Earth-Science Ret'iews, 34 (1993) 1 - 4 5

E l sev ie r Sc ience P u b l i s h e r s B.V. , A m s t e r d a m

History of the Earth's obliquity

George E. Williams Department of Geology and Geophysics, University of Adelaide, GPO Box 498, Adelaide, S.A. 5001, Australia

(Received October 9, 1991; revised and accepted August 18, 1992)

A B S T R A C T

Williams, G.E., 1993. History of the Earth 's obliquity. Earth-Sci. Rev., 34: 1-45.

The evolution of the obliquity of the ecliptic (E), the Earth 's axial tilt of 23.5 °, may have greatly influenced the Earth 's dynamical, climatic and biotic development. For e > 54 °, climatic zonation and zonal surface winds would be reversed, low to equatorial latitudes would be glaciated in preference to high latitudes, and the global seasonal cycle would be greatly amplified. Phanerozoic palaeoclimates were essentially uniformitarian in regard to obliquity, with normal climatic zonation and zonal surface winds, circum-polar glaciation and little seasonal change in low latitudes. Milankovitch-band periodicity in early Palaeozoic evaporites implies ~ ~- 26.4 +_ 2.1 ° at ~ 430 Ma, suggesting that the obliquity during most of Phanerozoic time was comparable to the present value. By contrast, the paradoxical Late Proterozoic ( ~ 800-600 Ma) glacial environment--frigid, strongly seasonal climates, with permafrost and grounded ice-sheets near sea let,el preferentially in low to equatorial palaeolatitudes--implies glaciation with e > 54 ° (assuming a geocentric axial dipolar magnetic field). Palaeotidal data accord with a large obliquity in Late Proterozoic time. Indeed, Proterozoic palaeoclimates in general appear non-uniformitarian with respect to climatic zonation, consistent with e > 54 °.

The primordial Earth 's obliquity is unconstrained by the widely-accepted single-giant-impact hypothesis for the origin of the Moon; an impact-induced obliquity > 70 ° is possible, depending on the impact parameters. Subsequent evolution of E depends on the relative magnitudes of the rate of obliquity-increase i t caused by tidal friction, and the rate of decrease ip due to dissipative core -mant le torques during precession (~ < 90 ° is required for precessional torques to move ~ toward 0°). Proterozoic palaeotidal data indicate i t = 0.0003-0.0006"/cy (seconds of arc per century) during most of Earth history, only half the rate est imated using the modern, large value for tidal dissipation. The value of ~p resulting from the combined effects of viscous, electromagnetic and topographic core-mant le torques cannot be accurately determined because of uncertainties in estimating, at present and for the geological past, the effective viscosity of the outer core, the nature of magnetic fields at the core-mant le boundary (CMB) and within the lower mantle, and the topography of the CMB. However, several est imates of ~p approximate, or exceed by several orders of magnitude, the indicated value of ~ . If ~p did indeed exceed ~t in the past, then the obliquity would have decreased during Earth history.

It is postulated here that the primordial Earth acquired an obliquity of ~ 70 ° (54 ° < e < 90 °) from the Moon-producing single giant impact at ~ 4500 Ma (approach velocity = 5-20 k m / s , impac to r /Ear th mass-ratio = 0.08-0.14). Secular decrease in g subsequently occurred under the dominant influence of dissipative core -mant le torques. From 4500-650 Ma, g slowly decreased to ~ 60 ° ( (~) = -0 .0009" /cy) . g then decreased relatively rapidly from ~ 60 ° to ~ 26 ° between 650 and 430 Ma ((~) = -0 .0556" /cy) ; climatic zonation changed from reverse to normal when g = 54 ° at - 610 Ma, and (~) and the rate of amelioration of global seasonality were maxima for g = 45 ° at - 550 Ma (the precessional rate 1) is maximum when E = 45 °, and ~p varies as f12). Since 430 Ma, (g) has been < --0.0025"/cy and g has remained near its Quaternary range.

The postulated relatively rapid decrease in ~ between 650 and 430 Ma may partly reflect special conditions at the CMB which caused significant increase in dissipative core-mant le torques at that time. This inflection in the curve of ~ versus time centred at g = 45 ° also may be partly explained by the function ~p ~ (f~2/~o)(sin 2e), where w is the Earth 's rate of rotation, and other dynamical effects on gp.

