The recent shear wave travel-time data of Ibrahim and Nuttli (1967) and Doyle and Hales (1967) is reinterpreted to yield a shear-velocity structure that is compatible with Johnson's (1967) compressional-velocity structure. The elastic parameters Φ, K/μ, and σ are calculated as a function of depth. All three parameters increase with depth in the homogeneous regions of the mantle but only Φ increases through the transition regions. Poisson's ratio is apparently less for the close-packed deeper mantle phases than it is for the normal phases of the upper mantle. The theoretical prediction that dμ/dP becomes negative before a phase change is verified by the seismic data

Anderson, Don L.

Julian, Bruce R.

Caltech Authors - Main

Jut;RNAL OF GEOPHYSICAL HESL\RCH VoL. 7-1, No. 15, 1%') 
Shear Velocities and Elastic Parameters of the Mantle I 
DoN L. ANDI<JRsox 
,_"JczsJ~nnlnr:ru~''' Laboratory, 
Pasadcnrr, 
BRUCE H. JULIAN 
Institnte of Technology 
'n/\iln·•·n·Jrt DJJOD 
?'he r:ecen~ :-hear >vaye tra:·ei-tinw (lata of Ibrahim and Nuttli (1967) and Doyle and Hales 
(196:) I;:< remtcr:r:m~ted to :ncld a structure that is eompatible with Johnson's 
(1961) cm:1presswnal-n~locit~· structure. The parame1N;:< <P. K/ fl, and cr an: cal('ulated 
as a funehon of depth. All three parameters increase 1vith depth in the regions 
of the mantle but only <P increases through the tnmsi!ion regions. Poisson's is anoa1·entlv 
less for !he elose-pa~ked mantle phases than it is for the normal phases of 
ma1_1tlc. The thco.ret~cal that dfl/dP become;,; ncgatiYe before a phase 
venfied by the sc1smrc data. 
lKTRODUCTIOX 
J\Iuch effort has been spent m the last few 
years in the collection and of compres-
sional velocity data and in the inversion of this 
data to obtain compressional structures. 
The travel apparent velocity, and ampli-
tude curves have been found to be Yerv com-
plicated out to about 40°, and thry [~re ob-
the result of more than one branch 
involved. The complications are caused 
of abnormally high-velocity gradients in 
he upper mantle and Anderson, 1965; 
Johnson, 1967; Kanamori, 1967; Julian and 
1968; Green and 1968; Leu·is 
and 111 eyer, 1968; and Archambeau et HJ69] 
That had previously been found surface \vave 
studies [Anderson and Toksoz, 1963]. A de-
tailed of these high UAinn,i-n 
ents in terms of phase 
Andersm1 
The 
that of Ibrahim 
for S waYes 
[1967]. 
ll1 
the shear 
they determined travel-time cnn·es out 
to about 50° for focal of 33 and 120 
km. The travel time curves were similar in their 
to the P travel-time curves. ::\Iuch 
of their data \vas to \Yestern North 
Contribution No. 1615, Division of uc:OH)grcal 
•::Jclertces. California Institute of Technology, 
adena. 
Copyright © 1969 by the American Geophysical Union. 
a studied l{iazi 
awl Anderson I1DG5], Johnson [1967], Julian 
and Anderson [1968], and Archambeau et al. 
[H169] \Yith P waws. Ibrahim and Nuttli 
[19(:)7] determined a shear structure 
that gave Yer~· good agreement \Yith their data 
for both foc,tl Although their model was 
in gross agreement with the recent P structnres 
in that it h:Hl a urlper mantle lmv-
velocity zone and discontinuities near 400 and 
700 km, it differed in some details. 
The main differences in the models are the 
to the zone and to the dis-
continuity between GOO nnd 7:30 km. An interest-
ing fe,lture of their model was the existence of 
regions of con~tant Fn,~n,'-'· 
In another notnble recent pa11er, Doyle and 
Ilales /10(17] determined a new 
tranl-timc cnrve between about 28 and 80°. 
These papers are in that 
a refined travel-time curve for S waves 
and proYide the of 
estimates of the Yariation of shear n"l~n'+'· 
de11th in the mantle. apart 
in its own this lYYlr\l"r"r"n'""d· 
e~sential in free oscillation 
the shear is the dominant parameter 
for most of the modes of free oscillation. If this 
parameter can be determined independently 
with good and the 
free oscillation data can be used to determine 
the distribution in the earth. In addition 
the data can be combined vvith 
the data in order to 
3281 
3282 ANDERSON AND JULIAN 
180 
-(.) ISO us Cl.> 
(/) 
(.) 
Cl.> 120 (/) 
' E 
.X: 
ro 
--l!) 
