocities, low P~ velocities and a pronounced low-velocity zone are features of most global inversion models that are stqipressed when anisotropy is allowed for in the inversion. The Preliminary Reference Earth Model, PREM, and auxiliary tables showing fits to the data are presented. Preamble and his models A and B were employed exten- sively. The study of precession and nutation in astron- Seismological studies of the structure of the omy and geodesy, and of Earth tides and free Earth have developed rapidly since 1950, much oscillations in geophysics, need knowledge of the aided by the fast improvement in computer tech- internal structure of the Earth. The importance of niques. free and forced nutations, for instance, polar mo- Expansion in the utilization of computers made tion, Chandler and annual components, and di- it possible to construct many types of Earth mod- urnal motion of the Earth, in different fields of els. The consequent proliferation of Earth models science, emphasizes the value of the contribution had two consequences: of seismology for these researches. (I) There was a difficulty of choice of an ade- It was very difficult to set up models of the quate Earth model for researchers that depend on Earth’s structure before the advent of computers; the structure of the Earth, such as those listed in the more important ones were set up by Bullen, the first paragraph. (2) Several researchers adopted some properties • With a preamble by the Standard Earth Committee of the from one model and other properties from a sec- I.U.G.G. Followed by “A note on the calculation of travel ond model, with the consequence that their models times in a transversely isotropic Earth model” by L~ were not self-compatible. Woodhouse (this issue, pp. 357-359). These difficulties were pointed out, at a Sym-
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Physics of the Earth and Planetary Interiors, 25 (1981) 297—356 297Elsevier Scientific PublishingCompany,Amsterdam— Printedin TheNetherlands
Preliminary referenceEarth model *
Adam M. Dziewonski’andDon L. Anderson2‘Departmentof GeologicalSciences,Harvard University, Cambridge,MA 02138(U.S.A.)
2 SeismologicalLaboratory, California Institute of Technology,Pasadena, CA 91125(U.S.A.)
A largedatasetconsistingof about1000 normal modeperiods,500 summarytravel time observations,100 normalmodeQ values,massandmomentof inertiahavebeeninvertedto obtaintheradialdistributionof elasticproperties,Qvaluesanddensityin theEarth’sinterior.Thedatasetwas supplementedwith aspecialstudyof 12 yearsof ISC phasedatawhichyieldedanadditional1.75X 106 travel timeobservationsfor P andS waves.In orderto obtainsatisfactoryagreementwith the entire datasetwe wererequiredto take into accountanelasticdispersion.The introduction oftransverseisotropyinto theouter220kmof themantlewasrequiredin orderto satisfytheshorterpenodfundamentaltoroidalandspheroidalmodetThis anisotropyalsoimprovedthe fit of thelargerdataset.Thehorizontalandverticalvelocitiesin the upper mantledifferby 2-4%, both for P andS waves.Themantlebelow220km is not requiredto beanisotropic.Mantle Rayleighwavesare surprisinglysensitiveto compressionalvelocity in the uppermantle.High S~velocities,low P~velocitiesand a pronouncedlow-velocity zoneare features of most global inversionmodels that arestqipressedwhenanisotropy is allowedfor in the inversion.
The Preliminary ReferenceEarth Model, PREM, andauxiliary tables showingfits to thedata are presented.
Preamble and his models A and B were employed exten-sively.
The study of precessionand nutation in astron- Seismological studies of the structure of theomy and geodesy,and of Earth tides and free Earth have developed rapidly since 1950, muchoscillations in geophysics,needknowledge of the aidedby the fast improvement in computer tech-internal structure of the Earth. The importanceof niques.free and forced nutations, for instance,polar mo- Expansionin the utilization of computersmadetion, Chandlerand annualcomponents, and di- it possibleto constructmany typesof Earth mod-urnal motion of the Earth, in different fields of els.The consequentproliferation of Earth modelsscience,emphasizesthe value of the contribution had two consequences:of seismologyfor theseresearches. (I) There was adifficulty of choiceof an ade-
It was very difficult to set up models of the quate Earth model for researchersthat depend onEarth’s structure before the advent of computers; the structure of the Earth, such as those listed inthe more importantoneswere set up by Bullen, the first paragraph.
(2) Severalresearchersadopted someproperties• With a preambleby the StandardEarth Committeeof the from one model andother propertiesfrom a sec-
I.U.G.G. Followed by “A note on the calculationof travel ond model,with the consequencethat their modelstimes in a transverselyisotropic Earth model” by L~ werenot self-compatible.Woodhouse(this issue,pp. 357-359). Thesedifficulties were pointed out, at a Sym-
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posium on Earth Tides, during the 1971 IUGG arately andproduce a consistentreferencemodel.GeneralAssemblyin Moscow(Vicente,R.O., 1973, Severalapproachesto the problem of setting up aBull. GeodesiqueNo. 107, p. 105), and informal reference model were discussed, including al-discussionson the subjectled to the setting up of a lowancefor attenuation; it was decided to inviteworking group, composedof membersof lAG and colleaguesto produce andpresent complete mod-ISPEI, called the “Standard EarthModel Commit- els worked out by themselvesand satisfying thetee”; the chairmanwas the late Professor K.E. guidelines laid down by the Committee. TheBullen. guidelines were published during 1976 in several
The objective of the working group was to set scientific journals (Bull. Seismol. Soc. Am., Geo-up a standard model for the structure of the Earth, phys.J., EOS, etc.) with the announcement thatfrom the center to the surface, defining the main proposed models should be presented during theparameters andprincipal discontinuities in such a IASPEI meeting in 1977.way that they could be adopted by the interna- The meeting of the Committee during thetional scientific community in any studies that IASPEI assembly in Durham (1977) was con-dependedon the Earth’s structure. cerned with the presentation and discussion of
The initial approach was to appoint several three different proposals, corresponding to re-sub-committees dealing with different regions of searchesdone by D,L. Anderson, B. Bolt andthe Earth, composed of scientists specialising in A.M. Dziewonski. It appeared to be possible tothoseareas.The original sub-committeeswere on: construct models taking accountof damping, that(I) the hydrostatic equilibrium problem; (2) the is, of Q values. The Committee memberspresentcrust; (3) the upper mantle; (4) region D”; (5) core considered that the effects of attenuation wereradius; (6) P-velocity distribution in the core; and important and should be considered; but, since Q(7) density andrigidity of the inner core. was not well determined, instead of having one
During the meeting of the Symposium on reference model, we should have two referenceMathematical Geophysics(Banff, 1972), threere- models—oneincluding Q values’ and the othersearchgroups, headedby D.L. Anderson, F. Gil- without Q values.bert and F. Press, presented models giving the At this meeting it wasevident that the originalmain parameters; in spite of the fact that these referencemodel envisagedwasgrowing more andmodelsemployed different data setsand computa- more detailed, thanks to the rapid progress oftion techniques, the values obtained for the core seismology. Several features that could not haveradius agreedwithin 0.2%, which was a remarkable been consideredin 1971 werenow feasible. It wasresult. The papers were published in Geophys.J., decided to entrust to D.L. Anderson and A.M.vol. 35 (1973); there wasby then a generalfeeling Dziewonskithe task of presenting a suitable refer-that it was possibleto setup an adequatestandard encemodel.Earth model. The first report on the reference model of
