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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.)

(ReceivedDecember3, 1980;acceptedfor publicationDecember5, 1980)

Dziewonski, A.M. andAnderson,D.L., 1981. Preliminary referenceEarth modeL Phys. Earth Planet. Inter., 25:297—356.

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

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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

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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

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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.

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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

inappropriate.Oncethestartingvelocity modelsfor theupper-

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

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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 hom*ogeneous.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

Region Radius Density Vp V~

(km) (gcm3) (kms~) (kms’)

Innercore 0— 13.0885 11.2622 3.6678 84.6 1327.71221.5 —8.8381x2 —6.3640x2 —4.4475x2

Outercore 1221.5— 12.5815 11.0487 0 578233480.0 — l.2638x —4.0362x

—3.6426x2 +4.8023x2—5.528lx3 —13.5732x3

Lower 3480.0— 7.9565 15.3891 6.9254 312 57823mantle 3630.0 —6.476lx —5.318lx + l.4672x

+5.5283x2 +5.5242x2 —2.0834x2—3.0807x3 —2.5514x3 +0.9783x3

3630.0— 7.9565 24.9520 11.1671 312 578235600.0 —6.476Ix —40.4673x —13.78l8x

+5.5283x2 +51.4832x2 + 17.4575x2—3.0807x3 —26.6419x3 —9.2777x3

5600.0— 7.9565 29.2766 22.3459 312 578235701.0 —6.4761x —23.6027x —l7.2473x

+5.5283x2 +5.5242x2 —2.0834x2—3.0807x3 —2.55l4x3 +0.9783x3

Transition 5701.0— 5.3197 19.0957 9.9839 143 57823zone 5771.0 — l.4836x —9.8672x —4.9324x

5771.0— 11.2494 39.7027 22.3512 143 578235971.0 —8.0298x —32.6l66x — 18.5856

5971.0— 7.1089 20.3926 8.9496 143 578236151.0 —3.8045x — 12.2569x —4.4597x

Vsv QK

LVZ* 6151.0— 2.6910 0.8317 5.8582 80 57823

6291.0 +0.6924x +7.2l80x — l.4678xVPH VSH 11

3.5908 — 1.0839 3.3687+4.6l72x +5.7176x —2.4778x

Vpv V~,,r QK

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

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 anisotropic 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 hom*ogeneousregions.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

100 24 4 betweenthe observedandpredictedvaluesof Q ofthe normalmodes.

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.

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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.~ ~- 04 U) .I’00 WI ‘C P. ‘C* 0 W) U) a 0 ‘C .., 0. 4.— ‘C 0 .-I U~4. U) 04 4’ 04 4. 01 P. II) ‘C a ‘C 0404 WI 0 4.4’ ‘C C’ P. 4

~ ~‘C~ 04. U)U’04’Ca’WI4.4,CC’01U)0..I4.P.0 0410P.OWIU)0004U)’C’C,CU)4.4.4’WIClJ —

0 (.1 ~II CII CII 114 WI WI III 4.44.4. 4’ 10 U) 10 ‘C ‘C ‘C P. P. P.0. 0000’ a’ a’ a’ 00 0 0 00 00 0 0000(S .4.4 — — — .4 — — — ~ — ~4 .‘~

• a’a’a’a’a’a’a’a’a’a’a’o0aI1)(I,.4.40eeo0oo0eoooooaooa’U%Oa’0~~~~I.4.40e0 0. a’ 0’ 01 a’ Dl C’ 0’ a’ a’ 0’ 0’ 0000000000000000000000000~ C’ 0’ a’ 00000000

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q COM GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC S SEC S S KM/S

O S 50 178.28 0.05 178.214 0.02 177.92 0.20 133.0 5.0 1143.2 3.620O 5 51 175.36 0.05 175.140 —0.02 175.07 0.17 1314.0 5.0 1142.1 3.6214O S 52 172.59 0.05 172.65 —O.O~4 172.31 0.16 136.0 5.0 140.9 3.629OS 53 169.99 0.05 169.98 0.00 169.63 0.21 139.0 5.0 139.9 3.63305 514 167.1410.05 167.39 0.01 167.03 0.22 136.0 5.0 138.8 3.637O 5 55 1614.88 0.05 1614.88 0.00 1614.51 0.23 1314.0 5.0 137.8 3.6141OS 56 162.1420.05 162.1414—0.01 162.05 0.22 133.0 5.0 136.9 3.6145O 5 57 160.11 0.05 160.06 0.03 159.67 0.28 131.0 5.0 135.9 3.6149O S 58 157.75 0.05 157.76 —0.00 157.35 0.25 135.0 3.653O 5 59 155.38 0.05 155.51 —0.09 155.10 0.18 1314.1 3.656O 5 60 153.214 0.05 153.33 —0.06 152.91 0.22 133.3 3.660O 5 61 151.19 0.05 151.20 —0.01 150.77 0.28 13?.5 3.663O S 62 1119.16 0.05 1149.13 0.02 1148.69 0.31 131.7 3.667O 5 63 1147.114 0.05 1147.12 0.02 1146.67 0.32 130.9 3.670O 5 614 11414.96 0.09 145.15 —0.13 11411.70 0.18 130.2 3.673O S 66 1141.22 0.09 1141.37 —0.11 1140.91 0.22 128.9 3.679O S 67 139.73 0.11 139.56 0.12 139.08 0.146 128.2 3.682O S 68 137.914 0.11 137.78 0.12 137.30 0.147 127.6 3.685O S 69 136.19 0.12 136.05 0.10 135.57 0.46 127.0 3.6880 5 70 1314.148 0.12 1314.36 0.09 133.87 0.45 126.11 3.691O S 71 132.79 0.13 132.71 0.06 132.21 0.143 125.8 3.6914O 5 72 131.114 0.13 131.10 0.03 130.60 0.141 125.3 3.696O S 73 129.50 0.13 129.53 —0.03 129.02 0.37 1214.8 3.6990 S 714 127.89 0.12 127.99 —0.08 127.148 0.32 1211.3 3.702O S 75 126.29 0.11 126.149 —0.16 125.97 0.25 123.8 3.7014O 5 76 125.014 0.30 125.03 0.01 1214.50 0.143 127.0 15.0 123.14 3.7070 S 80 119.51 0.30 119.147 0.03 118.93 0.48 121.8 3.717O S 85 113.22 0.30 113.17 0.014 112.61 0.53 120.3 3.728O S 90 107.514 0.30 107.118 0.05 106.91 0.58 119.1 3.7390 S 100 97.73 0.30 97.63 0.10 97.05 0.70 118.0 3.758O 5 105 93.46 0.140 93.314 0.13 92.75 0.76 117.9 3.768O S 110 89.514 0.50 89.140 0.15 88.81 0.81 118.1 3.776O 5 115 85.91 0.60 85.77 0.16 85.18 0.85 118.6 3.7814O 5 120 82.57 0.60 82.142 0.19 81.83 0.90 119.3 3.792O 5 125 79.149 0.70 79.31 0.22 78.73 0.96 120.3 3.799O S 130 76.60 0.70 76.43 0.23 75.814 0.99 121.14 3.806O 5 135 73.93 0.80 73.714 0.26 73.16 1.011 122.8 3.812O 5 1140 71.143 0.80 71.23 0.28 70.66 1.09 1214.3 3.817O S 1115 69.10 0.80 68.89 0.31 68.32 1.13 126.1 3.822o 5 150 66.90 0.80 66.69 0.32 66.13 1.16 128.0 3.827O S 155 611.85 0.80 614.62 0.314 614.07 1.20 130.1 3.831O S 160 62.91 0.80 62.68 0.36 62.13 1.23 132.3 3.8314O S 165 61.08 0.80 60.85 0.38 60.31 1.27 1314.8 3.837

1 5 2 11470.85 0.08 11470.98 —0.01 11471.32 —0.03 310.3 10.9131 S 3 1063.96 0.11 10614.014 —0.01 10614.36 _O.014 282.7 9.8811 S 4 852.67 0.05 852.63 0.00 852.84 —0.02 271.1 8.7121 5 5 730.56 0.06 729.79 0.11 729.83 0.10 291.9 6.9751 S 6 657.61 0.05 657.02 0.09 657.00 0.09 3145.7 5.14721 S 7 603.92 0.05 6014.05 —0.02 6014.05 —0.02 4811.0 17.6 37?.2 5.146141 S 8 556.03 0.07 555.77 0.05 555.78 0.014 379.4 6.1701 S 9 509.96 0.05 509.23 0.114 509.23 0.114 380.3 7.0391 S 10 465.46 0.06 1465.46 0.00 1465.145 0.00 378.3 7.7451 S 16 299.57 0.05 299.53 0.01 299.52 0.02 165.9 6.3631 5 17 286.22 0.07 286.22 0. 286.19 0.01 158.5 6.0914

319

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q COM GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC S SEC S S KM/S

1 5 19 263.63 0.07 263.59 0.02 263.52 0.04 155.6 5.9211 5 20 253.97 0.07 253.72 0.10 253.63 0.13 155.14 5.8791 S 22 236.21 0.07 236.17 0.02 236.06 0.06 155.8 5.8221 S 23 228.142 0.09 228.33 0.014 228.21 0.09 156.1 5.7981 5 214 220.99 0.07 221.02 —0.01 220.89 0.05 156.5 5.77141 S 26 207.71 0.07 207.80 ~O.o14 207.65 0.03 157.0 5.7251 5 27 201.70 0.07 201.80 —0.05 201.614 0.03 157.2 5.6971 S 28 196.31 0.07 196.17 0.07 196.00 0.16 157.2 5.6681 S 35 1614.60 0.10 1611.78 —0.11 164.55 0.03 153.9 5.14021 S 36 161.38 0.05 161.20 0.11 160.97 0.26 153.0 5.3581 S 37 157.67 0.10 157.80 —0.08 157.56 0.07 152.0 5.3131 5 38 1514.73 0.05 154.57 0.10 1511.32 0.26 150.9 5.2671 5 39 151.614 0.07 151.50 0.09 151.24 0.26 149.7 5.2211 5 140 148.61 0.07 1148.57 0.03 1148.31 0.20 1148.5 5.1751 5 41 1145.78 0.05 145.77 0.00 1145.51 0.19 1117.2 5.1301 5 142 1143.12 0.07 143.11 0.01 1142.83 0.20 145.9 5.0851 5 143 1110.61 0.07 1140.56 0.014 140.27 0.211 144.6 5.0411 S 44 138.25 0.09 138.12 0.10 137.83 0.30 1143.3 14.9981 S 50 125.33 0.10 125.41 —0.07 125.10 0.18 135.8 4.7731 5 52 121.87 0.05 121.79 0.06 121.46 0.33 133.6 4.7121 5 53 120.00 0.05 120.07 —0.06 119.74 0.22 132.5 14.6841 S 54 118.50 0.10 118.40 0.08 118.08 0.36 131.5 4.6581 5 55 116.81 0.13 116.79 0.01 116.146 0.30 130.5 14.6341 5 56 115.32 0.10 115.24 0.07 1114.90 0.36 12916 4.6111 5 58 112.25 0.10 112.26 —0.01 111.93 0.29 127.9 14.5711 5 59 110.91 0.10 110.84 0.06 110.51 0.37 127.1 14.5531 5 75 92.148 0.10 92.51 —0.04 92.20 0.31 119.1 4.399

2S 14 724.87 0.05 725.08 —0.03 725.36 —0.07 350.0 5.0 380.2 5.3362 S 5 660.41 0.05 660.12 0.014 660.55 —0.02 302.2 6.0052 5 6 594.80 0.05 594.96 —0.03 595.114 —0.11 237.9 7.2012 S 8 488.18 0.05 488.00 0.014 488136 —0.04 197.7 7.2852 S 9 1448.35 0.05 448.69 —0.08 4149.00 ~0.114 188.2 7.0692 S 10 415.92 0.05 416.17 —0.06 1416.142 —0.12 181.2 6.8582 5 12 365.13 0.05 365.33 —0.06 365.50 —0.10 173.3 6.5362 S 13 31411.72 0.05 344.85 —0.04 3144.97 —0.07 1714.3 6.4812 S 114 326.59 0.05 326.42 0.05 326.51 0.03 188.0 6.6852 5 15 308.42 0.05 308.56 —0.04 308.60 —0.06 2144.0 20.0 258.1 7.61452 5 26 179.214 0.05 179.13 0.06 179.40 —0.09 194.2 6.5682 5 27 174.03 0.05 174.07 —0.02 174.33 —0.17 188.1 6.4512 5 28 169.29 0.05 169.32 —0.02 169.58 —0.17 185.4 6.141142 5 29 164.714 0.05 1614.85 —0.07 165.09 —0.21 183.1 6.3842 5 30 160.53 0.05 160.63 —0.06 160.86 —0.20 181.0 6.3532 5 31 156.58 0.05 156.614 ~0.014 156.85 —0.17 179.1 6.3222 S 33 149.27 0.05 1149.28 —0.01 1149.146 —0.13 175.5 6.2562 S 34 145.95 0.05 145.88 0.05 146.05 —0.07 173.9 6.2222 S 36 139.58 0.05 139.57 0.01 139.71 —0.09 171.0 6.1532 S 37 136.66 0.05 136.64 0.02 136.76 —0.07 169.8 6.1182 5 38 133.88 0.05 133.85 0.02 133.96 —0.06 168.6 6.0822 S 39 131.10 0.05 131.18 —0.06 131.28 —0.13 179.0 20.0 167.5 6.0472 S 40 128.57 0.05 128.64 —0.05 128.72 —0.11 166.5 6.0132 S 42 123.84 0.05’ 123.87 —0.02 123.92 —0.06 164.8 5.9442 S 143 121.65 0.05 121.63 0.01 121.67 —0.02 1614.0 5.9102 S 44 119.49 0.05 119.149 0. 119.52 —0.02 163.3 5.8772 S 45 117.34 0.05 117.43 —0.08 117.145 —0.09 162.6’ 5.8414

320

TABLE V (continued)

M 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q COM GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC S SEC S S KM/S-p

2 S 448 111.87 0.20 111.73 0.13 111.71 0.14 160.8 5.71452 S 149 110.07 0.20 109.96 0.10 109.914 0.12 160.3 5.7132 S 50 108.37 0.20 108.27 0.10 108.23 0.13 159.7 5.6802 5 51 106.71 0.20 106.63 0.07 106.59 0.11 159.2 5.6472 S 58 96.61 0.20 96.65 _0.014 96.57 0.05 155.1 5.14052 S 60 914.14 0.20 94.20 —0.06 94.11 0.03 151.0 20.0 153.8 5.3332 S 614 89.66 0.20 89.75 —0.10 89.614 0.02 151.0 5.1882 S 65 88.65 0.20 88.72 —0.07 88.61 0.05 150.3 5.1522 S 66 87.66 0.22 87.71 —0.06 87.60 0.07 1149.6 5.1182 S 71 82.97 0.20 83.12 —0.18 83.00 —0.03 146.1 14.9562 S 714 80.53 0.20 80.65 —0.14 80.52 0.01 144.2 14.8722 5 76 78.89 0.20 79.10 —0.26 78.97 —0.10 1143.1 11.823

3 5 1 1058.10 0.08 1059.40 —0.12 1059.45 —0.13 1020.0 20.1 826.9 7.9513 S 2 9014.30 0.05 904.00 0.03 904.10 0.02 366.6 7.5863 S 6 392.34 0.05 392.21 0.03 392.30 0.01 275.5 5.5723 S 8 3514.41 0.05 3514.66 —0.07 3514.79 —0.11 263.6 5.2973 S 9 338.97 0.05 338.80 0.05 338.96 0.00 258.7 5.2923 S 11 310.45 0.05 310.1414 0.00 310.64 —0.06 2149.9 5.5423 S 12 297.145 0.05 297.144 0.01 297.66 —0.07 2145.14 5.7233 S 13 285.10 0.05 285.11 —0.00 285.35 —0.09 2140.9 5.9023 S 114 273.33 0.05 273.144 ~0.014 273.70 —0.14 236.2 6.0633 5 15 262.42 0.05 262.1414 —0.01 262.71 —0.11 231.5 6.1973 5 16 252.17 0.05 252.09 0.03 252.38 —0.08 226.9 6.3033 S 17 242.46 0.05 242.39 0.03 2112.69 —0.09 222.4 6.3823 S 18 233.25 0.05 233.32 —0.03 233.63 —0.16 218.1 6.14383 S 19 2214.99 0.05 224.85 0.06 225.15 —0.07 213.9 6.4763 5 20 216.99 0.05 216.93 0.03 217.214 —0.11 229.0 20.0 210.1 6.11983 S 21 209.63 0.05 209.53 0.05 209.84 —0.10 206.4 6.5093 S 22 202.69 0.05 202.61 0.04 202.92 —0.11 203.0 6.5123 S 23 196.18 0.06 196.114 0.02 196.44 —0.13 200.1 6.5113 S 214 190.07 0.05 190.07 0. 190.35 —0.15 198.0 6.5163 S 25 184.32 0.06 1814.32 0.00 184.56~—0.13 207.0 6.7083 S 141 113.35 0.05 113.38 —0.03 113.50 —O.1’l 227.3 6.2613 5 42 111.41 0.05 111.41 0.00 111.53 —0.11 224.5 6.2323 S 43 109.42 0.06 109.51 —0.08 109.614 —0.20 221.8 6.2043 S 144 107.77 0.05 107.68 0.08 107.81 —0.04 219.1 6.1783 S 145 106.00 0.06 105.92 0.08 106.05 —0.05 216.6 6.1533 S 46 104.20 0.10 1014.23 —0.03 1014.36 —0.15 2144.1 6.1303 S 147 102.51 0.06 102.59 —0.08 102.72 —0.21 211.7 6.1083 S 48 101.08 0.05 101.01 0.07 101.114 —0.06 209.14 6.087

3 5 149 99.146 0.08 99.148 —0.02 99.61 —0.15 207.3 6.0663 5 50 97.99 0.05 98.00 —0.01 98.13 —0.114 205.2 6.01463 S 53 93.73 0.06 93.85 —0.13 93.97 —0.26 199.7 5.9893 S 56 90.10 0.05 90.07 0.014 90.17 —0.08 195.1 5.9333 S 57 88.83 0.05 88.88 —0.06 88.98 —0.17 193.8 5.9153 S 58 87.65 0.05 87.73 —0.09 87.82 —0.20 192.6 5.8973 S 63 82.38 0.10 82.143 —0.06 82.50 —0.14 187.7 5.8153 S 67 78.76 0.10 78.68 0.11 78.72 0.05 185.1 5.7573 S 70 76.11 0.10 76.10 0.01 76.13 —0.03 183.7 5.7173 S 73 73.78 0.10 73.70 0.11 73.72 0.08 182.4 5.676

14 5 2 580.81 0.12 580.62 0.03 580.59 0.04 14311.2 13.261‘4 3 3 1489.04 0.07 488.05 0.20 488.02 0.21 1480.2 13.38614 S 4 439.17 0.11 438.68 0.11 1138.73 0.10 290.2 5.018

321

M 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC 5 SEC 5 5 KM/S

14 5 5 1414.62 0.06 14114.69 —0.02 14111.76 —0.03 282.14 5.5314

4 S 9 269.63 0.05 269.63 —0.00 269.61 0.01 339.0 6.61314 S 10 258.75 0.05 258.76 —0.01 258.76 —0.00 302.14 5.97514 5 11 2149.38 0.05 2149.35 0.01 2149.36 0.01 2814.6 5.7144~4S 12 240.78 0.05 2140.79 —0.00 2140.82 —0.01 2714.5 5.681I4 5 13 232.75 0.05 232.82 —0.03 232.85 —0.04 268.2 5.71314 5 114 225.08 0.05 225.27 —0.08 225.31 —0.10 288.0 20.0 2614.3 5.801414 5 15 218.19 0.05 218.07 0.05 218.11 0.03 261.8 5.930

4 S 16 211.214 0.05 211.16 0.04 211.21 0.02 260.3 6.07114 5 17 204.66 0.05 �O’4.53 0.06 2014.58 0.014 259.5 6.21214 S 18 198.16 0.05 198.16 —0.00 198.22 —0.03 259.1 6.314314 5 19 191.96 0.05 192.07 —0.06 192.13 —0.09 291.0 20.0 258.9 6.145714 5 20 186.33 0.05 186.25 0.011 186.31 0.01 258.9 6.55214 5 214 165.68 0.05 165.67 0.01 165.714 —0.03 258.8 6.73514 5 30 141.97 0.05 1141.97 0.00 142.05 —0.05 253.9 6.6514S 31 138.72 0.05 138.70 0.02 138.78 —0.05 2611.020.0 252.3 6.6184 5 32 135.65 0.05 135.59 0.014 135.68 —0.02 , 250.5 6.5834S 314 129.87 0.05 129.83 0.03 129.92—0.014 2311.020.0 2146.2 6.50914 5 35 127.18 0.05 127.15 0.02 127.25 —0.05 246.0 20.0 243.8 6.147114 5 36 1214.66 0.05 1214.59 0.06 1214.69 —0.02 2141.2 6.143314 5 37 122.22 0.05 122.15 0.05 122.26 —0.03 238.5 6.3964 S 38 119.87 0.05 119.82 0.014 119.93 —0.05 235.8 6.3604 S 39 117.65 0.05 117.58 0.06 117.69 —0.014 233.0 6.3254 S 40 115.142 0.05 115.’1~4 —0.01 115.55 —0.11 230.7 6.30514 S 63 76.65 0.10 76.67 —0.03 76.69 —0.05 237.14 6.221