90 
' <J 
I 
1--
60 
• 
3010 40 
!::., deg. 
Fig. 1. Reduced travel-time curve for shear waves from shallow focus earthquakes. Depth 
of focus, 33 km. Data: open circle, Doyle and Hales [1967]; solid dot, Ibrahim and Nuttli 
[1967]. 
determine the depth variation of such impor-
tant parameters as the seismic parameter cf> and 
and Poisson's ratio a. These quantities are in-
volved in the interpretation of seismic data in 
terms of composition and petrology of the 
various regions of the mantle. 
It is the purpose of this paper to invert this 
data in such a way that the resulting shear-
velocity profile is similar to recent compres-
sional velocity profiles that are based on a much 
larger body of data. By 'similar' we mean that 
such features as low-velocity zones and transi-
tion regions should occur at roughly the same 
depth in both profiles. These compatible profiles 
can then be combined to yield the other param-
eters noted above. In addition the degree of 
non-uniqueness of the structures resulting from 
the inversion of this kind of data is clearly 
demonstrated. Lateral variations are still a 
problem in all studies of this type, and studies 
in different regions are clearly desirable. 
DATA 
The raw data of Ibrahim and Nuttli [1967] 
were used and were independently corrected to 
either 33 km or 120 km, depending on whether 
the earthquake was shallow or intermediate. 
The first arrival data beyond 28° was taken 
from Doyle and Hales [1967] and was corrected 
to 33 km by taking their tabulated J-B resi-
duals and applying the correction to the J-B 
tables. Figure 1 shows that the two sets of data 
are compatible although the scatter is substan-
tial. 
ANALYSIS AND RESULTS 
The inversion was accomplished by trial and 
error using the travel-time program TVT3 de-
scribed by Julian and Anderson [1968]. John-
son's [1967] P-wave model CIT204 was used as 
a guide, and we attempted to have the locations 
and thicknesses of the low-velocity zone and 
the transition regions be the same as in this 
model. 
Figures 1, 2, and 3 show the fit of the Ibrahim-
Nuttli model and our model, US26. Both models 
fit the data out to 40° about equally well. 
The models are shown in Figure 4. By intro-
ducing negative gradients for shear waves where 
Ibrahim and Nuttli [1967] had constant ve-
0 
(]) 
(/) 
0 
(]) 
(/) 
' E 
~ 
a:> 
l{) 
' <l 
I 
r-
BRIEF REPORTS 3283 
150 
120 
90 
60 
30 
• ----= 
. ----!_. 
~~~~~~~~~~~c=-~-Jl~-~-~~~--~;--~~-·- ~. ~~~ 
""' o;ttractecT --
THEORETICAL CURVES 
IBRAHIM 8 NUTTLI 
us 26 
20 
!J., deg. 
30 
Fig. 2. Reduced travel-time curve for shear waves from intermediate focus earthquakes. 
270 
u 260 
Q) 
(/) 
u 250 Q) 
(/) 
' E 
..:.:: 
co 240 
' <J 
I 
1-
230 
Depth of focus, 120 km; data from Ibrahim and Nuttli [1967]. 
" 
" 
" 
THEORETICAL CURVES 
IBRAHIM 
us 26 
B NU TTL I 
60 
de g. 
" '\. 
'\ 
'\ 
\ 
\ 
\ 
\ 
Fig. 3. Reduced travel-time curve for shear waves between 25° and 80°. Depth of focus, 33 
km; data from Doyle and Hales [1967]. 
40 
3284 ANDERtiON AND JULIAN 
Fig. 4. ~hear nloeity model of Ibrahim and 
Nuttli [1967] and present work and compress-
ional velocity model of Johnson [1967]. 
locity gradients, it has been possible to find a 
model that is nearly compatible with the com-
pressional velocity model. As expected from the 
natbre of travel-time data the two shear-
Yelocity solutions oscillate about each other. The 
large negatiYe gradient between 500 and 650 km 
in 1JS26 prevents any ray from bottoming in 
this region; the corresponding braneh of the 
travel-time curve for this model therefore rep-
resents diffracted energy (see Figures 1 and 2). 
The negative velocity gradients above 400 km 
can easily be explained by a modest C--5°C/km) 
temperature gradient that, for shear waves, 
cancels out the effect of presmre in increasing 
the velocity. The large negative gradient be-
tween 500 and 650 km, however, requires that 
the material in this region, presumably mainly 
olivine in the spinel strueture, have a low 
(ilVs/ilP)T or a high (ilVs/ilT)P or both. There 
is, of course, a large uncertainty in the actual 
gradient. 
