Physics of the Earth and Planetary Interiors, 9 (1974) 28—35© North-Holland Publishing Company, Amsterdam — Printed in The Netherlands

THE RADIUS OF THE CORE—MANTLE BOUNDARY INFERREDFROM TRAVELTIME AND FREE OSCILLATION DATA;

A CRITICAL REVIEW

A.M. DZIEWONSKIDepartment of Geological Sciences, Harvard University,

Cambridge, Mass. (U.S.A.)

and

R.A.W. HADDONDepartment ofApplied Mathematics, The University of Sydney

Sydney, N. S. W. (Australia)

Submitted for publication February 7, 1974;accepted July 29, 1974

A review is givenof the present status of the information on the core radius, indicating its most likely value, butwith the understanding that it must be made compatible with the remaining features of the Standard Earth Model,which are not known to us at the present time.

1. Introduction tam point, and that adjustments may be necessary atall levels within the earth interior with the core radius

The core—mantle boundary represents the most being only a single, though important, parameter.significant discontinuity within the earth’s interior,and precise knowledge of the radius at which thisdiscontinuity occurs is of importance in investigation 2. Determination of the core radius from travel timesof the internal structure of the earth. The question of of body wavessmoothness of this boundary has a bearing on someaspects of the dynamo theory. The first close estimate of the core radius is due toDetermination of the core radius cannot be consid- Gutenberg (1913) who inferred a value of 3471 km

ered separately from the physical properties of the from determination of the distance at which themantle; P-velocity distribution if the core radius is P-wave becomes diffracted. The precision of his esti-determined from PcP reflections, S-velocity distribu- mate obtained in days of a very scarce seismographtion if ScS reflections are used, or density in addition station network, poor time service, inaccurate epicen-to both velocity distributions for the entire earth, if ter location and, above all, inherent insensitivity ofthe free oscillation data are used. Therefore, it is the method he used can be compared to the successdifficult to recommend a particular value for the of Eratosthenes in his measurement of the earth’sradius of the core if the structure of the mantle is not circumference.established. Jeffreys (1939a) proposed a method of determina-

It is obvious that the internal consistency of the tion of the core radius from the travel times of coreStandard Earth Model must be ascertained at a cer- reflections which, with some modifications, is still

THE RADIUS OF THE CORE-MANTLE BOUNDARY 29

being used. This method represents one of the first advantages over interpretation of the absolute travelapplications of linear approximation to a solution of times. In the distance range analyzed by Hales anda non-linear seismological inverse problem. Roberts (48—70°)the ray paths are at shallow depthsTo apply the method of Jeffreys it is necessary to very close to the vertical for both S and ScS, thus the

know the velocity distribution in the mantle, and effect of the source and station anomalies are elimi-assume an approximate value of the core radius, rt. nated; also, the errors in determination of depth andHavingmeasured travel times T?of, say, ScS phase at origin time become relatively insignificant. The meth-a series of epicentral distances, n.j, one calculates the od of interpretation is the same as discussed above,theoretical travel time Tf = T(~i,rc= rt) and differen- except that the calculations of the starting values andtial kernelsK~= aT(~j,rc= r~)/ar.Then, the correc- differential kernels are performed for a parametertion to the core radius is found from the least-squares TSCSS (z~).Hales and Roberts (1970b) used twocondition: models of S-velocity distribution (SLUTD1 and

SLUTD2) and obtained estimates of core radiusAl 3489.92 ±4.66 km and 3486.10 ±4.59 km, thus~ [(Ta~ Tf) — K1Sr]

2 = mm. strongly indicating a need for a significant increase ini~’1 the core radius over the value of Jeffreys. Jordan

(1972) has collected a significantly larger set of ScS-Swhich leads to: (also PcP-P as well as other phases not relevant to this

N N report) differential travel times. He incorporated— ~ 1T~ T~’~ K these data with free oscillation data and invertedr — ~ ~ i — ~ i I them to obtain the structure of the entire earth.