5 5 3 14~1~7~0.05 460.90 —0.03 460.911 —0.03 292.14 3.870

5 S 11 1420.36 0.05 420.25 0.03 420.20 0.014 1489.1 13.2335 5 5 369.92 0.05 369.91 0.00 369.814 0.02 502.5 12.7225 5 6 332.11 0.05 332.15 —0.01 332.07 0.01 506.3 11.8535S 7 303.98 0.05 303.88 0.03 303.79 0.06 1496.020.0 1192.810.11585 S 8 283.56 0.05 283.64 —0.03 283.57 —0.00 1118.2 8.2725 5 11 2214.145 0.05 224.39 0.03 224.25 0.09 3714.7 9~7355 S 13 203.09 0.05 203.07 0.01 202.91 0.09 386.1 8.8505 S 114 1914.61 0.05 194.68 —0.03 1914.52 0.05 371.6 8.1185 S 19 166.78 0.05 166.79 —0.00 166.73 0.03 2814.7 6.3995 S 20 162.145 0.05 162.144 0.00 162.140 0.03 279.14 6.14155 S 23 150.57 0.05 150.58 —0.00 15O.5’4 0.02 268.8 6.5165 S 214 1146.98 0.05 146.96 0.01 1146.93 0.03 265.9 6.5345 S 25 143.59 0.05 1143.52 0.05 143.148 0.08 263.0 6.51405 S 26 1140.25 0.05 1140.23 0.02 1140.19 0.011 260.0 6.5325 5 27 137.12 0.05 137.09 0.02 137.05 0.05 257.0 6.5135 5 28 1314.08 0.05 1314.10 —0.02 1314.06 0.01 253.9 6.14855 5 29 131.18 0.05 131.25 —0.06 131.21 —0.03 250.8 6.14525 5 30 128.149 0.05 128.514 —0.03 128.50 —0.00 2148.0 20.0 247.9 6.14185 5 31 125.90 0.05 125.914 —0.03 125.91 —0.01 2145.1 6.3865 5 32 123.140 0.05 123.116 —0.05 123.143 —0.02 242.6 6.3575 5 33 121.02 0.05 121.09 —0.05 121.06 —0.03 2140.14 6.3355 5 34 118.76 0.05 118.81 —0.05 118.78 —0.02 238.6 6.3205 S 35 116.65 0.05 116.62 0.02 116.59 0.05 237.1 6.3125 S 36 114.57 0.05 114.52 0.014 114.149 0.07 236.0 6.3105 5 37 112.55 0.05 112.118 0.06 112.45 0.09 235.3 6.3155 S 38 110.57 0.05 110.52 0.05 110.49 0.08 223.0 20.0 2314.9 6.3255 S 39 108.66 0.05 108.62 0.014 108.59 0.07 2314.8 6.3395 S 140 106.84 0.05 106.77 0.06 106.75 0.08 234.9 6.355

322

TABLE V (continued)

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC S SEC S 5 KM/S

5 5 41 105.06 0.05 1014.99 0.07 104.97 0.09 235.3 6.3725 5 42 103.36 0.05 103.26 0.10 103.214 0.12 235.9 6.3895 5 43 101.69 0.05 101.58 0.11 101.56 0.12 236.5 6.14065 5 414 100.09 0.05 99.95 0.114 99.914 0.15 237.3 6.14215 ~ 145 98.45 0.05 98.37 0.08 98.36 0.09 238.1 6.14345 5 46 97.01 0.05 96.814 0.18 96.83 0.19 239.0 6.1445

5 5 47 95.51 0.05 95.35 0.17 95.314 0.18 239.8 6.4535 5 51 89.91 0.05 89.82 0.10 89.81 0.11 2142.3 6.455

6 S 9 252.63 0.07 252.19 0.18 252.10 0.21 292.0 20.0 320.6 9.6386 5 114 185.15 0.05 1811.814 0.17 184.80 0.19 259.3 7.3686 5 15 178.76 0.07 178.149 0.15 178.141 0.19 272.2 8.0026 5 16 172.29 0.05 172.16 0.07 172.05 0.14 287.9 8.11186 S 17 166.09 0.06 166.08 0.01 165.93 0.10 300.8 8.5716 5 18 160.146 0.07 160.37 0.05 160.20 0.16 309.0 8.51406 5 19 155.08 0.05 155.10 —0.01 1514.91 0.11 312.7 8.3896 5 20 150.13 0.05 150.28 —O.~1O 150.07 0.014 312.2 8.1586 5 21 1145.75 0.05 1145.88 —0.09 1145.67 0.05 308.0 7.8756 S 22 141.87 0.05 1141.88 —0.01 1141.67 0.114 300.8 7.5726 5 23 138.23 0.05 138.214 —0.01 138.03 0.15 292.0 7.2886 5 214 1314.82 0.05 1314.90 —0.06 1314.69 0.09 282.9 7.0536 5 25 131.80 0.05 131.80 —0.00 131.61 0.15 274.7 6.8826 5 26 128.79 0.05 128.90 —0.09 128.72 0.06 267.9 6.7716 5 27 125.96 0.05 126.16 —0.16 125.99 —0.02 262.4 6.7076 5 28 123.149 0.05 123.55 —0.05 123.39 0.08 258.3 6.6776 5 29 121.01 0.05 121.06 _O.014 120.90 0.09 255.2 6.6696 5 30 118.75 0.07 118.66 0.07 118.51 0.20 253.0 6.6736 S 31 116.40 0.07 116.36 0.014 116.21 0.16 251.5 6.6846 5 33 112.06 0.07 111.99 0.06 111.85 0.18 , 250.0 6.7086 5 34 109.90 0.07 109.92 —0.02 109.79 0.10 249.7 6.7166 5 35 107.96 0.07 107.93 0.03 107.80 0.15 2149.6 6.7206 5 36 106.06 0.07 106.01 0.05 105.88 0.17 249.6 6.7186 5 37 104.18 0.07 1014.15 0.02 1014.03 0.114 2149.7 6.7116 5 38 102.38 0.07 102.37 0.01 102.214 0.13 2149.7 6.6986 5 39 100.68 0.07 100.614 0.014 100.52 0.16 2149.7 6.6806 5 40 98.97 0.07 98.98 —0.01 98.86 0.11 249.6 6.6576 S 142 95.80 0.07 95.814 —0.04 95.72 0.09 2149.1 6.5986 S 143 914.32 0.07 914.35 —0.03 94.23 0.10 248.6 6.5636 5 148 87.62 0.07 87.66 —0.05 87.55 0.08 24’4.7 6.3606 S 149 86.141 0.07 86.46 —0.06 86.35 0.07 214358 6.3216 5 51 84.07 0.07 814.17 —0.12 814.06 0.01 2111.9 6.2516 5 52 82.99 0.07 83.08 —0.11 82.97 0.02 241.1 6.2226 5 53 81.93 0.07 82.02 —0.11 81.92 0.02 240.4 6.1986 5 55 79.95 0.07 79.99 —0.06 79.90 0.07 239.2 6.1646 5 56 78.92 0.07 79.02 —0.13 78.93 —0.01 238.9 6.1566 5 57 77.97 0.07 78.07 —0.13 77.98 —0.01 238.7 6.1526 5 58 77.11 0.07 77. 114 _O.O14 77.06 0.07 238.7 6.1536 5 59 76.20 0.07 76.214 —0.05 76.16 0.06 238.8 6.1586 S 60 75.33 0.07 75.35 —0.03 75.28 0.07 239.0 6.1676 S 61 711.~I6 0.07 74.49 —0.03 714.141 0.06 239.4 6.179

7 5 2 397.37 0.05 397.25 0.03 397.22 0.014 3141.14 15.3117 S 14 293.25 0.05. 292.98 0.09 292.914 0.11 333.8 7.7037 S 5 273.43 0.05 273~214 0.07 273.20 0.09 1477.14 11.6387 5 6 252.66 0.05 252.61 0.02 252.56 0.011 504.3 12.075

323

N 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC 5 SEC S ‘ SEC S 5 KM/S

7 5 7 236.04 0.05 235.97 0.03 235.93 0.05 1415.1 10.0867 5 8 2214.36 0.10 224.59 —0.10 2214.56 —0.09 321.5 7.3667 5 9 216.62 0.10 216.55 0.03 216.52 0.014 281.9 6.1677 S 10 209.142 0.10 209.714 —0.15 209.72 —0.15 266.3 5.9387 5 11 203.09 0.10 203.38 ~0.114 203.36 —0.13 258.14 6.0467 S 12 197.12 0.10 197.20 ~0.014 197.18 —0.03 254.1 6.31147 S 18 147.82 0.07 147.79 0.02 1147.76 0.014 2141.0 6.14147 5 20 1141.23 0.07 1141.20 0.02 1141.17 0.014 239.2 6.5077 S 21 138.06 0.07 137.98 0.06 137.93 0.09 240.1 6.71437 S 22 134.81 0.07 134.78 0.02 134.73 0.06 2142.3 6.9927 S 24 128.57 0.07 .128.53 0.03 128.144 0.10 2149.2 7.39147 5 25 125.48 0.07 125.52 —O.0~4 125.42 0.05 252.5 7.5077 5 28 117.21 0.07 117.18 0.02 117.03 0.15 258.0 7.51497 S 29 114.65 0.07 1114.65 —0.00 1114.149 0.114 258.4 7.5097 5 30 112.16 0.07 112.214 —0.07 112.08 0.07 258.4 7.14597 S 35 101 .714 0.07 101.78 —O.O~4 101.61 0.13 255.9 7.1887 5 36 99.98 0.07 99.96 0.02 99.79 0.19 255.3 7.1377 S 37 98.19 0.07 98.21 —0.02 98.05 0.15 2514.7 7.0877 5 38 96.51 0.07 96.514 —0.03 96.37 0.111 254.1 7.0387 5 39 914~90.07 94.93 —0.04 914.77 0.13 253.6 6.9907 5 143 88.99 0.07 89.09 —0.11 88.914 0.05 251.9 6.8287 S 145 86.37 0.07 86.47 —0.11 86.33 0.05 251.6 6.7707 S 14~ 85.13 0.07 85.22 —0.11 85.09 0.05 251.5 6.71487 ~ ~ 82.76 0.07 82.84 —0.10 82.72 0.04 251.8 6.716

7 S 55 75.53 0.07 75.51 0.02 75.43 0.14 255.0 6.6827 S 56 74.59 0.07 714.57 0.02 74.49 0.13 255.6 6.6777 5 57 73.68 0.07 73.66 0.03 73.58 0.114 256.0 6.671

8 5 1 348.12 0.05 3148.02 0.03 347.98 0.04 930.2 14.1778 5 5 239.96 0.05 2140.03 —0.03 239.95 0.01 611.6 12.14578 S 6 225.28 0.05 225.47 —0.08 225.38 —0.04 1441.0 9.2028 S 7 215.13 0.05 215.03 0.014 214.95 0.08 351.6 9.0118 5 9 191.89 0.07 191.87 0.01 191.76 0.07 1483.0 20.0 501.3 12.141488 S 15 158.50 0.07 158.30 0.12 158.26 0.15 250.6 5.8788 S 23 120.87 0.07 120.67 0.16 120.62 0.21 237.8 6.0528 S 24 118.67 0.07 118.48 0.16 118.143 0.20 237.5 6.1768 S 29 108.08 0.07 108.02 0.06 107.98 0.09 243.1 6.8958 5 30 106.04 0.07 106.02 0.01 105.98 0.05 2414.9 7.0198 S 32 102.20 0.07 102.16 0.014 102.12 0.08 248.5 7.2198 S 38 91.81 0.07 91.79 0.02 91.73 0.09 256.1 7.14358 5 41 87.28 0.07 87.33 —0.05 87.26 0.03 257.9 7.4008 5 146 80.79 0.07 80.85 —0.08 80.78 0.01 258.5 7.21478 5 147 79.78 0.07 79.69 0.12 79.61 0.21 258.3 7.2088 5 148 78.57 0.07 78.56 0.01 78.149 0.11 257.9 7.167

9 S 3 281.39’O.O5 281.30 0.03 281.23 0.06 777.7 13.2669 5 14 258.10 0.07 257.87 0.09 257.80 0.12 515.2 13.1979 5 6 216.37 0.05 216.141 —0.02 216.37 0. 331.1 8.5109 S 7 205.16 0.05 205.23 —0.011 205.18 —0.01 489.9 11.0729 S 8 194.22 0.07 1914.38 —0.08 194.314 —0.06 1472.3 10.5819 5 11 170.01 0.05 169.90 0.07 169.80 0.12 1413.9 11.9729 S 12 161.64 0.05 161.62 0.01 161.50 0.09 ‘ 1465.0 12.0179 S 13 1514.30 0.07 1514.24 0.014 1514.10 0.13 4814.6 11.6599 5 114 1147.87 0.05 1147.75 0.08 1147.60 0.18 14811.7 11.0629 5 15 1142.23 0.05 1112.25 —0.02 142.10 0.09 1430.1 9.635

324

TABLE V (continued) -

M 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC 5 SEC S SEC 5 5 KM/S

9 S 18 132.147 0.07 132.40 ~0.O5 132.33 0.11 255.9 5.8609 5 19 129.87 0.07 129.90 —0.02 129.83 0.03 248.2 5.7979 S 29 100.32 0.07 100.27 0.05 100.20 0.12 243.14 6.3739 5 35 91.16 0.07 91.18 —0.02 91.13 0.03 242.7 6.85119 5 37 88.149 0.07 88.39 0.11 88.35 0.16 241.6 6.956

10 5 2 2147.714 0.05 2147.99 —0.10 2147.96 —0.09 192.14 20.148610 S 10 161.65 0.05 161.53 0.08 161.49 0.10 376.2 10.611410 5 13 145.146 0.07 145.147 —0.00 145.142 0.03 277.7 6.86110 5 114 142.06 0.05 142.07 —0.01 1112.02 0.03 259.1 6.149110 5 17 130.314 0.05 130.28 0.05 130.13 0.16 387.5 10.1441410 5 18 126.00 0.05 125.97 0.02 125.81 0.15 1410.7 10.149010 5 19 121.93 0.05 121.98 —0.05 121.80 0.10 1411.8 10.21810 5 20 118.37 0.05 118.39 —0.02 118.21 0.114 390.5 9.59910 5 21 115.20 0.05 115.30 —0.09 115.12 0.07 342.3 8.145710 S 28 95.58 0.07 95.59 —0.01 95.143 0.15 300.1 7.71510 5 29 93.90 0.07 93.93 —0.03 93.78 0.13 279.9 1.18010 5 31 91.14 0.07 91.00 0.15 90.88 0.28 257.0 6.60610 5 32 89.78 0.07 89.67 0.13 89.56 0.25 251.1 6.149610 S 314 87.21 0.07 87.15 0.07 87.05 0.18 2144.1 6.414110 S 36 814.86 0.07 814.76 0.12 814.68 0.22 240.2 6.148910 S 37 83.58 0.07 83.61 —0.03 83.53 0.06 238.9 6.53010 5 141 79.18 0.07 79.21 —0.04 79.15 0.014 236.2 6.731410 S 44 76.05 0.07 76.13 —0.11 76.08 —O.O~1 236.1 6.873

11 5 1 271.36 0.09 271.33 0.01 271.28 0.03 663.6 15.15211 5 3 223.93 0.05 224.09 —0.07 2214.02 —0.O~1 1447•5 10.68011 5 14 209.55 0.05 209.78 —0.11 209.70 —0.07 652.0 20.0 701.6 12.69011 S 5 197.114 0.05 197.07 0.011 196.99 0.08 665.4 12.01311 5 6 186.83 0.05 186.86 —0.01 186.79 0.02 1463.14 10.02211 5 7. 179.70 0.10 179.714 —0.02 179.69 0.01 280.6 7.57011 5 9 155.49 0.05 155.35 0.09 155.22 0.17 627.1 11.961411 5 10 1149.03 0.05 148.98 0.03 1118.85 0.12 1426.3 9.148311 S 13 1314.99 0.07 1314.82 0.13 1314.76 “0.17 1420.14 11.09511 S 15 126.44 0.07 126.28 0.13 126.22 0.18 332.1 8.314711 5 16 123~’.22 0.07 123.35 —0.11 123.29 —0.05 2814.6 6.84911 5 17 120.89 0.07 120.95 —0.05 120.88 0.01 261.8 6.11414

11 5 21 112.16 0.07 112.30 —0.13 112.214 —0.07 277.3 7.66811 S 22 109.66 0.07 109.75 —0.08 109.65 0.00 317.1 8.83111 5 23 107.15 0.07 107.05 0.09 106.93 0.21 3149.1 9.41111 5 24 1014.36 0.05 104.38 —0.02 1014.23 0.12 363.1 9.501411 5 31 87.29 0.07 87.142 —0.15 87.30 —0.01 335.4 8.64111 5 32 85.78 0.07 85.81 _O.O1l 85.68 0.12 332.1 8.48611 5 314 82.87 0.07 82.90 —0.03 82.75 0.14 307.3 7.81414

11 5 35 81.145 0.07 81.60 —0.18 81.146 —0.01 291.9 7.47311 5 37 79.15 0.07 79.28 —0.16 79.15 0. 268.3 6.92911 S 39 77.24 0.07 77.19 0.06 77.08 0.20 255.9 6.70811 S 140 76.21 0.07 76.21 0.00 76.11 0.114 252.14 6.67811 S 141 75.21 0.07 75.25 —0.05 75.15 0.07 250.0 6.67811 5 143 73.39 0.07 73.140 —0.01 73.31 0.11 2147.3 6.72611 5 414 72.53 0.07 72.50 0.014 72.142 0.15 2146.6 6.76011 S 146 70.68 0.07 70.76 —0.11 70.68 0. 2145.6 6.8214

12 S 7 170.67 0.05 170.77 —0.06 170.65 0.01 1423.8 10.27112 S 10 1145.67 0.05 1115.74 —0.05 1145.69 —0.01 330.9 9.171

325

M 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q 085 Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC S SEC S S KM/S

12 S 11 1110.25 0.05 1140.08 0.12 139.99 0.18 511.1 12.321412 S 12 134.214 0.05 1314.114 0.07 1314.03 0.15 570.0 12.85912 5 13 128.68 0.05 128.59 0.08 128.147 0.17 568.6 12.88312 S 114 123.57 0.05 123.50 0.06 123.37 0.16 552.7 12.74312 S 15 118.93 0.05 118.89 0.03 118.75 0.15 5143.2 12.22812 5 16 115.11 0.05 115.05 0.05 1114.911 0.15 1449.6 10.26112 S 17 111.79 0.07 111.93 —0.13 111.814 —0.014 382.9 9.13112 5 18 109.39 0.07 109.311 0.05 109.25 0.13 325.3 7.86512 S 22 102.08 0.07 102.05 0.02 101.99 0.09 253.5 6.02712 S 23 100.148 0.07 100.50 —0.02 100.1414 0.014 252.0 6.09412 5 26 95.80 0.07 95.87 —0.07 95.82 —0.02 265.14 6.91412 S 33 81 .143 0.07 81.142 0.01 81.37 0.07 267.4 6.970

13 5 1 222.27 0.05 222.143 —0.08 222.35 _O.O11 735.1 114.36913 S 2 206.57 0.05 206.39 0.09 206.30 0.13 878.5 13.93913 5 3 192.71 0.05 192.514 0.09 192.45 0.13 908.6 14.03913 S 8 152.39 0.10 152.59 —0.13 152.52 —0.08 278.14 5.35813 S 12 125.76 0.10 125.71 0.011 125.64 0.10 2147.11 5.13413 S 14 120.96 0.10 121.08 —0.10 121.02 —0.05 285.7 7.58713 S 18 106.77 0.10 106.71 0.06 1O6.~9 0.17 490.5 12.19613 S 19 103.141 0.05 103.36 0.05 103.23 0.17 1486.8 11.78913 S 21 97.65 0.10 97.68 —0.03 97.54 0.12 14140.0 10.56613 5 22 95.32 0.10 95.36 _O.O11 95.23 0.10 378.6 9.23713 S 23 93.62 0.10 93.148 0.15 93.38 0.26 316.8 7.65213 S 25 90.52 0.10 90.62 —0.11 90.514 —0.03 267.8 6.22813 5 26 89.31 0.10 89.38 —0.08 89.31 —0.00 259.6 6.04213 S 29 85.914 0.10 85.93 0.02 85.87 0.08 251.6 6.07313 5 37 73.52 0.10 73.51 0.02 73.146 0.09 250.1 6.143113 5 38 72.74 0.10 72.63 0.114 72.59 0.20 254.2 6.6314

114 5 14 180.81 0.10 180.145 0.20 180.36 0.25 742.14 13.843114 5 7 147.79 0.05 1147.65 0.10 1147.59 0.14 330.11 9.582114 S 8 142.02 0.05 1141.89 0.10 1141.83 0.14 1483.1 12.058114 5 9 136.13 0.05 135.98 0.11 135.92 0.16 528.14 12.226114 S 10 131.27 0.10 130.96 0.23 130.91 0.27 388.14 9.76014 5 17 104.97 0.07 1014.97 0.00 104.92 0.05 316.2 8.2141114 S 19 99.99 0.05 100.02 —0.03 99.98 0.01 1106.9 10.02214 S 25 87.15 0.07 87.30 —0.17 87.16 —0.02 1434.3 10.145114 S 28 82.07 0.07 82.08 —0.02 81.914 0.15 331.8 8.221114 5 31 78.89 0.07 78.79 0.13 78.70 0.214 253.9 6.0314

15 5 3 165.83 0.05 165.69 0.08 165.61 0.13 805.8 14.32715 S 11 122.85 0.07 122.99 —0.11 122.87 —0.02 500.5 11.35515 S 12 118.59 0.05 118.59 0.00 118.48 0.09 572.3 12.141715 S 16 100.69 0.05 100.71 —0.02 100.59 0.10 538.1 13.25415 5 18 96.03 0.07 96.07 _O.014 95.99 0.04 281.3 6.541415 S 28 80.39 0.07 80.45 —0.07 80.39 0. 3211.14 8.14215 S 30 77.63 0.07 77.63 —0.00 77.53 0.13 392.7 9.53815 S 31 76.21 0.07 76.22 —0.01 76.10 0.114 392.2 9.471415 S 32 714.83 0.07 714.89 —0.08 711.77 0.08 371.5 9.071

16 S 5 1116.145 0.05 1146.28 0.12 1146.19 0.18 581.1 12.141516 S 6 139.87 0.05 139.79 0.06 139.69 0.13 739.3 12.89016 S 7 133.90 0.07 133.80 0.08 133.69 0.16 800.0 12.77016 S 10 118.58 0.05 118.52 0.06 118.143 0.13 7714~312.609

326

TABLE V (continued)

