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Is the lower mantle homogeneous?
JOURNAL OF GEODYNAM1CS 1, 3--9 (1984)
3
IS THE LOWER MANTLE H O M O G E N E O U S ?
A. L. HALES
Research School of Earth Sciences, Australian National University. Canberra, Australia (Received August 17, 1983; accepted August 31, 1983)
ABSTRACT Hales, A. L., 1984. Is the lower mantle homogeneous? Journal of Geodynamics, l: 3-9. Comparison of some array dt/dzl studies with the global travel times of Dziewonski and Anderson (1983) leads to the conclusion that a discontinuity in the P travel times between 80 ° and 85 ° is consistent with both sets of data. This discontinuity in dt/dA corresponds to an increase in velocity of about 0.1 km/sec between depths of 2400 and 2600 km. Models of the P velocity distribution which match the Dziewonski and Anderson travel times reasonable well have the shadow zone for short period "diffracted" P beginning at about 110 ° arc distance.
The early array dt/dA studies by Niazi and Anderson (1965) Johnson (1967 and 1969), Chinnery (1969), Corbishley (1970) and Vinnik and Nikolayev (1970) were interpreted consistently in terms of discontinuities in dt/dA between 24 ° and 100 ° and therefore as indicating the existence of discontinuities in the velocity in the lower mantly. On the other hand dt/dA's derived from global travel time analyses show that dt/dA varies almost linearly with A from about 40 ° to 90 ° arc distance (Hales and Herrin, 1972). More recent array studies of dt/dA (Wright and Cleary, 1972; Wright, 1973; Datt and Muirhead, 1977; Wright and Lyons, 1981)are consistent with the earlier array studies in showing that there are discontinuities in dt/dA beyond the onset at 24 ° which corresponds to the discontinuity in velocity at a depth of about 650 kin. Furthermore, the travel times determined from long profiles in Australia have been shown by Muirhead and Hales (1980) to correspond more closely to straight line segments terminated by discontinuities in dt/dA than to smooth travel times such as those of the Herrin (1968) travel time tables. It must, of course, be recognised that if dt/dA is constant the amplitudes calculated on geometrical ray theory, which have a term Id2t/dA21j/z, would be zero, and this is unrealistic. The Muirhead and Hales (1980) results, and a similar interpretation of travel times in terms of straight line segments by Evernden and Clark (1970) must therefore be inter0264-3707/84/$3.00
,c: 1984 Geophysical Press Ltd.
4
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preted as meaning that d2t/dA 2 is significantly less than the average value of about 0.07 sec deg 2 from 40 ° to 90 ° given by the global travel time studies. If travel times which are quadratic are fitted by a straight line the maximum deviations are 0.44, 0.28 and 0.19 sec. for 10° segments if Id2t/dA 2 ]= 0 . 0 7 . 0.05 and 0.03 respectively. Deviations such as these would be masked by reading errors in analyses such as those of Evernden and Clark (1970). In the long profile studies such as those of Muirhead and Hales (1980) the curvature would not be detected if]d2t/dA 2] were less than 0.02 and the effect on the amplitudes which are proportional to [d2t/dA 211/2 would not be significant. The most recent analysis of global travel times by Dziewonski and Anderson (1983) was based on two independent sets of data: Class I for events away from subduction zones, Class II for events near subduction zones. The analysis included determination of station corrections and tentative relocation of epicenters. Dziewonski and Anderson report their observations as means for 1° cells, dt/dA's calculated by differencing the 1° cell means are shown in Fig. I for both sets of data. Fig. I illustrates even more clearly than earlier global travel time studies the change in the character of the dt/dA to A relation at 90 ° arc distance. This change has been associated with the existence of a thermal boundary at the base of the mantle, or with changing composition in that region (Jones, 1977; Jeanloz and Richter, 1979: Doornbos and Mondt, 1979a and 1979b; Doornbos, 1983). Dziewonski and Anderson (1983) remark that "In view of the effect that station corrections had on both curves it would be difficult to defend an argument in favour of major, global scale discontinuities in the lower mantle between a depth of some 800 km and the top of the D" layer. The residual