TABLE 1. Velocities and Elastic Parameters as Function of Depth 
Depth, Vs,, * Vs,,* Vp,** iP,, ()?2, 
km km/sec km/sec km/sec (km/sec)2 (km/sec)2 (K/11l1 
35 4.60 4.60 7.85 33.4 33.4 1.38 
50 4.60 4.59 7.87 3:3.7 33.8 1.59 
6.5 4.60 4.59 7.70 (31.1) (31. 2) (1.47) 
80 4.60 4.40 7.60 (29 .5) 31.9 (1.40) 
100 4.60 4.40 7.61 (29.7) 32.1 (1.40) 
125 4.60 4.40 7.70 (:31.1) (:3:3 .5) (1.47) 
150 4.5:3 4.55 7.93 (3i).5) (35.3) (I.n) 
180 4.00 4.60 8.30 (47 .6) 40.7 (2.97) 
200 4.60 4.64 8.:31 (40.8) (40.3) (1. 93) 
2.50 4.65 4.60 8.42 42.1 42.7 1.94 
300 4.65 4.58 8 . .54 (44.1) 4.5.0 (2. 04) 
350 4.57 4 . .55 8.67 (47 .3) (47.6) (2.27) 
400 5.13 4.90 9.:30 51.4 (54.5) 1. 93 
450 5.30 5.:39 9.6:) 55.3 54.0 1.97 
500 5.37 5.44 9.75 .56.6 5.5.6 1.96 
550 5.:37 5.29 9.84 (58.4) 59 . .5 (2.02) 
600 5.37 5.15 9.95 (60.5) (63.6) (2.10) 
650 5.:37 5.00 10.55 (72.8) (78. 7) (2. 53) 
700 5.33 5.75 10.95 (82.0) (75. 8) (2.89) 
750 6.14 6.2:3 11.0:3 71.4 (69.9) 1.89 
800 6.38 6.30 11.11 69.2 70.5 1.70 
900 6.38 6.33 11.30 (73 .4) 74.3 (1.80) 
1000 6.40 6.38 11.47 76.9 77.:3 1.88 
1200 6.49 6.51 11.80 83.1 82.7 1.97 
1400 6.60 6.6:3 12.08 87.8 87.3 2.02 
1600 6.68 6.74 12.34 92.8 91.7 2.09 
1800 6.73 6.8:3 12.55 97.1 95.3 2.14 
*Subscript 1 refers to Ibrahim and Nuttli structure; subscript 2 is US26. 
** CIT204 [Johnson, 1967]. 
(K/p)z <T! 
"' 
1. ;)8 0.2:)8 0.238 
1.61 0.240 0.242 
(1.48) (0.222) (0.224) 
1.6.5 (0.211) 0.248 
1.66 (0.212) 0.249 
(1. 73) (0.222) (0.258) 
(1. 70) (0.258) (0. 255) 
1. 92 (0.349) 0.278 
(1. 87) (0. 279) (0.273) 
2.02 0.281 0.287 
2.14 (0.289) 0.298 
(2 .30) (0.:308) (0.310) 
(2. 27) 0.281 (0.308) 
1.86 0.28:3 0.272 
1.88 0.282 0.274 
2.13 (0.288) 0.297 
(2 .40) (0. 294) (0.317) 
(3 .12) (0.:325) (0.355) 
(2.29) (0.345) (0.310) 
(1.80) 0.275 (0.266) 
1. 78 0.254 0.263 
1.85 (0.266) 0.271 
1.90 0.274 0.276 
1.95 0.283 0.281 
1.99 0.287 0.284 
2.02 0.293 0.287 
2.04 0.298 0.290 
BRIEF REPORTS 3285 
The shear-velocity structures obtained by 
Ibrahim and Nuttli [1967] and reported in this 
paper are tabulated in columns 2 and 3 of Table 
1. These are combined with Johnson's model 
CIT204 (column 4) to obtain the elastic param-
eters in the remaining columns. No attempt has 
been made to smooth the results. Values in 
parentheses are in transition regions or repre-
sent regions where the shear velocity model i8 
incompatible with the compressional velocit~· 
model. If these values are ignored, there is a 
relati;-ely uniform increase of rp with depth a8 
>:hown in Figure 5, except for the low-wlocity 
zone that has a lower ·¢ than the adjacent re-
gions of the mantle. K/i-t and cr increase rather 
uniformly with depth to at least 300 km. The 
values for these parameters are less in the 
region between the major discontinuities, i.e. 
the 'spinel' section of the mantle, than at 30J 
km, but increase with depth in this region. 