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC 5 SEC 5 SEC S S KM/S

16 S 19 91.18 0.07 91.20 —0.02 91.08 0.11 5143.2 13.031416 5 20 88.61 0.07 88.62 —0.01 88.149 0.114 521.2 12.145716 5 25 80.23 0.07 80.23 0.01 80.17 0.07 393.3 9.37316 S 26 78.81 0.07 78.77 0.05 78.71 0.12 373.6 8.914316 S 31 73.61 0.07 73.57 0.06 73.52 0.12 272.9 6.6011

17 S 12 109.11 0.07 109.27 —0.15 109.19 —0.07 1462.0 10.80017S 13 105.93 0.07 105.98 —0.05 105.89 0.014 553.8’ 11.50117 S 114 102.96 0.07 102.96 0. 102.88 0.08 1459.1 10.15717 5 15 100.148 0.07 100.60 —0.12 100.52 _O.O14 350.7 8.11717 S 22 83.514 0.07 83.149 0.07 83.40 0.17 1406.5 10.52817 S 23 81.61 0.07 81.59 0.03 81.147 0.17 1465.9 11.45017 5 26 76.147 0.07 76.39 0.11 76.27 0.26 1427.8 10.52517 S 28 73.56 0.07 73.51 0.07 73.142 0.18 4111.0 9.961417 S 29 72.26 0.07 72.22 0.05 72.15 0.16 386.7 9.3149

17 5 30 71.11 0.07 71.08 0.05 71.01 ‘ 0.15 3147.8 8.147617 S 31 69.98 0.07 70.07 —0.13 70.01 —0.014 3111.6 7.635

18 S 3 1145.28 0.05 1145.10 0.12 1145.00 0.19 851.14 14.05618 S 14 138.11 0.05 138.10 0.00 138.00 0.08 9143.1 13.72618 S 15 95.68 0.07 95.65 0.03 95.60 0.08 381.7 9.76218 S 16 93.28 0.07 93.28 0.00 93.23 0.05 14714.4 11.33218 S 17 90.814 0.07 90.86 —0.02 90.81 0.03 480.2 11.16918 S 25 76.19 0.07 76.11 0.11 76.06 0.17 307.9 7.51818 5 27 73.62 0.07 73.63 —0.02 73.59 0.05 1425.14 10.101

19 S 9 110.62 0.05 110.53 0.08 110.43 0.17 612.14 12.16519 S 10 106.86 0.05 106.87 —0.00 106.77 0.09 675.8 12.140219 5 11 103.66 0.05 103.55 0.10 103.146 0.19 531.14 11.08219 5 14 93.36 0.07 93.37 —0.01 93.23 0.13 6116.14 11.60019 5 15 90.91 0.07 90.99 —0.09 90.85 0.07 521.3 10.321

20 5 14, 123.18 0.05 123.20 —0.02 123.12 0.05 782.5 15.08720 5 5 118.06 0.05 118.014 0.02 117.96 0.08 636.8 12.814420 S 15 89.12 0.05 89.12 0.00 89.07 0.06 301.9 6.60120 5 16 87.39 0.07 87.146 —0.07 87.140 —0.01 1458.8 10.148120 5 17 85.30 0.07 85.31 —0.01 85.24 0.07 606.2 12.08820 S 18 83~16 0.07 83.114 0.02 83.06 0.12 634.14 12.27320 S 19 81.12 0.07 81.11 0.01 81.03 0.11 565.7 11.67720 5 20 79.146 0.07 79.35 0.13 79.28 0.23 1417.9 10.101420 5 25 70.75 0.07 70.60 0.22 70.53 0.31 5147.0 12.876

21 5 6 112.96 0.05 112.99 —0.02 112.87 0.08 739.8 12.73621 5 7 109.02 0.05 109.01 0.01 108.90 0.11 799.9 12.97021 S 8 105.37 0.05 105.30 0.07 105.19 0.17 667.3 13.014321 5 10 98.70 0.05 98.71 —0.01 98.60 0.10 833.9 12.81221 5 11 95.814 0.05 95.75 0.09 95.65 0.20 747.8 12.11121 S 12 93.32 0.05 93.25 0.08 93.15 0.18 516.9 10.000

22 5 12 89.88 0.07 , 89.87 0.02 89.81 0.08 309.0 6.97122 S 13 88.23 0.07 88.114 0.10 88.09 0.16 14142.9 10.36522 S ill 86.08 0.07 85.98 0.11 85.93 0.18 591.3 12.08822 S 23 70.88 0.07 70.93 —0.06 70.89 —0.02 3914.9 9.572

327

H 0 D E ‘OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SE~ S SEC S S KM/S

23 S 14 111.88 0.05 111.814 0.014 111.73 0.13 809.3 13.92023 5 5 107.57 0.05 107.65 —0.07 107.514 0.03 899.2 13.97123 S 7 100.114 0.07 100.114 0.00 100.04 0.09 660.4 13.59323 S 8 97.06 0.07 96.90 0.16 96.81 0.26 740.2 12.991

.23 5 9 914.16 0.07 914.12 0.04 914.014 0.13 553.6 10.98523 5 10 92.114 0.07 92.21 —0.08 92.114 —0.00 322.0 6.60823 5 22 69.59 0.07 69.57 0.03 69.149 0.14 509.4 11.659

214 S 10 89.52 0.10 89.62 —0.11 89.54 —0.02 4149.2 9.875214 S 11 87.33 0.10 87.42 —0.10 87.32 0.01 673.3 12.088214 5 12 85.06 0.10 85.12 —0.07 85.02 0.05 1125.0 20.0 7144.1 12.472214 5 114 80.65 0.10 80.70 —0.06 80.63 0.03 742.8 12.516211 5 15 78.63 0.10 78.69 —0.08 78.62 0.02 8114.6 12.714724 5 16 76.71 0.10 76.77 —0.08 76.70 0.01 795.8 12.53224 5 17 75.20 0.10 75.10 0.13 75.014 0.22 482.8 9.5772~l 5 18 714.26 0.10 74.19 0.09 74.13 0.18 277.8 5.1146

25 5 1 115.46 0.07 115.511 —0.07 115.143 0.02 843.4 114.31525 5 2 110.89 0.05 110.83 0.05 110.73 0.15 787.6 15.43125 5 3 106.05 0.05 106.11 —0.05 106.02, 0.03 376.8 16.61825 5 5 98.65 0.10 98.66 —0.02 98.57’ 0.08 766.3 1~4.55225 S 6 95.32 0.10 95.39 —0.07 95.29 0.03 7214.1 13.15525 S 10 811.78 0.10 814.82 —0.05 84.70 0.09 537.1 10.39725 S 18 72.99 0.10 72.99 0. 72.93 0.09 574.1 11.733

26 S 8 89.19 0.07 89.25 —0.07 89.15 0.05 698.3 12.314726 S 9 86.82 0.07 86.76 0.06 86.67 0.17 325.0 14.11126 5 11 81.77 0.07 81.68 0.11 81.63 0.17 536.0 11.714826 S 12 79.66 0.07 79.62 0.05 79.56 0.12 763.9 13.15926 S 13 77.58 0.07 77.61 —0.011 77.56 0.03 7014.6 12.533

27 5 2 101.144 0.07 101.35 0.09 101125 0.19 797.3 14.80227 5 14 914.37 0.07 914.37 0.00 94.27 0.10 576.7 13.19827 5 114 75.18 0.15 75.06 0.16 714.98 0.26 1420.9 9.75227 5 15 73.143 0.15 73.145 —0.03 73.38 0.07 680.1 12.149527 5 16 71.60 0.15 71.82 —0.31 71.76 —0.22 625.0 11.971

28 5 5 91.39 0.07 91.19 0.21 91.09 0.33 683.8 13.241428 S 6 88.61 0.07 88.147 0.15 88.37 0.27 756.4 13.55528 5 10 78.59 0.07 78.47 0.16 78.40 0.211 762.0 13.26428 5 11 76.75 0.07 76.78 —0.04 76.72 0.014 288.0 5.868

29 S 1 97.014 0.10 96.99 0.05 96.89 0.16 7314.5 15.708

30 S 3 90.61 0.07 90.149 0.13 90.39 0.24 715.6 15.391130 S 7 79.69 0.07 79.69 0.01 79.61 0.10 848.0 114.17730 S 8 77.52 0.07 77.53 —0.02 77.146 0.07 798.1 13.5914

32 5 1 90.03 0.07 89.94 0.10 89.93 0.11 89.8 11.653

33 S 6 77.00 0.10 76.82 0.24 76.75 0.33 606.6 14.012

314 5 1 83.83 0.10 83.76 0.08 83.68 0.18 630.0 20.0 754.0 15.822

328

TABLE V (continued)

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC 5 SEC S SEC 5 5 KM/S

0 T 2 2636.38 0.08 2637.145 —0.O~4 2639.140 —0.11 250.11 9.1790 T 3 1705.95 0.15 1706.07 —0.01 1707.61 —0.10 2140.0 7.613O T 14 1305.92 0.07 1306.11 —0.01 1307.55 —0.13 228.2 6.796O T 5 1075.98 0.12 1077.314 —0.13 1078.79 —0.26 216.14 6.233O T 6 925.814 0.09 926.96 —0.12 928.145 —0.28 205.14 5.826O T 7 819.31 0.08 819.22 0.01 820.77 —0.18 195.6 5.528O T 8 736.86 0.20 737.142 —0.08 739.03 —0.29 170.0 20.0 187.1 5.30140 T 9 671.80 0.20 672.69 —0.13 6714.35 —0.38 180.0 20.0 179.7 5.132O T 10 618.97 0.20 619.88 —0.15 621.59 ~0.142 173.3 4.995O T 12 538.05 0.20 538.25 —O.O~l 540.05 —0.37 162.9 14.7914O T 13 506.07 0.20 505.814 0.05 507.67 —0.32 158.8 4.7200 T i~4 1477.53 0.20 1477.149 0.01 1479.35 —0.38 155.3 14.659O T 16 1430.01 0.20 1430.08 —0.02 1432.00 —0.146 1149.5 11.567O T 17 1410.214 0.20 410.00 0.06 ‘411.93 ~0.141 1147.2 14.533O T 18 391.82 0.20 391.83 —0.00 393.77 —0.50 1145.2 14.505O T 20 360.03 0.08 360.16 —0.03 362.11 —0.58 141.9 ‘4.462O T 21 3146.50 0.08 3146.25 0.07 3148.20 ~0.149 1110.5 14.14147O T 22 333.69 0.08 333.141 0.08 335.37 —0.50 1114.0 20.0 139.3 14.1434O T 23 321.70 0.08 321.52 0.05 323.148 —0.55 138.3 14.1423

0 T 214 310.63 0.07 310.148 0.05 312.143 —0.58 137.14 ~4.4114O T 25 300.37 0.06 300.18 0.06 302.13 —0.59 110.0 23.0 136.6 14.1407OT 26 29O.77O.06 290.56 0.07 292.50—0.60 113.022.3 135.9 14.1402

O T 27 281.75 0.06 281.55 0.07 283.148 —0.61 115.0 21.11 135.2 14.397

O T 28 273.27 0.06 273.09 0.07 275.01 ~0.614 116.0 20.0 1314.7 14.393O T 29 265.30 0.06 265.12 0.07 267.014 —0.65 115.0 18.0 1314.2 14.390O T 30 257.76 0.06 257.62 0.06 259.52 —0.68 113.0 16.1 133.7 14.3880 T 31 250.66 0.06 250.53 0.05 252.142 —0.70 112.0 15.0 133.3 14.386O T 32 2143.95 0.06 243.82 0.05 2145.70 —0.72 112.0 15.2 133.0 14.385O T 33 237.59 0.05 237.146 0.05 239.33 —0.73 112.0 16.5 132.7 14.3814

O T 34 231.56 0.05 231.143 0.06 233.29 —0.75 113.0 18.3 132.14 4.383O T 35 225.83 0.05 225.70 0.06 227.514 —0.76 113.0 20.0 132.2 4.3820 T 36 220.37 0.05 220.214 0.06 222.07 —0.77 113.0 21.2 132.0 4.382O T 37 215.17 0.05 215.05 0.06 216.86 —0.79 112.0 22.0 131.8 4.382O T 38 210.21 0.05 210.09 0.06 211.90 —0.80 111.0 22.5 131.7 14.382O T 39 205.147 0.05 205.35 0.06 207.15 —0.82 111.0 22.8 131.5 14.381O T 40 200.95 0.05 200.83 0.06 202.61 —0.83 111.0 23.0 131.4 14.382O T 41 196.60 0.05 196.50 0.05 198.26 —0.85 112.0 23.3 131.3 11.382O T 42 192.50 0.05 192.35 0.08 1914.10 —0.83 113.0 23.6 131.2 4.382O T 143 188.51 0.05 188.38 0.07 190.12 —0.85 115.0 23.9 131.2 4.382O T 1414 1814.70 0.05 184.56 0.08 186.29 —0.86 117.0 214.2 131.1 4.382O T 145 181 .011 0.05 180.89 0.08 182.61 —0.87 119.0 24.5 131.1 4.382O T 146 177.52 0.05 177.37 0.08 179.07 —0.87 121.0 214.8 131.1 14.383O T 147 174.10 0.05 173.99 0.06 175.68 —0.91 122.0 25.0 131.1 14.383O T 148 170.87 0.05 170.72 0.09 172.140 —0.90 .123.0 25.1 131.1 14.383O T 49 167.73 0.05 167.58 0.09 169.25 —0.90 123.0 25.1 131.1 14.383O T 50 1614.70 0.05 1614.56 0.09 166.21 —0.91 122.0 25.1 131.1 14.3814

0 T 51 161.78 0.05 161.611 0.09 163.27 —0.92 121.0 25.1 131.1 4.3814O T 52 158.95 0.05 158.82 0.08 160.1414 ~0.914 120.0 25.0 131.1 4.384O T 53 156.23 0.05 156.10 0.09 157.71 —0.95 119.0 25.0 131.2 14.3814

0 T 514 153.59 0.05 153.46 0.08 155.07 —0.96 118.0 25.0 131.3 14.3814O T 55 151.04 0.05 150.92 0.08 152.51 —0.97 117.0 25.0 131.3 14.385O T 56 1148.57 0.05 1148.46 0.07 150.014 —0.99 116.0 25.1 131.4 4.385O T 57 146.19 0.05 1146.08 0.08 1147.614 —0.99 116.0 25.1 131.4 14.385O T 58 1143.87 0.05 143.77 0.07 1145.33 —1.01 115.0 25.5 131.5 4.3850 T 59 1141.63 0.05 1141.514 0.07 1143.08 —1.02 115.0 25.8 131.6 14.385

329

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC 5 SEC 5 5 KM/S

O T 60 139.116 0.05 139.37 0.06 140.90 —1.03 116.0 26.2 131.7 14.385O T 61 137.35 0.05 137.27 0.06 138.79 —1.05 116.0 26.6 131.8 14.385O T 62 135.30 0.06 135.23 0.05 136.74 —1.07 116.0 27.1 131.9 14.385O T 63 133.32 0.06 133.25 0.05 1311.75 —1.07 117.0 27.6 132.0 14.385O T 614 131.39 0.06 131.33 0.05 132.82 —1.09 117.0 28.1 132.1 14.385O T 65 129.51 0.06 129.46 0.04 130.94 —1.10 118.0 28.7 132.3 14.385O T 66 127.69 0.06 127.65 0.03 129.12 —1.12 118.0 29.3 132.14 4.385O T 67 125.92 0.07 125.88 0.03 127.314 —1.13 119.0 30.0 132.5 14.385

1 T 2 756.57 0.08 757.50 —0.12 757.514 —0.13 256.14 4.1031 T 3 695.18 0.07 694.86 0.05 6914.95 0.03 252.9 5.3611 T 6 519.09 0.06 519.32 ~0.014 519.45 —0.07 242.2 7.1021 T 7 475.17 0.13 475.33 —0.03 475.47 —0.06 238.0 20.0 237.3 7.1121 T 8 1438.149 0.05 438.55 —0.01 438.70 —0.05 232.1 6.9791 T 9 407.74 0.07 407.75 —0.00 407.91 —0.04 227.3 6.7901 T 10 381.65 0.10 381.68 —0.01 381.814 —0.05 223.3 6.6071 T 11 359.13 0.05 359.28 ~0.014 359.145 —0.09 220.0 6.14511

1 T 12 339.514 0.06 339.76 —0.07 339.93 —0.12 195.0 20.0 217.14 6.33141 T 13 322.814 0.12 322.53 0.10 322.70 0.014 215.1 6.2401 T 15 293.35 0.05 293.314 0.00 293.51 —0.06 211.3 6.0971 T 16 280.56 0.05 280.84 —0.10 281.00 —0.16 209.14 6.0361 T 17 269.51 0.05 269.147 0.02 269.63 —0.04 207.3 5.9771 T 18 259.00 0.05 259.08 —0.03 259.24 —0.09 205.2 5.9191 T 19 249.141 0.05 2149.55 —0.06 249.71 —0.12 195.0 20.0 202.9 5.8601 T 20 240.88 0.05 240.79 0.014 2140.95 —0.03 200.14 5.8001.T 21 232.53 0.05 232.70 —0.07 232.86 ~0.114 197.8 5.71401 T 22 225.22 0.05 225.21 0.00 225.37 —0.07 195.2 5.678iT 23 218.31 0.05 218~26 0.0? 218.113—0.05 182.0 20.0 192.14 5.6171 T 214 211.91 0.05 211.80 0.05 211.96 —0.03 1611.0 20.0 189.6 5.555iT 25 205.80 0.05 205.78 0.01 205.911—0.07 192.0 20.0 186.7 5.14931 T 26 200.24 0.05 200.15 0.05 200.31 —O.O~4 183.9 5.4321 T 27 194.83 0.05 1914.87 —0.02 195.04 —0.11 181.0 5.3731 T 28 189.911 0.05 189.93 0.01 190.09 —0.08 178.2 5.31141 T 29 185.26 0.05 185.27 —0.00 185.43 —0.09 175.5 5.2571 T 30 180.80 0.05 180.88 —0.05 181.05 —0.14 172.9 5.2031 T 31 176.85 0.07 176.714 0.06 176.90 —0.03 170.14 5.1501 T 32 172.98 0.05 172.82 0.09 172.99 —0.01 168.0 5.1001 T 33 169.22 0.05 169.11 0.06 169.27 —0.03 165.8 5.0531 T 314 165.72 0.05 165.59 0.08 165.75 —0.02 163.6 5.0081 T 35 162.34 0.05 162.23 0.06 162.140 ~0.014 161.6 ‘4.9661 T 36 159.09 0.05 159.04 0.014 159.20 —0.07 159.7 4.9271 T 37 156.03 0.05 155.99 0.03 156.15 —0.08 157.9 14.8901 T 38 153.13 0.05 153.08 0.04 153.24 —0.07 156.3 4.8561 T 39 150.26 0.05 150.29 —0.02 150.45 —0.12 154.7 4.8251 T 40 147.63 0.05 1117.62 0.01 1147.78 —0.10 153.3 14.7951 T 41 145.05 0.05 1115.05 0. 1’45.22 —0.11 152.0 14.7681 T 42 142.60 0.05 142.59 0.00 1142.75 —0.11 150.8 14.7431 T 43 140.21 0.05 140.22 —0.01 1140.38 —0.12 149.6 4.7201 T 145 135.64 0.214 135.74 —0.08 135.90 —0.19 147.7 4.6801 T ‘46 133.63 0.05 133.62 0.01 133.78 —0.11 1146.8 14.6621 T 47 131.54 0.05 131.57 —0.03 131.73 —0.15 1116.0 4.6461 T 48 129.56 0.05 129.59 —0.02 129.75 —0.15 1145.3 4.6311 T 49 127.72 0.05 127.68 0.03 127.83 —0.09 11414.6 4.6181 T 50 125.92 0.10 125.82 0.08 125.98 —0.05 1414.0 4.6051 T 51 1214.18 0.10 124.02 0.12 124.18 —0.00 143.14 4.594

330

TABLE V (continued)

M 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC S SEC S S KM/S

1 T 52 122.26 0.10 122.28 —0.02 122.1414 —O.i’l 1142.9 11.5831 T 514 118.99 0.10 118.95 0.03 119.10 —0.09 1112.0 ‘4.5651 T 57 1114.141 0.10 1114.30 0.09 114.145 _o.014 1140.9 ~4.5~421 T 58 112.92 0.10 112.811 0.07 112.99 —0.06 1140.6 14.5361 7 59 111.40 0.10 111.141 —0.01 111.56 ~0.111 1314.0 20.0 1140.14 4.5301 T 60 110.214 0.10 110.02 0.20 110.17 0.07 140.1 14.52141 T 62 107.44 0.10 107.35 0.09 107.149 —0.05 138.0 20.0 139.8 14.51141 T 64 1014.914 0.10 104.81 0.13 1014.95 —0.01 139.14 14.5061 T 66 102.59 0.10 102.39 0.20 102.53 0.06 139.2 14.498