roughness of these curves seems to be uncorrelated". Fig. 1 shows, however, that the uniform behaviour of dt/dA with respect to A does not begin until about 40 °. The changes between 30 ° and 40 ° correspond to the second order discontinuity in the velocity at a depth of 771 km in the PREM model of Dziewonski and Anderson (1981). They could equally well be accounted for in terms of discontinuities as Muirhead and Hales (1980) suggest. There is an indication also that the uniform behaviour of dt/dA with respect to A may end between 80 ° and 85 ° arc distance. Similar roughness patterns occur in both sets of data at some points between 40 ° and 85 °. These patterns are of the order of the overall roughness so that, as Dziewonski and Anderson (1983) suggest, more detailed studies will be required for the detection of discontinuities in dt/dA between 40 ° and 85 ° with reasonable certainty. It is possible that lateral heterogeneity of the upper mantle, and possibly lateral variations in the depths to the discontinuities, could account for some of the difficulty in recognising the discontinuity in global travel time analyses, and for the inconsistencies in different array studies of dt/dA. In 1972 David Brown, a student at the University of Texas at Dallas, made
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ARC DISTANCE(deg) Fig. 1. Plots of dt/dA found by differencing the 1° cell roans of D z i e w o n s k i and Anderson (I 983). In the top portion of the figure the Class II dt/dA's have been increased by 0.1 sec/deg to facilitate comparison. In the lower figure the dt/dA's are plotted as dt/dA -(11.06 0.07A).
a careful comparison of the various array dt/dA studies and concluded that the only discontinuities for which the dt/dA's of different authors were sufficiently consistent that a discontinuity could be established with reasonable certainty was that between 80 ° and 85 ° . Brown concluded that this would correspond to a step increase in velocity at a depth of 2460 km. A comparison of some of the dt/dA data is shown in Fig. 2. The data plotted are: (1) the smoothed dt/dA given by Dziewonski and Anderson (1983) for Class I events. (2) the dt/dd calculated from the observed Class II cell means of Dziewonski and Anderson from 25 ° to 45 ° and from 77 ° to 100 °. (3) the straight line segment of Evernden and Clark (1970) from 24 ° to 35 °. (4) the dt/dA's at the mid-points of the other Everden and Clark (1970) segments. (5) the Johnson (1969) data (6) the 1° means of the Corbishley (1970) data. (7) the Vinnik and Nikolayev (1970) data after Fourier series analysis. Fig. 2 shows clearly that all the dt/dA array studies and the Class II data indicate a moderately sharp decrease in dt/dA between 80 ° and 85 °.
6
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Preliminary calculations showed that it was possible to fit the dt/dA data of Fig. 2 by minor modificatins of the Herrin (1968) and PREM (Dziewonski and Anderson, 1981) P velocity distributions with a velocity increase of 0.10 km/sec between depths of 2400 and 2600 km. The dt/dA's corresponding to one such model, Model A, are shown in fig. 2. The model is shown in Fig. 3. Also shown in Fig. 3 are the deviations of the calculated times for this model from the smoothed times for Class II events of Dziewonski and Anderson (1983). The deviations of the Class I observed cell means from the smoothed Class II times are shown for comparison. The largest deviations of the model A times from the smoothed Class II times occur between 86 ° and 89 ° and are less than 0.21 sec. A second model B for which the calculated times deviate even less from the observed times was constructed by reducing the velocity gradient of Model A between depths of 2471 and 2646 km and introducing a 0.05km/sec step increase in velocity at 2646km. This corresponds to a discontinuity in dt/dA at about 88 ° as suggested by Wright and Cleary (1972) and Wright and Lyons (1981). A third model, Model C, was developed to correspond to the most extreme interpretation of the data of Fig. 2. The dt/dA's for this model are shown on Fig. 2. The increase in velocity is 0.2 km/sec at a depth of 2431 km. In order to make possible so large an increase in velocity, it was necessary to reduce the PREM velocities progressively below a depth of 1671 km. Then departures of the calculated times from the Class II smoothed times are shown in Fig. 3.