During the IASPEI meeting in Lima (1973) Anderson and Dziewonski was presented at thethere was agreement about the needfor a para- meetingof the Committee on Mathematical Geo-metrisation of the model to be adopted. It was physics (Caracas, 1978), with the statement thatdecided to call the model for the Earth’s structure the grossEarthdata employedfor the constructiona “reference model”, following the example of of the model was being enlarged,using the ISCgeodesywhere there is a reference ellipsoid. In tapes. -
spite of this change in the name, it was agreedto During the 1979 IUGG General Assemblykeep the samename for the Committee.The re- (Canberra) a preliminary report on the Interimports of the sub-committees were published in Reference Earth Model was presented by A.M.Phys. Earth Planet. Inter., vol. 9 (1974). DziewonskiandD.L. Anderson. It was agreedby
By the time of the 1975 IUGG GeneralAssem- the Committeethat the report should be submittedbly (Grenoble) it was evident that it would be to Physicsof theEarth andPlanetaryInteriors, anddifficult for several sub-committeesto work sep- that interested seismologistsshould be encouraged
299
to use the Preliminary Earth Model and send within which the properties are assumedto varycommentsto the authors. In order that the authors smoothlypredeterminesthe generalfeatures of theshould be able to considersuch comments,and to final modelandmustbe donewith care.In generalmodify themodel in the light of them if they think terms, we follow the recommendationsof the Sub-fit, such comments should be in the hands of committee on Parainetenzation, whose findingsDziewonski andAnderson as soon as possible. were published among reportsof the other sub-
ProfessorsDziewonskiandAndersonhavebeen committees in Phys. Earth Planet. Inter., vol.9asked to make a further Report, which the Corn- (1974).mitteehopesto be able to regard as the conclusion Section3 contains a description of the datasetsof its work, at the IASPEI Assemblyin 1981. that weuse in inversion for the final model. Sec-
tion 4 describes proceduresadopted in formula-E.R. Lapwood,Chairman tion of the starting model. In Section6 weprovide
R.O. Vicente,Secretary a brief outline of the inversion method used, theFor theStandard Earth Mode~:n~m~~ final (in terms of thisreportonly, of course)model
anddiscussionof the fit to the data.There havebeen a number of important prob-
1. Infroduction lems and decisionsthat we have faced during thecourseof this work. Some of thesedecisionsre-
A variety of geophysical, geochemicaland as- quiredchoicesbetweenconflicting datasets.Otherstronomicalstudies requirean accuratedescription were resolved by acceptingthat the velocities inof the variation of elasticproperties anddensity in the real Earth are dispersive. The most difficultthe interior of the Earth. This paper containsa decisionto make was whether we should drop thebrief descriptionof a new Earth model, PREM, assumption of isotropy. A large amountof im-that satisfies the guidelines establishedby the portant data could not be fit adequately with theStandard Earth Model (S.E.M.) Committeeat its preliminary isotropic Earth models. So we viewmeeting in Grenoble in 1975. In order to satisfy anisotropy and anelastic dispersion as essentialthe large amount of precisenormal mode, surface complexities.We have, however, tabulated resultswaveand bodywave data, wehave found it neces- for the “equivalent” isotropic Earth. “Equivalent”saiy to introduce anelasticdispersionand anisot- meansthat the model has approximately the sameropy. The model is therefore frequency-dependent bulk modulus and shear modulus as the aniso-and, for the upper mantle, transversely isotropic. tropic model, not that it provides an equivalent,orWe present tablescontaining the velocities,elastic satisfactory, fit to the data. The isotropic moduliconstantsand Q as a function of radius, and arecalculated with a Voigt averagingschemeand,auxiliary parameters such as gravity, pressure, therefore, represent the least upper bound. WedK/dP and the Bullen parameter, ilB. encouragethe geophysicalcommunity to test and
The model is parametric in nature, a concept evaluate the modeland the tables and to contrib-discussed,and, in generalterms, found acceptable ute to refinement of what we call the Preliminaryduring the meeting of the S.E.M. Committee, ReferenceEarth Model, or PREM.chaired by the late Professor Keith Bullen, inLima, 1973. We have provided analyticformulaefor the~seismicvelocities,density and quality fac- 2. The concept of themodeltor Q asa function of radius. For this purposeweuselow-order polynomialsin radius, of order be- An average Earth model, the subject of thistweenzero andthree, to describeseismicvelocities, work, is a mathematical abstraction. The lateraldensity and attenuation in the variousregions of heterogeneityin the first few tensof kilometers isthe Earth. solarge that an averagemodel doesnot reflect the
Section2 deals with the basic concept of the actual Earth structure at any point. In construc-model. The division of the Earth into regions tion of the structure within the first 100 km we
300
have adopted the concept of weighted average: of free oscillations or travel times of body waves,assuming that oceaniccrust covers two-thirds of but there are no equivalent expressionsfor dif-the Earth’s surfaceandthat the average depth to fused transitions.the Moho is II km under oceansand35 km under The preceding discussion dealt only with thecontinents, we arrive at a figure of 19 lan for the elastic properties of the Earth. One fundamentaldepth to the Moho for the averageEarth. This is assumption that wemake an interpretation of theusedasthe trial starting value, data in the seismic frequency band is that the
We recognizethe following principal regions seismic quality factor Q is independent of thewithin the Earth: frequency. This hypothesisseemsto be consistent(I) Oceanlayer. with most of the currently available information(2) Upper andlower crust. except perhaps for periods shorter than 5—10 s.(3) Region above the low velocity zone (LID), We in no way imply that Q is exactly independent
consideredto be the main part of the seismic of frequency at all depths and over the entirelithosphere. When we finally dropped the as- seismic frequency band but only that most datasumption of isotropy the distinction between can be satisfactorily fitted with this assumption.LID and LVZ becamelesspronounced.
(4) Low velocity zone(LVZ).(5) Region betweenlow velocity zoneand400 km 3. The grossEarthdataset
discontinuity.(6) Transition zone spanning the region between There arethree principal subsetsof data:
the 400 and 670 km discontinuities.(7) Lower mantle. In our work we found it neces- 1. Astronomic-geodeticdata
sary to subdivide this region into three parts Radius of the Earth: 6371 km. Mass: 5.974Xconnectedby second-orderdiscontinuities. 1024kg. I/MR2: 0.3308.Thesevalues, listed in the
(8) Outer core. guideline of the SEM Committee, were used as(9) Inner core. constraints.While the existenceof most of the regions listedabove has been recognized for some time, the 2. Free oscillation and long-periodsurface wavesubdivision of the upper mantle is still subject to datasomedifferencesof opinion. We feel that evidence There is an impressive set of measurementsoffor the world-wide existence of a zone of low eigenfrequenciesfor over 1000 normal modes.Thevelocity gradient in the upper mantle is very strong precisionof measurementsvariesappreciably: fromand that the sameis true with respect to at least up to 4 X l0~for someof the toroidal overtonestwo major discontinuities, although the actual to the 4X 106 recentlyreported for the funda-velocity gradientsare still unresolved, mental radial mode.