2 T 4 420.46 0.07 1120.19 0.06 1420.21 0.06 209.14 3.8032 T 7 363.65 0.07 363.14 0.114 363.19 0.13 223.14 6.0922 T 8 3143.34 0.06 3143.17 0.05 3143.22 0.014 229.2 6.6972 7 17 219.95 0.05 220.03 —0.03 220.06 —0.05 235.6 6.8442 T 18 211.90 0.05 212.10 —0.10 212.13 —0.11 233.6 6.7382 T 19 2014.63 0.05 2014.83 —0.10 2014.86 —0.11 231.6 6.61462 T 21 191.91 0.05 191.91 —0.00 191.94 —0.01 227.3 6.14942 T 22 186.19 0.05 186.114 0.03 186.16 0.02 225.2 6.14302 T 25 171.12 0.12 170.98 0.08 171.00 0.07 219.3 6.2662 T 26 166.50 0.05 166.5Z1 —0.02 166.55 —0.03 217.5 6.2202 T 28 158.142 0.05 158.38 0.03 158.140 0.02 2114.3 6.1372 7 29 154.614 0.05 154.63 0.00 154.65 —0.01 212.9 6.1002 T 31 147.71 0.05 147.70 0.01 147.71 —0.00 210.3 6.0332 7 32 1144.59 0.06 1144.149 0.07 11414.50 0.06 209.1 6.0012 T 33 141.54 0.05 141.113 0.08 1141.44 0.07 207.9 5.9702 7 34 138.62 0.05 138.51 0.08 138.52 0.07 206.7 5.9392 T 35 ‘135.73 0.05 135.72 0.00 135.73 —0.00 205.6 5.9082 7 36 133.114 0.05 133.06 0.06 133.07 0.06 183.0 20.0 2014.4 5.8772 7 38 128.15 0.05 128.08 0.05 128.08 0.05 172.0 20.0 201.8 5.8122 7 140 123.56 0.05 123.50 0.05 123.51 0.05 199.0 5.71422 T 41 121 .143 0.05 121.36 0.06 121.36 0.06 197.14 5.7052 T 144 115.149 0.05 115.42 0.06 115.142 0.06 192.3 5.5862 7 47 110.22 0.05 110.15 0.06 110.15 0.07 182.0 20.0 186.6 5.4582 T 49 106.98 0.05 106.96 0.02 106.95 0.03 207.0 20.0 182.7 5.3702 T 51 104.01 0.05 103.99 0.02 103.99 0.02 178.0 20.0 178.6 5.2822 T 52 102.60 0.05 102.59 0.01 102.58 0.02 162.0 20.0 176.7 5.2392 T 514 99.93 0.05 99.92 0.01 99.91 0.02 172.8 5.1562 T 55 98.61 0.05 98.65 —0.04 98.65 —0.011 170.9 5.1162 T 56 97.140 0.05 97.143 —0.03 97.142 —0.02 169.1 5.0772 T 58 95.08 0.05 95.09 —0.01 95.08 —0.00 165.6 5.0042 T 61 91.85 0.05 91.814 0.01 91.814 0.02 160.9 ‘4.907

3 7 9 259.26 0.07 259.48 —0.09 259.148 —0.08 233.9 5.14543 T ii 2140.149 0.07 240.86 —0.15 2140.86 —0.15 2140.1 6.14393 T 18 184.09 0.07 1814.26 —0.09 1814.25 —0.09 236.3 7.3173 T 19 178.13 0.05 178.31 —0.10 178.30 —0.10 232.8 7.1563 T 20 172.714 0.05 172.85 —0.07 172.85 —0.06 229.5 7.0043 T 21 167.69 0.05 167.82 —0.08 167.81 —0.07 226.7 6.8733 T 214 1514.67 0.05 1514.70 —0.02 154.68 —0.01 221.14 6.6283 T 26 147.11 0.05 1147.20 —0.06 1147.18 —0.05 219.9 6.51463 T 27 1143.67 0.05 1143.74 —0.05 143.73 _O.014 219.5 6.5173 T 28 140.40 0.05 1140.46 —0.014 1140.1414 —0.03 219.2 6.4923 T 29 137.21 0.05 137.33 —0.08 137.31 —0.07 219.1 6.4703 T 30 1314.23 0.05 1314.35 —0.09 134.33 —0.07 215.0 20.0 219.0 6.4483 T 31 131.37 0.05 131.50 —0.10 131.48 —0.09 218.9 6.427

331

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. - PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC 5 SEC S 5 KM/S-p

3 T 32 128.68 0.05 128.78 —0.08 128.76 —0.06 218.7 6.14053 T 33 126.16 0.05 126.18 —0.02 126.16 —0.00 218.5 6.3823 T 34 123.75 0.05 123.70 0.04 123.68 0.06 218.3 6.3583 T 37 116.89 0.05 116.814 0.014 116.82 0.06 217.0 6.2773 T 38 114.66 0.05 1114.74 —0.07 114.72 —0.05 216.4 6.21483 7 14~ 108.87 0.05 108.92 —0.05 108.90 —0.03 2114.2 6.1573 T 42 107.011 0.05 107.13 —0.08 107.10 —0.06 213.4 6.1273 T 46 100.56 0.05 100.58 —0.02 100.56 0.00 210.2 6.0153 T 147 99.08 0.05 99.09 —0.01 99.06 0.02 209.5 5.9903 T 54 89.90 0.07 89.86 0.014 89.84 0.07 206.1 5.8513 7 57 86.41 0.07 86.146 —0.06 86.144 —0.03 205.0 5.8033 T 58 85.33 0.07 85.39 —0.07 85.37 —0.014 204.6 5.7863 7 59 814.35 0.07 84.35 —0.00 814.33 0.03 2014.2 5.7693 T 62 81.1414 0.07 81.39 0.06 81.37 0.09 202.6 5.7133 7 65 78.69 0.07 78.66 0.03 78.614 0.06 200.14 5.6473 T 68 76.19 0.07 76.114 0.06 76.12 0.09 197.14 5.5683 T 69 75.142 0.07 75.35 0.10 75.32 0.13 196.3 5.5393 T 72 73.16 0.07 73.08 0.11 73.06 0.114 192.3 5.4463 7 73 72.36 0.07 72.36 0.00 72.34 0.03 190.8 5.413

14 7 11 199.714 0.15 200.114 —0.20 200.10 —0.18 221.1 4.726

4 T 20 155.64 0.15 155.75 —0.07 155.72 —0.05 231.7 7.118214 T 21 151.15 0.15 151.33 —0.12 151.30 —0.10 232.2 7.4934 T 25 136.30 0.15 136.18 0.09 136.15 0.11 231.6 7.16214 T 27 - 130.03 0.15 129.91 0.09 129.88 0.11 231.1 6.9984 T 40 101.27 0.07 101.43 —0.16 101.39 —0.12 219.9 6.35214 T 141 99.71 0.07 99.82 —0.11 99.79 —0.08 219.0 6.3204 T 145 93.79 0.07 93.94 —0.16 93.90 —0.12 217.3 6.231

‘4 7 47 91.11 .0.07 91.27 —0.18 91.24 —0.14 217.3 6.2064 T 50 87.46 0.07 87.56 —0.11 87.52 —0.07 217.9 6.1854 T 54 82.95 0.07 83.06 —0.14 83.03 —0.10 219.1 6.16414 T 62 75.146 0.45 75.38 0.10 75.36 0.14 219.0 6.08214 7 614 73.77 0.07 73.70 0.10 73.68’ 0.13 218.2 6.0514 T 65 72.914 0.07 72.89 0.07 72.86 0.10 217.6 6.03144 T 67 71.07 0.147 71.32 —0.35 71.30 —0.32 . 216.5 5.99814 T 80 63.06 0.45 62.77 0.145 62.76 0.48 206.5 5.740

4 T 90 57.69 0.145 57.67 0.03 57.66 0.05 197.8 5.51611 T 95 55.43 0.45 55.149 —0.11 55.48 —0.09 192.1 5.3814 T 97 54.95 0.145 54.68 0.50 54.66 0.52 189.6 5.3234 7 98 514.50 0.145 514.28 0.141 514.27 0.143 188.3 5.29414 T 99 53.914 0.145 53.89 0.08 53.88 0.10 187.0 5.265

5 7 38 97.11 0.07 97.25 —0.15 97.21 —0.10 2214.5 6.58145 7 40 94.12 0.07 914.24 —0.13 94.20 —0.08 225.4 6.5695 7 14~ 92.65 0.07 92.80 —0.16 92.76 —0.12 226.1 6.568

5 T 142 91.34 0.07 91.141 —0.07 91.37 —0.03 227.0 6.5695 T 43 89.97 0.07 90.05 —0.09’ 90.02 —0.05 227.9 6.5725 T 414 88.614 0.07 88.74 —0.11 88.71 —0.07 228.9 6.5755 T 45 87.47 0.07 87.146 0.01 87.143 0.05 229.8 6.5765 T 146 86.26 0.07 86.22 0.014 86.19 0.08 230.7 6.5775 T 47 85.08 0.07 85.02 0.07 84.99 0.11 231.5 6.5755 7 50 81.60 0.07 81.60 0. 81.57 0.04 233.1 6.5545 T 51 80.55 0.07 80.52 0.03 80.50 0.07 233.4 6.5415 T 52 79.52 0.07 79.148 0.05 79.45 0.09 233.4 6.5265 7 55 76.52 0.07 76.51 0.01 76.149 0.014 232.6 6.462

332

TABLE V (continued)

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC 5 SEC S SEC 5 5 KM/S

5 7 56 75.67 0.07 75.58 0.12 75.55 0.15 232.0 6.14365 T 57 714.75 0.07 714.68 0.10 74.65 0.14 231.2 6.14085 T 60 72.13 0.42 72.10 0.014 72.08 0.07 228.3 6.31145 7 77 60.87 0.142 60.80 0.11 60.78 0.114 212.3 5.8845 7 79 59.69 0.42 59.73 —0.07 59.71 —0.03 211.7 5.86145 T 105 148.79 0.142 48.76 0.07 ‘48.75 0.09 2014.9 5.7205 T 107 147.94 0.145 148.09 —O~31 48.08 —0.29 2014.1 5.7025 T 109 147.68 0.43 147.144 0.50 117.143 0.52 203.3 5.6805 T 110 147.23 0.42 117.12 0.23 ‘47.11 0.25 202.8 5.6675 T 111 146.77 0.42 146.81 —0.09 146.80 —0.07 202.2 5.6535 T 118 1411.68 0.142 44.76 —0.18 44.7s —0.17 197.0 5.519

6 7 314 97.13 0.07 97.14 —0.01 97.10 0.03 233.1 7.1386 T 35 95.46 0.07 95.149 —0.04 95.146 0.01 233.7 7.0816 7 37 92.29 0.07 92.39 —0.11 92.35 —0.07 235.6 7.0076 T 141 86.70 0.07 86.80 —0.11 86.76 —0.07 239.9 6.9416 T 145 81.85 0.07 81.88 —0.04 81.85 —0.01 2141.7 6.8686 T 147 79.71 0.07 79.65 0.07 79.62 0.11 2141.3 6.8116 7 49 77.65 0.07 77.56 0.12 77.53 0.15 239.9 6.71406 T 71 60.82 0.140 60.98 —0.26 60.96 —0.23 223.3 6.2016 7 72 60.12 0.40 60.41 —0.48 60.39 ~0.1414 223.5 6.2006 7 81 56.02 0.110 55.72 0.514 55.70 0.57 222.9 6.114146 7 89 51.97 0.110 52.18 ~0.140 52.16 —0.37 218.0 6.0276 T 91 51.38 0.140 51.37 0.01 51.36 0.014 216.7 5.9976 7 92 51.02 0.140 50.98 0.09 50.96 0.12 216.1 5.9826 T 98 148.62 0.40 148.76 —0.29 148.75 —0.26 212.9 5.9d36 T 117 ‘ 43.214 0.140 42.98 0.62 ‘42.96 0.65 207.2 5.72146 T 125 140.98 0.110 40.97 0.014 ‘40.96 0.06 2014.5 5.6676 T 131 39.67 0.140 39.59 0.19 39.58 0.21 202.14 5.6286 T 132 39.143 0.140 39.37 0.14 39.37 0.16 202.1 5.6206 7 1141 37.36 0.140 37.52 ~0.141 37.51 ~0.140 197.9 5.5266 7 145 36.89 0.140 36.76 0.35 36.76 0.37 195.2 5.14606 T 149 35.90 0.40 36.04 _0.141 36.04 —0.39 191.9 5.3796 T 154 . 35.19 0.140 35.20 ~0.014 35.19 —0.02 186.9 5.2596 T 163 33.71 0.140 33.82 —0.32 33.82 —0.31 176.8 5.020

7 T 8 129.66 0.38 129.58 0.06 129.50 0.13 211.2 2.0977 T 314 ‘91.46 0.10 91.414 0.02 91.40 0.06 246.6 7.701.7 7 38 85.45 0.10 85.47 —0.02 85.1411 0.01 2149.5 7.149147 T 140 82.84 0.10 82.85 —0.01 82.82 0.03 2118.6 7.313

7 T 42 80.51 0.10 80.414 0.09 80.141 0.13 2146.9 7.11197 7 145 77.23 0.10 77.16 0.09 77.13 0.13 2142.8 6.9387 T 46 76.18 0.10 76.114 0.05 76.11 0.09 241.1 6.87147 T 148 74.28 0.10 74.22 0.09 714.18 0.13 237.6 6.757

7 7 49 73.36 0.10 73.30 0.08 73.27 0.13 235.9 6.7047 T 66 60.54 0.38 60.91 —0.61 60.88 —0.57 232.6 6.14887 T 77 514.70 0.38 55.00 —0.54 514.98 —0.50 227.2 6.3007 T 81 53.014 0.38 53.16 ~0.211 53.15 —0.21 223.8 6.2197 T 82 52.76 0.38 52.73 0.06 52.71 0.09 223.1 6.2027 T 83 52.15 0.38 52.30 —0.29 52.28 —0.26 222.5 6.1887 T 102 45.31 0.38 145.38 ~0.114 145.37 —0.11 222.14 6.0987 7 106 144.26 0.38 414.16 0.22 ~414.i5 0.25 221.1 6.0517 7 109 43.12 0.38 113.29 ~0.111 143.28 —0.38 219.14 6.0057 7 130 38.33 0.38 38.22 0.29 38.21 0.32 207.7 5.7267 T 144 35.65 0.38 35.51 0.39 35.50 0.111 206.0 5.679

333

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC S SEC S SEC 5 S KM/S

7 7 151 311.43 0.38 34.30 0.37 314.30 0.39 204.1 5.61437 T 152 34.23 0.38 314.114 0.27 314.13 0.29 203.8 5.6377 7 165 32.18 0.38 32.15 0.12 32.14 0.13 197.4 5.14917 7 178 30.45 0.38 30.143 0.06 30.113 0.07 186.7 5.2287 T 187 29.37 0.38 29.40 —0.09 29.40 —0.08 177.3 5.0237 T 191 28.75 0.38 28.97 —0.79 28.97 —0.79 ‘ 173.0 14.940

8 7 9 113.82 0.38 113.88 —0.06 113.79 0.03 202.3 1.9678 T 114 109.65 0.38 110.02 —0.34 109.93 —0.26 2014.9 2.9578 7 75 53.33 0.38 53.59 —0.50 53.57 —0.46 227.6 6.3918 T 88 147.99 0.38 48.23 ~0.149 48.21 —0.46 ‘ 231.3 6.3938 7 92 146.70 0.38 46.79 —0.19 146.77 —0.15 231.6 6.3628 T 93 46.58 0.38 46.44 0.29 46.143 0.32 231.14 6.3488 T 94 ‘46.09 0.38 46.10 —0.02 146.09 0.01 230.9 6.3328 T 95 145.64 0.38 45.77 —0.29 45.75 —0.26 230.4 6.3148 T 116 39.88 0.38 39.92 —0.10 39.91 —0.06 217.14 5.9778 T 121 38.79 0.38 38.76 0.08 38.75 0.11 219.3 6.0038 7 123 38.15 0.38 38.32 —0.42 38.30 —0.39 220.1 6.0138 T 125 37.85 0.38 37.88 —0.06 37.87 —0.03 220.7 6.0198 T 173 30.10 0.38 30.014 0.21 30.03 0.22 199.2 5.5518 T 188~ 28.26 0.38 28.26 —0.02 28.26 —0.01 195.7 5.5858 T 193 27.70 0.38 27.72 —0.07 27.72 —0.06 193.14 5.5528 T 195 27.45 0.38 27.51 —0.22 27.51 —0.21 192.3 5.5308 7 202 26.84 0.38 26.80 0.13 26.80 O.i~4 187.4 5.14138 T 212 25.92 0.38 25.89 0.13 25.89 0.114 178.9 5.1638 T 216 25.143 0.38 25.55 —0.49 25.55 —0.49 175.3 5.052

9 T 10 101.29 0.37 101.63 —0.34 101.55 —0.26 213.3 2.0329 T 84 47.69 0.37 47.82 —0.28 47.80 —0.25 237.9 6.5799 7 99 142.76 0.37 142.91 —0.36 42.89 —0.31 223.6 6.1889 T 103 41.76 0.37 41.80 —0.11 41.79 —0.07 223.3 6.1719 T 1014 141.67 0.37 141.53 0.314 41.52 0.38 223.7 6.1759 T 105 41.24 0.37 41.27 —0.08 ~41.25 ~0.014 224.2 6.1829 T 106 ‘40.86 0.37 141.01 —0.36 40.99 —0.32 224.8 6.1919 T 130 35.59 0.37 35.58 0.04 35.57 0.07 219.9 6.0199 T 135 34.77 0.37 34.66 0.32 34.65 0.35 214.8 5.8919 T 136 314.51 0.37 314.148 0.08 34.47 0.12 2114.1 5.8709 T 138 34.08 0.37 314.14 —0.18 34.13 —0.15 212.9 5.8359 7 1140 33.814 0.37 33.80 0.12 33.79 0.15 212.1 5.8109 T 183 28.05 0.37 27.92 0.46 27.92 0.148 198.9 5.6619 7 185 27.76 0.37 27.70 0.20 27.70 0.22 198.3 5.6429 T 194 26.83 0.37 26.77 0.21 26.77 0.22 196.9 5.5669 T 211 25.19 0.37 25.19 —0.01 25.19 —0.00 195.6 5.4619 T 217 214.65 0.37 24.68 —0.15 214.68 —0.15 194.5 5.14239 7 220 214.33 0.37 214.414 —0.45 214.44 ~0.414 193.6 5.3999 7 229 23.68 0.37 23.714 —0.23 23.74 —0.23 189.4 5.2999 T 237 23.19 0.37 23.16 0.114 23.16 0.14 183.5 5.1679 T 241 22.81 0.37 22.89 —0.32 22.89 —0.32 180.1 5.089

10 T 11 91.24 0.36 91.07 0.19 91.00 0.26 228.9 2.04510 7 18 87.29 0.36 87.41 —0.114 87.35 —0.07 231.1 3.18210 7 109 38.80 0.36 38.90 —0.25 38.88 —0.22 236.8 6.145310 T 113 38.03 0.36 37.95 0.22 37.93 0.26 233.9 6.38610 T 115 37.70 0.36 37.49 0.55 37.48 0.58 231.6 6.33410 7 117 37.10 0.36 37.06 0.11 37.04 0.114 229.0 6.276

334

TABLE V (continued)

H 0 D E OBSERVATION ANISOTROPIC ISOTROPIC Q OBS Q CON GROUPPERIOD S.D. PERIOD DEV PERIOD DEV VALUE S.D. VEL.

SEC 5 SEC S SEC S 5 KM/S

10 T 118 36.78 0.36 36.814 —0.17 36.83 ~0.114 227.7 6.2141410 T 1314 314.01 0.36 33.82 0.57 33.80 0.60 220.3 6.00010 T 11414 32.16 0.36 32.17 —0.03 32.16 0. 221.9 6.05510 T 1149 31.52 0.36 31.140 0.36 31.140 0.39 219.0 6.03510 T 152 30.914 0.36 30.96 —0.09 30.96 —0.07 216.5 6.00710 T 15~4 30.75 0.36 30.68 0.22 30.67 0.214 214.7 5.98510 T 199 25.79 0.36 25.514 0.95 25.511 0.97 203.1 5.611410 T 202 25.142 0.36 25.27 0.57 25.27 0.59 201.8 5.571410 T 210 214.79 0.36 214.58 0.83 214.58 0.811 199.7 5.51110 T 213 214.52 0.36 214.33 0.76 214.33 0.77 199.3 5.50210 T 2111 24.314 0.36 2~4.25 0.37 211.25 0.38 199.2 5.50010 T 233 22.81 0.36 22.81 0.02 22.81 0.02 195.9 5.148010 T 245 21.85 0.36 21.99 —0.62 21.99 —0.63 191.7 5.39510 T 262 20.98 0.36 20.95 0.114 20.95 0.12 182.9 5.16710 7 265 20.75 0.36 20.78 ~0.114 20.78 —0.16 180.9 5.119

11 7 13 82.63 0.35 82.29 0.141 82.21 0.50 221.9 2.06711 T 20 79.27 0.35 79.37 —0.12 79.29 —0.03 219.9 3.035

12 T 114 75.81 0.35 75.74 0.09 75.67 0.19 216.1 2.02112 T 22 72.62 0.35 72.91 —0.39 72.814 —0.31 220.9 3.108

13 T 15 70.011 0.35 69.97 0.10 69.91 0.19 226.5 2.06213 7 24 67.02 0.35 67.19 —0.26 67.114 —0.18 229.1 3.170

114 7 16 65.10 0.314 614.98 0.19 614.92 0.28 222.2 1.983114 T 25 62.52 0.314 62.70 —0.29 62.65 —0.21 219.7 2.970

15 T 17 60.79 0.314 60.83 —0.06 60.78 0.03 216.5 1.96015 7 27 58.33 0.314 58.59 —O.~45 58.55 —0.37 222.8 3.0711

16 T 18 57.03 0.314 57.02 0.01 56.98 0.08 229.7 2.03516 T 29 514.67 0.314 514.77 —0.19 514.714 —0.12 2314.3 3.177

17 T 20 53.514 0.314 53.140 0.26 53.36 0.314 228.5 2.08117 7 31 51.145 0.34 51 .116 —0.02 51.41 0.06 223.9 3.0148

18 T 21 50.59 0.33 50.53 0.11 50.148 0.20 216.8 1.96118 T 33 148.58 0.33 48.69 —0.23 148.65 ~0.111 222.2 3.028

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

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

25.00 327.09 325.00 0.06 325.08 —0.09 9.135 3214.714 0.26 9.128 0.926.00 336.31 334.20 0.06 334.19 0.01 9.083 333.814 0.36 9.075 0.927.00 3145.43 3143.31 0.06 343.25 0.06 9.021 3142.88 0.143 9.011 0.928.00 354.38 352.26 0.06 352.23 0.03 8.947 351.85 0.41 8.936 0.929.00 363.32 361.18 0.06 361.114 0.014 8.8614 360.75 0.43 8.851 0.930.00 372.14 370.00 0.06 369.98 0.03 8.810 369.59 0.41 8.807 0.931.00 381.05 378.9O’O.O6 378.78 0.12 8.806 378.140 0.50 8.797 0.932.00 389.89 387.74 0.06 387.56 0.17 8.765 387.18 0.56 8.758 0.933.00 398.149 396.32 0.06 396.31 0.02 8.718 395.91 0.41 8.712 0.934.00 1407.28 405.11 0.06 405.01 0.10 8.668 4014.60 0.51 8.658 0.935.00 1115.90 413.72 0.06 413.64 0.08 8.614 ‘413.23 0.149 8.608 0.936.00 4214.148 1422.29 0.06 1422.23 0.07 8.556 1421.81 0.48 8.5149 0.937.00 1432.91 430.71 0.06 1430.75 —0.05 8.1496 1430.33 0.38 8.488 0.938.00 441.143 1439.22 0.06 439.22 0.00 8.1134 ‘438.79 0.43 8.428 1.039.00 449.79 14147.57 0.06 14147.62 —0.05 8.369 1447.18 0.39 8.360 1.0110.00 458.20 455.97 0.06 455.96 0.01 8.303 455.51 0.46 8.297 1.0141.00 1466.49 464.26 0.06 14614.23 0.02 8.235 1463.77 0.148 8.228 1.042.00 474.66 1472.142 0.06 1472.1414 —0.02 8.166 1171.97 0.45 8.159 1.0143.00 1482.77 1480.52 0.06 1480.57 —0.05 8.096 1180.09 0.143 8.090 1.0