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Fig. 3. Top Figure. Deviations of the calculated times for Models A, B a n d C from the smoothed times of Dziewonski and Anderson (1983) for Class lI events. Also plotted are the deviations of the C l a s s l cell means from the smoothed Class II times. Lower Figure. The velocity models A. C compared with the PREM model.
These departures are unacceptably large unless the analysis of global travel times introduces more smoothing than I consider likely. The standard deviations of the 1° cell observations of Dziewonski and Anderson (1983) are of order of 1.2 sec with from 1750 to 8000 observations per cell for Class II events. It might be expected therefore that the standard errors of the means would be less than 0.03 sec over the distance range from 25 ° to 100 °. However the scatter of the data of Fig. 2 shows a larger range. It is probable that the variance between events is larger than other sources of error. The discussion thus far has concentrated on arc distances between 80 ° and 90 °. It does not seem likely that step discontinuities of more than 0.05 km/sec could be introduced between depths of 1000 km (corresponding to 40 ° arc distance) and 2400 km without unacceptable departures from the global travel times. On the other hand discontinuities of 0.05 km/sec or less cannot be excluded on the basis of these data. It should be recognised that the existence, or non-existence, of discontinuities in the velocity in the lower mantle is not merely a matter of seismological nicety, but has considerable significance in discussions of the composition of the Earth and the processes which have shaped it. For example if there are discontinuities in the lower mantle then the value of dK/dP, K being the incompressibility and P the pressure, between
8
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discontinuities would be reduced significantly and thus the Ko's estimated using Murnaghan's equation, or any similar equation, increased. The existence or non-existence, of discontinuities in the lower mantle is also significant in discussions of mantle convection. Lay and Helmberger (1983) inferred from a study of S H records that there is a discontinuity in the S H travel times at 83 ° and that this corresponded to an increase in the S velocity of 2.75 ± 0.25 % at a depth of about 2600 kin. A 2.75 + 0.25 % increase in the P velocity would amount to 0.33 to 0.40 km/sec. It does not appear that an increase in P velocity of this order would be consistent with the Dziewonski and Anderson travel times. Recently Jeanloz and Ahrens (1980) have interpreted shock wave data on Fe0 in terms of a phase transformation to a denser phase at a pressure of 70 GPa. This would correspond to a depth within the Earth of about 1800 kin. However the discussion by McCammon, Ringwood and Jackson (1983) suggests that, at the temperatures prevailing in the Earth, the transformation would occur at a depth between 2400 and 2500 km (see their Fig. 3). The decrease in velocity at a depth of about 2800 km is not required to fit the travel time data although the calculated times are consistent with the observations. Similar distributions occur in the models of Wright and Cleary (1972) and Doornbos (1983). The reduction in velocity has the consequence that the shadow zone for short period P does not begin until about 110 °. The bottoming depths for 1 sec period waves lie more than two wavelengths above the core-mantle boundary for these models up to a distance of about 107 °. Thus the onset times of the short period P phases would not be affected by the boundary at lesser distances. Diffracted P would only begin at about 110 °, a possibility discussed by Clearly (1974). ACKNOWLEDGEMENTS
A first draft of this paper was written while I was a visitor at the Institute for the Study of Earth and Man, Southern Methodist University. My thanks are due to Dr J. E. Brooks, President of the Institute and the staff of the Institute and the Department of Geological Sciences for the help they gave me while I was ar S.M.U. I thank also my colleagues at A.N.U., especially K. J. Muirhead, C. Wright and Ian Jackson, for much helpful discussion, and A. M. Dziewonski, D. L. Anderson, T. Lay and D. Helmberger for preprints.
REFERENCES Chinnery, M. A., 1969. Velocity anomalies in the lower mantle. Phys. Earth Planet. Inter., 2 : 2 Cleary, J. R., I974. The D" region. Phys. Earth Planet. Interiors, 9: 13-27.
10.
IS THE L O W E R M A N T L E H O M O G E N E O U S ?