Jordan’s results will be discussed in the followingUsing tl~e~1atafrom the earthquakes whose epicen- section.

tral location and depth were determined as accurately Hales and Roberts have observed that the residualsas possible, Jeffreys obtained a value for the core of their observed differential travel timeswith respectradius of 3473 ±4.2 km. Soon afterwards, Jeffreys to TSCSS (~)computed for the model SLUTDI with(1939b) added new measurements of ScS and PcP a core radius of 3471 km are event-dependent. Fortravel times and obtained a new estimate of rc = example, the average residual for the event KAM 2673473.1 ±2.5 km. This value has withstood many is roughly —4 sec, while it is +2 sec for the event RATsubsequent investigations, and only in the most re- 116 in the same range of epicentral distances. Thecent years a need for revision became evident. events would haveto be mislocated by approximatelyTaggart and Engdahl (1968) haveused a large 1°to account for such a large difference, and this

number of travel times of PcP phases from nuclear does not appear likely. Hales and Roberts indicatedexplosions, where location and the origin timewere that the alternative explanation may be provided by:exactly known. They have also applied station correc- (1) lateral heterogeneities in the lower mantle; or (2)tions determined by Herrin and Taggart (1968) and lateral variations in the radius of the core—mantleassumed that these station corrections include the boundary. In future studies it would be appropriatedifferences between the model (Herrin et al., 1968) to examine the alternative (1) first, because if theand the world-wide average crust and upper mantle. answer is affirmative, there is very little that can beAs the earthquakes tend to occur in the regions said about alternative (2).characterized by an anomalous crustal and upper- A studyby Julian and Sengupta (1973) has pro-mantle structure, this assumption may not be sus- vided convincing evidence that there are substantialtam. Taggart and Engdahl gave a value of 3477 ± lateral variations (of the order of at least 1%) of the2.0 km as their estimate of the core radius. compressional velocity in the last 500 km of theHales and Roberts (1970b) have used the differen- mantle. They have shown that the rays bottoming

tial travel times of (T~cs— 7’s) obtained by measur- within this depth range and within particular regionsing the elapsedtime between the corresponding peaks determined by geographical coordinates show similarof the SH and SCSH pulses in a particular recording. travel time anomalies irrespective of the source orThe use of differential travel times has distinct receiver.

30 AM. DZIEWONSKI AND R.A.W. HADDON

Julianand Sengupta have also found a significant ellipticity) are not justified at this time, because ofdifference between their P-wave travel time data the complications discussed in point (2).beyond 90°and those of Herrin et al. (1968). Theyconcluded that this difference results from a bias insampling. Since the data set of Julian and Sengupta 3. Determination of the core radius from inversion ofwas equally extensive as that of Herrin, their conflict- normal mode dataing results indicate that much more data has yet to becollected, in order that the average structure of the A newkind of seismic data — periods of freeearth in this depth range could be established from oscillations of the earth, became available for the firstthe body wave studies alone. Even a larger effect has time from the analysis of a number of recordings ofbeen reported by Jordan and Lynn (1973) for the the great Chilean earthquake of May 22, 1960.travel times of the S-waves bottoming near the core— Information that can be obtained through observa-mantle boundary (up to 10 sec). tions of free oscillations of the earth is important notThe presence of the lateral variations of shear only because of the sensitivity of their eigenperiods

velocity in the deep mantle can be deduced indirectly to the density distribution, but also because of theirfrom fig. 6 of Hales and Roberts (1970a) where the property of averaging the lateral inhomogeneities inscatter of residual travel times with respect to the the earth structure.Jeffreys-Bullen tables increases suddenly by a factor Rotation, ellipticity and lateral inhomogeneities inof 3 for distances greater than 82°(bottoming depth the distribution of elastic parameters within the earthof approximately 2300 km). interior will cause splitting of spectral peaks; thus, aRecently Engdahl and Johnson (1972) have ana- multiplet of a mode withan angular order number l is