These values drop again in going through the 
()50-lnn phase change and increase relatively 
~lowly thereafter. The general tendency is for 
the Poisson's ratio to increase with depth in rela-
tively homogeneous regions of the mantle. This 
increase is to be expected since both tempera-
ture and pressure increase Poisson's ratio. The 
¢, (km/sec) 2 
0 
GUTENBERG 
Fig. 5. Seismic parameter if> versus depth in 
the homogeneous regions of 1JS26 compared with 
the Gutenberg model. 
TABLE 2. Properties of Simple Oxides 
Substance Coordination (M) Po P.I. 0"1 
BeO 4-4 1') c ~.;; 3.00 7.2 .205 
ZnO 4-4 40.7 5.62 5.3 .357 
AlzO" 6-4 20.4 3.97 7.2 .236 
Fe,o, 6-4 31.9 5.25 6.6 .308 
:VI gO 6-6 20.2 3.58 6.3 .182 
CaO 6-6 28.0 3.29 5.3 .210 
I Anderson et al. [1969] 
drop in Poioson's ratio upon passing through 
the transition regions was unexpected. There 
is not enough ultrasonic data available to say 
v;hether this effect is due to composition or 
cry8tal structure. Since most of the increase of 
velocity through the transition regions is due 
to phase changes, most of the drop in Poisson's 
ratio is probably clue to change in crystal struc-
tnre. If this probability is tru8, one would pre-
dict cr1 (olivine) > a" (spinel) > cr3 (post-
spinel), or dcr1/ clZ > da"/ dZ > da3/ dZ, or both. 
Table 2 gives Poisson's ratio for 6 simple 
oxides. (111) is the mean atomic weight, Po is the 
zero-pressure density, and P.I. is the packing 
index of Fairbairn [1963], a measure of how 
effectively the ions are packed into a unit cell. 
For a given coordination Poisson's ratio de-
crra~es as the packing index increases. For a 
given mean atomic weight Poisson's ratio de-
creases as the coordination increases. For the 
olivine-spinel phase change there is an increase 
iu flacking index with no change in coordination 
while for the spinel-post-spinel phase change 
there is an increase in both the packing index 
and the coordination. The seismic data seems 
consistent, therefore, with the limited amount of 
]Jertincnt ultrasonic data. 
Note added in proof: G. Barsch and 0. L. 
~~nderson (personal communicn.tions) have sug-
gested that a negative dp/dP implies an un-
stable crystal lattice. It follows that the shear 
Yelocity should decrease vvith depth above each 
~hangc in the enrth's mantle. This is consistent 
1vith the interpretations given here and by 
Ibrahim and N uttli [1967]. 
Acknowledgments. This re8earch was sup-
ported b~· the Advanced Research Projects 
Agency of the Department of Defens" and was 
monitored by the Air Force Office of Scientific 
3286 ANDERSON AND JULIAN 
Research under. Contract No: F44620-69-C-0067 
and National Science FoundatiOn grant GA 1003. 
We would like to thank A. Ibrahim, 0. Nuttli, 
A. Hales and H. Doyle for advance copies of their 
manuscripts. 
REFERENCES 
Anderson, Don L., Phase changes in the upper 
mantle, Science, 157, 1165-1173, 1967. 
Anderson, Don L., and M. N. Toksoz, Surface 
waves on a spherical Earth, 1, Upper mantle 
structure from Love waves, J. Geophys. Res., 
68, 3483-3500, 1963. 
Anderson, 0. L., E. Schreiber, R. C. Liebermann, 
and N. Soga, Some elastic constant data on 
minerals relevant to geophysics, Rev. Geophys., 
6, 491-524, 1969. 
Archambeau, C. B., E. A. Flinn, and D. G. Lam-
bert, Fine structure of the upper mantle, (in 
press) 1969. 
Doyle, H. A., and A. L. Hales, An analysis of the 
travel times of S waves to North American sta-
tions in the distance range 28• to 82°, Bull. 
Seism. Soc. Am., 57, 761-772, 1967. 
Fairbairn, H. W., Packing in ionic minerals, Bull. 
Geol. Soc. Am., 54, 1305-1374, 1943. 
Green, R. W. E., and A. L. Hales, The travel 
times of P waves to 30° in the central United 
States and upper mantle structure, Bull. Seism. 
Soc. Am., 58, 267, 1968. 
Ibrahim, A. K., and 0. W. Nuttli, Travel-time 
curves and upper mantle structure from long-
period S waves, Bull. Scism. Soc. Am., 57, 1063-
1092, 1967. 
Johnson, L. R., Array measurements of P veloci-
ties in the upper mantle, J. Geophys. Res., 72, 
6309-6325, 1967. 
Julian, B. R., and Don L. Anderson, Travel times, 
apparent velocities and amplitudes of body 
waves, Bull. Seism. Soc. Am., 58(1), 339-366, 
1968. 