From a practical viewpoint, such a modular Qur set of normal mode data consistsof aboutconstruction is very convenient. It is much easier 900 modescollectedfrom early observationscorn-to perturb a particularfeature of a model when it piled by Derr (1969), Dziewonski and Gilbertis separated from the remaining onesby clearly (1972, 1973), Mendiguren (1973), Gilbert anddefined discontinuities than to alter a model that Dziewonski (1975),and Buland et al. (1979). l’hisby definition is continuous. Other practical rea- datasethas beensupplementedby measurementssonshave to do with numerical applications. Many of dispersionof surfacewavesby Kanamori (1970),methodsof construction of synthetic seismograms Dziewonski (1971),Dziewonski et al. (1972),Millscan satisfactorily treat abrupt discontinuities, but (1977), and Robert North (personal communica-arenot suitable for regionswith very steepvelocity tion, 1980).gradients. Another important issueis the inverse The data on attenuation are important in theproblem: there exist formulae for the effect of context of thisreport only to a limited extent. Thechangein the radius of a discontinuity on periods anelastic component of our model is primarily
301
meantas a tool for taking into accountthe small, equality of the area. Averagetravel times werebut important,frequency-dependenceof theelastic computedonly if at leastfive readingsfor a givenparameters.The publisheddataon attenuationof 10 cell were available.Figures1 and 2 show thenormal modes is of variable quality. We have deviationsof our global averagetravel-timecurvechosena relatively small set of data basedon from Jeffreys—Bullen travel times.Also shownaremeasurementsof Kanamon(1970), Dratler et a!. residualsfor other travel-time studies; these two(1971),Sailor (1978),SailorandDziewonski(1978), figureswill bediscussedmore extensivelylater onSteinandGeller(1978),Bulandetal. (1979),Geller in the text.andStein(1979),andSteinandDziewonski(1980). All events analyzedwere shallow, between0
and 100 km in depth. For reasonsthat, at least3. Bodywaves originally, were not particularly relevant to thisObservationsof travel timesof body wavesare report, we have also derivedaveragetravel-time
most numerous; there have been hundredsof curves separatelyfor regions with shallow andstudiesdealingwith thissubject.The advantageof deepseismicity(but for shalloweventsonly).Therethe body wave data over the normal mode ob- aresignificantandsystematicdifferencesbetweenservationsis that, becauseof shorterperiods,they thesetwo types of regions.The P-waveinterceptarecapableof higher radial resolution.The disad- time for shallow seismicity regions is earlier byvantagelies in the somewhatrelative nature of about0.6 s; thedeepseismicityareasareearlierbytheir absolutevalues. The problem of base-line about0.4s at 90°.This is not purelya problemofdifferencesis well known and neednot be dis- a tilt in the travel-timecurvesas thereare atleastcussedhere.There is also the questionof small two intersectionsof the curves at intermediatedifferencesin the overall slope of the teleseismic distances.While the broad-scalefeaturesfor bothtravel-time curve; some of the controversieson curvesarevirtually identical,the shortwavelength-
this subject are now over a decadeold and still structureis markedlydifferent.remainunresolved.The body wave datasetis im- For the S-wavedata,differencesbetweentravelportantin definingtheregionsof the mantlewhich times for regions of deepand shallow seismicitywedisc~issedaboveandin improvingthe resolving are muchgreater.The differencein the interceptpowerof the dataset. time is 5—6 s and, what is evenmore surprising,
In order to obtainarepresentativeglobal body- there is a systematicdifference of 3—4 s in thewave datasetwe havestudiedthe P- and S-wave distancerangefrom 90 to 1000. The wide scattertravel timesusingthearrival time datafrom Bul- of data in the interval 80—90°can probably beletinsof theInternationalSeismologicalCentrefor explainedby interferencewith the SKS phase,years1964—1975.Rejectingeventswith fewer than which beginsto arrive before S at approximately30 stationsreporting, one retains approximately 82°.26000 eventswith reportsof nearly 2000000P- It would appearthattheeventsfor regionswithwave arrival times and 250000 S-wave arrival deep seismicity(trenches)are systematicallymis-times.Sinceneitherthedistributionof stationsnor located. The near-source stations tend to beearthquakesis uniform, thereexists theimportant groupedonly on one side of the event, andanquestionof anappropriateaveragingmethod.After epicentralmislocation is very plausible, particu-manyexperiments,a decisionwasmadeto divide larly if S-wavedataarenot used.This errorin thethe Earthinto a numberof sectionsof equalarea, positionandthe origin tunemustbecompensatedderive a travel-timecurve for sourcesin eachof by anequivalenterrorin depth.This is reflectedinthe areasand then averageall thesetravel-time thebaselineandtilt of aderivedtravel-timecurve.curves.This would tendto eliminatethebiasintro- Becauseof the very large differencesbetweenduced by unequalseismicity in the presenceof variousdatasets,a meaningfulaverageis difficultlateral heterogeneity.In actual experimentswe to determine.Variousdatasetsareshownin Fig.2.haveused72 regions,each30°wide in longitude Substantialadjustmentsin the absolutevalues ofandof the appropriatelatitudinalextentto assure the travel timesappearto benecessary.
302
0 I-v I I
—10C1~
— ci(a ci
- 00 ci
8 ci ci ciw ci --
-2 - ci0 ~D /
Es ~‘ ciI I -. ci Dcl ,~
Es ~ \~/ ~%%%%%%% 0 ci~
“.. ,/
4 I — I I I I I I I
0 20 40 60 80 100
Epicentral distance (degrees)
Fig. 1. SurfacefocusP-wave travel-time residuals with respect to JB times. Crosses are ISC data. Boxes arefrom Hales et al. (1968).Dashedline is from Herrin et al. (1968). Solid line is anisotropic PREM. ISC times have been corrected with —1.88 s baseline and— 0.0085s deg —‘ slope. Residuals calculated at a period of 1 s.
Becauseof the baselineand tilt uncertaintyof P (EngdahlandJohnson,1974)andScS—S (Jordantravel-time observationsfrom natural sourceswe andAnderson, 1974), areimportant for the con-usebody-wavedata as a constrainton the fine trol of theoutercoreradius.structure of velocity variations ratherthan as a If the issuesaresomewhatunclearwith respectstrongconstrainton absolutevelocities.Thus, we to the mantletravel times,the difficulties increasearemainly concernedwith fitting the shapeof the by an order of magnitudein the outer core. Totravel-time curves. Differential travel times and obtain reasonablygood control over velocities inthe normal mode datasetprovide constraintson the outercore, one must combinethe data fromabsolutevelocities.Even thesedatasetscontain a four travel-time branches:SKKS, SKS, PKP(AB)sourceandpathbiasbut wehavebeenableto find and PKP(BC). Some attemptsto combinethesea sphericallysymmetricEarthmodel which satis- data haveresultedin a markedroughnessof thefies thesedatato high precision. derivedmodelat depthintervalscorrespondingto
Other subsetsof teleseismictravel times, used juncturesbetweensegments.In addition, SKKSmostlyfor comparison,includedeepsourceP-wave dataarelikely to suffer from a sr/2 phaseshiftdata of SenguptaandJulian (1976) and S-wave with respectto theSKSphase(ChoyandRichards,data of Sengupta(1975), Haleset al. (1968), and 1975),unlessSKKS is Hilbert transformedbeforeGognaetal. (1981).Differential travel times,PcP— cross-correlationwith SKS(or vice versa).
303
I ~‘ I I I I I I
6—I $
- St xit
4 xH ‘ Xix.
0$, t x-~ :: ~o t~9o x ~
I : ~ :/~~ :~~s~*P~ ~‘?o “ / ~+ + ~ %~S 0 0 0
- b~ ~:J~+~~‘- ~
Es -2 - -
.1- -
+A +
+
- + +
+ +
-6- + + -
I I I I I I I I
20 40 60 80 100
Epicentral distance (degrees)
Fig.2. SurfacefocusS-wavetravel-timeresidualswith respectto JB. BoxesareISC data.+: from Gognaet at. (1981). X: from HalesandRoberts(1970). Solid line is for theverticallypolarized(SV) shearwaveanddashedline is for the horizontallypolarized(SH)shearwavein theanisotropicPREMmodel.Nobaselineor slopecorrections.Residualscalculatedat aperiodof I S.