44.00 490.85 488.59 0.06 488.64 —0.05 8.026 488.15 0.411 8.015 1.045.00 1498.814 496.57 0.06 1496.61 —0.04 7.955 1196.13 0.115 7.948 1.0146.O~ 506.60 5011.52 0.06 504.53 —0.01 7.883 5014.014 0.148 7.873 1.0147.00 514.53 512.25 0.06 512.38 —0.13 7.811 511.88 0.37 7.8011 1.0‘48.00 522.38 520.09 0.06 520.15 —0.06 7.738 519.64 0.145 7.728 .1.0149.00 530.111 527.83 0.06 527.85 —0.02 7.665 527.314 0.50 7.659 1.0

50.00 537.70 535.39 0.06 535.48 —0.09 7.592 5314.96 0.43 7.581 1.051.00 545.36 5113.014 0.06 543.014 0.00 7.519 5142.51 0.53 7.513 1.152.00 552.81 550.48 0.06 550.52 —O.O~4 7.4146 5119.98 05O 7.1436 1.153.00 560.22 557.88 0.06 557.93 ~0.014 7.372 557.38 0.50 7.366 1.154.00 567.59 565.25 0.06 565.26 —0.01 7.300 5614.71 0.514 7.292 1.155.00 574.88 572.52 0.06 572.52 0.00 7.226 571.97 0.55 7.219 1.156.00 582.06 579.70 0.06 579.71 —0.02 7.153 579.15 0.55 7.147 1.157.00 589.28 586.91 0.06 586.83 0.08 7.080 586.26 0.64 7.072 1.158.00 596.25 593.87 0.06 593.87 0.00 7.007 593.29 0.58 7.002 1.159.00 603.26 600.87 0.06 600.814 0.03 6.9314 600.26 0.61 6.925 1.160.00 610.20 607.80 0.06 607.73 0.07 6.861 607.15 0.65 6.855 1.161.00 616.99 6114.58 0.06 6114.56 0.02 6.788 613.97 0.61 6.782 1.1

(continued)

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

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

62.00 623.75 621.33 0.06 621.31 0.02 6.715 620.71 0.62 6.709 1.163.00 630.38 627.96 0.06 627.99 ~0.011 6.6143 627.39 0.57 6.638 1.1614.00 636.98 6314.55 0.06 6314.60 —0.05 6.570 633.99 0.56 6.562 1.165.00 6143.143 640.99 0.06 6141.13 ~O.1’4 6.1497 6140.52 0.147 6.1492 1.166.00 6149.96 6147.51 0.06 647.59 —0.08 6.425 646.97 0.514 6.1119 1.267.00 656.40 653.94 0.06 653.98 —0.03 6.352 653.35 0.59 6.346 1.268.00 662.81 660.35 0.06 660.29 0.06 6.279 659.66 0.69 6.2714 1.269.00 668.96 666.149 0.06 666.53 —0.05 6.206 665.90 0.59 6.199 1.270.00 675.11 672.63 0.06 672.71 —0.08 6.133 672.06 0.56 6.128 1.271.00 661.31 678.82 0.06 678.80 0.02 ‘ 6.061 678.15 0.67 6.056 1.272.00 687.30 684.81 0.06 6814.83 —0.02 5.987 6811.17 0.63 5.980 1.273.00 693.27 690.76 0.06 690.78 —0.02 5.9114 690.12 0.614 5.909 1.2714.00 699.15 696.63 0.06 696.65 —0.03 5.8141 6~5.99 0.614 5.836 1.2

75.00 7011.914 702.42 0.06 702.146 ~0.014 5.767 701.79 0.63 5.760 1.276.00 710.72 708.19 0.06 708.19 0.00 5.693 707.51 0.68 5.688 1.277.00 716.141 713.87 0.06 713.814 0.03 5.619 713.16 0.71 5.6114 1.278.00 721.95 719.140 0.06 719.142 —0.02 5.51414 718.714 0.66 5.539 1.279.00 727.1414 7214.88 0.06 7214.93 —0.04 5.469 7214.211 0.614 5.11614 1.280.00 732.90 730.33 0.06 730.36 —0.02 5.3914 729.67 0.66 5.389 1.281.00 738.33 735.75 0.06 735.71 0.04 5.316 735.02 0.714 5.313 1.282.00 7143.55 7140.97 0.06 7140.99 —0.02 5.2141 7140.30 0.67 5.236 1.283.00 7148.75 7146.16 0.06 7146.20 _O.O11 5.165 7115.149 0.67 5.160 1.284.00 753.93 751.33 0.06 751.32 0.01 5.088 750.61 0.72 5.083 1.285.00 758.87 756.26 0.06 756.37 —0.11 5.010 755.66 0.60 5.005 1.386.00 763.92 761.30 0.06 761.34 —0.04 4.931 760.62 0.68 4.926 1.387.00 768.89 766.26 0.06 766.23 0.03 4.852 765.51 0.75 14.8147 1.388.00 773.614 771.00 0.06 771 .011 —0.011 ‘4.772 770.32 0.69 4.767 1.389.00 778.36 775.72 0.06 775.77 —0.06 14.691 775.014 0.67 11.686 1.390.00 783.17 780.52 0.06 780.43 0.09 ~4.617 779.70 0.82 4.6111 1.391.00 787.79 785.13 0.06 785.05 0.08 4.597 7811.33 0.80 11.595 1.392.00 792.140 789.73 0.06 789.66 0.07 ‘4.606 788.914 0.78 14.601 1.393.00 797.02 7914.314 0.06 7914.25 0.09 14.606 793.53 0.80 14.591 1.3914.00 801.66 798.97 0.06 798.814 0.13 14.573 798.11 0.86 14.566 1.3

95.00 806.011 803.35 0.06 803.110 —0.05 4.51414 802.67 0.68 11.539 1.396.00 810.63 807.93 0.06 807.93 —0.00 14.513 807.19 0.73 14.509 1.397.00 815.26 812.55 0.06 812.143 0.12 4.1479 811.68 0.86 14.1477 1.398.00 819.67 816.95 0.06 816.89 0.06 14.14144 816.15 0.80 14.14142 1.3

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

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

27.00 343.98 3143.014 0.30 3113.25 —0.21 9.021 3142.88 0.15 9.011 0.9ag.oo 362.02 361.09 0.30 361.111 —0.05 8.8611 360.75 0.314 8.851 0.931.00 379.89 378.98 0.30 378.78 0.20 8.806 378.40 0.58 8.797 0.933.00 397.50 396.61 0.30 396.31 0.30 8.718 395.91 0.70 8.712 0.935.00 4111.814 ‘413.97 0.30 1413.64 0.32 8.6114 1413.23 0.73 8.608 0.937.00 431.90 431.04 0.30 430.75 0.29 8.1496 1430.33 0.71 8.1488 0.939.00 1448.70 14147.86 0.30 14147.62 0.214 8.369 14117.18 0.68 8.360 1.0141.00 1465.21 14614.39 0.30 464.23 0.15 8.235 1463.77 0.61 8.228 1.043.00 481.115 1480.614 0.30 ‘480.57 0.07 8.096 ‘480.09 0.55 8.090 1.0145.00 497.141 496.62 0.30 496.61 0.01 7.955 1496.13 0.50 7.948 1.047.00 513.09 512.32 0.30 512.38 —0.06 7.811 511.88 0.1411 7.804 1.0149.00 528.50 527.75 0.30 527.85 —0.10 7.665 527.314 0.111 7.659 1.051.00 5143.62 5142.88 0.30 5143.04 —0.15 7.519 5142.51 0.37 7.513 1.153.00 558.146 557.714 0.30 557.93 —0.19 7.372 557.38 0.36 7.366 1.155.00 573.02 572.32 0.30 572.52 —0.20 7.226 571.97 0.35 7.219 1.157.00 587.30 586.62 0.30 586.83 —0.21 7.080 586.26 0.36 7.072 1.159.00 601.30 600.63 0.30 600.814 —0.21 6.9314 600.26 0.37 6.925 1.161.00 615.00 614.35 0.30 6114.56 —0.21 6.788 613.97 0.38 6.782 1.163.00 628.143 627.80 0.30 627.99 —0.19 6.643 627.39 0.111 6.638 1.165.00 641.56 6140.95 0.30 6141.13 —0.18 6.1497 6140.52 0.143 6.492 1.167.00 6514.141 653.81 0.30 653.98 —0.16 6.352 653.35 0.116 6.3146 1.269.00 666.97 666.39~O.3O 666.53 ~0.114 6.206 665.90 0.149 6.199 1.271.00 679.23 678.67 0.30 678.80 —0.13 6.061 678.15 0.52 6.056 1.273.00 691.21 690.66 0.30 690.78 —0.11 5.9114 690.12 0.54 5.909 1.275.00 702.90 702.37 0.30 702.146 —0.09 5.767 701.79 0.58 5.760 1.277.00 7114.29 713.78 0.30 713.811 —0.06 5.619 713.16 0.62 5.6114 1.279.00 725.39 724.90 0.30 7211.93 —0.03 5.469 7214.214 0.65 5.1164 1.281.00 736.19 735.71 0.30 735.71 0.00 5.318 735.02 0.70 5.313 1.283.00 7146.70 7146.214 0.30 7146.20 0.014 5.165 7145.149 0.75 5.160 1.285.00 756.92 756.148 0.30 756.37 0.11 5.010 755.66 0.82 5.005 1.387.00 766.83 766.41 0.30 766.23 0.18 4.852 765.51 0.90 4.847 1.389.00 776.145 776.014 0.30 775.77 0.27 14.691 775.014 1.00 4.686 1.391.00 785.76 785.37 0.30 785.05 0.32 14.597 7814.33 1.014 14.595 1.393.00 7914.82 794.145 0.30 794.25 0.20 14.606 793.53 0.91 ‘4.591 1.3

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

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

25.00 3214.39 3214.98 0.10 325.08 —0.11 9.135 3214.711 0.23 9.128 0.926.00 333.63 3314.20 0.10 3314.19 0.01 9.083 333.8’! 0.37 9.075 0.927.00 3142.71 3143.27 0.10 343.25 0.02 9.021 342.88 0.38 9.011 0.928.00 351.68 352.23 0.10 352.23 —0.01 8.9147 351.85 0.37 8.936 0.929.00 360.60 361.111 0.10 361.111 —0.00 8.8614 360.75 0.38 8.851 0.930.00 369.51 370.03 0.10 369.98 0.05 8.810 369.59 0.144 8.807 0.931.00 378.38 378.88 0.10 378.78 0.10 8.806 378.110 0.148 8.797 0.932.00 387.19 387.68 0.10 387.56 0.12 8.765 387.18 0.50 8.758 0.933.00 395.96 396.144 0.10 396.31 0.13 8.718 395.9.1 0.53 8.712 0.934.00 14014.68 405.114 0.10 1405.01 0.111 8.668 14014.60 0.55 8.658 0.935.00 1413.314 1413.79 0.10 1413.614 0.15 8.6114 413.23 0.56 8.608 0.936.00 ‘421.95 1422.38 0.10 1422.23 0.15 8.556 1421.81 0.57 8.5149 0.937.00 1430.149 1430.91 0.10 1130.75 0.16 8.1496 1430.33 0.58 8.1488 0.938.00 1438.96 439.37 0.10 1439.22 0.15 8.11311 1138.79 0.58 8.1428 1.039.00 14147.37 1447.76 0.10 14147.62 0.13 8.369 4147.18 0.57 8.360 1.0140.00 1455.70 1456.08 0.10 1155.96 0.12 8.303 1455.51 0.57 8.297 1.0141.00 1463.97 11614.33 0.10 1464.23 0.10 8.235 1463.77 0.56 8.228 1.0112.00 1472.17 1472.52 0.10 1472.1414 0.09 8.166 ‘471.97 0.55 8.159 1.043.00 1480.31 1180.614 0.10 1180.57 0.07 8.096 1480.09 0.55 8.090 1.01411.00 1488.37 488.69 0.10 1488.64 0.05 8.026 488.15 0.514 8.015 1.0

‘45.00 1496.36 1496.67 0.1O~. 1196.61 0.05 7.955 496.13 0.514 7.9118 1.0‘46.00 5014.28 5014.57 0.10 5014.53 0.014 7.883 5011.04 0.53 7.873 1.0147.00 512.12 512.140 0.10 512.38 0.03 7.811 511.88 0.52 7.8014 1.0148.00 519.89 520.16 0.10 520.15 0.00 7.738 519.614 0.51 7.728 1.0149.00 527.58 527.83 0.10 527.85 —0.02 7.665 527.311 0.149 7.659 1.050.00 535.20 535.44 0.10 535.48 —O.O~4 7.592 5314.96 0.118 7.581 1.051.00 5142.711 5142.97 0.10 543.014 —0.07 7.519 542.51 0.116 7.513 1.152.00 550.22 550.112 0.10 550.52 —0.09 7.14116 5149.98 0.1414 7.1436 1.1

53.00 557.62 557.81 0.10 557.93 —0.12 7.372 557.38 0.143 7.366 1.1514.00 564.95 565.13 0.10 565.26 —0.13 7.300 564.71 0.112 7.292 1.155.00 572.21 572.38 0.10 572.52 —O.1~4 7.226 571.97 0.141 7.219 1.156.00 579.140 579.55 0.10 579.71 —0.16 7.153 579.15 0.140 7.1147 1.157.00 586.51 -586.65 0.10 586.83 —0.18 7.080 586.26 0.39 7.072 1.158.00 593.55 593.68 0.10 593.87 —0.19 7.007 593.29 0.38 7.002 1.159.00 600.52 600.63 0.10 600.811 —0.21 6.93’! 600.26 0.37 6.925 1.160.00 607.142 607.51 0.10 607.73 —0.22 6.861 607.15 0.36 6.855 1.161.00 614.214 6111.33 0.10 614.56 —0.214 6.788 613.97 0.35 6.782 1.1

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

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

62.00 621.01 621.08 0.10 621.31 —0.23 6.715 620.71 0.36 6.709 1.163.00 627.71 627.76 0.10 627.99 —0.23 6.6143 627.39 0.37 6.638 1.164.00 6314.35 6311.38 0.10 6314.60 —0.22 6.570 633.99 0.40 6.562 1.165.00 6140.91 6140.94 0.10 6141.13 —0.19 6.1497 640.52 0.142 6.1492 1.166.00 6147.141 6147.’42 0.10 6147.59 —0.17 6.1425 646.97 0.45 6.419 1.267.00 653.85 653.814 0.10 653.98 —0.13 6.352 653.35 0.49 6.3146 1.268.00 660.22 660.20 0.10 660.29 —0.10 6.279 659.66 0.53 6.274 1.269.00 666.51 666.148 0.10 666.53 —0.05 6.206 665.90 0.58 6.199 1.270.00 672.714 672.69 0.10 672.71 —0.01 6.133 672.06 0.63 6.128 1.271.00 678.88 678.82 0.10 678.80 0.02 6.061 678.15 0.67 6.056 1.272.00 6814.914 684.86 0.10 684.83 0.04 5.987 6814.17 0.69 5.980 1.273.00 690.91 690.82 0.10 690.78 0.04 5.9114 690.12 0.70 5.909 1.2714.00 696.81 696.70 0.10 696.65 0.05 5.841 695.99 0.71 5.836 1.275.00 702.63 702.51 0.10 702.146 0.05 5.767 701.79 0.73 5.760 1.276.00 708.38 708.25 0.10 708.19 0.07 5.693 707.51 0.7’4 5.688 1.277.00 71~4.07713.92 0.10 713.84 0.08 5.619 713.16 0.76 5.6114 1.278.00 719.67 719.51 0.10 719.142 0.09 5.51414 718.714 0.77 5.539 1.279.00 725.19 725.02 0.10 7214.93 0.09 5.469 7211.24 0.78 5.1464 1.280.00 730.63 730.45 0.10 730.36 0.09 5.3914 729.67 0.78 5.389 1.281.00 736.00 735.80 0.10 735.71 0.09 5.318 735.02 0.78 5.313 1.282.00 7141.29 741.07 0.10 7140.99 0.08 5.2141 7140.30 0.78 5.236 1.283.00 746.49 746.26 0.10 7146.20 0.07 5.165 745.149 0.77 5.160 1.2811.00 751.61 751.36 0.10 751.32 0.04 5.088 750.61 0.75 5.083 1.285.00 756.63 756.37 0.10 756.37 —0.00 5.010 755.66 0.71 5.005 1.386.00 761.56 761.29 0.10 761.34 —0.05 14.931 760.62 0.67 14.926 1.387.00 766.143 766.15 0.10 766.23 —0.08 4.852 765.51 0.64 14.847 1.388.00 771.25 770.95 0.10 771.014 —0.10 4.772 770.32 0.63 14.767 1.389.00 776.01 775.69 0.10 775.77 —0.08 4.691 775.04 0.65 14.686 1.390.00 780.72 780.39 0.10 780.143 —0.0~4 4.617 779.70 0.69 14.6114 1.391.00 785.40 785.06 0.10 785.05 0.01 14.597 784.33 0.73 11.595 1.392.00 790.06 789.70 0.10 789.66 0.05 4.606 788.914 0.76 4.601 1.393.00 7914.69 794.32 0.10 7914.25 0.07 14.606 793.53 0.78 14.591 1.3914.00 799.30 798.91 0.10 798.84 0.07 14.573 798.11 0.80 4.566 1.395.00 803.89 803.49 0.10 803.40 0.09 4.5414 802.67 0.82 4.539 1.396.00 808.47 808.05 0.10 807.93 0.13 14.513 807.19 0.86 4.509 1.397.00 813.04 812.61 0.10 812.43 0.18 14.1179 811.68 0.93 14.1477 1.398.00 817.60 817.16 0.10 816.89 0.27 14.14411 816.15 1.01 4.4112 1.3

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

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

23.00 263.30 263.57 0.30 262.87 0.70 8.888 262.68 0.89 8.883 0.625.00 279.90 280.13 0.30 280.61 ~O.148 9.021 280.35 —0.22 8.812 0.627.00 297.40 297.60 0.30 298.10 —0.50 8.741 297.91 —0.31 8.739 0.629.00 315.40 315.56 0.30 315.50 0.07 8.6148 315.29 0.27 8.6145 0.631.00 332.70 332.83 0.30 332.69 0.114 8.5143 332.48 0.35 8.539 0.733.00 3149.40 3119.149 0.30 3149.66 —0.17 8.1428 349.145 0.05 8.1127 0.735.00 366.40 366.116 0.30 366.140 0.06 8.307 366.17 0.29 8.305 0.737.00 382.90 382.92 0.30 382.89 0.03 8.181 382.66 0.26 8.175 0.739.00 399.10 399.09 0.30 399.13 —0.05 8.051 398.89 0.20 8.0147 0.741.00 1415.40 1115.35 0.30 1415.09 0.26 7.919 14114.85 0.50 7.915 0.843.00 1430.90 430.82 0.30 1430.79 0.03 7.7814 1430.514 0.28 7.781 0.8145.00 14146.30 14116.19 0.30 14146.22 —0.04 7.6148 Z145.97 0.22 7.6145 0.8147.00 461.70 1461.55 0.30 1461.38 0.17 7.511 ‘461.12 0.43 7.509 0.8149.00 476.140 476.22 0.30 1476.26 —0.05 7.3714 476.00 0.21 7.371 0.8

51.00 1491.00 490.78 0.30 1490.88 —0.10 7.236 1490.60 0.18 7.2311 0.853.00 505.30 505.05 0.30 505.21 —0.16 7.098 5014.93 0.11 7.095 0.955.00 519.30 519.01 0.30 519.27 —0.25 6.960 518.98 0.03 6.957 0.957.00 533.140 533.08 0.30 533.05 0.03 6.823 532.76 0.32 6.819 0.959.00 546.90 5116.514 0.30 5146.56 —0.02 6.684 546.26 0.28 6.680 0.961.00 560.20 559.81 0.30 559.79 0.02 6.5117 559.149 0.32 6.5143 0.963.00 573.30 572.87 0.30 572.74 0.13 6.409 572.113 0.144 6.1106 0.965.00 585.80 585.34 0.30 585.112 —0.08 6.270 585.11 0.23 6.268 0.967.00 598.140 597.90 0.30 597.82 0.08 6.131 597.51 0.110 6.129 0.969.00 610.40 609.87 0.30 609.911 —0.07 5.992 609.62 0.25 5.988 1.071.00 622.30 621.73 0.30 621.78 —0.05 5.852 621.46 0.27 5.8119 1.073.00 6314.20 633.60 0.30 633.35 0.25 5.711 633.02 0.58 5.709 1.075.00 645.30 644.66 0.30 6144.63 0.04 5.568 644.29 0.38 5.565 1.077.00 656.50 655.83 0.30 655.62 0.21 5.1425 655.28 0.55 5.423 1.079.00 667.10 666.140 0.30 666.33 0.07 5.280 665.98 0.111 5.278 1.081.00 677.60 676.86 0.30 676.73 0.13 5.133 676.39 0.147 5.130 1.083.00 687.50 686.73 0.30 686.85 —0.13 ‘4.984 686.50 0.23 14.982 1.085.00 697.50 696.69 0.30 696.67 0.02 14.832 696.31 0.38 14.830 1.087.00 707.10 706.26 0.30 706.18 0.08 14.678 705.82 0.44 14.676 1.189.00 716.20 715.32 0.30 715.145 —0.13 14.598 715.10 0.23 14.597 1.191.00 725.30 7214.39 0.30 7214.65 —0.26 14.603 7214.30 0.09 14.589 1.1