lyzed the differential travel times PcP-P from three characterized by 21 + 1 spectral lines. But Gilbertnuclear explosions in the Aleutian Islands. They have (1971a) has shown that the meanvalue of all eigen-concluded that the radius of the core should be periods belonging to a multiplet is the multiplet’sincreased from 5 to 15 km over the value of Taggart completely degenerate eigenperiod (“terrestrialand Engdahl (1968) of 3477 km. Engdahl and John- monopole”) belonging to the spherically averagedson have used a three-dimensional ray tracing tech- earth.nique to account for scattering of the seismic waves Theoretically, a bias could be introduced becauseby a descending slab. It would appear that uncertain- of nonuniform distribution of stations and sources,ties connected with the model representing this but Dziewonski and Gilbert (1973a) compared eightstructural complication may contribute significantly different sets of average eigenperiods of fundamentalto the uncertainty of their results. spheroidal modes and have shown that the bias, if itWe can summarize the results of determination of does exist, is not greater than 0.05—0.03%, and that

the core radius from body wave travel times. it is probably less for overtone modes with high phase(1) Recent results in which differential travel times velocities.

have been used (T~cs— T5 Tpcp — Tp) favour a Thus, the normal mode method provides absolutecore radius between 3482 and 3492 kin; a significant information on the properties of the sphericallyincrease from the values deduced by Jeffreys symmetric average earth; no station or source correc-(l939a,b) and Taggart and Engdahl (1968). tions are necessary. This property of the normal(2) At the same time, a strong evidence for lateral modes makes them ideally suited to become a refer-

variations of the velocities in the lowermost mantle ence data set for derivation of the Standard Earthhas been found. This raises the question whether the Model, and they can be used to establish the absolutesampling of the inhomogeneous mantle has been base-line values for travel times (Gilbert et al., 1973;sufficiently adequate, such that the figures quoted Jordan, 1972).above could represent an unbiased world-wideaverage. 3.1. Review ofdevelopments until 1971(3) Any inferences with respect to the large wave-

length lateral variations in the core radius (other than Numerical calculations of the free oscillation

THE RADIUS OF THE CORE-MANTLEBOUNDARY 31

periods for a number of the earth models representing While these models were of course not intended to becombinations of the velocity distributions of Jeffreys final, it is interesting to note that many of theiror Gutenberg and density distributions of Bullen essential characteristics have survived in currently(models A’ and B) have shown that the observations preferred models.of normal modes confirm the basic validity of these An important result demonstrated was that travelmodels. However, it also became obvious that some time and oscillation data could be reconciled with aadjustments in the radial distribution of the physical postulated Adams-Williamson density gradient in theparameters were necessary since there were system- lower mantle by increasing the core radius by 15—20atic differences of the order of 1 or 2% between the km from the Jeffreys’s (l939b) value of 3473 km.observed and computed eigenfrequencies. The large core radii of the HB1 models were sub-One of the first attempts at inversion of normal sequently, for a time, thought to be unacceptable

mode data was made by MacDonald and Ness (1961) because they were in disagreement with the result ofwho improved the agreement between the observed Taggart and Engdahl (1968; 3477 ±2 km; see discus-and computed periods of low-order toroidal osdilla- sion in the previous section). Muirhead and Clearytions by perturbing the shear velocity distribution in (1969) proposed an alternative solution in whichthe lower mantle. However, their solution was obvi- shear velocity in the D” layer has been reduced ac-ously unsatisfactory, because the S-wave travel times cording to Cleary (1969) and the core radius wascomputed for their model had residuals of over 25 reduced to an “acceptable” 3478 km, with all theseconds at teleseismic distances, other parameters of the HB1 model being retained.The observed travel times of body waves represent However, the recent discovery of the lateral variations

a serious limitation on the permissible range of per- of velocities in the lowermost mantle and uncertain-turbations in velocity distributions. Realizing this, ties connected with the applicability of ray theoryLandisman et al. (1965) attempted to satisfy the cast some doubt on the interpretation of Clearyavailable free oscifiation data by perturbing the densi- (1969).ty distribution. They obtained agreement with the A different approach has been adopted by Pressdata for a model in which the density was nearly (1968, 1969, 1 970a and b) who, recognizing non-constant in a depth range from 1600 to 2800 km. uniqueness of the inverse problem, used the MonteAlthough this solution is considered implausible from Carlo method to generate trial earth models, testedthe viewpoint of geochemical and thermal consider- them against the data and then investigated the corn-ations, it attracted attention to the non-uniqueness of mon properties of those models that satisfied the datathe free oscillation inverse problem. Soon after publi- within prescribed error limits. The successful modelscation of the paper by Landisman et al., Dorman et in his most recent study (1970b) have not showna!. (1965) have suggested an alternative solution in strong preference for any particular value of the corewhich the core radius was increased by 10 km and a radius within the bounds from 3463 to 3483 km.“soft” layer was introduced at the base of the mantle. Dziewonski (1970) in his investigation of theThus, for the first time the importance of the value of singularities of the auto-correlation matrix of differ-the core radius in inverting the free oscillation data ential kernels (partial derivatives) explained thehas been recognized. reason for the failure of free oscillationdata to nar-Bullen and Haddon (1967) were the first authors row the range of permissible solutions based on the