9
Corbishly, D. J., 1970. Multiple array measurements of the P-wave travel-time derivative. Geophys. J. Roy. Astron. Soc., 19: 1-14. Dart, R. and Muirhead, K. J., 1977. Evidence for multiplicity in the P travel-time curve beyond 30 °. Phys. Earth Planet. Onter., 1 5 : 2 8 38. Doornbos, D. J., 1983. Present seismic evidence for a boundary layer at the base of the mantle. J. Geophys. Res., 8 8 : 3 4 9 8 3505. Doornbos, D. J. and Mondt, J. C., 1979a. Attenuation of P and S waves diffracted round the core. Geophys. J.R. Astron. Soc., 5 7 : 3 5 3 379. Doornbos, D. J. and Mondt, J. C., 1979b. P and S waves diffracted round the core and the velocity structure at the base of the mantle. Geophys. J. R. Astron. Soc., 57: 381-395. Dziewonski, A. M. and Anderson, D. L., 1981. Preliminary reference earth model (PREM). Phys. Earth Planet. Inter., 35: 297-356. Dziewonski, A. M. and Anderson, D. L., 1983. Travel times and station corrections for P waves at teleseismic distances. J. Geophys. Res., 8 4 : 3 2 9 5 - 3 3 1 4 . Evernden. J. F. and Clark, D. M.. 1970. Study of teleseismic P 1 travel-time data. Phys. Earth Planet. Interiors, 4 : 1 23. Hales, A. L. and Herrin, E., 1972. Travel times of seismic waves, Chapter 8 in The Nature of the Solid Earth ed. E. C. Robertson, McGraw-Hill, New York. Herrin, E.. 1968. 1968 seismological tables for P phases. Bull. Seism. Soc. Am., 5 8 : 1 1 9 3 1241. Jeanloz, R. and Ahrens, T., 1980. Equations of state of Fe0 and Ca0. Geophys. J.R. astr. Soc., 62: 505 528. Jeanloz, R. and Richter, F. M., 1979. Convection, composition and the thermal state of the lower mantle. J. Geophys. Ref., 8 4 : 5 4 9 7 5504. Johnson, J. R., 1967. Array measurements of P velocities in the upper mantle. J. Geophys. Res., 72: 5309-6325. Johnson, L. R., 1969. Array measurements of P velocities in the lower mantle. Bull. Seism. Soc. Amer.. 5 9 : 9 7 3 1008. Jones, G. M., 1977. Thermal interaction of the core and the mantle and long term behavior of the geomagnetic field. J. Geophys. Res., 8 2 : 1 7 0 3 1709. Lay. T. and Helmberger, D. V., 1983. A lower mantle S wave triplication and the shear velocity structure of D". Submitted for publication. M c C a m m o n , C. A., Ringwood, A. E. and Jackson, I., 1983. Thermodynamics of the system Fe Fe0 Mg0 at high pressure and temperature and a model for formation of the Earth's core. Geophys. J.R. astr. Soc., 7 2 : 5 7 7 595. Muirhead, K. J. and Hales, A. L., 1980. Evidence for P wave velocity discontinuities at depths greater than 650 km in the mantle. Phys. Earth Planet Interiors, 2 3 : 3 0 4 313. Niazi, M. and Anderson. D. L., 1965. Upper mantle structure of western North America from apparent velocities of P waves. J. Geophys. Res., 70: 4633-4640. Vinnik, L. P. and Nikolayev, A. V., 1970. The velocity profile of the lower mantle from direct measurement of dt/dA. Izv. Akad. Nauk SSSR Fiz. Zemli, 11 : 699-708. Wright, C., 1973. Array studies of the P phases and the structure of the D" region of the mantle. J. Geophys. Res., 78: 4 9 6 5 4 9 8 2 . Wright, C. and Cleary, J. R., 1972. P wave travel time gradient measurements at the Warramunga seismic array and lower mantle structure. Phys. Earth Planet Interiors, 5 : 2 1 3 230. Wright, C. and Lyons, J. A., 1981. Further evidence for radial velocity anomalies in the lower mantle. Pure Appl. Geophys., 119:137 162.
3
IS THE LOWER MANTLE H O M O G E N E O U S ?