Kanamori, H., Upper mantle structure from ap-
parent velocities of P waves recorded at vVak-
ayomo Micro-Earthquake Observatory, Bull. 
Earthquake Res. lnst., Tokyo Univ., 45, 657-
678, 1967. 
Lewis. B. T. R., and R. B. Meyer, A seismic in-
vestigation of the upper mantle to the west of 
Lake Superior, Bull. Seism. Soc. Am., 58, 565-
596, 1968. 
Niazi, M., and Don L. Anderson, Upper mantle 
structure of western North America from ap-
parent velocities of P waves, J. Geophys. Res., 
70, 4633-4640, 1965. 
(Received February 17, 1969; 
revised March 12, 1969.) 


Shear Velocities and Elastic Parameters of the Mantle

Jut;RNAL OF GEOPHYSICAL HESL\RCH VoL. 7-1, No. 15, 1%') 
Shear Velocities and Elastic Parameters of the Mantle I 
DoN L. ANDI<JRsox 
,_"JczsJ~nnlnr:ru~''' Laboratory, 
Pasadcnrr, 
BRUCE H. JULIAN 
Institnte of Technology 
'n/\iln·•·n·Jrt DJJOD 
?'he r:ecen~ :-hear >vaye tra:·ei-tinw (lata of Ibrahim and Nuttli (1967) and Doyle and Hales 
(196:) I;:< remtcr:r:m~ted to :ncld a structure that is eompatible with Johnson's 
(1961) cm:1presswnal-n~locit~· structure. The parame1N;:< <P. K/ fl, and cr an: cal('ulated 
as a funehon of depth. All three parameters increase 1vith depth in the regions 
of the mantle but only <P increases through the tnmsi!ion regions. Poisson's is anoa1·entlv 
less for !he elose-pa~ked mantle phases than it is for the normal phases of 
ma1_1tlc. The thco.ret~cal that dfl/dP become;,; ncgatiYe before a phase 
venfied by the sc1smrc data. 
lKTRODUCTIOX 
J\Iuch effort has been spent m the last few 
years in the collection and of compres-
sional velocity data and in the inversion of this 
data to obtain compressional structures. 
The travel apparent velocity, and ampli-
tude curves have been found to be Yerv com-
plicated out to about 40°, and thry [~re ob-
the result of more than one branch 
involved. The complications are caused 
of abnormally high-velocity gradients in 
he upper mantle and Anderson, 1965; 
Johnson, 1967; Kanamori, 1967; Julian and 
1968; Green and 1968; Leu·is 
and 111 eyer, 1968; and Archambeau et HJ69] 
That had previously been found surface \vave 
studies [Anderson and Toksoz, 1963]. A de-
tailed of these high UAinn,i-n 
ents in terms of phase 
Andersm1 
The 
that of Ibrahim 
for S waYes 
[1967]. 
ll1 
the shear 
they determined travel-time cnn·es out 
to about 50° for focal of 33 and 120 
km. The travel time curves were similar in their 
to the P travel-time curves. ::\Iuch 
of their data \vas to \Yestern North 
Contribution No. 1615, Division of uc:OH)grcal 
•::Jclertces. California Institute of Technology, 
adena. 
Copyright © 1969 by the American Geophysical Union. 
a studied l{iazi 
awl Anderson I1DG5], Johnson [1967], Julian 
and Anderson [1968], and Archambeau et al. 
[H169] \Yith P waws. Ibrahim and Nuttli 
[19(:)7] determined a shear structure 
that gave Yer~· good agreement \Yith their data 
for both foc,tl Although their model was 
in gross agreement with the recent P structnres 
in that it h:Hl a urlper mantle lmv-
velocity zone and discontinuities near 400 and 
700 km, it differed in some details. 
The main differences in the models are the 
to the zone and to the dis-
continuity between GOO nnd 7:30 km. An interest-
ing fe,lture of their model was the existence of 
regions of con~tant Fn,~n,'-'· 
In another notnble recent pa11er, Doyle and 
Ilales /10(17] determined a new 
tranl-timc cnrve between about 28 and 80°. 
These papers are in that 
a refined travel-time curve for S waves 
and proYide the of 
estimates of the Yariation of shear n"l~n'+'· 
de11th in the mantle. apart 
in its own this lYYlr\l"r"r"n'""d· 
e~sential in free oscillation 
the shear is the dominant parameter 
for most of the modes of free oscillation. If this 
parameter can be determined independently 
with good and the 
free oscillation data can be used to determine 
the distribution in the earth. In addition 
the data can be combined vvith 
the data in order to 
3281 
3282 ANDERSON AND JULIAN 
180 
-(.) ISO us Cl.> 
(/) 
(.) 