to derive a model which was reasonably consistent fundamental mode data alone. He has pointed outwith both free oscillation and travel time data avail- that only acquisition of particular overtone data orable by 1965 and which at the same time was satisfac- relevant body wave information free of usual un-tory in other essential respects. Theirmodel HB1 was certainties may remedy the situation.derived by modifying the original model A’ of Bullen Perhaps the only important conclusion that couldon only those respects which appeared to be de- have been made on the basis of the results obtainedmanded by all the evidence brought to bear. Full during the period 1961—1970 was that it is possiblenumerical details of the model HB1 and some variant to satisfy the observed normal mode data with amodels were published by Haddon and Bullen (1969). model in which density distribution in the lower

32 A.M. DZIEWONSKI AND R.A.W. HADDON

mantle follows closely the Adams-Williamson equa- limited by the broken lines envelops the range oftion. All the published solutions in which this condi- solutions obtained from the inversion experiment. Ittion was fulfilled had either the core radius substan- is easily seen that the range of permissible densitytially greater than the value of Jeffreys (l939b) or solutions in the lower mantle has been reduced by aanomalous velocity gradients in the region D”. How- factor of 2 or 3 by the application of the overtoneever, the possibility of a significant super-adiabatic constraints. The range of shear velocity solutions isdensity gradient in the lower mantle could not be also somewhat less even though the travel time dataexcluded on the basis of the limited set of free oscilla- were not used as a constraint. The average sheartion data brought to bear. velocity from 41 solutions is very close to that of

Hales and Roberts (l970b). The upper mantle has3.2. Recent developments in identification ofnormal beenobviously overparameterized and, as a result, the

mode data bounds were not appreciably changed in this region.Fig. 2 shows the histogram of the core radius

Dziewonski and Gilbert (1972) identified and values before (broken line) and after inversion (solidmeasured eigenperiods of 70 spheroidal and toroidal line). All solutions after inversion fall within a rela-overtone modes from the spectra of 84 recordings of tively narrow range between 3486 and 3491 km,the Alaskan earthquake of March 28, 1964. It became while for the starting models they were scatteredobvious from the first attempts at inversion (Dzie- between 3463 and 3483 km.wonski, l971b) that these overtone data impose new The experiment described above was not entirelyconstraints on the distribution of elastic parameters satisfactory from the formal point of view. Thewithin the earth’s interior. parameterization of the models (pivotal depths) wasThe following unpublished experiment of Dzie- the same as in the study of Press, and it appears that

wonski may serve as a graphical illustration of the the models were underparameterized in the lowerincreased resolving power of the new data set. The mantle with respect to the increased resolving powerdata set of Dziewonski and Gilbert (1972)was in- of the augmented data set. Thus, certain bias mightverted using the approach of Dziewonski (197la,b) have been introduced to the solutions. For example,for 41 successful models of Press (l970b; oceanic the models UTD124A’ and B’ of Dziewonski andstructure). The solid lines in Fig. 1 designate the Gilbert (1972) represent successful solutions with theextreme range of solutions of Press; the hatched area core radius of only 3482 km.

_______________________ _______________________ Fig. 2. Comparison of the histogram of the core radii in theI I I

DEPTH ~ 20 HJ set of 41 models ofPress (1970b, oceanic structure) —

dashed line, with the histogram of the core radii in the mod-Fig. 1. Comparison of the extreme bounds of 41 models of els obtainedby perturbing the models of Press to satisfy thePress (1970b, oceanic structure) — solid lines, bounds of the data of Dziewonski and Gilbert (1972) — solid line. Themodels obtained by perturbing the models of Press to satisfy values on the abscissa represent excess of core radius in athe data ofDziewonski and Gilbert (1972) — stapled area, model over a value of 3473 km.