The Proterozoic-Phanerozoic transition may record profound change in global state caused by reduction in g through the critical values of 54 ° and 45 °. The postulated flip-over of climatic zonation at ~ 610 Ma (g = 54 °) coincides with the widespread appearance of the Ediacaran metazoans at ~ 620-590 Ma, and the interval of most rapid reduction of obliquity

0 0 1 2 - 8 2 5 2 / 9 3 / $ 2 4 . 0 0 © 1993 - E l s ev i e r Sc ience P u b l i s h e r s B.V. All r i gh t s r e s e r v e d

2 G.E. WILLIAMS

and seasonality at ~ 550 Ma (g = 45 °) with the "Cambrian explosion" of biota at 550 ± 20 Ma. These two most spectacular radiations in the history of life thus may mark the passage from an inhospitable global state of reverse climatic zonation and extreme seasonality (the Earth's Precambrian "Uranian" obliquity state) to a relatively benign state of normal climatic zonation and moderate seasonality.

Further geological, palaeomagnetic and geochronological studies of Precambrian glaciogenic and aeolian deposits can test the predictions of a large obliquity (e > 54 °) and reverse climatic zonation and zonal surface winds during the pre-Ediacaran Precambrian.

CONTENTS

I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2. CLIMATIC EFFECTS OF MAJOR CHANGE OF OBLIQUITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1 Increase in obliqui ty (e >> 23 °) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Decrease in obliqui ty (e < 23 °) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3. EVIDENCE FOR OBLIQUITY IN THE GEOLOGICAL PAST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1 Phanerozo ic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2 L a t e Proterozoic ( ~ 800-600 M a ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.2.1 The paradoxical Late Proterozoic glacial climate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . l0 3.2.2 Global refrigeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2.3 Equatorial ice-ring system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.2.4 Geomagnetic field non-axial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.5 Large obliquity (e > 54 °) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2.6 Discrimination between hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3 Prior to ~ 800 Ma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4. ORIGIN AND LIMITS OF THE PRIMORDIAL EARTH'S OBLIQUITY . . . . . . . . . . . . . . . . . . . . . . 24

George Williams received his PhD in 1966 from

the Sedimentology Research Laboratory, Univer-

sity of Reading, where he held an 1851 Exhibit ion

Overseas Scholarship, and an MSc from the

Universi ty of Melbourne in 1963. His PhD re-

search investigated the pa laeoenv i ronment and

palaeoclimatology of the Late Proterozoic Torri-

donian sediments and palaeosols of northwest

Scotland, after which he s tudied Qua te rnary

sed imenta t ion and palaeosols in the nor the rn

Sahara and central Austral ia . Since then his main

research interests have been Precambr ian cli-

matic history and the past dynamics of the

E a r t h - M o o n system as revealed by the sedimen-

tary and pedological records, and the effects of

major meteor i te impact on the Earth. He was

elected a Fellow of the Geological Society of

Amer ica in 1979. His discovery of the Late

Proterozoic A c r a ma n impact structure, the largest

known impact s t ructure on the Aus t ra l ian conti-

nent , was honoured by the In te rna t iona l Astro-

nomical U n i o n in 1988. Will iams was awarded

the 1991 Research Medal of the Royal Society of

Victoria for research in the earth sciences in

Austra l ia dur ing 1985-1990. Formerly Principal

Geologist with BHP Minera ls In te rna t iona l in

Austral ia, he is now Senior Research Fellow in

the Depa r tmen t of Geology and Geophysics,

Universi ty of Adelaide.