We use the SKS data of Hales andRoberts the ISC travel time datafor distancesup to 25°,(1970), corephasedata for the AB, BC andDF allowing for an arbitrary base-linecorrection. Abranchesof Geeand Dziewonski (unpublished) decreasein S-velocity gradientbelow600km wasandPKiKP-PcPdifferential travel timesof Eng- dictatedby the needto obtain intersectionwithdahlet a!. (1974). The latter studygives the best the teleseismicbranchat24°;without that featureavailablecontrolof theinner coreradius. the intersectionoccursat 21.5°,whichis distinctly
4. Thestaim~gmo~iet most 670 km were designed,it was possible tostrip theuppermantleandinvert thestrippeddata
Design of the velocity models for the upper to obtainthelower mantlestructure.It was atthismantlerepresentedthe mostinvolved part of this stagethattheneedfor introductionof thefeaturesstageof our work. Our decisionto locate discon- in the lower mantle becameobvious. One, andtinuities at 220, 400 and 670 km was basedon perhapsthe most important, is the second-orderresultsof manyotherstudies.The bottomof the discontinuitysome150 km abovethecore-mantlelithospherewas initially placedat a depth of 80 boundary. The velocity gradient at this depthkm. Then, the velocities were adjustedto satisfy changesabruptlyandcouldbecomenegative.This
304
featureis clearon adT/d~ plot, whereasudden Moho to the core).Our choiceof the freeparame-changein the slopeof dT/d~occursat90°.The terswas —0.5,5.55, and3.32 g cm3,respectively.otherfeatureis a region of steepvelocity gradient Thisyielded a centraldensityof 12.97g cm3 andjustbelowthe670 km discontinuityextendingto a a densityjump at 670km of —0.35 g cm3.Thesedepth that is not particularly easy to define ex- assignedand derived parameterswere free toactly, but 771 km (5600km radius)appearedto be changein the inversion.Derivation of the startinga reasonableestimate.The model of the lower density distribution completes this stageof ourmantlewas formed by representingthe velocity work.between3485 and 3630 km as well as between5600 and 5701 km by linear segmentsand theregion betweenby acubic in radiusrequiringthat 5. Anisotropythereshould be continuityat the pointsof junc-tion. The starting model for P-velocitiespredicts Global inversionsof seismicdata, suchas pre-travel timesthat matchobservationswith an r.m.s. sentedhere,usuallygiveveryhigh shearvelocities,error of 0.06 s, roughly the averages.e.m. of a 4.8 km s~,in the uppermostmantle. Suchsingle observationin our global averagingproce- modelsdo not satisfyshortperiod (<200 s)Lovedure. andRayleighwave dataor shearwave travel times
Thescatterof the S-wavedatais largerby more at short distances(<20°).Very pronouncedlow-thanan order of magnitude,andthesedata could velocity zones(LVZ) are a prominent feature ofnot be expectedto reveal independentlythe fine most models. We have found it impossible tofeaturesdemandedby theP-wavedata.TheS-wave simultaneouslysatisfythe datawhich arerelevantdatawereinvertedassumingthatfirst- andsecond- to the upper200 km or soof the mantlewith anorderdiscontinuitiesexistatthe samedepthsasin isotropic model. The discrepancybetween Lovethe P-velocitymodel, waveand Rayleigh wave data suggeststhat the
In view of the fact that our knowledgeof the uppermantleis anisotropic(Anderson,1966).Thestructureof theinnerandoutercoreis still rather discrepancyis also pronouncedfor relatively ho-poor,webeganwith thehypothesisthat bothcores mogeneousoceanicpaths(Forsyth,I 975a,b;Schlueareindividually homogeneous.For this reasonwe andKnopoff, 1977; Yu and Mitchell, 1979). Thhaveusedthe resultsof fourth-orderfinite strain suggeststhat lateralvariationsarenot theprimarytheoryto constructthestartingmodelof P-velocity causeof the discrepancies.Although azimuthalin the outer core, and P- and S-velocitiesin the anisotropyis importantjust below the Moho ininner core. The starting densitydistribution was oceanicenvironments(Hess, 1964; Backus, 1965;obtainedby a variation of the methodproposed Raitt et a!. 1969), it appearsto be lessimportantby Birch (1964). We assumedthat the Adams— atsurfacewave periods(Forsyth, l975a; Yu andWilliamsonequationis satisfiedin eachsubregion Mitchell, 1979). Transverseisotropy, or polariza-from the center of the Earthup to the 670 km tion anisotropy,hasbeeninvoked to explain thediscontinuity.Following Birch, we assumethatthe Love wave—Rayleighwave discrepancy.Sinceourdensityin the uppermantleis linearly relatedto datarepresentanaverageovermanyazimuthsanyP-velocity: p = a+ bv~.Given the mass and the residualazimuthal anisotropywill be effectivelymomentof inertia of the Earth,we can find the averagedout. We thereforedeal only with thedensityatthecenterof theEarthandthejump of sphericalequivalentof transverseisotropy. Thedensityat the 670 kin discontinuityif we specify symmetryaxis is vertical (radial).the following parameters:densityjump acrossthe For this typeof anisotropytherearefive elasticinner—outercoreboundary;densityat thebaseof constants,A, C, F, L and N, following the nota-the mantle; and densitybelow the Mohoroviëiá tion of Love (1927, p. 196). A and C can bediscontinuity(Birch had only onefree parameter, determinedfrom measurementsof the velocity ofbut he did not treatthe innercoreseparatelyand P wavespropagatingperpendicularandparalleltohis densitydistributionwas continuousfrom the the axis of symmetry.Sincein our casethe axis of
305
symmetryis vertical (radial) I I
A=pV~H 8.0U,
C—pvI~v
wherep is thedensity.UIn general,the shear-wavevelocity dependson
polarizationanddirection of propagation.In the ~ 1.1 0.90-ldirectionperpendicularto theaxis of symmetry: 00
NPVIH
U,U,
a,L=pV~~ ~7.8
UIn the radial direction,parallel to the symmetryaxis, thereis no splitting and both polarizations I I I I I I
arecontrolledby theelasticconstantL. Therefore, ________________________________bothhorizontallyandverticallytravellingSV waveshave the samevelocity. The elastic constantNcontrols the propagationof fundamentalmodeLove waves.All five elastic constantsenter intothe dispersionequationfor Rayleighwavesbut L ?
is themore importantshear-typemodulus(Ander- ~ 44v-~.III
son, 1965). For this reason,vertically travelling Sor ScS waves are controlled by the sameset of ~ 4.2
elastic constantsthat control Rayleighwave dis-persion.tiesatintermediateincidenceangles.It is conveni- 4.1
The fifth constant,F, is a functionof theveloci-ent to introduceanon-dimensionalparameter~ = I I I I I I
F/(A — 2L) (Anderson, 1961; Harkrider and U 120 180Anderson, 1962; Takeuchiand Saito, 1972). InFig. 3 we showtheP andS velocitiesasa function Angle of incidence (degrees)
of incidence angle for five values of ,~ranging Fig.3. P- andS-velocitiesasa function of angleof incidencefrom 0.9 to 1.1. For an isotropic solid, A = C, andthe anisotropicparameter~, whichis varied from 0.9 to 1.1
L = N, and j= I. It is clear that variationsin ~ at intervalsof 0.05c The valuesof velocitiesusedin thecalcula-can lead to substantialdifferencesin velocitiesat tion areVpv = 7.752km s~1VPH = 7.994km s- and V~v=4.343km s~.intermediateincidenceanglesandalsoin averagevalues of velocity. Anderson(1966) showedthatfundamentalmode Rayleigh wave dispersion isalsovery sensitiveto this parameter. almost independentof SV and SH, respectively,
It is often assumedthat Rayleigh waves are but Rayleighwavesaresensitiveto tj, PV andPH.controlledby the horizontal SV velocity so that In thissenseanisotropicsolidis adegeneratecase.isotropicprogramscanbeusedto computedisper- We shall show later that it is possibleto satisfysion curves. It is also often assumedthat the the global datasetwith anisotropyrestrictedto thecompressionalvelocity is unimportantin Rayleigh upper 200 km of the mantle.The anisotropyre-wave inversion.Theseassumptionsarenot strictly quired is about2—4% for both P andS waves.Thevalid (Anderson, 1966) and we have inverted for resultingmodelsdo not havethe pronouncedde-the five independent elastic parameters. The creasein velocity from the LID to the LVZ thatfundamentalmode Loveand Rayleighmodesare characterizesmost surfacewave models, particu-
306
larly for global and oceanicpaths. In fact, the 0.217 DE a s 80
variationswith depthof all the velocitiesis rathermild in this region of the mantle. It appearsthatsome of the features of isotropic or pseudo-isotropic(SH, SV) modelsaredueto theneglectofparameters,such as i~, PV and PH, which areimportant in anisotropicRayleigh wave disper-sion.