THE RADIUS OF THE CORE-MANTLE BOUNDARY 33

Regardless of these reservations with respect to the It is difficult at the present time to predict theexperiment described above, it is clear that this new progress in identification of normal modes that maynormal mode information can be instrumental in take place during the next few years, particularly nowimproving our knowlegde of the structure of the that the stacking and stripping methods can be usedearth’s interior, in processing simultaneously records from differentDziewonski and Gilbert (1973a) have continued earthquakes. It appears, however, that the quality

their interpretation of the Alaskan data and were able rather than quantity of the data will be of paramountto identify 87 additional spheroidal overtones with importance.periods from 285 to 100 seconds. More than one halfof these new overtone data have an effective control 3.3, Results ofrecent inversion studies that includeover the structure of the outer or inner core. the augmented set offree oscillation dataMendiguren (1972, 1973) proposed a method

which has revolutionized the problem of identifica- Publication of the extensive set of overtone datation of normal modes. Ifthe earthquake mechanism by Dziewonski and Gilbert (1972) has renewed inter-is known, the theory of excitation of normal modes est ofgeophysicists in inversion studies, as it was clear(Saito, 1967; Gilbert, l97lb) makes it possible to that the additional information contained in thesecalculate for a particular mode the sign and amplitude data could be instrumental in resolving questions withof the initial displacement at any point on the surface regard to the density gradient in the lower mantle orof the earth. If the data from many stations are the value of the core radius. The overtone data set ofavailable, it is possible to “stack” their spectra for a Dziewonski and Gilbert has been considered in theparticular angular order number 1. This is achieved by following studies: Johnson (1972), Jordan (1972),multiplying each individual spectrum by the theoreti- Wang (1972), and Worthington (1973); Gilbert et al.cal amplitude (including its sign) predicted for the (1973) included in their study also additional data ofparticular location and component and summing the Dziewonski and Gilbert (1973a). Although the de-results. Should the coverage be continuous, the effect tailed composition of the data sets and the inversionof all modes with the angular order number other methods used were different in each of these studies,than 1 would be eliminated, because of the ortho- the results, with the exception of the upper mantle,gonality of spherical harmonics. In practice, the are very similar and basically conform to the classicalcoverage is limited, but the experiments have shown concepts of the structure of the earth’s interior.that even using as few as 10 or 15 stations the enhance- Of the studies quoted above, the work by Jordanment is sufficient to isolate the modes which some- and Anderson (1974) and Gilbert et al. (1973) istimes cannot be seen in the spectra of individual re- perhaps the most relevant to the problem of thecordings. Standard Earth Model, as the attempt was made inDziewonskiand Gilbert (1973b, full report now in these reports to integrate the entire available seismic

preparation) have analyzed spectra of 165 recordings information with regard to the deep structure of theof the Colombian earthquake of July 31, 1970 and earth’s interior.using the technique described above as well as a more Jordan and Anderson (1974) have used the normalrefined method which they call “stripping”, have mode data (primarily those of Dziewonski and Gil-identified over400 new spheroidal and toroidal bert, 1972) and differential travel times (PcP-P,overtone modes. The shortest period of an identified ScS-S, PAB-PDF and PBC-PDF) to derive their modelmode is at the present time 83 seconds, but it appears Bl. Having used the inversion method of Jordan andlikely that the process can be extended to periods as Franklin (1971), they were able to assure smoothnessshort as 40 seconds and perhaps even further. of their final model in the lower mantle and the outerMany of the identified modes have body-wave core,while their upper mantle contains two dis-

equivalences (Dziewonski and Gilbert, 1972, 1973a) continuities at 420 and 670 km. The two main con-of the type ScS and PScS, in addition to the mantle troversial features of their model are the negativemodes of S and PS type. It may be expected, there- gradient of shear velocity between 420 and 670 kmfore, that the entire data set will be sensitive to the and the systematic difference in slowness of thevalue of the core radius. S-waves computed for the mode! Bl and derived from