A. L. HALES
Research School of Earth Sciences, Australian National University. Canberra, Australia (Received August 17, 1983; accepted August 31, 1983)
ABSTRACT Hales, A. L., 1984. Is the lower mantle homogeneous? Journal of Geodynamics, l: 3-9. Comparison of some array dt/dzl studies with the global travel times of Dziewonski and Anderson (1983) leads to the conclusion that a discontinuity in the P travel times between 80 ° and 85 ° is consistent with both sets of data. This discontinuity in dt/dA corresponds to an increase in velocity of about 0.1 km/sec between depths of 2400 and 2600 km. Models of the P velocity distribution which match the Dziewonski and Anderson travel times reasonable well have the shadow zone for short period "diffracted" P beginning at about 110 ° arc distance.
The early array dt/dA studies by Niazi and Anderson (1965) Johnson (1967 and 1969), Chinnery (1969), Corbishley (1970) and Vinnik and Nikolayev (1970) were interpreted consistently in terms of discontinuities in dt/dA between 24 ° and 100 ° and therefore as indicating the existence of discontinuities in the velocity in the lower mantly. On the other hand dt/dA's derived from global travel time analyses show that dt/dA varies almost linearly with A from about 40 ° to 90 ° arc distance (Hales and Herrin, 1972). More recent array studies of dt/dA (Wright and Cleary, 1972; Wright, 1973; Datt and Muirhead, 1977; Wright and Lyons, 1981)are consistent with the earlier array studies in showing that there are discontinuities in dt/dA beyond the onset at 24 ° which corresponds to the discontinuity in velocity at a depth of about 650 kin. Furthermore, the travel times determined from long profiles in Australia have been shown by Muirhead and Hales (1980) to correspond more closely to straight line segments terminated by discontinuities in dt/dA than to smooth travel times such as those of the Herrin (1968) travel time tables. It must, of course, be recognised that if dt/dA is constant the amplitudes calculated on geometrical ray theory, which have a term Id2t/dA21j/z, would be zero, and this is unrealistic. The Muirhead and Hales (1980) results, and a similar interpretation of travel times in terms of straight line segments by Evernden and Clark (1970) must therefore be inter0264-3707/84/$3.00
,c: 1984 Geophysical Press Ltd.
4
HALES
preted as meaning that d2t/dA 2 is significantly less than the average value of about 0.07 sec deg 2 from 40 ° to 90 ° given by the global travel time studies. If travel times which are quadratic are fitted by a straight line the maximum deviations are 0.44, 0.28 and 0.19 sec. for 10° segments if Id2t/dA 2 ]= 0 . 0 7 . 0.05 and 0.03 respectively. Deviations such as these would be masked by reading errors in analyses such as those of Evernden and Clark (1970). In the long profile studies such as those of Muirhead and Hales (1980) the curvature would not be detected if]d2t/dA 2] were less than 0.02 and the effect on the amplitudes which are proportional to [d2t/dA 211/2 would not be significant. The most recent analysis of global travel times by Dziewonski and Anderson (1983) was based on two independent sets of data: Class I for events away from subduction zones, Class II for events near subduction zones. The analysis included determination of station corrections and tentative relocation of epicenters. Dziewonski and Anderson report their observations as means for 1° cells, dt/dA's calculated by differencing the 1° cell means are shown in Fig. I for both sets of data. Fig. I illustrates even more clearly than earlier global travel time studies the change in the character of the dt/dA to A relation at 90 ° arc distance. This change has been associated with the existence of a thermal boundary at the base of the mantle, or with changing composition in that region (Jones, 1977; Jeanloz and Richter, 1979: Doornbos and Mondt, 1979a and 1979b; Doornbos, 1983). Dziewonski and Anderson (1983) remark that "In view of the effect that station corrections had on both curves it would be difficult to defend an argument in favour of major, global scale discontinuities in the lower mantle between a depth of some 800 km and the top of the D" layer. The residual roughness of these curves seems to be uncorrelated". Fig. 1 shows, however, that the uniform behaviour of dt/dA with respect to A does not begin until about 40 °. The changes between 30 ° and 40 ° correspond to the second order discontinuity in the velocity at a depth of 771 km in the PREM model of Dziewonski and Anderson (1981). They could equally well be accounted for in terms of discontinuities as Muirhead and Hales (1980) suggest. There is an indication also that the uniform behaviour of dt/dA with respect to A may end between 80 ° and 85 ° arc distance. Similar roughness patterns occur in both sets of data at some points between 40 ° and 85 °. These patterns are of the order of the overall roughness so that, as Dziewonski and Anderson (1983) suggest, more detailed studies will be required for the detection of discontinuities in dt/dA between 40 ° and 85 ° with reasonable certainty. It is possible that lateral heterogeneity of the upper mantle, and possibly lateral variations in the depths to the discontinuities, could account for some of the difficulty in recognising the discontinuity in global travel time analyses, and for the inconsistencies in different array studies of dt/dA. In 1972 David Brown, a student at the University of Texas at Dallas, made
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ARC DISTANCE(deg) Fig. 1. Plots of dt/dA found by differencing the 1° cell roans of D z i e w o n s k i and Anderson (I 983). In the top portion of the figure the Class II dt/dA's have been increased by 0.1 sec/deg to facilitate comparison. In the lower figure the dt/dA's are plotted as dt/dA -(11.06 0.07A).