Cl.> 
120 (/) 
' E 
.X: 
ro --l!) 
90 
' <J 
I 
1--
60 
• 
3010 40 
!::., deg. 
Fig. 1. Reduced travel-time curve for shear waves from shallow focus earthquakes. Depth 
of focus, 33 km. Data: open circle, Doyle and Hales [1967]; solid dot, Ibrahim and Nuttli 
[1967]. 
determine the depth variation of such impor-
tant parameters as the seismic parameter cf> and 
and Poisson's ratio a. These quantities are in-
volved in the interpretation of seismic data in 
terms of composition and petrology of the 
various regions of the mantle. 
It is the purpose of this paper to invert this 
data in such a way that the resulting shear-
velocity profile is similar to recent compres-
sional velocity profiles that are based on a much 
larger body of data. By 'similar' we mean that 
such features as low-velocity zones and transi-
tion regions should occur at roughly the same 
depth in both profiles. These compatible profiles 
can then be combined to yield the other param-
eters noted above. In addition the degree of 
non-uniqueness of the structures resulting from 
the inversion of this kind of data is clearly 
demonstrated. Lateral variations are still a 
problem in all studies of this type, and studies 
in different regions are clearly desirable. 
DATA 
The raw data of Ibrahim and Nuttli [1967] 
were used and were independently corrected to 
either 33 km or 120 km, depending on whether 
the earthquake was shallow or intermediate. 
The first arrival data beyond 28° was taken 
from Doyle and Hales [1967] and was corrected 
to 33 km by taking their tabulated J-B resi-
duals and applying the correction to the J-B 
tables. Figure 1 shows that the two sets of data 
are compatible although the scatter is substan-
tial. 
ANALYSIS AND RESULTS 
The inversion was accomplished by trial and 
error using the travel-time program TVT3 de-
scribed by Julian and Anderson [1968]. John-
son's [1967] P-wave model CIT204 was used as 
a guide, and we attempted to have the locations 
and thicknesses of the low-velocity zone and 
the transition regions be the same as in this 
model. 
Figures 1, 2, and 3 show the fit of the Ibrahim-
Nuttli model and our model, US26. Both models 
fit the data out to 40° about equally well. 
The models are shown in Figure 4. By intro-
ducing negative gradients for shear waves where 
Ibrahim and Nuttli [1967] had constant ve-
0 
(]) 
(/) 
0 
(]) 
(/) 
' E 
~ 
a:> 
l{) 
' <l 
I 
r-
BRIEF REPORTS 3283 
150 
120 
90 
60 
30 
• ----= . ----!_. 
~~~~~~~~~~~c=-~-Jl~-~-~~~--~;--~~-·- ~. ~~~ 
""' o;ttractecT --
THEORETICAL CURVES 
IBRAHIM 8 NUTTLI 
us 26 
20 
!J., deg. 
30 
Fig. 2. Reduced travel-time curve for shear waves from intermediate focus earthquakes. 
270 
u 260 
Q) 
(/) 
u 250 Q) 
(/) 
' E 
..:.:: 
co 240 
' <J 
I 
1-
230 
Depth of focus, 120 km; data from Ibrahim and Nuttli [1967]. 
" " " 
THEORETICAL CURVES 
IBRAHIM 
us 26 
B NU TTL I 
60 
de g. 
" '\. '\ 
'\ 
\ 
\ 
\ 
\ 
Fig. 3. Reduced travel-time curve for shear waves between 25° and 80°. Depth of focus, 33 
km; data from Doyle and Hales [1967]. 
40 
3284 ANDERtiON AND JULIAN 
Fig. 4. ~hear nloeity model of Ibrahim and 
Nuttli [1967] and present work and compress-
ional velocity model of Johnson [1967]. 
locity gradients, it has been possible to find a 
model that is nearly compatible with the com-
pressional velocity model. As expected from the 
natbre of travel-time data the two shear-
Yelocity solutions oscillate about each other. The 
large negatiYe gradient between 500 and 650 km 
in 1JS26 prevents any ray from bottoming in 
this region; the corresponding braneh of the 
travel-time curve for this model therefore rep-
resents diffracted energy (see Figures 1 and 2). 
The negative velocity gradients above 400 km 
can easily be explained by a modest C--5°C/km) 
temperature gradient that, for shear waves, 
cancels out the effect of presmre in increasing 
the velocity. The large negative gradient be-
tween 500 and 650 km, however, requires that 
the material in this region, presumably mainly 
olivine in the spinel strueture, have a low 
(ilVs/ilP)T or a high (ilVs/ilT)P or both. There 
is, of course, a large uncertainty in the actual 
gradient. 