34 A.M. DZIEWONSKI AND R.A.W. HADDON

observations of Hales and Roberts (1970a). Jordan 4. Conclusionsand Anderson estimated the value of the core radiusas 3485 km. A value of 3485 ±3 km is suggested as the bestGilbert et al. (1973) have used the normal mode available estimate of the outer core radius. This value

data of Dziewonski and Gilbert (1972, l973a) and is concordant with what we consider to be the bestBrune and Gilbert (1974), P-wave travel times of current evidence.Carder et a!. (1966), travel times of 5, SKS and SKKS However, it must be realized that this estimate isphases of Hales and Roberts (1970a and 1971) and based on the assumption that the earth models thatPKIKP travel times of Cleary and Hales (1971). The were used in derivation of the core radius are linearlytotal number of data was 497 (including the earth’s close to the real earth. Should some new observa-mass and moment of inertia), and hence the name of tions, or a more refined analysis of the existing datathe final model B497 (for the listing see Appendix I set, prove that this assumption is incorrect (for ex-in Dziewonski and Gilbert, 1973a). ample, if it were shown that a major discontinuity isHowever a set of 196 carefully selected normal associated with the D” region), it will be necessary to

mode data with a very conservative estimate of stan- revaluate all the results obtained so far for the lowerdard errors was inverted before the final inversion mantle and the core, including the estimate of therun, yielding a model C198 (ibid.) This model was core radius.used to calculate the absolute base-line values for thetravel time data sets specified above. The computedbase-line correction for the P-travel times is +2 ±0.4 Acknowledgmentssec, for S-travel times +4 ±0.9 sec, and for SKS andSKKS +3.4 ±0.9 sec. The computed PKIKP travel The research effort of A.M.D. was supported bytime at 180°is 1213 ±0.2 sec. The P-wave travel time the Committee on Experimental Geology and Geo-corrections of Jordan and Anderson are approximate- physics, Harvard University and the National Sciencely 1 second less from those of Gilbert et al., while the Foundation grant GA-32320.S-wave base-line corrections are in good agreement.The reason for this discrepancy is not clear at thistime. ReferencesGilbert et al. have computed a table of resolving

lengths for calculation of local averages of Vp VS and Brune, J.N. and Gilbert, F., 1974. Toroidal overtone disper-p at a 0.5% error level. The core radius for model sion from correlations of S-waves and SS-waves. Bull.B497 is 3482.6 km, and recently Gilbert and Dzie- SeismoL Soc. Am., 64: 3 13—320.Bullen, K.E. and Haddon, R.A.W. 1967. Derivation of anwonski (1973) estimated the error limits to be±2.8 —earth model from free oscillation data. Proc. Nail. Acad.km. Sci., 58: 846—852.

The other recent determinations of the core radius Carder, D.S., Gordon, D.W. and Jordan, J.N., 1966. Analysisare: Wang(1972) — 3481 kin; Johnson (1972) — of surface-foci travel times. Bull. Seismol. Soc. Am., 56:3481.4 kin; Dziewonski and Gilbert (1972) — 3482 815840.kin’ Gilbert et al. (1973) — 3484.9 km for the model Qeary, J., 1969. The S-velocity at the core—mantle bound-ary, fromobservations of diffracted S. Bull. Seismol. Soc.C198. Am., 59: 1399—1405.It is important to state that the inversion and error Cleary, J.R. and Hales, AL., 1971. PKIKP-times and 5-

analysis based on the linear inverse theory of Backus station anomalies. J. Geophys. Res., 76: 7249—7259.and Gilbert is valid only if the starting model is linear- Dorman, J., Ewing, J. and Alsop, L., 1965. Oscillations of theearth: new core—mantle boundary model based on low-ly close to the real earth. Ifwe are willing to assume order free vibrations. Proc. Nail, Acad. Sci., 54:that this is the case, then a value of the core radius of 364—368.3485 ±3 km appears to be an estimate of the radius Dziewonski, A.M., 1970. Correlation properties of free pe-of the core—mantle boundary that is consistent with nod partial derivatives and their relation to the resolutionall the recent observations of normal modes and of grossearth data. Bull. Seismol. Soc. Am., 60:travel times. —