a careful comparison of the various array dt/dA studies and concluded that the only discontinuities for which the dt/dA's of different authors were sufficiently consistent that a discontinuity could be established with reasonable certainty was that between 80 ° and 85 ° . Brown concluded that this would correspond to a step increase in velocity at a depth of 2460 km. A comparison of some of the dt/dA data is shown in Fig. 2. The data plotted are: (1) the smoothed dt/dA given by Dziewonski and Anderson (1983) for Class I events. (2) the dt/dd calculated from the observed Class II cell means of Dziewonski and Anderson from 25 ° to 45 ° and from 77 ° to 100 °. (3) the straight line segment of Evernden and Clark (1970) from 24 ° to 35 °. (4) the dt/dA's at the mid-points of the other Everden and Clark (1970) segments. (5) the Johnson (1969) data (6) the 1° means of the Corbishley (1970) data. (7) the Vinnik and Nikolayev (1970) data after Fourier series analysis. Fig. 2 shows clearly that all the dt/dA array studies and the Class II data indicate a moderately sharp decrease in dt/dA between 80 ° and 85 °.
6
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and Anderson and Anderson
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(1983) smoolhed values for Class l evenls {1983) observed l°celt means
Straight dine segment of Evernden and Clark (1970) d t / d & s at mid points of other IEvernden and Clark (1970) segments Johnson !1969) dat a • 1Gmeans of Corbishley d a t a [~ Vinnlk and NTkolaev ( 1 9 7 0 ) d a l a afler Fourier analys,s :%
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,
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,
L 100
(deg)
details).
Preliminary calculations showed that it was possible to fit the dt/dA data of Fig. 2 by minor modificatins of the Herrin (1968) and PREM (Dziewonski and Anderson, 1981) P velocity distributions with a velocity increase of 0.10 km/sec between depths of 2400 and 2600 km. The dt/dA's corresponding to one such model, Model A, are shown in fig. 2. The model is shown in Fig. 3. Also shown in Fig. 3 are the deviations of the calculated times for this model from the smoothed times for Class II events of Dziewonski and Anderson (1983). The deviations of the Class I observed cell means from the smoothed Class II times are shown for comparison. The largest deviations of the model A times from the smoothed Class II times occur between 86 ° and 89 ° and are less than 0.21 sec. A second model B for which the calculated times deviate even less from the observed times was constructed by reducing the velocity gradient of Model A between depths of 2471 and 2646 km and introducing a 0.05km/sec step increase in velocity at 2646km. This corresponds to a discontinuity in dt/dA at about 88 ° as suggested by Wright and Cleary (1972) and Wright and Lyons (1981). A third model, Model C, was developed to correspond to the most extreme interpretation of the data of Fig. 2. The dt/dA's for this model are shown on Fig. 2. The increase in velocity is 0.2 km/sec at a depth of 2431 km. In order to make possible so large an increase in velocity, it was necessary to reduce the PREM velocities progressively below a depth of 1671 km. Then departures of the calculated times from the Class II smoothed times are shown in Fig. 3.