TABLE VIe

PKPtravel times, ARbranch: Gee and Dziewonski (unpublished). Baseline correction —4.22 s

DELTA OBSERVATION - ANISOTRÔPIC ISOTROPIC 7’7 OBS 7 CORE ERROR 7 COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

152.00 1209.51 1205.29 0.50 12011.90 0.39 4.151 12014.15 1.114 4.153 1.21514.00 1217.67 1213.145 0.50 1213.27 0.18 4.2111 1212.52 0.93 14.216 1.2156.00 1226.08 1221.860.50 1221.75 0.11 14.262 1221.00 0.86 4.263 1.2158.00 12311.60 1230.380.50 1230.31 0.07 4.301 1229.57 0.81 4.302 1.2160.00 12143.25 1239.030.50 1238.95 0.08 11.332 1238.21 0.83 14.333 1.2162.00 1251.52 12147.300.50 12147.63 —0.33 4.356 1246.90 0.111 14.357 1.21614.00 1260.04 1255.820.50 1256.37 —0.55 4.376 1255.63 0.19 4.376 1.2166.00 1269.17 12614.95 0.50 1265.1’! —0.18 14.391 12614.40 0.55 11.392 1.3168.00 1278.36 1274.111 0.50 1273.93 0.22 14.1402 1273.20 0.95 4.4014 1.3

341TABLE VI fPKP travel times, BC branch: Gee and Dziewonski (unpublished). Baseline correction —2.18 S

DELTA OBSERVATION ANISOTROPIC ISOTROPIC 7’7 OBS T CORE ERROR T COMP (0—C) P 7 COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

146.00 1182.67 1180.50 0.30 1180.51 —0.01 3.025 1179.72 0.78 3.017 1.0147.00 1185.28 1183.11 0.30 1183.143 —0.32 2.822 1182.63 0.148 2.815 1.048.00 1188.28 1186.11 0.30 1186.16 —0.06 2.660 1185.36 0.75 2.655 1.0149.00 1191.02 1188.85 0.30 1188.75 0.09 2.515 1187.914 0.91 2.510 1.050.00 1193.42 1191.25 0.30 1191.20 0.05 2.385 1190.39 0.86 2.382 1.051.00 1195.80 1193.63 0.30 1193.52 0.10 2.262 1192.70 0.92 2.257 1.052.00 1198.014 1195.87 0.30 1195.72 0.14 2.1147 11911.90 0.96 2.143 1.0TABLE VI g

PKIKP travel times: Gee and Dziewonski (unpublished). Baseline correction —2.18 s

DELTA OBSERVATION ANISOTEOPIC ISOTROPIC T’T OBS 7 CORE ERROR T COMP (0—C) P 7 COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

122.00 1136.94 11314.75 0.30 11314.78 —0.03 1.934 1133.97 0.79 1.933 1.01214.00 11110.76 1138.57 0.30 1138.63 —0.06 1.929 1137.82 0.75 1.929 1.0126.00 11411.69 11142.50 0.30 1142.148 0.03 1.9211 11111.66 0.811 1.923 1.0128.00 1148.68 11116.149 0.30 1146.31 0.18 1.917 1145.50 0.99 1.917 1.0130.00 1152.59 1150.40 0.30 1150.14 0.26 1.910 1149.33 1.07 1.910 1.0132.00 1156.111 11511.22 0.30 1153.95 0.27 1.901 1153.14 1.08 1.900 1.01314.00 1160.22 1158.03 0.30 1157.711 0.29 1.888 1156.93 1.10 1.888 1.1136.00 1163.94 1161.75 0.30 1161.51 0.25 1.873 1160.69 1.06 1.872 1.1138.00 1167.70 1165.51 0.30 1165.23 0.28 1.852 11614.142 1.10 1.852 1.1152.00 1191.18 1188.99 0.30 1189.23 —0.24 1.506 1188.40 0.59 1.505 1.21514.00 11914.30 1192.11 0.30 1192.17 —0.06 1.~121 1191.33 0.78 1.421 1.3156.00 1196.90 11914.71 0.30 11914.93 —0.22 1.329 11914.08 0.63 1.329 1.3158.00 1199.68 1197.149 0.30 1197.149 0.00 1.232 1196.614 0.85 1.231 1.3160.00 1202.02 1199.83 0.30 1199.85 —0.01 1.130 1199.00 0.83 1.129 1.3162.00 1204.08 1201.89 0.30 1202.02 —0.13 1.022 1201.15 0.714 1.023 1.14164.00 1205.78 1203.59 0.30 1203.98 —0.38 0.912 1203.09 0.50 0.913 1.4166.00 1207.51 1205.32 0.30 1205.69 —0.37 0.801 12011.81 0.51 0.803 1.14168.00 1209.34 1207.15 0.30 1207.20 —0.0~4 0.688 1206.30 0.85 0.690 1.11170.00 1210.82 1208.63 0.30 1208.51 0.12 0.568 1207.57 1.06 0.577 1.4172.00 1211.64 1209.145 0.30 1209.59 ~0.114 0.4147 1208.61 0.814 0.1162 1.14

TABLE VI hPKIKP travel times: Engdahl et al. (1974). Baseline correction —2.59 SDELTA OBSERVATION ANISOTROPIC ISOTROPIC 7’

7 OBS T CORE ERROR 7 COMP (0—C) P 7 COMP (0—C) PDEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/PEG SEC

1.00 995.80 993.21 0.30 992.87 0.314 0.022 992.03 1.18 0.022 0.910.00 996.90 9914.31 0.30 993.98 0.33 0.221! 993.111 1.17 0.2211 0.920.00 1000.10 997.51 0.30 997.33 0.18 0.445 996.49 1.02 0.14145 0.930.00 1005.70 1003.11 0.30 1002.85 0.26 0.659 1002.02 1.09 0.660 0.9140.00 1013.20 1010.61 0.30 1010.49 0.12 0.865 1009.65 0.96 0.865 0.950.00 1022.80 1020.21 0.30 1020.12 0.09 1.060 1019.29 0.92 1.060 0.960.00 1034.20 1031.61 0.30 1031.63 —0.02 1.240 1030.80 0.81 1.241 0.970.00 10147.110 10144.81 0.30 10414.88 —0.06 1.1405 1014’4.O5 0.76 1.406 0.980.00 1062.20 1059.61 0.30 1059.69 —0.07 1.554 1058.86 0.75 1.554 0.990.00 1078.20 1075.61 0.30 1075.89 —0.28 1.6814 1075.06 0.55 1.684 0.9

100.00 1095.50 1092.91 0.30 1093.29 —0.38 1.795 1092.148 0.1414 1.795 1.0110.00 1113.80 1111.21 0.30 1111.72 —0.50 1.886 1110.90 0.31 1.887 1.0

342

TABLE ViiDifferential travel times, PcP—P: Engdahi and Johnson (1974)

DELTA OBSERVATION ANISOTROPIC ISOTROPIC 7’

7 OBS 7 CORE ERROR T COMP (0—C) P 7 COMP (0—C) PDEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

32.00 169.00 169.00 0.20 169.73 —0.73 —6.052 169.31 —0.31 _6.0144 0.135.00 151.50 151.50 0.20 152.08 —0.58 —5.711 151.69 —0.19 —5.704 0.138.00 135.20 135.20 0.20 135.48 —0.28 —5.354 135.11 0.09 —5.346 0.0‘41.00 119.20 119.20 0.20 119.95 —0.75 —‘4.992 119.62 —O.~l2 —4.983 0.0114.00 105.10 105.10 0.20 105.50 —0.40 —‘4.632 105.21 —0.11 ~14.620 0.0‘47.00 92.00 92.00 0.20 92.16 —0.16 —4.279 91.87 0.13 ~11.271 0.050.00 79.140 79.140 0.20 79.84 —0.1111 —3.935 79.58 —0.18 —3.923 0.053.00 68.140 68.140 0.20 68.53 —0.13 —3.603 68.31 0.09 —3.595 0.056.00 58.10 58.10 0.20 58.22 —0.12 —3.281 58.01 0.09 —3.2711 0.059.00 48.80 48.80 0.20 148.84 ~0.011 —2.971 48.66 0.114 —2.961 —0.062.00 40.20 110.20 0.20 140.38 —0.18 —2.671 40.22 —0.02 ~2.6614—0.065.00 32.70 32.70 0.20 32.81 —0.11 —2.382 32.66 0.011 —2.376 —0.075.00 13.140 13.140 0.20 13.58 —0.18 ~1.1175 13.51 —0.11 —1.468 —0.0TABLE VIj

Differential travel times, PKiKP—PcP: Engdahl et al. (1974)

DELTA OBSERVATION ANISOTROPIC ISOTROPIC T’7 OBS T CORE ERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

10.90 1477.50 1477.50 0.40 ‘477.311 0.16 —0.784 1177.314 0.16 —0.785 0.011.73 1477.20 1477.20 0.110 ‘476.67 0.53 ~0.8142 1476.67 0.53 —0.8~$3—0.021.34 14611.90 1464.90 0.110 1465.514 —0.64 ~1.1457 1465.53 —0.63 ~1.1459—0.026.614 1457.40 1457.110 0.140 1457.02 0.38 —1.752 1457.01 0.39 —1.753 —0.027.71 1454.80 454.80 0.140 1455.12 —0.32 —1.807 455.10 —0.30 —1.808 —0.029.69 451.15 451.15 0.40 451.144 —0.29 —1.9011 451.112 —0.27 —1.906 —0.030.50 450.140 450.110 0.110 1449.89 0.51 —1.943 14119.86 0.54 —1.944 —0.030.60 449.50 4149.50 0.40 449.69 —0.19 —1.947 14119.67 —0.17 —1.949 —0.031.08 4148.20 448.20 0.140 4118.75 —0.55 —1.969 14148.73 —0.53 —1.971 —0.035.914 438.35 438.35 0.140 438.67 —0.32 —2.177 1438.63 —0.28 —2.178 —0.136.04 438.75 438.75 0.40 1438.145 0.30 —2.181 1438.141 0.314 —2.182 —0.138.17 433.50 1133.50 0.40 1133.72 —0.22 —2.261 1433.68 —0.18 —2.263 —0.147.18 1411.85 1411.85 0.40 412.014 —0.19 -‘—2.533 1411.99 —0.14 ~2.5314 —0.1

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

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

32.00 701.116 700.614 0.75 701.81 —1.17 15.14814 702.02 —1.38 15.11714 11.0

33.00 717.27 716.148 0.75 717.27 —0.78 15.1429 717.146 —0.97 15.417 4.0314.00 732.96 732.21 0.75 732.67 —0.46 15.369 732.85 —0.614 15.360 4.135.00 7148.52 7147.80 0.75 7148.00 —0.20 15.305 748.19 —0.39 15.296 4.136.00 763.914 763.25 0.75 763.28 —0.03 15.236 763.1114 —0.19 15.225 14.237.00 779.20 778.55 0.75 778.117 0.07 15.163 778.63 —0.08 15.1149 14.238.00 7911.34 793.72 0.75 793.60 0.12 15.086 793.75 —0.03 15.076 14.239.00 809.38 808.79 0.75 808.65 0.114 15.005 808.78 0.01 14.995 14.3110.00 824.33 823.77 0.75 823.60 0.17 111.922 823.73 0.04 14.907 4.341.00 839.18 838.66 0.75 838.49 0.17 14.835 838.60 0.06 14.825 4.4142.00 853.94 853.45 0.75 853.29 0.16 14.746 853.38 0.07 114.7314 4.443.00 868.60 868.114 0.75 867.99 0.16 114.6514 868.06 0.08 111.6110 14~141114.00 883.16 882.74 0.75 882.60 0.114 114.560 882.66 0.07 114.5149 4.5145.00 897.63 897.211 0.75 897.12 0.12 14.4614 897.17 0.07 114.1450 4.5

46.00 912.00 911.614 0.75 911.52 0.13 114.366 911.56 0.09 114.355 14.547.00 926.26 925.93 0.75 925.83 0.11 114,266 925.86 0.07 114.253 11.6148.00 9140.43 9140.114 0.75 9140.014 0.10 114.165 940.07 0.07 111.151 11.6149.00 954.149 9514.23 0.75 954.15 0.08 14.061 9514.16 0.07 14.050 11.6

50.00 968.146 968.23 0.75 968.16 0.07 13.957 968.17 0.07 13.940 14.7

51.00 982.31 982.12 0.75 982.07 0.014 13.851 982.05 0.07 13.8140 14.752.00 996.07 995.91 0.75 995.86 0.05 13.71414 995.811 0.07 13.729 14.853.00 1009.72 1009.59 0.75 1009.55 0.04 13.637 1009.52 0.08 13.626 11.8514.00 1023.26 1023.17 0.75 1023.114 0.03 13.528 1023.08 0.08 13.513 ‘4.855.00 1036.70 1036.614 0.75 1036.61 0.03 13.419 1036.55 0.09 13.1108 14.9

56.00 1050.03 1050.00 0.75 1O’49.98 0.02 13.308 1049.90 0.10 13.293 14.957.00 1063.25 1063.25 0.75 1063.22 0.03 13.197 1063.15 0.11 13.186 4.958.00 1076.36 1076.140 0.75 1076.37 0.03 13.085 1076.27 0.13 13.070 5.059.00 1089.37 1089.1411 0.75 1089.140 0.011 12.973 1089.28 0.16 12.962 5.060.00 1102.26 1102.36 0.75 1102.31 0.05 12.860 1102.19 0.17 12.81111 5.061.00 1115.014 1115.18 0.75 1115.11 0.07 12.747 11114.98 0.20 12.736 5.162.00 1127.70 1127.87 0.75 1127.80 0.07 12.632 1127.66 0.21 12.619 5.163.00 11140.26 11140.146 0.75 11140.37 0.09 12.518 1140.23 0.24 12.507 5.1614.00 1152.70 1152.93 0.75 1152.814 0.10 12.1103 1152.67 0.26 12.392 5.265.00 1165.02 1165.29 0.75 1165.18 0.11 12.287 1165.01 0.28 12.276 5.266.00 1177.23 1177.53 0.75 1177.141 0.12 12.172 1177.22 0.31 12.161 5.2

(continued)

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

67.00 1189.32 1189.65 0.75 1189.52 0.13 12.055 1189.33 0.32 12.042 5.368.00 1201.30 1201.67 0.75 1201.52 0.15 11.939 1201.31 0.36 11.929 5.369.00 1213.15 1213.55 0.75 1213.110 0.15 11.821 1213.18 0.37 11.809 5.370.00 1224.89 1225.32 0.75 1225.15 0.17 11.704 12214.93 0.39 11.693 5.471.00 1236.50 1236.96 0.75 1236.80 0.16 11.586 1236.56 0.41 11.576 5.14

72.00 12148.00 12148.50 0.75 12148.33 0.17 11.467 1248.08 0.142 11.1155 5.1473.00 1259.37 1259.90 0.75 1259.73 0.17 11.349 1259.48 0.42 11.339 5.4714.00 1270.62 1271.18 0.75 1271.02 0.16 11.229 1270.75 0.143 11.219 5.575.00 1281.75 1282.35 0.75 1282.19 0.16 11.109 1281.91 0.43 11.099 5.576.00 1292.75 1293.38 0.75 1293.24 0.114 10.989 1292.96 0.142 10.980 5.577.00 1303.63 13014.29 0.75 13011.17 0.13 10.868 1303.87 0.112 10.856 5.678.00 1314.38 1315.08 0.75 13111.97 0.11 10.747 13114.66 0.141 10.737 5.679.00 1325.01 1325.74 0.75 1325.66 0.08 10.625 1325.34 0.40 10.616 5.680.00 1335.50 1336.26 0.75 1336.22 0.014 10.502 1335.89 0.37 10.491 5.781.00 13115.87 1346.66 0.75 1346.66 0.00 10.379 13146.32 0.314 10.369 5.782.00 1356.11 1356.914 2.25 1356.98 —0.011 10.255 1356.63 0.30 10.2146 5.783.00 1366.22 1367.08 2.25 1367.17 —0.09 10.131 1366.81 0.27 10.120 5.7814.00 1376.19 1377.08 2.25 1377.214 —0.16 10.005 1376.88 0.21 9.995 5.885.00 1386.014 1386.97 2.25 1387.18 —0421 9.879 1386.81 0.16 9.870 5.886.00 1395.75 1396.71 2.25 1396.99 —0.28 9.753 1396.62 0.09 9.7143 5.887.00 11405.33 11406.32 2.25 1406.68 —0.36 9.625 11406.30 0.03 9.615 5.888.00 14111.77 1415.79 2.25 11416.211 _0.145 9.1496 11115.814 —0.05 9.1487 5.989.00 114214.08 1425.114 2.25 1425.67 —0.53 9.367 11425.27 —0.13 9.358 5.990.00 11433.25 14314.314 2.25 14314.98 —0.63 9.236 14314.56 —0.22 9.227 5.991.00 14142.28 14143.40 2.25 1111414.15 —0.75 9.105 114143.72 —0.32 9.096 5.992.00 11451.18 11452.314 2.25 11153.18 —0.84 8.973 11452.75 —0.112 8.9611 6.093.00 1459.911 11461.13 2.25 11462.09 —0.96 8.840 11461.65 —0.52 8.831 6.094.00 1468.56 11469.78 2.25 11170.86 —1.08 8.708 11170.41 —0.63 8.700 6.095.00 11177.04 1478.29 2.25 1479.55 —1.26 8.713 11479.12—0.83 8.666 6.196.00 11185.1414 11486.73 2.25 11488.22 —1.50 8.7914 11487.83 —1.10 8.681 6.197.00 11493.85 11495.17 2.25 11496.90 —1.73 8.766 11196.50 —1.33 8.653 6.198.00 1502.26 1503.61 2.25 1505.57 —1.96 8.631 1505.13 —1.52 8.6114 6.199.00 1510.67 1512.06 2.25 1514.17 —2.11 8.577 1513.72 —1.66 8.568 6.2

100.00 1519.07 1520.49 2.25 1522.72 —2.23 8.5214 1522.26 —1.77 8.518 6.2

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

DEG SEC SEC SEC SEC SEC SEC/PEG SEC SEC SEC/DEG SEC

32.00 701.46 701.77 0.75 702.914 —1.17 15.1474 702.02 —0.26 15.1174 11.0

33.00 717.27 717.60 0.75. 718.39 —0.79 15.418 717.146 0.111 15.1417 14.0314.00 732.96 733.31 0.75 733.78 ~0.117 15.358 732.85 0.146 15.360 11.135.00 7148.52 7148.89 0.75 7119.10 —0.22 15.292 7148.19 0.70 15.296 14.136.00 763.914 7611.32 0.75 764.35 —0.03 15.223 763.1114 0.88 15.225 14.237.00 779.20 779.60 0.75 779.514 0.06 15.1149 778.63 0.98 15.1149 14.238.00 7914.34 7911.76 0.75 7914.66 0.11 15.072 793.75 1.02 15.076 14.239.00 809.38 809.82 0.75 809.69 0.13 114.991 808.78 1.04 14.995 14.3140.00 824.33 824.79 0.75 824.614 0.15 114.907 823.73 1.06 14.907 14.3141.00 839.18 839.66 0.75 839.50 0.16 114.820 838.60 1.06 111.825 14.11142.00 853.914 8511.1111 0.75 854.29 0.15 114.730 853.38 1.06 114.7314 14.4143.00 868.60 869.12 0.75 868.98 0.114 114.638 868.06 1.05 114.6140 14~4144.00 883.16 883.69 0.75 883.57 0.12 114.5414 882.66 1.03 114.5119 14.5145.00 897.63 898.18 0.75 898.06 0.12 111.14148 897.17 1.02 114.1450 11.5146.00 912.00 912.57 0.75 912.144 0.13 114.350 911.56 1.02 114.355 14.5147.00 926.26 926.85 0.75 926.711 0.11 14.250 925.86 0.99 111.253 11.648.00 9140.143 941.014 0.75 9140.911 0.10 114.1149 9140.07 0.97 114.151 11.6149.00 9514.149 955.12 0.75 955.014 0.08 114.0145 9514.16 0.96 114.050 14.6

50.00 968.146 969.11 0.75 969.03 0.07 13.941 968.17 0.911 13.9110 11.751.00 982.31 982.98 0.75 982.92 0.05 13.836 982.05 0.93 13.8140 14.752.00 996.07 996.76 0.75 996.70 0.05 13.729 995.811 0.91 13.729 ‘4.853.00 1009.72 1010.142 0.75 1010.38 0.014 13.621 1009.52 0.91 13.626 14.8514.00 1023.26 1023.98 0.75 1023.94 0.014 13.512 1023.08 0.90 13.513 14.8

55.00 1036.70 1037.1114 0.75 1037.140 0.014 13.1403 1036.55 0.89 13.1408 14.956.00 1050.03 1050.79 0.75 1050.76 0.03 13.293 10119.90 0.89 13.293 11.9