The anisotropicupper mantle reconciles the
ity data.ntisis importantfor surfacewavestudies .2730 100 200 300 400 600RayleighandLove wave dataand also permits afit of the shortperiod Rayleighwave groupveloc -_______________________________of seismicsources. —vs ---- VSV ——-VSH
In the courseof this studywe have,of course, Fig.4. Partial derivativesfor a relative change in periodofcalculatedpartial derivativesfor anisotropicstruc- modeoSso(T—. 120s) asa function of depth.The shortdashedtures.Theresultscan be summarizedas follows: line correspondsto perturbationin SVvelocityandlong dashed
line SH velocity; S~and~H of eq. A6 of the Appendix. TheAs expectedthe fundamentaltoroidal mode is continuousline correspondsto theisotropic case(eq. A9).
primarily controlledby SH. The toroidal over-tones,however,aresensitiveto both SV andSH.The spheroidalmodesareonly slightly sensitiveto importantnearthe top of the structure.At depthSH. However, PV, PH, SV, and ij all have a the PV and PH partials are nearly equal andsignificant effect on the spheroidalmodes and opposite. Individually they are significantbut inthere is no a priori relationshipbetween these the isotropiccasetheynearly cancel.Changesofparameters.It is necessary,therefore,to invert for oppositesign of thecomponentvelocitiescauseanfive elastic parameters.We cannot assume,for additive effect and the net partial is nearly asexample,that P-wavevelocities areisotropicand significantas the SV partial. The sameeffect per-invert only for P, SV, and SH. This would be a sistsfor all the spheroidalmodesso that thereisreasonableprocedureonly if the compressional good control on the anisotropicP-velocitiesandwavepartials werevery much lessthan the shear bettercontrol on P-velocitiesin the uppermantlewavepartials or if naturally occurringupperman- in general than is usually consideredto be thetle minerals had a more pronouncedshear waveanisotropy.Neitheris the case. MODE 0 S 80
Figures 4, 5, and 6 show the effects of per- 1 /turbing the shearand compressionalvelocities in / .
/an anisotropicEarthmodel.The formulaeusedto /
evaluatethesepartials are given in theAppendix.As expected,fundamentalmode Rayleigh waves, ‘ /
in this casethemode0S~with aperiod of 120s, /a~emainlycontrolledby SV (shortdashes)andare (___1~~little influencedby SH (long dashes).The totalshearwave partial derivativeis shownas the solid I
curve.Theparameterplottedis therelativechange ________________________________in periodof ~ for achangein shearvelocity as a _2.438~ (00 200 300 400 600function of depth. —VP VPV ~“vPM
A more surprising effect is the natureof per- Fig. 5. Partial derivativesfor a relativechange in periodofturbationsin the PV and PH velocities,shown in modeoS’o (T—. 120s) as afunction of depth. The short dashedline correspondsto perturbationinPV velocityand long-dashedFig. 5. The isotropicpartial derivative(solid line) line in PH velocity; ~v and~H of eq. A6of theAppendix.Theshowsthat compressionalwave velocitiesare only solid line correspondsto theisotropiccase(eq. A9).
307
MODE 0 S 80 where~rrepresentseither the period of free oscil-lation (T = Tin thatcase)or theappropriateperiod
for the body wave underconsideration.The per-~ (2)
It is clear that giventhe observedvaluesfor the, ,./ travel times, periodsof free oscillationsand their
/ attenuationfactors, the inverse problemsfor theI ~ I I elastic and anelasticparameterscan be solved
-s .273 0 100 200 300 400 500 simultaneously.An additional advantageof pro-ETA VP ~~VS ceedingin this manneris that presenceof the
Fig.6. Partial derivativesgiving the relativechangein period. 8q~termsin eq. 1 abovemayprovideadditionalwith respectto theanisotropicparametero~(solid line) andthe resolutionfor the anelasticstructure,sinceIn ‘r inisotropicvelocitiesV~(short-dashedline) andV~(long-dashed the seismic frequencyband varies from 0 to 8,hne). Seeeqs. A6 andA9 of the Appendix.
roughly. Generalizationof eq. 1 for the caseoftransverseanisotropyis consideredin theAppen-dix.
case. Mantle Rayleigh wave data are often in- Another featureof our particularinversionpro-verted for shearvelocity alone. Even in the iso- cedurewas that we optionally could introduceatropiccasethisis not good practicesincea wrong baseline correction or linear slope for a givenP-velocity at shallow depths can cause a large branchof the travel timesas additionalunknowns.perturbationin shearvelocityatgreaterdepth. Our startingmodelandperturbationstheretowere
The isotropic P and S partials are shown in assumedto have,for eachof the regions,aform ofFig. 6 along with the q partial; it is clear that a low-orderpolynomial in radius.For exampleperturbationsin the anisotropicparameteri~can — 2 3
OVp — a0 -r a1r + a2r + a3r ior r1 a~r ~leadto substantialchangesm the penodsof freeoscillations. Substitutioninto the integral leads to a familiar
form of thesystemof equationsof conditionwhichthen can be solved by standardprocedures.The
6. Inversionandthefinal model orderof thepolynomialsneededto satisfythe datawas determinedby trial anderror.
Our startingmodelatareferenceperiodof, say, The method was extendedto the problem of1 s is definedby a set of five functionsof radius transverseisotropy by modifying equationsgiven(Vp, V~,p, q~,‘i~c)’whereq Q~andq~,andq,, by TakeuchiandSaito(1972),as describedin therelate to isotropic dissipationof the shear and Appendix and utilizing the formulas derived bycompressionalenergy, respectively.For an iso- Woodhouse(1981), in the noteaccompanyingthistropicregionof the Earth,perturbationin aperiod report, for the travel times. We solve for fiveof free oscillation or travel time of abody wave elastic constantswhich we take as the horizontalcan be expressedby P-velocity,PH; verticalP-velocity,PV; horizontal
andverticalS-velocities,SH andSV; and an an-
— (I ( . - - - isotropic parameter(Anderson, 1966; TakeuchiT J~ ‘ and Saito, 1972).We found it necessaryto intro-
+8q ~-lnT +8qJ.Inr) (1) duceanisotropyinto the outerpart of the uppermantlebut not elsewhere.
+ (termsrelatedto changesin radii of discos- Parametersof the final model are listed intinuities) TableI. Graphicalrepresentationof the model is
TABLE ICoefficients of thepolyno~mialsdescribingthePreliminaryReferenceEarthModel (PREM).Thevariablex is thenormalizedradius:xr/a wherea6371 km. The parameters listed arevalid at a referenceperiodof I s
LID * 6291.0— 2.6910 0.8317 5.8582 600 578236346.6 +O.6924x + 7.2180x — I .4678x
VPH VSH
3.5908 — 1.0839 3.3687+4.6172x +5.7l76x —2.4778x
QKCrust 6346.6— 2.900 6.800 3.900 600 57823
6356.0
6356.0— 2.600 5.800 3.200 600 578236368.0
Ocean 6368.0— 1.020 1.450 0 578236371.0
* The region between24.4 and 220 kin depthsis transverselyisotropic with the symmetry axis vertical.The effective isotropicvelocitiesoverthis interval canbeapproximatedbyVp 4.l875+3.9382x
= 2. 15 19+2.348Ix
309
shownin Figs.7 and 8. It is important to remem- morecompatiblewith observations.The problember that theseparametersarevalid at a reference is highlynon-uniqueandits early resolutionis notperiod of 1 s. Forotherperiodsthevelocitiesmust likely.)be modified according to equations given in Thevelocities,densityandseveralotherparam-KanamoriandAnderson(1977) etersof geophysicalinterestarelisted in Table II.
I hi T \ In the depthrangefrom 24.4 to 220 km. in whichv5(T)= V~(l). ~l — —~,L) our structureis anisotropic,we alsogive thevalues
hi T for the “equivalent” isotropic solid. This corre-V~(T)= V~(l).{1— —[(1 — E) q~+ Eq,jJ spondsto anappropriateaveragingover all angles
IT of incidence;thegeneralequationshavebeengiven(3) by WoodhouseandDahlen(1978).For thecaseof
where transverseisotropy,the Voigt bulk andshearmod-
E=~(V5/V~)2 uliare
K=~(4A+C+4F—4N)(The particular distribution of bulk dissipation =J-( — )and sheardissipationm the inner core given mTableI should be only understoodas a way to theserepresentupper bounds on the effectivelower theQ of radialmodesin order to makethem elasticmoduli.
06~~~10~
7200 400 600 800
Depth (km)
Fig. 7. Uppermantlevelocities,densityandanisotropicparameter~iin PREM. Thedashedlines arethehorizontal componentsofvelocity. The solidcurvesareij, p andthevertical, or radial,componentsof velocity.
310
4:
-
11
I I I I I I
0 2000 4000 6000
Depth (kin)Fig. 8. The PREMmodel. Dashedlines arethehorizontalcomponentsof velocity. Where i~is I themodel is isotropic.Thecoreisisotropic.