IS T H E L O W E R
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Fig. 3. Top Figure. Deviations of the calculated times for Models A, B a n d C from the smoothed times of Dziewonski and Anderson (1983) for Class lI events. Also plotted are the deviations of the C l a s s l cell means from the smoothed Class II times. Lower Figure. The velocity models A. C compared with the PREM model.
These departures are unacceptably large unless the analysis of global travel times introduces more smoothing than I consider likely. The standard deviations of the 1° cell observations of Dziewonski and Anderson (1983) are of order of 1.2 sec with from 1750 to 8000 observations per cell for Class II events. It might be expected therefore that the standard errors of the means would be less than 0.03 sec over the distance range from 25 ° to 100 °. However the scatter of the data of Fig. 2 shows a larger range. It is probable that the variance between events is larger than other sources of error. The discussion thus far has concentrated on arc distances between 80 ° and 90 °. It does not seem likely that step discontinuities of more than 0.05 km/sec could be introduced between depths of 1000 km (corresponding to 40 ° arc distance) and 2400 km without unacceptable departures from the global travel times. On the other hand discontinuities of 0.05 km/sec or less cannot be excluded on the basis of these data. It should be recognised that the existence, or non-existence, of discontinuities in the velocity in the lower mantle is not merely a matter of seismological nicety, but has considerable significance in discussions of the composition of the Earth and the processes which have shaped it. For example if there are discontinuities in the lower mantle then the value of dK/dP, K being the incompressibility and P the pressure, between
8
HALES
discontinuities would be reduced significantly and thus the Ko's estimated using Murnaghan's equation, or any similar equation, increased. The existence or non-existence, of discontinuities in the lower mantle is also significant in discussions of mantle convection. Lay and Helmberger (1983) inferred from a study of S H records that there is a discontinuity in the S H travel times at 83 ° and that this corresponded to an increase in the S velocity of 2.75 ± 0.25 % at a depth of about 2600 kin. A 2.75 + 0.25 % increase in the P velocity would amount to 0.33 to 0.40 km/sec. It does not appear that an increase in P velocity of this order would be consistent with the Dziewonski and Anderson travel times. Recently Jeanloz and Ahrens (1980) have interpreted shock wave data on Fe0 in terms of a phase transformation to a denser phase at a pressure of 70 GPa. This would correspond to a depth within the Earth of about 1800 kin. However the discussion by McCammon, Ringwood and Jackson (1983) suggests that, at the temperatures prevailing in the Earth, the transformation would occur at a depth between 2400 and 2500 km (see their Fig. 3). The decrease in velocity at a depth of about 2800 km is not required to fit the travel time data although the calculated times are consistent with the observations. Similar distributions occur in the models of Wright and Cleary (1972) and Doornbos (1983). The reduction in velocity has the consequence that the shadow zone for short period P does not begin until about 110 °. The bottoming depths for 1 sec period waves lie more than two wavelengths above the core-mantle boundary for these models up to a distance of about 107 °. Thus the onset times of the short period P phases would not be affected by the boundary at lesser distances. Diffracted P would only begin at about 110 °, a possibility discussed by Clearly (1974). ACKNOWLEDGEMENTS
A first draft of this paper was written while I was a visitor at the Institute for the Study of Earth and Man, Southern Methodist University. My thanks are due to Dr J. E. Brooks, President of the Institute and the staff of the Institute and the Department of Geological Sciences for the help they gave me while I was ar S.M.U. I thank also my colleagues at A.N.U., especially K. J. Muirhead, C. Wright and Ian Jackson, for much helpful discussion, and A. M. Dziewonski, D. L. Anderson, T. Lay and D. Helmberger for preprints.
REFERENCES Chinnery, M. A., 1969. Velocity anomalies in the lower mantle. Phys. Earth Planet. Inter., 2 : 2 Cleary, J. R., I974. The D" region. Phys. Earth Planet. Interiors, 9: 13-27.
10.
IS THE L O W E R M A N T L E H O M O G E N E O U S ?