57.00 1063.25 10614.03 0.75 1063.98 0.04 13.182 1063.15 0.88 13.186 11.958.00 1076.36 1077.16 0.75 1077.12 0.011 13.070 1076.27 0.89 13.070 5.059.00 1089.37 1090.19 0.75 1090.13 0.06 12.958 1089.28 0.90 12.962 5.060.00 1102.26 1103.10 0.75 1103.03 0.07 12.8145 1102.19 0.91 12.81414 5.061.00 1115.04 1115.89 0.75 1115.82 0.08 12.732 11114.98 0.91 12.736 5.162.00 1127.70 1128.57 0.75 1128.148 0.09 12.619 1127.66 0.92 12.619 5.163.00 11140.26 1141.15 0.75 11141.04 0.11 12.5014 11140.23 0.93 12.507 5.1614.00 1152.70 1153.61 0.75 1153.50 0.11 12.389 1152.67 0.914 12.392 5.265.00 1165.02 1165.95 0.75 1165.82 0.13 12.273 1165.01 0.914 12.276 5.266.00 1177.23 1178.18 0.75 1178.04 0.111 12.158 1177.22 0.95 12.161 5.2

(continued)

Appendix. Differential kernelsfor perturbationof ~= (‘ri dr(8A.A+6C~(~+8F~freigenfrequenciesof normal modesin afransversely ~,2 J

0isotropicmediuni +6L.L+6N.1~’+8p.E) (Al)

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

67.00 1189.32 1190.29 0.75 1190.15 0.14 12.042 1189.33 0.96 12.0112 5.368.00 1201.30 1202.29 0.75 1202.12 0.16 11.925 1201.31 0.98 11.929 5.369.00 1213.15 1214.15 0.75 1213.99 0.16 11.808 1213.18 0.97 11.809 5.370.00 12214.89 1225.91 0.75 1225.714 0.18 11.691 1224.93 0.98 11.693 5.1471.00 1236.50 1237.514 0.75 1237.37 0.18 11.573 1236.56 0.98 11.576 5.1472.00 12148.00 1249.06 0.75 12148.88 0.18 11.14511 1248.08 0.99 11.455 5.473.00 1259.37 1260.145 0.75 1260.27 0.18 11.336 1259.148 0.97 11.339 5.11

7’4.0O 1270.62 1271.72 0.75 1271.55 0.17 11.217 1270.75 0.96 11.219 5.575.00 1281.75 1282.87 0.75 1282.71 0.16 11.097 1281.91 0.95 11.099 5.576.00 1292.75 1293.89 0.75 1293.75 0.114 10.977 1292.96 0.93 10.980 5.577.00 1303.63 13014.780.75 1304.66 0.12 10.856 1303.87 0.91 10.856 5.678.00 1314.38 1315.55 0.75 1315.145 0.10 10.735 13114.66 0.89 10.737 5.679.00 1325.01 1326.20 0.75 1326.12 0.08 10.613 1325.314 0.86 10.616 5.680.00 1335.50 1336.71 0.75 1336.68 0.03 10.491 1335.89 0.82 10.1491 5.781.00 13145.87 13147.10 0.75 1347J.1 —0.01 10.367 13146.32 0.78 10.369 5.782.00 1356.11 1357.36 2.25 1357.111 —0.05 10.21414 1356.63 0.73 10.2146 5.783.00 1366.22 1367.149 2.25 1367.59 —0.10 10.120 1366.81 0.68 10.120 5.7814.00 1376.19 1377.118 2.25 1377.65 —0.18 9.994 1376.88 0.60 9.995 5.885.00 1386.014 1387.35 2.25 1387.58 —0.23 9.868 1386.81 0.514 9.870 5.886.oo 1395.75 1397.07 2.25 1397.38 —0.31 9.742 1396.62 0.115 9.7143 5.887.00 1405.33 1406.67 2.25 1407.06 —0.39 9.614 11406.30 0.38 9.615 5.888.00 111114.77 1416.13 2.25 11416.61 ~0.118 9.1186 11415.814 0.29 9.487 5.989.00 11424.08 11425.146 2.25 11426.03 —0.57 9.357 11425.27 0.19 9.358 5.990.00 11433.25 14314.65 2.25 11435.32 —0.67 9.227 114314.56 0.09 9.227 5.991.00 111112.28 114143.70 2.25 114114.148 —0.78 9.095 11443.72 —0.02 9.096 5.992.00 11151.18 11452.62 2.25 11453.51 —0.89 8.963 11452.75 —0.13 8.9614 6.093.00 11159.914 11461.140 2.25 1462.110 —1.01 8.830 11461.65 —0.25 8.831 6.0914.00 11468.56 11470.03 2.25 1471.17 —1.1~l 8.702 11470.41 —0.38 8.700 6.095.00 11177.014 11478.53 2.25 1479.86 —1.32 8.719 11479.12 —0.59 8.666 6.196.00 1485.1114 11486.952.25 11488.52 —1.57 8.798 11487.83 —0.88 8.681 6.197.00 11493.85 11495.38 2.25 11197.20 —1.82 8.755 1496.50 —1.12 8.653 6:198.00 1502.26 1503.81 2.25 1505.87 —2.06 8.626 1505.13 —1.32 8.614 6.199.00 1510.67 1512.24 2.25 1514.46 —2.23 8.573 1513.72 ~1.148 8.568 6.2

100.00 1519.07 1520.66 2.25 1523.01 —2.36 8.520 1522.26 —1.61 8.518 6.2

but their expressionsare inconvenientto apply in J~= r 2( (1 + 2)(1 + 1)1(1— I) V2 — [2U— 1(1+ 1) V]2our formulationof the parameterssoughtin inver- . . . . .

wherethe dot signifiesdifferentiationwith respectto the radius and the eigenfunctionsare normal-The expressionsfor the differential kernels in d

terms of the eigenfunctionsfor spheroidalmodes izeare fl

~ii~Jp~U2+ 1(1+ 1)V2jr2dr 1c=02 °

A = r2[2U— 1(1+ l)v]2 For toroidal modes

F2r’U[2U—l(l+ 1)V] (A2) L(W— W/r)2

L1(i+ i)[J~+(u—V)/r]2 !1=(l+2)(!— 1)(W/r)2 (A3)

347

TABLE VImS travel times (SH): Hales and Roberts, (1970). Baseline correction — 1.14 s; slope —0.0068 s deg —

DELTA OBSERVATION ANISOTROPIC ISOTROPIC T*7 OBS T CORRERROR T COMP (0—c) p T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

30.00 671.97 670.62 0.75 670.714 —0.12 15.580 670.98 —0.35 15.567 3.931.00 687.09 685.73 0.75 686.30 —0.57 15.5314 686.52 —0.78 15.5214 14.0

32.00 702.82 701.46 0.75 701.81 —0.35 15.11814 702.02 —0.57 15.474 4.033.00 717.59 716.22 0.75 717.27 —1.05 15.1129 717.116 —1.24 15.417 4.034.00 733.143 732.05 0.75 732.67 —0.61 15.369 732.85 —0.79 15.360 4.135.00 7148.55 7147.17 0.75 7148.00 ~0.811 15.305 7148.19 —1.02 15.296 4.136.00 7611.22 762.83 0.75 763.28 —0.45 15.236 763.1414 —0.61 15.225 14.237.00 779.20 777.80 0.75 778.47 —0.67 15.163 778.63 —0.82 15.149 4.238.00 794.32 792.92 0.75 793.60 —0.68 15.086 793.75 —0.83 15.076 14.239.00 809.83 808.42 0.75 808.65 —0.23 15.005 808.78 —0.36 114.995 11.3

40.00 824.97 823.55 0.75 823.60 —0.05 14.922 823.73 —0.18 114.90, 4.3141.00 8110.99 839.57 0.75 838.49 1.08 14.835 838.60 0.97 114.825 14•4

42.00 856.40 8511.97 0.75 853.29 1.68 14.7116 853.38 1.59 114.7311 4.4143.00 870.23 868.79 0.75 867.99 0.81 114.6514 868.06 0.73 14.6140 4.4411.00 885.01 883.57 0.75 882.60 0.97 114.560 882.66 0.90 14.549 4.5145.00 899.50 898.05 0.75 897.12 0.93 114.4614 897.17 0.88 111.450 4.5‘46.00 914.02 912.56 0.75 911.52 1.05 114.366 911.56 1.01 114.355 4.5147.00 927.50 926.04 0.75 925.83 0.21 114.266 925.86 0.17 114.253 4.648.00 9141.12 939.65 0.75 9110.014 —0.39 114.165 940.07 —0.42 114.151 4.6149.00 955.142 953.911 0.75 9514.15 —0.21 114.061 9514.16 —0.22 114.050 4.6

50.00 969.79 968.31 0.75 968.16 0.14 13.957 968.17 0.14 13.940 4.751.00 983.74 982.25 0.75 982.07 0.18 13.851 982.05 0.20 13.840 4.752.00 997.143 995.93 0.75 995.86 0.07 13.744 995.814 0.09 13.729 4.853.00 1011.142 1009.92 0.75 1009.55 0.36 13.637 1009.52 0.140 13.626 4.8514.00 1025.07 1023.56 0.75 1023.14 0.42 13.528 1023.08 0.47 13.513 4.855.00 1038.33 1036.81 0.75 1036.61 0.20 13.419 1036.55 0.26 13.408 4.956.00 1051.86 1050.33 0.75 10149.98 0.35 13.308 1049.90 0.414 13.293 4.957.00 1065.26 1063.73 0.75 1063.22 0.51 13.197 1063.15 0.58 13.186 4.958.00 1077.80 1076.26 0.75 1076.37 —0.11 13.085 1076.27 —0.01 13.070 5.059.00 1091.24 1089.69 0.75 1089.110 0.30 12.973 1089.28 0.41 12.962 5.060.00 11O~4.061102.51 0.75 1102.31 0.20 12.860 1102.19 0.32 12.8414 5.061.00 1116.50 1114.914 0.75 1115.11 —0.17 12.747 1114.98 —0.04 12.736 5.162.00 1129.56 1127.99 0.75 1127.80 0.19 12.632 1127.66 0.34 12.619 5.163.00 1142.141 1140.814 0.75 11110.37 0.47 12.518 11140.23 0.61 12.507 5.1614.00 11514.10 1152.52 0.75 1152.84 —0.32 12.1403 1152.67 —0.15 12.392 5.2

(continued)

with the nonnalization non-dimensionalparameter~

w2fIpW2r2 dr = I VPH = (A/p)”2

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

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

65.00 1166.76 1165.17 0.75 1165.18 —0.00 12.287 1165.01 0.17 12.276 5.266.00 1178.97 1177.38 0.75 1177.141 —0.03 12.172 1177.22 0.15 12.161 5.267.00 1190.65 1189.05 0.75 1189.52 ~0.147 12.055 1189.33 —0.28 12.042 5.368.00 1202.58 1200.97 0.75 1201.52 —0.55 11.939 1201.31 —0.34 11.929 5.369.00 1214.71 1213.10 0.75 1213.140 —0.30 11.821 1213.18 —0.08 11.809 5.370.00 1226.21 12214.59 0.75 1225.15 —0.57 11.704 1224.93 —0.34 11.693 5.1471.00 1237.29 1235.66 0.75 1236.80 —1.14 11.586 1236.56 —0.90 11.576 5.14

72.00 1249.15 12147.52 0.75 1248.33 —0.81 11.1467 1248.08 —0.56 11.1455 5.473.00 1260.88 1259.24 0.75 1259.73 —0.49 11.3119 1259.48 ~0.21% 11.339 5.14

714.00 1272.31 1270.66 0.75 1271.02 —O.36.~.11.229 1270.75 —0.09 11.219 5.575.00 1284.18 1282.53 0.75 1282.19 0.34 11.109 1281.91 0.61. 11.099 5.576.00 1295.42 1293.76 0.75 1293.211 0.52 10.989 1292.96 0.80 10.980 5.577.00 1305.57 1303.90 0.75 13014.17 —0.26 10.868 1303.87 0.03 10.856 5.678.00 1316.50 1314.83 0.75 1314.97 —0.14 10.747 13114.66 0.16 10.737 5.679.00 1326.97 1325.29 0.75 1325.66 —0.37 10.625 1325.34 —0.05 10.616 5.680.00 1337.93 1336.211 0.75 1336.22 0.02 10.502 1335.89 0.35 10.1491 5.781.00 13119.50 13117.80 0.75 1346.66 1.114 10.379 13146.32 1.148 10.369 5.782.00 1358.61 1356.91 0.75 1356.98 —0.07 10.255 1356.63 0.28 10.246 5.783.00 1367.94 1366.23 2.25 1367.17 ~0.914 10.131 1366.81 -.0.58 10.120 5.7814.00 1379.114 1377.1422.25 1377.24 0.19 10.005 1376.88 0.55 9.995 5.885.00 1392.14 1390.42 2.25 1387.18 3.24 9.879 1386.81 3.61 9.870 5.886.00 1400.31 1398.58 2.25 1396.99 1.59 9.753 1396.62 1.96 9.743 5.887.00 11407.314 1405.60 2.25 1406.68 —1.08 9.625 1406.30 —0.69 9.615 5.888.00 1419.57 1417.83 2.25 11416.24 1.58 9.1496 11415.814 1.99 9.487 5.989.00 11428.414 11426.692.25 11425.67 1.02 9.367 11125.27 1.142 9.358 5.990.00 11436.02 14314.26 2.25 111314.98 —0.71 9.236 114314.56 —0.30 9.227 5.991.00 114116.15 111144.39 2.25 141414.15 0.24 9.105 14113.72 0.66 9.096 5.992.00 11455.30 1453.53 2.25 1453.18 0.35 8.973 1452.75 0.78 8.9614 6.093.00 1463.20 1461.1122.25 1462.09 —0.67 8.8140 1461.65 —0.23 8.831 6.0914.00 11473.47 11471.69 2.25 1470.86 0.82 8.708 11170.41 1.27 8.700 6.095.00 1482.35 1480.56 2.25 11179.55 1.01 8.713 11179.12 1.1411 8.666 6.196.00 1489.66 1487.86 2.25 11488.22 —0.36 8.7914 1487.83 0.03 8.681 6.197.00 1496.69 114911.89 2.25 11496.90 —2.01 8.766 11496.50 —1.61 8.653 6.198.00 1505.38 1503.57 2.25 1505.57 —2.00 8.631 1505.13 —1.56 8.6114 6.1

We seekan expressionfor a relative perturba- ~H = —T2PVPH(A+ ~P) (A6)

tion in a period of a normalmodein the form

6T ~ / , - - Svr2pVsv(L2~P)dr~&pR+&VPVPv+&VPHPH

+&Vsv~Sv+8VSH..~H +&~.E) (AS) SH = —r2pV~~NAfter simplealgebraictransformations,the ap- E = — ~r2PP(VP2H— 2P~)

propriateexpressionsare - - -

— — I 2F - 2 - I - \ 2 For toroidalmodes,A, C, andF areset to zero,— ~r jR + Vpv~C+~A+7JF)VpH of course.

+ (L — 2nP)V~~ + &V~~] In calculationof the kernelsfor and QK we- - usethe conceptof an equivalentisotropicmedium

= r2pVpvC (WoodhouseandDahlen, 1978) with the bulk and

349

TABLEYInS travel times (SV): Hales and Roberts (1970). Baseline correction 0.44 s; slope —0.021 s deg —‘

DELTA OBSERVATION ANISOTROPIC ISOTROPIC7 OBS T CORE ERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

30.00 671.97 671.78 0.75 671.90 —0.12 15.571 670.98 0.80 15.567 3.931.00 687.09 686.88 0.75 687.145 —0.57 15.525 ~86.52 0.36 15.5211 14.032.00 702.82 702.59 0.75 702.914 —0.35 15.4714 702.02 0.56 15.14714 ~1.033.00 717.59 717.314 0.75 718.39 —1.06 15.418 717.46 —0.12 15.1417 14.034.00 733.43 733.16 0.75 733.78 —0.62 15.358 732.85 0.31 15.360 11.135.00 7118.55 748.25 0.75 7149.10 —0.85 15.292 748.19 0.07 15.296 14.136.00 764.22 763.90 0.75 7611.35 ~0.145 15.223 763.144 0.146 15.225 4.237.00 779.20 778.86 0.75 779.54 —0.68 15.1119 778.63 0.214 15.1119 14.238.00 7914.32 793.96 0.75 7911.66 —0.69 15.072 793.75 0.21 15.076 4.239.00 809.83 809.145 0.75 809.69 —0.24 14.991 808.78 0.67 111.995 4.3140.00 824.97 824.57 0.75 824.64 —0.07 114.907 823.73 0.84 114.907 4.3111.00 840.99 840.57 0.75 839_,5O 1.07 111.820 838.60 1.97 14.825 4~14

112.00 856.40 855.96 0.75 854.29 1.67 114.730 853.38 2.58 14.734 11.4143.00 870.23 869.77 0.75 868.98 0.79 14.638 868.06 1.70 114.6140 4.14414.00 885.01 884.53 0.75 883.57 0.95 14.5414 882.66 1.86 14.549 4.5

45.00 899.50 898.99 0.75 898.06 0.93 14.1148 897.17 1.83 14.1450 4.546.00 9114.02 913.149 0.75 912.114 1.05 114.350 911.56 1.914 14.355 14.5

‘47.00 927.50 926.95 0.75 926.74 0.21 14.250 925.86 1.09 14.253 ‘4.648.00 941.12 940.55 0.75 9110.914 —0.39 114.1149 940.07 0.149 14.151 4.649.00 955.42 9514.83 0.75 955.04 —0.21 14.045 954.16 0.67 14.050 14.6

50.00 969.79 969.18 0.75 969.03 0.15 13.941 968.17 1.01 13.940 4.751.00 983.74 983.11 0.75 982.92 0.19 13.836 982.05 1.06 13.840 4.752.00 997.143 996.78 0.75 996.70 0.07 13.729 995.814 0.911 13.729 11.8

53.00 1011.42 1010.75 0.75 1010.38 0.36 13.621 1009.52 1.23 13.626 11.854.00 1025.07 1024.38 0.75 1023.914 0.43 13.512 1023.08 1.29 13.513 14.855.00 1038.33 1037.61 0.75 1037.140 0.21 13.403 1036.55 1.06 13.408 4.956.00 1051.86 1051.12 0.75 1050.76 0.37 13.293 1049.90 1.22 13.293 4.957.00 1065.26 10611.50 0.75 1063.98 0.52 13.182 1063.15 1.36 13.186 14.958.00 1077.80 1077.02 0.75 1077.12 —0.10 13.070 1076.27 0.76 13.070 5.059.00 1091.214 1090.44 0.75 1090.13 0.31 12.958 1089.28 1.16 12.962 5.060.00 11011.06 1103.24 0.75 1103.03 0.21 12.845 1102.19 1.05 12.8144 5.061.00 1116.50 1115.66 0.75 1115.82 —0.16 12.732 1114.98 0.68 12.736 5.162.00 1129.56 1128.70 0.75 1128.48 0.21 12.619 1127.66 1.04 12.619 5.163.00 11142.41 1141.53 0.75 1141.04 0.48 12.504 11110.23 1.30 12.507 5.1614.00 1154.10 1153.20 0.75 1153.50 —0.30 12.389 1152.67 0.52 12.392 5.2

(continued)

shearmoduli definedas where

K=(I/9)(4A+C+4F—4N) i=A+ë+P~~=(1/I5)(A+c—2F+5N+6L) and

Attenuation of a normal mode is evaluated ~ = + i~— (AS)from an integral For theisotropic (or “equivalent”)structurethe

kernelsfor perturbationsin thedensityandveloci-Q =1 r2dr(!t)l~Q,~ +K.kQ~’) (A7) ties are

350

TABLE VI n (continued)

DELTA OBSERVATION ANISOTROPIC ISOTROPIC TaT OBS T COER ERROR T COMP~(O—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

65.00 1166.76 1165.83 0.75 1165.82 0.01 12.273 1165.01 0.83 12.276 5.266.00 1178.97 1178.02 0.75 1178.014 —0.02 12.158 1177.22 0.80 12.161 5.267.00 1190.65 1189.68 0.75 1190.15 _0.146 12.0112 1189.33 0.35 12.042 5.368.00 1202.58 1201.59 0.75 1202.12 —0.53 11.925 1201.31 0.28 11.929 5.369.00 12114.71 1213.70 0.75 1213.99 —0.29 11.808 1213.18 0.52 11.809 5.370.00 1226.21 1225.18 0.75 1225.714 —0.56 11.691 12214.93 0.25 11.693 5.471.00 1237.29 1236.214 0.75 1237.37 —1.13 11.573 1236.56 —0.32 11.576 5.14

72.00 1249.15 1248.08 0.75 12118.88 —0.80 11.1454 124&.O8 0.00 11.1455 5.1473.00 1260.88 1259.79 0.75 1260.27 ~0.149 11.336 1259.148 0.31 11.339 5.1474.00 1272.31 1271.20 0.75 1271.55 —0.35 11.217 1270.75 0.1114 11.219 5.575.00 1284.18 1283.04 0.75 1282.71 0.33 11.097 1281.91 1.13 11.099 5.576.00 1295.42 12914.26 0.75 1293.75 0.52 10.977 1292.96 1.31 10.980 5.577.00 1305.57 1304.39 0.75 13014.66 —0.27 10.856 1303.87 0.52 10.856 5.678.00 1316.50 1315.30 0.75 1315.45 —0.15 10.735 13111.66 0.64 10.737 5.679.00 1326.97 1325.75 0.75 1326.12 —0.37 10.613 1325.311 0.111 10.616 5.680.00 1337.93 1336.69 0.75 1336.68 0.01 10.491 1335.89 0.80 10.1191 5.781.00 13149.50 1348.2110.75 13147.11 1.13 10.367 13116.32 1.92 10.369 5.782.00 1358.61 1357.33 0.75 1357.41 —0.08 10.2414 1356.63 0.70 10.246 5.783.00 1367.94 1366.614 2.25 1367.59 —0.95 10.120 1366.81 —0.18 10.120 5.784.00 1379.114 1377.82 2.25 1377.65 0.16 9.9914 1376.88 0.914 9.995 5.885.00 1392.111 1390.79 2.25 1387.58 3.22 9.868 1386.81 3.99 9.870 5.886.00 1400.31 1398.914 2.25 1397.38 1.56 9.742 1396.62 2.32 9.7143 5.887.00 1407.314 1405.95 2.25 11407.06 —1.11 9.6111 11106.30 ~0.314 9.615 5.888.00 11119.57 11418.16 2..25 11416.61 1.55 9.1186 11415.811 2.32 9.1487 5.989.00 1428.144 11427.01 2.25 11426.03 0.98 9.357 11425.27 1.714 9.358 5.990.00 11136.02 11434.57 2.25 1435.32 —0.75 9.227 114314.56 0.01 9.227 5.991.00 114146.15 1444.68 2.25 1141111.118 0.20 9.095 114113.72 0.96 9.096 5.992.00 11155.30 11453.81 2.25 11153.51 0.30 8.963 1452.75 1.06 8.9614 6.093.00 11163.20 1461.69 2.25 11462.110 —0.72 8.830 1461.65 0.011 8.831 6.094.00 11173.147 1471.94 2.25 11471.17 0.77 8.702 11470.41 1.52 8.700 6.095.00 1482.35 1480.79 2.25 11479.86 0.94 8.719 11479.12 1.67 8.666 6.196.00 11489.66 1488.08 2.25 1488.52 —0.~I3 8.798 1487.83 0.26 8.681 6.197.00 1496.69 1495.09 2.25 1497.20 —2.10 8.755 1496.50 ~1.1I1 8.653 6.198.00 1505.38 1503.76 2.25 1505.87 —2.11 8.626 1505.13 —1.37 8.6114 6.1

= — ~r2[E + (~siQ+ K~A~)/p] covered.The errorwas in a term associatedwith

— — 2 - the gravitational potential in the fluid core and,— r pV~K (A9) therefore, it only affects results for the gravest

S —r2pv~(Jt~t—4~) modes.For example,for OS,,andall following0S,

modes the results in TableV are correct to all

decimalplaceslisted.Also, noneof the theoreticalNoteaddedin ~ calculationsof periodsof normalmodeshavebeen

correctedfor the secondorder effects. For exam-An error in codefor evaluationof groupveloc- pie, the appropriatecorrectionof theperiod of 0S0

ity of spheroidalmodes has recently been dis- brings it muchcloserto the observedvalue.