One of the entriesin Table II is the parameter bedeterminedfrom eq. 3. Table IV lists the amso-tiB of Bullen (to be distinguishedfrom the aniso- tropic and anelasticparametersin the crust andtropicparameter‘i), whichrepresentsameasureof uppermantlecomputedata referencefrequencydeviationof amodelfrom theAdams—Williamson of 1 s (above)and200s (below). Notice that theequation effect of the velocity dispersiondueto anelasticity
dK 1 d~ leadsto the development,at long periods,of a low+ ~ -~j-,- (4) velocity zonein adepthrangefrom 80 to 220 km.
This is dueto thelow ~ in this region.For the mostpart ~ in thecoreandlower mantle In Fig. 9 the relativechangesin P- andS-waveis veryclosetounity. Small deviationsare, in some velocities are shown as a function of incidencecases,anartifact of thepolynomialrepresentation, anglefor threedepths:24.4, 100and200 km. TheThe parameterdK/dP is anothermeasureof ho- angulardependenceof SV and SH explainsthemogeneity.Thevaluesfor thelowermantle(except fact that the “effective” shearvelocity atadepthfor the region inunediatelyabovethecore—mantle of 200 kin is lower thaneither SV or SH.boundary)and outercorecan be considerednor- The Q distribution is modelledwith a smallmal. numberof homogeneousregions.Theradialmodes
In TableIII we give the modelparametersata arethe main control on QK and theseessentiallyperiod of 200s; thevelocitiesat otherperiodscan constrainonly the averagevaluein largeregions.
3Il
4 ferencesare substantial.Group velocities corn-I I I I I
puted for the anisotropic model are consistentwith the observations of Mifis (1977) andKanamori(1970). Thereis satisfactoryagreement
The theoreticalperiodsfor the“equivalent” iso-tropic model are systematicallytoo short for thefundamentalspheroidalmode.Thereverseis thecasefor thefundamentaltoroidalmode.The sametrend is evident for the first overtones.The iso-tropicmodelis anadequatefit to thelongerperiod.;;ispheroidalovertonesbut the fit degeneratesat theshorter periods. All of this is suggestiveof an
________________________________ anisotropicuppermantle,suchas wehaveadopted1 ~.-—--~~ I I here.We seeno needto invokedeepanisotropy.
14
The highly anisotropicmineralsolivine andpyrox-~ 4 ‘~24.4vs /1 ene, in fact, are restrictedto the upper mantle.4.,* /
/100 The travel-time data and theoretical fits are/ ~ given in TableVI. Theoriginal dataarealsogiven.
/ .7 \ In somecaseswe correctthedatafor anoffset anda tilt. The baselinefor most travel-timestudiesis
24arbitraryand,for ourpurposes,adjustable.
Thereareseveraleffectswhichcontributeto anoffset and tilt amongvarioustravel-time datasetsandbetweentheseandglobal models.First, thereare the well known sourceand receiver effects.h—200
________________________________ Secondly,the origin timeandlocationof theeventI I I I I I-2 are in error if the travel-timetable used in their
0 60 120 180 location is in error. An error in assigneddepthofAngle of incidence (degrees)
an eventalsocausesanerrorin both baselineandFig.9. Velocityasafunctionof directionof angleof incidence tilt. Published depths are sometimesbased onfor threedepthsin the anisotropicregionof thePR.EM model, minimizationof theresidualvs.distancerelativetoUpper curvesarecompressionalvelocities;lower panel gives a standardcurve.Thirdly, theeffectof attenuationV~(solid) andVSH (dashed). makesthe frequencycontentof the arrivals vary
with distance.In addition,in calculatingtheoreti-cal travel times we must assumea period and
TableV lists the observedand computedpert- correctfor Q. Uncertaintiesin Q anda frequencyods of the normalmodedata usedin this study. dependenceof Q give rise to achangein. baselineFor comparisonwelist the theoreticalresultsfor and tilt. The effects of dispersionand the depththe “equivalent”isotropicmodeldiscussedabove, variation of Q give an offset anda variation ofIt may be noted that at high phasevelocitiesor travel timewith distancethat dependson period.very long periods, the equivalentisotropicmodel Differential travel timesalsocontaintheseeffectsfits the data nearly as well as the anisotropic andhavedifferenteffectiveQ ‘s for the two phasesmodeL For example,the periodsof radial modes iii question. For these reasonswe calculate allpredictedby both modelsarenearly identicaland theoreticaltravel times at a period of one-secondthe sameis true with respectto modesoS2-oSd. and, in TablesVIa-v, computethe baselineand,But for short-periodfundamentalmodesthe dif- in some cases,a tilt that gives the best match
312
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TABLE VObservedandtheoreticalparametersof thenormalmodesusedin thisstudyincluding periodandQ. Periodsaregivenfor anisotropicPREM and anisotropic modelhaving thebulk modulusandrigidity evaluatedaccording to a Voigt averagingscheme.The groupvelocity is calculated for theanisotropicmodel; see Note addedin proof
M 0 D E OBSERVATION AMISOTROPIC ISOTROPIC Q OBS Q COM GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.
between theory andobservation.The uncorrected mula isdataarealsogiven. . lnf
The parameterT* is equalto the ratio of the Tcorr =7~ef— — .
travel timeto Q of agiven phase.In addition toitsapplication in calculations of a change in the If we assume,for example,that the appropriatespectrum of a phase, it can be usedto correct the frequencyfor observationsof the travel times oftheoreticaltravel timescomputedatacertainref- the S.wavesby Hales andRoberts (1970) is 0.2erencefrequency(1 s in our case)to the frequency Hz, thenat 30°distancethe correction is 2 s andappropriatefor the observedwaveform.The for- at 90°,3 s. The sameapproachcan be used to
335
TABLE VI aP travel times: global average from ISC data. Baseline correction — 1.88 s; slope —0.0085 s deg —‘
DELTA OBSERVATION ANISOTROPIC ISOTROPICT OBS 7 CORR ERROR 7 COMP (0—C) P T COMP (0—C) P
correctthe differentialtravel times,suchas ScS—S, these“static” valuesfrom one travel-time study to
and in this casethe parameter7’* hasa meaning another.
only in terms of this specific application. This The observedtravel times from TablesVIa—cillustratesthelargeeffecton bothbaselineandtilt arecomparedwith the resultsof calculationsforthat canoccurby this processalone.Eachsource modelPREMin Fig. I. After the globalaverageofregion has its own upper mantlevelocity and Q the ISC data is correctedfor baselineandslope,and thesevariations contributeto variationsin the fit of the predictedtravel timesis verygoodto
336
TABLE VIa (continued)
DELTA OBSERVATION ANISOTROPIC ISOTROPIC 7’T OBS 7 CORR ERROR T COMP (0—C) P T COMP (0—c) P
distancesas short as 20°; in particular, the 24° et al. (1981, Table VIk) and Hales and Robertsdiscontinuityis well matched.At shorterdistances, (1970, Table VIm) are comparedwith the globalthe differencebetweenthe upper mantlevelocity averageof the ISC dataand SV and SH travelof model PREM (8.2 km s’) and the apparent timesof the PREM model in Fig. 2. The overallvelocity of the P,~phasefrom the ISC data(—.‘ 8.0 shapeof the SV first arrival travel timesmatcheskm s ~‘) leadsto a severalseconddifference.The that of the ISC data well up to a distanceofdataof Haleset al. (1968)andHerrin et al. (1968) approximately80°.In a distancerangefrom 30 toshow differencesin slope of opposite sign with 80°all threedatasetsarein reasonableagreementrespectto PREM,but reproducewell thedetailsof if allowance for tilt and baselinecorrectionsarethe travel—timecurve. made. Beyond 80°,the shapeof the SV and SH
The surfacefocusS-wavetravel timesof Gogna travel—time curves are most consistentwith thedata of HalesandRoberts.