TABLE 1. Velocities and Elastic Parameters as Function of Depth 
Depth, Vs,, * Vs,,* Vp,** iP,, ()?2, 
km km/sec km/sec km/sec (km/sec)2 (km/sec)2 (K/11l1 
35 4.60 4.60 7.85 33.4 33.4 1.38 
50 4.60 4.59 7.87 3:3.7 33.8 1.59 
6.5 4.60 4.59 7.70 (31.1) (31. 2) (1.47) 
80 4.60 4.40 7.60 (29 .5) 31.9 (1.40) 
100 4.60 4.40 7.61 (29.7) 32.1 (1.40) 
125 4.60 4.40 7.70 (:31.1) (:3:3 .5) (1.47) 
150 4.5:3 4.55 7.93 (3i).5) (35.3) (I.n) 
180 4.00 4.60 8.30 (47 .6) 40.7 (2.97) 
200 4.60 4.64 8.:31 (40.8) (40.3) (1. 93) 
2.50 4.65 4.60 8.42 42.1 42.7 1.94 
300 4.65 4.58 8 . .54 (44.1) 4.5.0 (2. 04) 
350 4.57 4 . .55 8.67 (47 .3) (47.6) (2.27) 
400 5.13 4.90 9.:30 51.4 (54.5) 1. 93 
450 5.30 5.:39 9.6:) 55.3 54.0 1.97 
500 5.37 5.44 9.75 .56.6 5.5.6 1.96 
550 5.:37 5.29 9.84 (58.4) 59 . .5 (2.02) 
600 5.37 5.15 9.95 (60.5) (63.6) (2.10) 
650 5.:37 5.00 10.55 (72.8) (78. 7) (2. 53) 
700 5.33 5.75 10.95 (82.0) (75. 8) (2.89) 
750 6.14 6.2:3 11.0:3 71.4 (69.9) 1.89 
800 6.38 6.30 11.11 69.2 70.5 1.70 
900 6.38 6.33 11.30 (73 .4) 74.3 (1.80) 
1000 6.40 6.38 11.47 76.9 77.:3 1.88 
1200 6.49 6.51 11.80 83.1 82.7 1.97 
1400 6.60 6.6:3 12.08 87.8 87.3 2.02 
1600 6.68 6.74 12.34 92.8 91.7 2.09 
1800 6.73 6.8:3 12.55 97.1 95.3 2.14 
*Subscript 1 refers to Ibrahim and Nuttli structure; subscript 2 is US26. 
** CIT204 [Johnson, 1967]. 
(K/p)z <T! "' 
1. ;)8 0.2:)8 0.238 
1.61 0.240 0.242 
(1.48) (0.222) (0.224) 
1.6.5 (0.211) 0.248 
1.66 (0.212) 0.249 
(1. 73) (0.222) (0.258) 
(1. 70) (0.258) (0. 255) 
1. 92 (0.349) 0.278 
(1. 87) (0. 279) (0.273) 
2.02 0.281 0.287 
2.14 (0.289) 0.298 
(2 .30) (0.:308) (0.310) 
(2. 27) 0.281 (0.308) 
1.86 0.28:3 0.272 
1.88 0.282 0.274 
2.13 (0.288) 0.297 
(2 .40) (0. 294) (0.317) 
(3 .12) (0.:325) (0.355) 
(2.29) (0.345) (0.310) 
(1.80) 0.275 (0.266) 
1. 78 0.254 0.263 
1.85 (0.266) 0.271 
1.90 0.274 0.276 
1.95 0.283 0.281 
1.99 0.287 0.284 
2.02 0.293 0.287 
2.04 0.298 0.290 
BRIEF REPORTS 3285 
The shear-velocity structures obtained by 
Ibrahim and Nuttli [1967] and reported in this 
paper are tabulated in columns 2 and 3 of Table 
1. These are combined with Johnson's model 
CIT204 (column 4) to obtain the elastic param-
eters in the remaining columns. No attempt has 
been made to smooth the results. Values in 
parentheses are in transition regions or repre-
sent regions where the shear velocity model i8 
incompatible with the compressional velocit~· 
model. If these values are ignored, there is a 
relati;-ely uniform increase of rp with depth a8 
>:hown in Figure 5, except for the low-wlocity 
zone that has a lower ·¢ than the adjacent re-
gions of the mantle. K/i-t and cr increase rather 
uniformly with depth to at least 300 km. The 
values for these parameters are less in the 
region between the major discontinuities, i.e. 
the 'spinel' section of the mantle, than at 30J 
km, but increase with depth in this region. 