TABLEVI oDeep focus (550 km) S travel times (SH): Sengupta (1975). Baseline correction 2.28 s; slope —0.0433 s deg I

DELTA OBSERVATION ANISOTROPIC ISOTROPICT OBS T CORR ERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

31.00 596.02 596.96 3.00 599.61 —2.65 15.241 599.71 —2.75 15.236 2.933.00 628.98 629.83 0.60 629.95 —0.11 15.099 630.03 —0.20 15.095 3.035.00 659.95 660.72 0.60 660.00 0.72 14.9114 660.07 0.614 14.937 3.137.00 689.81 690.149 0.60 689.73 0.76 14.779 689.78 0.71 114.7714 3.239.00 719.34 719.93 0.60 719.12 0.82 114.604 719.14 0.79 114.599 3.341.00 748.38 748.89 0.60 748.15 0.74 14.1121 7148.17 0.72 114.412 3.3143.00 776.32 776.74 0.60 776.79 —0.05 14.232 776.81 —0.07 114.225 3.4145.00 804.11 804.44 0.60 805.05 —0.61 14.037 805.07 —0.63 114.032 3.547.00 833.60 833.85 0.60 832.92 0.92 13.838 832.93 0.92 13.833 3.649.00 861.37 861.53 0.60 860.40 1.13 13.634 860.39 1.111 13.629 3.751.00 886.17 886.211 0.60 887.46 —1.22 13.426 887.43 —1.19 13.422 3.753.00 912.18 912.17 0.60 914.10 —1.93 13.216 9114.07 —1.90 13.211 3.855.00 939.75 939.65 0.60 940.32 —0.67 13.003 9110.27 —0.62 12.998 3.957.00 9614.84 964.65 0.60 966.10 —1.45 12.787 966.05 —1.40 12.783 4.059.00 991.84 991.57 0.60 991.146 0.10 12.570 991.110 0.17 12.565 4.061.00 1017.14 1016.78 0.60 1016.38 0.40 12.350 1016.30 0.148 12.346 14.1

63.00 1040.714 1040.29 0.60 1040.86 —0.56 12.129 10140.77 _O.118 12.1211 ~4.265.00 1064.96 1064.143 0.60 1064.89 —0.47 11.906 1064.80 —0.37 11.901 ~4.267.00 1088.39 1087.77 0.60 1088.118 —0.71 11.681 1088.37 —0.60 11.675 4.369.00 1113.09 1112.38 0.60 1111.62 0.77 11.454 1111.50 0.88 11.447 14.4

71.00 1136.64 1135.85 0.60 1134.30 1.55 11.227 11311.17 1.67 11.221 4•14

73.00 1157.00 1156.12 0.60 1156.52 _0.110 10.997 1156.38 —0.26 10.992 4.575.00 1179.51 1178.54 0.60 1178.28 0.27 10.7614 1178.13 0.142 10.759 4.677.00 1200.23 1199.18 0.60 1199.57 —0.39 10.529 1199.41 —0.24 10.5211 4.679.00 1221.03 1219.89 0.60 1220.38 —0.49 10.293 1220.23 —0.34 10.288 14.7

81.00 1241.47 12140.214 0.60 12140.73 —0.49 10.053 1240.56 —0.32 10.049 4.883.00 1261.23 1259.92 0.60 1260.60 —0.68 9.811 1260.111 —0.50 9.806 4.885.00 1281.21 1279.81 0.60 1279.97 —0.16 9.567 1279.78 0.03 9.561 4.987.00 1301.62 1300.13 3.00 1298.85 1.28 9.317 1298.66 1.48 9.313 4.989.00 1318.88 1317.31 3.00 1317.24 0.07 9.066 1317.03 0.28 9.060 5.091.00 1337.81 1336.15 0.60 1335.11 1.04 8.810 1334.90 1.25 8.805 5.093.00 1355.44 1353.69 0.60 1352.514 1.15 8.725 1352.35 1.34 8.670 5.195.00 1373.80 1371.97 3.00 1369.89 2.07 8.730 1369.72 2.25 8.648 5.1

352

TABLEVI pDeep focus (550 km) S travel times (SV): Sengupta (1975). Baseline correction 3.OOs; slope —0.0495 s deg —

DELTA OBSERVATION ANISOTROPIC ISOTROPIC TaT OBS T CORE ERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

31.00 596.02 597.148 3.00 . 600.15 —2.66 15.235 599.71 —2.22 15.236 2.933.00 628.98 630.35 0.60 630.148 —0.13 15.092 630.03 0.31 15.095 3.035.00 659.95 661.22 0.60 660.52 0.70 114.937 660.07 1.114 14.937 3.137.00 689.81 690.98 0.60 690.22 0.75 114.771 689.78 1.20 14.774 3.239.00 719.34 720.41 0.60 719.60 0.81 114.596 719.114 1.26 14.599 3.3‘41.00 748.38 749.35 0.60 748.62 0.73 111.414 748.17 1.18 14.1412 3.343.00 776.32 777.19 0.60 777.25 —0.06 14.225 776.81 0.38 14.225 3.4145.00 8014.11 804.88 0.60 805.50 ~0.62 14.030 ~O5.07 —0.19 14.032 3.5147.00 833.60 834.27 0.60 833.35 0.92 13.830 832.93 1.314 13.833 3.649.00 861.37 861.914 0.60 860.80 1.14 13.626 860.39 1.55 13.629 3.751.00 886.17 886.611 0.60 887.86 —1.21 13.419 887.43 —0.79 13.422 3.753.00 912.18 912.56 0.60 9114.149 —1.93 13.209 9114.07 —1.51 13.211 3.855.00 939.75 940.03 0.60 940.68 —0.66 12.996 9140.27 ~0.214 12.998 3.957.00 9614.814 965.02 0.60 966.46 —1.45 12.780 966.05 ~1.014 12.783 11.059.00 991.84 991.92 0.60 991.80 0.12 12.563 991.40 0.52 12.565 4.061.00 1017.14 1017.12 0.60 1016.71 0.41 12.344 1016.30 0.82 12.3146 4.163.00 10140.74 1040.62 0.60 10111.18 -0.56 12.122 1040.77 —0.15 12.1211 4.265.00 10614.96 10614.74 0.60 1065.19 ~0.145 11.900 1064.80 —0.06 11.901 4.267.00 1088.39 1088.07 0.60 1088.76 —0.69 11.675 1088.37 —0.30 11.675 11.3

69.00 1113.09 1112.67 0.60 1111.89 0.78 11.448 1111.50 1.17 11.447 4.471.00 1136.611 1136.12 0.60 11314.56 1.56 11.221 1134.17 1.95 11.221 4.473.00 1157.00 1156.38 0.60 1156.76 —0.38 10.991 1156.38 0.00 10.992 4.575.00 1179.51 1178.80 0.60 1178.52 0.27 10.758 1178.13 0.67 10.759 4.677.00 1200.23 1199.42 0.60 1199.79 —0.38 10.5214 1199.141 0.00 10.5214 14.6

79.00 1221.03 1220.12 0.60 1220.61 —0.49 10.288 1220.23 —0.11 10.288 14.781.00 12141.47 1240.46 0.60 12110.911 —0.48 10.048 1240.56 —0.11 10.0149 4.883.00 1261.23 1260.12 0.60 1260.80 —0.68 9.806 1260.141 —0.30 9.806 4.885.00 1281.21 1280.00 0.60 1280.16 —0.16 9.561 1279.78 0.22 9.561 4.987.00 1301.62 1300.31 3.00 1299.03 1.28 9.312 1298.66 1.66 9.313 .14,989.00 1318.88 1317.147 3.00 1317.40 0.08 9.061 1317.03 0.114 9.060 5.091.00 1337.81 1336.30 0.60 1335.27 1.04 8.805 1334.90 1.41 8.805 5.093.00 1355.44 1353.83 0.60 1352.77 1.06 8.727 1352.35 1.118 8.670 5.195.00 1373.80 1372.09 3.00 1370.06 2.03 8.722 1369.72 2.38 8.648 5.1

TABLE VIqDeep focus (550 km) ScS travel times (SH): Sengupta (1975). Baseline correction —0.57s

DELTA OBSERVATION ANISOTEOPIC ISOTROPIC TaT OBS T CORE ERROR T COMP (0—C)• P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

32.50 909.93 909.36 1.00 908.142 0.914 5.227 908.13 1.23 5.229 3.637.50 936.92 936.35 1.00 936.01 0.34 5.796 935.73 0.63 5.798 3.7142.50 966.147 965.90 1.00 966.27 —0.36 6.2914 965.99 —0.09 6.296 3.8147.50 998.014 997.147 1.00 998.814 —1.36 6.723 998.57 —1.10 6.725 3.9

52.50 1032.81 1032.214 1.00 1033.39 —1.15 7.088 1033.13 —0.89 7.089 4.057.50 1068.02 1067.145 1.00 1069.62 —2.17 7.3914 1069.37 —1.92 7.395 4.262.50 1109.314 1108.77 1.00 1107.214 1.53 7.6147 1107.00 1.78 7.648 4.367.50 1146.76 11146.19 1.00 1146.01 0.18 7.852 1145.77 0.42 7.853 14•4

72.50 1187.62 1187.05 1.00. 1185.69 1.36 8.015 1185.46 1.59 8.016 14•577.50 1227.35 1226.78 1.00 1226.09 0.69 8.140 1225.86 0.92 8.141 11.7

353

TABLE VI rDeep focus (550 km) ScS travel times (SV): Sengupta (1975). Baseline correction —0.47 s

DELTA OBSERVATION ANISOTROPIC ISOTROPICT OBS T CORE ERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

32.50 909.93 909.146 1.00 908.48 0.99 5.230 908.13 1.33 5.229 3.637.50 936.92 936.45 1.00 936.08 0.38 5.799 935.73 0.73 5.798 3.7142.50 966.47 966.00 1.00 966.35 —0.35 6.296 965.99 0.01 6.296 3.8147.50 998.04 997.57 1.00 998.92 —1.35 6.725 998.57 —1.00 6.725 3.9

52.50 1032.81 1032.34 1.00 1033.149 —1.15 7.090 1033.13 —0.79 7.089 14.0

57.50 1068.02 1067.55 1.00 1069.72 —2.17 7.396 1069.37 —1.82 7.395 11.2

62.50 1109.34 1108.87 1.00 1107.36 1.51 7.648 1107.00 1.88 7.648 4.367.50 1146.76 11146.29 1.00 1146.13 0.16 7.853 1145.77 0.52 7.853 4•14

72.50 1187.62 1187.15 1.00 1185.82 1.33 8.016 1185.46 1.69 8.016 14.5

77.50 1227.35 1226.88 1.00 1226.23 0.65 8.1111 1225.86 1.02 8.1141 4.7TABLE VI s

SKS travel times (SV): Hales and RObCZIS (1970). Baseline correction —3.13 s

DELTA OBSERVATION ANISOTROPIC ISOTROPICT OBS T CORE ERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC ‘SEC/DEG SEC SEC SEC/DEG SEC

84.00 1377.11 1373.98 2.00 1374.70 —0.72 6.510 1373.99 —0.01 6.509 11.885.00 1385.70 1382.57 2.00 1381.16 1.41 6.409 1380.45 2.12 6.410 4.886.00 1392.06 1388.932.00 1387.52 1.141 6.308 1386.81 2.12 6.311 4.887.00 1397.90 1394.77 2.00 1393.78 0.99 6.207 1393.07 1.70 6.206 4.788.00 1404.10 1400.97 2.00 1399.94 1.04 6.107 1399.23 1.74 6.107 4.789.00 11408.63 1405.50 2.00 1405.99 —0.49 6.007 1405.29 0.22 6.010 4.790.00 14114.03 11410.90 2.00 1411.95 —1.011 5.910 1411.24 —0.34 5.909 4.791.00 1419.44 11(16.31 2.00 1417.81 —1.50 5.812 1417.11 —0.80 5.810 4.692.00 1425~961422.83 2.00 11(23.57 ~0.711 5.716 1422.87 —0.04 5.718 4.693.00 1432.41 11429.28 2.00 1429.211 0.04 5.622 1428.54 0.74 5.623 4.694.00 1438.41 11435.28 2.00 1~34.820.47 5.528 114314.11 1.17 5.525 11.695.00 14142.97 1439.84 2.00 1~41l0.30—0.46 5.437 11439.60 0.24 5.1438 14.6

96.00 1449.20 14116.07 2.00 11145.69 0.39 5.3116 11444.99 1.08 5.3149 4.697.00 11454.34 1451.21 2.00 1450.99 0.22 5.257 1450.29 0.92 5.254 4.598.00 1459.55 1456.1(2 2.00 11456.20 0.22 5.169 1455.50 0.92 5.170 14.5

99.00 14614.11 11460.98 2.00 1461.33 _0.314 5.083 11460.63 0.35 5.085 4.5100.00 11469.99 11466.86 2.00 11466.36 0.50 11.998 1465.67 1.19 4.997 4.5101.00 1475.02 1471.89 2.00 1471.32 0.57 14.913 1470.63 1.26 14.913 4.5102.00 11480.18 11477.05 2.00 11176.19 0.86 14.830 1475.50 1.55 11.832 4.5103.00 1485.55 11482.142 2.00 11180.98 1.145 14.7119 1480.29 2.13 4.749 4.51014.00 1491.73 11488.60 2.00 1485.69 2.92 14.667 1485.00 3.60 4.666 4.5105.00 1495.28 1492.15 2.00 1490.31 1.84 4.588 1489.63 2.53 11.589 4.5106.00 11498.73 1495.60 2.00 14914.86 0.74 11.509 11494.17 1.143 4.510 ‘4.4107.00 1502.30 1499.17 2.00 11199.33 —0.16 4.430 11198.64 0.53 14.428 4.11108.00 1506.62 1503.149 2.00 1503.72 —0.23 14.353 1503.03 0.146 4.354 4.4109.00 1511.82 1508.69 2.00 1508.014 0.66 4.277 1507.35 1.34 4.278 4.4110.00 1517.59 15114.116 2.00 1512.28 2.18 4.201 1511.59 2.88 4.199 4.4111.00 1519.03 1515.90 2.00 1516.414 —0.54 14.127 1515.75 0.15 ‘4.127 4.4112.00 1521.40 1518.27 2.00 1520.52 —2.25 4.053 1519.8’l —1.57 4.054 4.4113.00 1527.40 15211.27 2.00 1524.514 —0.27 3.979 1523.86 0.142 3.976 4.4114.00 1532.11 1528.98 2.00 1528.48 0.50 3.906 1527.80 1.18 3.906 4.4115.00 1536.32 1533.19 2.00 1532.35 0.814 3.83Z1 1531.67 1.52 3.835 4.4

(continued)

354

TABLE VI s (continued)

116.00 1538.58 1535.145 2.00 1536.15 —0.70 3.763 1535.47 —0.02 3.762 14~4

117.00 15140.86 1537.73 2.00 1539.88 —2.15 3.691 1539.20 ~1.116 3.691 14~14118.00 15145.67 15142.54 2.00 15143.53 —0.99 3.621 1542.85 —0.31 3.622 4.14

119.00 15149.66 15146.53 2.00 15147.12 —0.58 3.552 15146.1414 0.10 3.551 4.4120.00 1551.99 15148.86 2.00 1550.614 —1.77 3.1181 1549.95 —1.09 3.480 4.3121.00 1555.93 1552.80 2.00 15514.08 —1.28 3.413 1553.140—0.60 3.1413 4.3122.00 1560.67 1557.514 2.00 1557.45 0.09 3.31114 1556.78 0.76 3.3144 14.3123.00 1563.67 1560.511 2.00 1560.77 —0.23 3.276 1560.09 0.146 3.274 14.3124.00 1566.87 1563.74 2.00 1564.01 —0.27 3.208 1563.33 0.111 3.208 4.3125.00 1568.57 1565.414 2.00 1567.18 ~1.714 3.1141 1566.50 —1.06 3.1141 4.3126.00 1572.53 1569.140 2.00 1570.29 —0.89 3.073 1569.61 —0.21 3.072 4.3

TABLE VI

Deep focus (600 km) differential travel times ScS(SH)—S(SH): Jordan and Anderson (1974). No baseline correction

DELTA OBSERVATION ANISOTEOPIC ISOTROPIC TaT OBS T COREERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

35.00 259.40 259.40 0.71 258.57 0.83 —9.352 258.22 1.18 ~9.3143 0.640.00 215.70 215.70 0.66 214.22 1.48 —8.386 213.91 1.79 —8.377 0.5145.00 1714.30 174.30 0.52 1714.67 —0.37 —7.449 174.39 —0.09 ~7.1439 0.14

50.00 138.60 138.60 0.69 139.70 —1.10 ~6.5149 139.145 —0.85 ~6.5140 0.355.00 108.50 108.50 0.58 109.11 —0.61 —5.690 108.91 —0.111 —5.684 0.260.00 82.00 82.00 0.52 82.73 —0.73 ~4.8711 82.55 —0.55 —4.866 0.265.00 59.70 59.70 0.144 60.32 —0.62 ~11.095 60.17 —0.47 —4.088 0.170.00 140.60 40.60 0.146 41.72 —1.12 —3.351 141.60 —1.00 —3.345 0.175.00 25:50 25.50 0.60 26.76 —1.26 —2.635 26.68 —1.18 —2.629 0.080.00 14.00 14.00 0.37 15.314 —1.34 —1.940 15.28 —1.28 —1.933 0.0

TABLE VI uDeep focus (600 km) differential travel times ScS(SH)—S(SH): Jordan and Anderson (1974). Baseline correction 0.68 s

DELTA OBSERVATION ANISOTROPIC ISOTROPICT OBS T CORR ERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

35.00 259.140 260.08 0.71 258.57 1.51 —9.352 258.22 1.86 —9.343 0.6140.00 215.70 216.38 0.66 214.22 2.16 —8.386 213.91 2.46 —8.377 0.5

45.00 174.30 1714.98 0.52 174.67 0.31 ~7.14149 174.39 0.59 —7.1139 0.450.00 138.60 139.28 0.69 139.70 —0.42 —6.549 139.145 —0.17 —6.540 0.355.00 108.50 109.18 0.58 109.11 0.06 —5.690 108.91 0.27 —5.684 0.260.00 82.00 82.68 0.52 82.73 —0.05 _1l.8711 82.55 0.13 —4.866 0.265.00 59.70 60.38 0.414 60.32 0.06 ~14.095 60.17 0.20 —4.088 0.170.00 40.60 41.28 0.46 111.72 —0.414 —3.351 141.60 —0.33 —3.3115 0.175.00 25.50 26.18 0.60 26.76 —0.58 —2.635 26.68 —0.50 —2.629 0.080.00 14.00 111.68 0.37 15.314 —0.66 ~1.9110 15.28 —0.60 —1.933 0.0

355

TABLEVI vDeep focus (600 km) differential travel times ScS(SV)—S(SV): Jordan and Anderson (1974). No baseline correction

DELTA OBSERVATION ANISOTROPIC ISOTROPICT OBS T CORE ERROR T COMP (0—C) P T COMP (0—C) P

DEG SEC SEC SEC SEC SEC SEC/DEG SEC SEC SEC/DEG SEC

35.00 259.110 259.110 0.71 258.11 1.29 —9.342 258.22 1.18 —9.3143 0.640.00 215.70 215.70 0.66 213.81 1.89 —8.376 213.91 1.79 —8.377 0.545.00 174.30 1714.30 0.52 174.31 —0.01 ~7.1439 174.39 —0.09 —7.439 0.1450.00 138.60 138.60 0.69 139.38 —0.78 —6.540 139.45 —0.85 —6.540 0.355.00 108.50 108.50 0.58 108.84 —0.34 —5.682 108.91 —0.111 —5.684 0.260.00 82.00 82.00 0.52 82.51 —0.51 —4.866 82.55 —0.55 —4.866 0.265.00 59.70 59.70 0.44 60.114 —0.44 —4.088 60.17 —0.47 —4.088 0.170.00 40.60 40.60 0.46 141.58 —0.98 ~3.3144 141.60 —1.00 ~3.3115 0.175.00 25.50 25.50 0.60 26.66 —1.16 —2.629 26.68 —1.18 —2.629 0.080.00 114.00 14.00 0.37 15.25 —1.25 —1.934 15.28 —1.28 —1.933 0.0

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.

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