H I S T O R Y O F T H E E A R T H ' S O B L I Q U I T Y 3

5. M E C H A N I S M S F O R S E C U L A R C H A N G E IN T H E E A R T H ' S O B L I Q U I T Y . . . . . . . . . . . . . . . . . . . 25

5.1 Tidal f r ic t ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.2 DissipatiL~e core-mant le torques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

6. A P R O P O S E D O B L I Q U I T Y HISTORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

7. THE P R O T E R O Z O I C - P H A N E R O Z O I C TRANSITION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

8. DISCUSSION AND POSSIBLE TESTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

9. C O N C L U S I O N S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

A C K N O W L E D G M E N T S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

10. R E F E R E N C E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

1. I N T R O D U C T I O N

The obliquity of the ecliptic (E)--the Earth's axial tilt of 23.5 ° (Fig. 1) or the angle between the equatorial plane and the plane of the Earth's orbit (the ecliptic plane)--ex- erts a fundamental influence on terrestrial climate and dynamics. The obliquity controls the seasonal cycle and strongly influences tidal rhythms. In addition, fluctuations of obliquity between 21.5 ° and 24.5 ° over a pe- riod of 41 ka constitute an important orbital element which, together with precession and variations in eccentricity, drives glacial and other medium-term (10-100 ka) climatic cy- cles (Berger et al., 1984). Indeed, the Earth's precession is maintained largely because the obliquity permits luni-solar torques to act strongly on the Earth's equatorial bulge.

As noted by Gold (1966), the obliquity of the ecliptic may represent a balance between the effects of tidal friction, which increases the obliquity, and internal dissipation within the Earth, which tends to erect the axis. Dynamical calculations (MacDonald, 1964; Goldreich, 1966; Mignard, 1982), which as- sume that the modern, large value of tidal friction applies for much of the geological past, have suggested that the obliquity is very slowly increasing under the action of luni- solar tidal friction and that early in Earth history the obliquity was perhaps ~ 10-15 °. Such calculations, however, do not consider possible geophysical mechanisms within the

Earth such as dissipative core-mantle cou- pling (e.g. Aoki, 1969; Bills, 1990a) or take account of evidence from the geological record concerning non-uniformitarian past climates and the history of the Earth's rota- tion and lunar orbit (e.g. Williams, 1975a, 1990).

Many of the planets have undergone or are subject to significant change in obliquity (Table 1), indicating that planetary obliquity may be regarded as a potential variable. Venus, Uranus and Pluto have large obliqui-

Rotation axis

Pole of ~l~ eclip

\ "

Fig. 1. Schematic representa t ion of the obliquity of the ecliptic (E), the Ear th ' s axial tilt of 23.5 ° or the angle between the equatorial plane and the ecliptic or orbital plane.

4 G l~. WILl JAMS

ties that could have resulted from several mechanisms including tidal torques, dissipa- tive core-mant le coupling, planetary impact, resonant axial-orbital precession and a twist of the orbital angular momentum vector. In addition, resonant axial-orbital precession causes large fluctuations in the obliquities of Mars and Pluto on time-scales of 10 6 years. Axial-orbital precession causes only small variations in the Earth's obliquity (_+l.5°); however, Ward (1982) suggested that with continued tidal evolution of the Ear th -Moon system, in less than 2000 Ma resonant axial- orbital precession will cause wider oscilla- tions of obliquity about an increased mean value (51.8 _+ 8.4°).

Geologists in general have given little at-

tention to the origin and evolution of the Earth's obliquity. However, if the obliquity in the geological past extended well beyond its Quaternary limits, the implications would be vital for the Earth's climatic and biotic histo- ries as well as for the dynamical evolution of the Ear th -Moon system. Despite the numer- ous mechanisms that may affect a planet's obliquity, a commonly held view is that no potential mechanism exists for substantial change of the Earth's obliquity. This percep- tion is without foundation. As discussed here, a recognised geophysical mechanism--dis- sipative core-mant le coupl ing--may indeed have accomplished geologically significant secular change in obliquity during Earth his- tory.