337
TABLE VIbP travel times: Hales et al. (1968). Baseline correction — 1.18 s; slope 0.0085 s deg —‘
DELTA OBSERVATION ANISOTROPIC ISOTROPIC T’T OBS 7 CORR ERROR T COMP (0—C) P T COMP (0—C) P
7. Discussion inversionwere61 and 126sfor fundamentalmodelRayleigh and Love waves, respectively.These
When the upper mantle was allowed to be modeshavewavelengthsof > 240 km so we cananisotropic, the inversion decreasedthe shear only determineaveragepropertiesof the uppervelocity of the LID and increasedthe velocity of mantle.Short-periodRayleighwaves,<20s, sug-the LVZ. The SH and SV velocities, although gest that sv in the uppermostmantleis about4.6different,wereindividuallyalmostcontinuousfrom km s-I, 5% greaterthan theaverageuppermantletheMoho to 220 km. It appearedthat the LID, or SV determinedin this study.seismic lithosphere, could not be resolvedwith the Since thethicknessof the LID andvelocitiesindatabeingused.The shortestperiodsusedin the theLID andLVZ can beexpectedto varywith the
338
TABLE VI cP travel times: Hemn et al. (1968). Baseline correction —0.94 s; slope —0.0141 s deg —
DELTA OBSERVATION ANISOTROPIC ISOTROPIC 7’T OBS 7 CORR ERROR 7 COMP (0—c) P T COMP (0—C) P
ageof the lithospherewe havechosento treatthe scatterwhich is typical of S-wave studies.Otherentire upper mantle to a depthof 220 km as a contributors to S-wavescatterare: (I) the diffi-smoothentity. culty of identifying andpicking later arrivals; (2)
The final modelpredictssignificantly different the longer period nature of 5; (3) the fact thattravel times for SV and SH waves.The effect is locationsare basedon P-wavetimes; and (4) themostpronouncedat short distances,<25°,but is finitenessof naturalsourcesand rupturevelocitiesmaintainedat teleseismicdistances.SH is fasterby which arecloseto shearvelocities.1.16 s at 30°and 0.34s at 90°.This, plus varia- As can be seen from Fig. 1 and the tables,tions in Q andperiod,maycontributeto the large PREM is an excellent fit to P-wave travel-time
339
DELTA OBSERVATION ANISOTROPIC ISOTROPICT OBS 7 CORE ERROR 7 COMP (0—C) P T COMP (0—C) P
datafrom about22 to 90°.The simplified upper- out to about94°.At larger distances,dz/di~formantlestructurewe adoptedis inappropriatefor PREM is up to 0.1 s deg—‘, low comparedto thelocal and regional travel-timestudies.In addition majority of recentdata. This indicatesthat veloci-to agood fit to the travel times, PREMis alsoan ties in the lowermostmantleshouldbe decreasedexcellentfit to dt/di~data. Gognaet al. (1981), slightly.hereafterGJS,tabulateresultsfrom arecentstudy. The dt/d~for S-wavesfor PREM falls in thePREM fits dt/d~ for P.waves,from this study, midstof the ratherwidely-scatteredpublishedval-with an averageerror of only 0.004s deg— ~, over ues in the distancerange 30—40°.Comparedtothe interval 40—77°.Maximumisolatederrorsare GJS the errors are 0.03 s deg—‘ (36—40°),0.04only 0.008s deg~. Beyond 77° PREM deviates (41—51°), 0.03 (51—60°),0.02 (61—70°),0.05 (71—from GJSbut is within the scatterof otherstudies 80°),0.11 (81—90°)and0.16(91—95°).Thecorrec-
340
TABLE VI dDeep focus (550 km) P travel times: Sengupta and Julian (1976). Baseline correction 0.67 s; slope —0.0 173 s deg —‘
DELTA OBSERVATION ANISOTROPIC ISOTROPIC7 OBS 7 CORE ERROR 7 COMP (0—C) P 7 COMP (0—C) P
tion to aperiodof S s increasesdt/d~of PREM in the GJS study, P-wave times are up to 3.2sby about 0.02s deg ‘. Beyond 95°,PREM has short and S-timesup to 6.9 s short in the Hindudt/di~valueswhichare0.17 to 0.38 sdeg—‘ higher Kush area compared to previous travel-timethanGJS.Thissuggeststhat theshearvelocitiesat studies,andthetilts from 30—90°differ by aboutthe baseof the mantleshouldbe increasedor that 0.01 s deg ‘. This is of theorderof the tilt correc-the structure in this region is more complicated tion requiredto reconcilePREMtravel timeswiththanthat givenby PREM. observedtravel times.
Consideringall datasets,the discrepancystartsto set in at about93°with dt/d~of 8.85s deg~. RegionD”Thismeansthat theerroris in thelower 195 km ofthe mantle. The lowermostmantle, region D” in Bullen’s
Travel timesout to distancesof about20°vary notation, clearly has a different velocity gradientsubstantiallyfrom region to region.For example, than the rest of the lower mantle. For simplicity
343
TABLE VI kS travel times (SH): Gogjia et al. (1981). Baseline correction —1.87s; slope 0.0329 deg —l
DELTA OBSERVATION ANISOTROPIC ISOTROPIC T’7 OBS T CORE ERROR 7 COMP (0—C) P T COMP (0—C) P
we haveassumedthat the top of this region is a velocity by about0.04km s— or by decreasingthesecond-orderdiscontinuity.The inversion results velocity gradient somewherenear3630 km radius.in anearlyconstant velocity in the lower 150 km The studyof amplitudesand wave-forms shouldof the mantle. The P-wave travel-times beyond 90° resolvethe possibilities.
are at least 0.08s fast relative to baseline-andtilt-corrected travel-time data. This is a smallerror Radiusofthe corebut is indicated by all datasets.Apparently, theaveragetime spent in region D” by rays at near The radiusof the outer corein PREMis 3480grazingincidenceshouldbelongerby about0.27%. km. It may be noted that PcP—Ptimes for theThis can be accomplishedby reducing the P. model are systematicallyslow with respectto the
344
TABLE VI k (continued)DELTA OBSERVATION ANISOTROPIC ISOTROPIC T’
T OBS 7 CORE ERROR T COMP (0—C) P T COMP (0—C) PPEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC
observations,indicating that the core should be Woodhouseparticipatedin numerousdiscussionsslightly larger. The ScS—S times are also margi- related to this work and assistedus in solvingnally too long. Taking into account the slower many problems.In particular, he derived equa-velocitieswhichmay exist in D”, good agreement tionsfor the traveltimesin a transverselyisotropicwith thesetwo datasetscan be obtainedwith a mediumandhisnoteon this subjectaccompaniescoreradius1.7 km larger,or 3481.7 km. thisreport. RobertNorth madeavailableto ushis
Love wave dataprior to publication.This research
Acknowledgements was supportedby National ScienceFoundationGrantsNo. EAR78-05353(Harvard)and EAR77-
Anton Haleswas an interestedobserverat all 14675 (California Institute of Technology).Con-stagesof this studyandwegratefullyacknowledge tribution No. 3531 of the Division of Geologicalhis advice. We also acknowledgehelpful corre- and Planetary Sciences, California Institute ofspondence with Sir Harold Jeffreys. John Technology,Pasadena,California 91125.