THE RADIUS OF THECORE-MANTLE BOUNDARY 35

Dziewonski, A.M., 1971a. Upper-mantle models from “pure Johnson, C.E., 1972. Regionalized earth Models from Linearpath” dispersiondata. J. Geophys. Res., 76: 2587—2601. Programming Methods. Thesis, Massachusetts Institute of

Dziewonski, A.M., 197 lb. Overtones of free oscillations and Technology.the structure of the earth’s interior. Science, 172: Jordan, T.H., 1972. Estimation of the Radial Variation of1336—1338. Seismic Velocities and Density in the Earth. Thesis, Call-

Dziewonski, A.M. and Gilbert, F., 1972. Observations of fornia Institute of Technology.normal modes from 84 recordings of the Alaskan earth- Jordan, T.H. and Anderson, D.L., 1974. Earth structure fromquake of 1964 March 28. Geophys. J. R. Astron. Soc., free oscillations and travel times. Geophys. JR. Astron.27: 393—446. Soc., 36: 4 11—459.

Dziewonski, A.M. and Gilbert, F., 1973a. Observations of Jordan, T.H. and Franklin, J., 1971. Optimal solutions to anormal modes from 84 recordings of the Alaskan earth- linear inverse problem in geophysics. Proc. NatI. Acad.quake of 1964 March 28. Part II: Further remarks based Sci.,68: 291—293.on new overtone data. Geophys. J.R. Astron. Soc., 35: Jordan, T.Fl. and Lynn, W.S., 1973. Lateral heterogeneity of401—437. the lower mantle from observations of ScS-S differential

Dziewonski, A.M. and Gilbert, F., 1973b. Identification of travel times. Trans. A.G.U., 54: 363 (abstract).normal modes using spectral stacking and stripping. Trans. Julian, BR. and Sengupta, M.K., 1973. Seismic travel timeAm. Geophys. Union, 54: 374 (abstract). evidence for lateral heterogeneity in the deep mantle.

Engdahl, E.R. and Johnson, L.E., 1972. A new PcP data set Nature, 242: 443—447.from nuclear explosions on Amchitka Island. Trans. Landisman, M., Satô, Y. and Nafe, J., 1965. Free vibrationsA.G.U., 53: 1045 (abstract). of the earth and the properties of the deep interior re-

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Gilbert, F. and Dziewonski, AM., 1973. The structure of the Oscillations. Thesis, Dept. of Earth and Planetary Science,earth retrieved from eigenspectra. Trans. A.G.U., 54: 374 M.I.T.(abstract). Mendiguren, J., 1973. Identification of free oscillation spec-

Gilbert, F., Dziewonski, A.M. and Brune, J., 1973. An infor- tral peaks for 1970 July 31, Colombian deep shock usingmative solution to a seismological inverse problem. Proc. the excitation criterion. Geophys. JR. Astron. Soc., 33:Natl. Acad. Sci., 70: 1410—1413. 281—321.

Gutenberg, B., 1913. Uber die Konstitution des Erdinnern, Muirhead, K.J. and Cleary, J., 1969. Free oscillations of theerschlossenaus Erdbebenbeobachtungen. Phys. Z., 14: earthand the D” layer. Nature, 223: 1146.1217—1218. Press, F., 1968. Earth models obtained by Monte Carlo

Haddon, R.A.W. and Bullen, K., 1969. An earth model incor- inversion. J. Geophys. Res., 73: 5223—5234.porating free earth oscillation data. Phys. Earth Planet. Press, F., 1969. The suboceanic mantle. Science, 165:Inter., 2: 35—49. 174—176.

Hales A.L. and Roberts, J.L., 1970a. The travel times of S Press, F., l970a. Earth models consistent with geophysicaland SKS. Bull. SeismoL Soc. Am., 60: 461—489. data. Phys. Earth Planet. Inter., 3: 3—22.

Hales, AL. and Roberts, J.L., 1970b. Shear velocities in the Press, F., l970b. Regionalized earth models. J. Geophys.lower mantle and the radius of the core. Bull Seismol. Res., 75: 6575—6581.Soc. Am., 60: 1427—1436. Saito, M., 1967. Excitation o free oscillations and surface

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