These values drop again in going through the 
()50-lnn phase change and increase relatively 
~lowly thereafter. The general tendency is for 
the Poisson's ratio to increase with depth in rela-
tively homogeneous regions of the mantle. This 
increase is to be expected since both tempera-
ture and pressure increase Poisson's ratio. The 
¢, (km/sec)
2 
0 
GUTENBERG 
Fig. 5. Seismic parameter if> versus depth in 
the homogeneous regions of 1JS26 compared with 
the Gutenberg model. 
TABLE 2. Properties of Simple Oxides 
Substance Coordination (M) Po P.I. 0"1 
BeO 4-4 1') c ~.;; 3.00 7.2 .205 
ZnO 4-4 40.7 5.62 5.3 .357 
AlzO" 6-4 20.4 3.97 7.2 .236 
Fe,o, 6-4 31.9 5.25 6.6 .308 
:VI gO 6-6 20.2 3.58 6.3 .182 
CaO 6-6 28.0 3.29 5.3 .210 
I Anderson et al. [1969] 
drop in Poioson's ratio upon passing through 
the transition regions was unexpected. There 
is not enough ultrasonic data available to say 
v;hether this effect is due to composition or 
cry8tal structure. Since most of the increase of 
velocity through the transition regions is due 
to phase changes, most of the drop in Poisson's 
ratio is probably clue to change in crystal struc-
tnre. If this probability is tru8, one would pre-
dict cr1 (olivine) > a" (spinel) > cr3 (post-
spinel), or dcr1/ clZ > da"/ dZ > da3/ dZ, or both. 
Table 2 gives Poisson's ratio for 6 simple 
oxides. (111) is the mean atomic weight, Po is the 
zero-pressure density, and P.I. is the packing 
index of Fairbairn [1963], a measure of how 
effectively the ions are packed into a unit cell. 
For a given coordination Poisson's ratio de-
crra~es as the packing index increases. For a 
given mean atomic weight Poisson's ratio de-
creases as the coordination increases. For the 
olivine-spinel phase change there is an increase 
iu flacking index with no change in coordination 
while for the spinel-post-spinel phase change 
there is an increase in both the packing index 
and the coordination. The seismic data seems 
consistent, therefore, with the limited amount of 
]Jertincnt ultrasonic data. 
Note added in proof: G. Barsch and 0. L. 
~~nderson (personal communicn.tions) have sug-
gested that a negative dp/dP implies an un-
stable crystal lattice. It follows that the shear 
Yelocity should decrease vvith depth above each 
~hangc in the enrth's mantle. This is consistent 
1vith the interpretations given here and by 
Ibrahim and N uttli [1967]. 
Acknowledgments. This re8earch was sup-
ported b~· the Advanced Research Projects 
Agency of the Department of Defens" and was 
monitored by the Air Force Office of Scientific 
3286 ANDERSON AND JULIAN 
Research under. Contract No: F44620-69-C-0067 
and National Science FoundatiOn grant GA 1003. 
We would like to thank A. Ibrahim, 0. Nuttli, 
A. Hales and H. Doyle for advance copies of their 
manuscripts. 
REFERENCES 
Anderson, Don L., Phase changes in the upper 
mantle, Science, 157, 1165-1173, 1967. 
Anderson, Don L., and M. N. Toksoz, Surface 
waves on a spherical Earth, 1, Upper mantle 
structure from Love waves, J. Geophys. Res., 
68, 3483-3500, 1963. 
Anderson, 0. L., E. Schreiber, R. C. Liebermann, 
and N. Soga, Some elastic constant data on 
minerals relevant to geophysics, Rev. Geophys., 
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Archambeau, C. B., E. A. Flinn, and D. G. Lam-
bert, Fine structure of the upper mantle, (in 
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Doyle, H. A., and A. L. Hales, An analysis of the 
travel times of S waves to North American sta-
tions in the distance range 28• to 82°, Bull. 
Seism. Soc. Am., 57, 761-772, 1967. 
Fairbairn, H. W., Packing in ionic minerals, Bull. 
Geol. Soc. Am., 54, 1305-1374, 1943. 
Green, R. W. E., and A. L. Hales, The travel 
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Johnson, L. R., Array measurements of P veloci-
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6309-6325, 1967. 
Julian, B. R., and Don L. Anderson, Travel times, 
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waves, Bull. Seism. Soc. Am., 58(1), 339-366, 
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Kanamori, H., Upper mantle structure from ap-
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Lewis. B. T. R., and R. B. Meyer, A seismic in-
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(Received February 17, 1969; 
revised March 12, 1969.) 


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Shear Velocities and Elastic Parameters of the Mantle

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