345
TABLE VIIS travel times (SV): (3ogna et al. (1981). Baseline correction —0.29s; slope 0.0188 s deg~
DELTA OBSERVATION ANISOTROPIC ISOTROPICT OBS 7 CORE ERROR T COMP (0—C) P T COMP (0—C) P
Equations for differential kernels given by whereA, C, F, N, and L are thefive independentBackusandGilbert (1967)can beeasilyexpanded elasticconstantsasdefmedby Love(1927,p. 196).to accommodatetransverselyisotropicmedium.A The problemof differential kernelsfor this caserelative changein the squaredeigenfrequencyis hasbeenpresentedby TakeuchiandSaito(1972),
346
TABLE VII (continued)
DELTA OBSERVATION ANISOTROPIC ISOTROPIC T*
T OBS T CORE ERROR T COMP (0—C) P T COMP(0—C) PDEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC
The differential kernel for the density,1~,is the ~pv = (C/p )h1~2
sameas givenby BackusandGilbert (1967). 1/2
As in our inversionwe considersimultaneously VSH (1’T/p) (A4)periods of free oscillations and travel times of ~ = (L/p)’12bodywaves,it is desirableto recasttheproblemin svterms of the perturbationsin velocities and,a ~g F/(A — 2L)
348
TABLE VIm (continued)
DELTA OBSERVATION ANISOTROPIC ISOTROPIC TaT OBS 7 COREERROR T COMP (0—C) P T COMP (0—C) P
References Dziewonski, A.M., Mills, J.M. andBlock, S., 1972. Residualdispersion measurement— a new method of surface wave
Anderson, DL., 1961. Elastic wave propagation in layered analysis, Bull. Seismol. Soc. Am., 62: 129—139.anisotropic media. I. Geophys. Res., 66: 2953-2963. Engdahl, ER. and Johnson, L.E., 1914. Differential PcP travel
Anderson, D.L., 1966. Recent evidence concerning the struc- times and the radius of the core. Geophys. J. R. Astron.tare and composition of the Earth~smantle. In: Physics and Soc., 39: 435—456.Chemistry of the Earth. VoL 6. Pergamon Press, Oxford, Engdahl, ER., Flinn, EA. and Masst, R.P., 1974. Differentialpp. 1—131. PKIKP travel times and the radius of the inner core.
Backus, G.E., 1965. Possible forms of seismic anisotropy of the Geophys. J. R. Astron. Soc., 39: 457—464.upper mantle under oceans. J. Geophys. Res., 70: 3249— Forsyth, D.W., 1975a. A new method for the analysis of3439. multimode surface wave dispersion; application to Love-
Backus, G.E and Gilbert, F., 1967. Numerical applications of a wave propagation in the east Pacific. Bull. Seismol. Soc.formalism for geophysical inverse problems. Geophys. J. R. Am., 65: 323—342.Astron. Soc., 13: 247—276. Forsyth, D.W., 1975b. The early structural evolution and ani-
Birch, F., 1964. Density and composition of mantle and core. i. sotropy of the oceanic upper mantle. Geophys. J. R. Astron.Geophys. Res., 69: 4377—4388. Soc., 43: 103— 162.
Buland, R., Berger, J. and Gilbert, F., 1979. Observations from Geller, R.J. and Stein, S., 1979. Time domain measurements ofthe IDA network of attenuation and splitting during a attenuation of fundamental spheroidal modes (0S6—0S28)recent earthquake. Nature (London), 277: 358—362. for the 1977 Indonesian earthquake. Bull. SeismoL Soc.
Choy, G.L. and Richards, P.G., 1975. Pulse distortion and Am., 69: 1671—1691.Hilbert transformation in multiply reflected and refracted Gilbert, F. and Dziewonski, A.M., 1975. An application ofbody waves. Bull. Seismol. Soc. Am., 65: 55-70. normal mode theory to the retrieval of structural parame.
Derr, 1, 1969. Free oscillation observations through 1968. Bull. ters and source mechanisms from seismic spectra. Philos.SeismoL Soc. Am., 59: 2079—2099. Trans. R. Soc. London, Ser. A, 278: 187—269.
Dratler, J., Farell, W.C., Block, B. and Gilbert, F., 1971. Gog!IS.~ML., Jeffreys, H. and Shimshoni, M., 1981. SeismicHigh.Q overtone modes of the Earth. Geophys. J.R. Astron. travel times for Central Asian epicenters Geophys. J. R.Soc., 23: 399—410. Astron. Soc. (in press).
Dziewonski, A.M., 1971. On regional differences in dispersion Hales, A.L. and Roberts, J.L., 1970. The travel times of S andof mantle Rayleigh waves. Geophys. J.R. Astron. Soc., 22: SItS. Bull. Seismol. Soc. Am., 60: 461—489.289- 325. Hales, A.L., Cleaiy, JR. and Roberts, J.L., 4968. Velocity
Dziewonski, A.M. and Gilbert, F., 1972. Observations of nor- distribution in the lower mantle. Bull. Seismol. Soc. Am.,mal modes from 84 recordings of the Alaskan earthquake of 58: 1975-1989.28 March 1964. Geophys. J. R. Astron. Soc., 27: 393—446. Harkrider, D.G. and Anderson, D.L., 1962. Computation of
Dziewonski, A.M. and Gilbert, F., 1973. Observations of nor- surface wave dispersion for multilayered anisotropic media.mal modes from 84 recordings of the Alaskan earthquake of Bull. Seismol. Soc. Am., 52: 321-332.28 March 1974, Part II: spheroidal overtones. Geophys. J. Herrin, E., Tucker, W., Taggart, J.N., Gordon, D.W. andR. Astron. Soc., 35: 401—437. Lobdell, J.L., 1968. Estimation of surface-focus P travel
times. Bull. Seismol. Soc. Am., 58: 1273—1929.
356
Hess, H., 1964. Seismic anisotropy of the uppermost mantle Schlue, J. and Knopoff, L., 1977. Shear-wave polarizationunder the oceans. Nature (London), 203: 629—63 1. anisotropy in the Pacific basin. Geophys. J. R. Astron. Soc.,
Jordan, T.H. and Anderson, D.L., 1974. Earth structure from 49: 145—165.free oscillations and travel times. Geophys. J. R. Astron. Sengupta, M., 1975. The structure of the Earth’s mantle fromSoc., 36: 411. body wave observations. Ph.D. thesis, Massachusetts In-
Kanamon, H., 1970. Velocity and Q of mantle waves. Phys. stitute of Technology, Cambridge, MA.Earth Planet. Inter., 2: 259—275. Sengupta, M. and Julian, B.R., 1976. P-wave travel times for
Kanamori, H. and Anderson, D.L., 1977. Importance of physi- deep earthquakes. Bull. Seismol. Soc. Am., 66: 1555—1580.cal dispersion in surface waves and free oscillation prob- Steim, J.M. and Dziewonski, A.M., 1980. A new approach tolems. Rev. Geophys. Space Phys., 15: 105—112. measurements of dispersion and attenuation of mantle
Love, A.E.H., 1927. A Treatise on the Mathematical Theory of waves. EOS Trans. Am. Geophys. Union, 61: 298 (abstract).Elasticity. 4th edn. Cambridge University Press, Cam- Stein, S. and Geller, R.J., 1978. Attenuation measurements ofbridge, 643 pp. split normal modes for the 1960 Chilean and 1964 Alaskan
Mendiguren, J.A., 1973. Identification of the free oscillation of earthquakes. Bull. Seismol. Soc. Am., 68: 1595—1611.spectral peaks for 1970 July 31, Colombian deep shock Takeuchi, H. and Saito, M., 1972. Seismic surface waves. In:using the excitation criterion. Geophys. J. R. Astron. Soc., Methods in Computational Physics. Academic Press, New33: 281—321. York, NY, ii: 217—295.
Mills, J.M., 1977. Rayleigh Wave Group Velocities and At- Woodhouse,J.H., 1981. A note on the calculation of traveltenuation Coefficients. Ph.D. thesis, Australian National times in a transversely isotropic earth model. Phys. EarthUniversity, Canberra. Planet. Inter., 25: 357—359.
Raitt, R., Shor, G., Francis, T. and Morris, G., 1969. Aniso- Woodhouse,J.H. and Dahlen, F.A., 1978. The effect of atropy of Pacific upper mantle. J. Geophys. Res., 74: 3095— general aspherical perturbation on the free oscillations of3109. the Earth. Geophys. J. R. Astron. Soc., 53: 263—280.
Sailor, R.V., 1978. Attenuation of Low Frequency Seismic Yu, G. and Mitchell, B.J., 1979. Regionalized shear velocityEnergy. Ph.D. thesis, Harvard University, Cambridge, MA. models of the Pacific upper mantle from observed Love and
Sailor, R.V. and Dziewonski, A.M., 1978. Measurements and Rayleigh wave dispersion. Geophys. J. R. Astron. Soc., 57:interpretation of normal mode attenuation. Geophys. J. R. 311—341.Astron. Soc., 53: 559—581.