9
Corbishly, D. J., 1970. Multiple array measurements of the P-wave travel-time derivative. Geophys. J. Roy. Astron. Soc., 19: 1-14. Dart, R. and Muirhead, K. J., 1977. Evidence for multiplicity in the P travel-time curve beyond 30 °. Phys. Earth Planet. Onter., 1 5 : 2 8 38. Doornbos, D. J., 1983. Present seismic evidence for a boundary layer at the base of the mantle. J. Geophys. Res., 8 8 : 3 4 9 8 3505. Doornbos, D. J. and Mondt, J. C., 1979a. Attenuation of P and S waves diffracted round the core. Geophys. J.R. Astron. Soc., 5 7 : 3 5 3 379. Doornbos, D. J. and Mondt, J. C., 1979b. P and S waves diffracted round the core and the velocity structure at the base of the mantle. Geophys. J. R. Astron. Soc., 57: 381-395. Dziewonski, A. M. and Anderson, D. L., 1981. Preliminary reference earth model (PREM). Phys. Earth Planet. Inter., 35: 297-356. Dziewonski, A. M. and Anderson, D. L., 1983. Travel times and station corrections for P waves at teleseismic distances. J. Geophys. Res., 8 4 : 3 2 9 5 - 3 3 1 4 . Evernden. J. F. and Clark, D. M.. 1970. Study of teleseismic P 1 travel-time data. Phys. Earth Planet. Interiors, 4 : 1 23. Hales, A. L. and Herrin, E., 1972. Travel times of seismic waves, Chapter 8 in The Nature of the Solid Earth ed. E. C. Robertson, McGraw-Hill, New York. Herrin, E.. 1968. 1968 seismological tables for P phases. Bull. Seism. Soc. Am., 5 8 : 1 1 9 3 1241. Jeanloz, R. and Ahrens, T., 1980. Equations of state of Fe0 and Ca0. Geophys. J.R. astr. Soc., 62: 505 528. Jeanloz, R. and Richter, F. M., 1979. Convection, composition and the thermal state of the lower mantle. J. Geophys. Ref., 8 4 : 5 4 9 7 5504. Johnson, J. R., 1967. Array measurements of P velocities in the upper mantle. J. Geophys. Res., 72: 5309-6325. Johnson, L. R., 1969. Array measurements of P velocities in the lower mantle. Bull. Seism. Soc. Amer.. 5 9 : 9 7 3 1008. Jones, G. M., 1977. Thermal interaction of the core and the mantle and long term behavior of the geomagnetic field. J. Geophys. Res., 8 2 : 1 7 0 3 1709. Lay. T. and Helmberger, D. V., 1983. A lower mantle S wave triplication and the shear velocity structure of D". Submitted for publication. M c C a m m o n , C. A., Ringwood, A. E. and Jackson, I., 1983. Thermodynamics of the system Fe Fe0 Mg0 at high pressure and temperature and a model for formation of the Earth's core. Geophys. J.R. astr. Soc., 7 2 : 5 7 7 595. Muirhead, K. J. and Hales, A. L., 1980. Evidence for P wave velocity discontinuities at depths greater than 650 km in the mantle. Phys. Earth Planet Interiors, 2 3 : 3 0 4 313. Niazi, M. and Anderson. D. L., 1965. Upper mantle structure of western North America from apparent velocities of P waves. J. Geophys. Res., 70: 4633-4640. Vinnik, L. P. and Nikolayev, A. V., 1970. The velocity profile of the lower mantle from direct measurement of dt/dA. Izv. Akad. Nauk SSSR Fiz. Zemli, 11 : 699-708. Wright, C., 1973. Array studies of the P phases and the structure of the D" region of the mantle. J. Geophys. Res., 78: 4 9 6 5 4 9 8 2 . Wright, C. and Cleary, J. R., 1972. P wave travel time gradient measurements at the Warramunga seismic array and lower mantle structure. Phys. Earth Planet Interiors, 5 : 2 1 3 230. Wright, C. and Lyons, J. A., 1981. Further evidence for radial velocity anomalies in the lower mantle. Pure Appl. Geophys., 119:137 162.