TABLE 1

Planetary obliquities (angles between equatorial and orbital planes)

Planet Present Range or past Mechanism obliquity obliquity for variation (o) (o)

Reference for variation of obliquity

Mercury 0 < 90

Venus 177 0 to ~ 180

0 to ~ 180

Earth 23.5 23 + 1.5 ~ 10 to 23 - 13 to 23

70 to 23 Moon 6.7 77 to 6.7 Mars 25.2 24.4 _+ 13.6

27.5 _+ 18.5

25.8 + 25.6 0 to ~ 20 +

Jupiter 3.1 Saturn * 26.7 Uranus 97.9

Neptune * 28.8 Pluto 104.5

118

tidal torque and core-mantle dissipation

tidal torques and core-mantle dissipation

tidal torques and core-mantle dissipation

axial-orbital precession tidal friction tidal friction core-mantle dissipation tidal torque axial-orbital precession axial-orbital precession

(prior to Tharsis uplift) axial-orbital precession polar ice-cap loading

Peale (1976)

Goldreich and Peale (1970)

Lago and Cazenave (1979)

Berger et al. (1984) Goldreich (1966) Mignard (1982) this study Ward (1975) Ward (1979) Ward et al. (1979)

Bills (1990b) Rubincam (1990)

0 to ~ 27 twist of orbital plane Tremaine (1991) 0 to ~ 98 planetary impact Safronov (1966) 0 to ~ 98 planetary impact Korycansky et al. (1990) 0 to ~ 98 tidal torque Greenberg (1974) 0 to ~ 98 twist of orbital plane Tremaine (1991) 0 to ~ 98 axial-orbital precession Harris and Ward (1982) 0 to ~ 29 twist of orbital plane Tremaine (1991) 99 _+ 14 axial-orbital precession Dobrovolskis (1989) 0 to 118 twist of orbital plane Tremaine (1991)

* Krimigis (1992) gives post-Voyager 2 obliquities of Saturn and Neptune as 29.0 ° and 29.6 °, respectively.

tIISTORY ()F THE EAR I'H'S OBLIQUITY 5

This review presents a new approach to the history of the Earth 's obliquity. Evidence from palaeoclimatology, geochronometry and geophysics, as well as the widely-accepted single-giant-impact hypothesis of lunar origin (which does not constrain the impact-in- duced obliquity), leads to a model of an evolving obliquity that has slowly decreased from a primordial large value (54 ° < • < 90 °) and has played a vital role in the Earth 's dynamical, climatic and biotic development.

2. C L I M A T I C E F F E C T S OF M A J O R C H A N G E OF O B L I Q U I T Y

2.1 Increase in obliquity (e >> 23 °)

As discussed by Williams (1975a), substan- tial increase in the Earth 's obliquity would cause major changes in global climate (Table 2):

(a) The amplitude of the global seasonal cycle would be greatly increased. With an obliquity of 60 °, for example, the tropics would be at 60 ° latitude and the polar circles at 30 ° latitude. Areas between 30-60 ° lati- tude thus would be within both the tropics and the polar circle! All areas poleward of 30 ° latitude would endure greatly contrasting seasons, with dark winters of deep cold and torrid summers under a continually circling Sun. Seasonal tempera ture contrasts would be most extreme in high latitudes, and large

seasonal oscillations of temperature would extend into low latitudes. The strongly sea- sonal climate experienced at all latitudes would likely be too stressful for all but rela- tively primitive organisms.

Moreover, a monotonic temperature gra- dient directed from the summer to the win- ter pole should exist for a large obliquity (Hunt, 1982). Substantial atmospheric circu- lation across the equator therefore would occur around solstices, when very cold air from the anticyclonic province in the winter hemisphere would flow toward the deep thermal depression in the summer hemi- sphere. At equinoxes the global climate would display a "normal" day-night cycle. Hence, low to equatorial latitudes would ex- perience frigid temperatures and very cold winds around solstices, alternating with more benign equinoctial conditions.

(b) The ratio of solar radiation received annually at either pole to that received at the equator would be increased (Fig. 2). For E = 54 °, all latitudes would receive equal ra- diation annually and the climatic zones would disappear. For E > 54 °, low to equatorial lati- tudes would receive less radiation annually than high latitudes. Figure 2b shows that minimum insolation occurs at +30 ° latitude for E = 60 ° , and at the equator for E > 60 ° . Williams (1975a) obtained the critical obliq- uity of 54 °, at which value the climatic zona- tion reverses, from Milankovitch (1930). This

T A B L E 2

Relat ion between the obliquity of the ecliptic and global climate (modified from Williams, 1975a)

Obliquity Seasonality Annual insolation, Climatic Preferred latitudes (°) either pole : equator * zonation of glaciation

(°)

23.5 moderate 0.4247 "normal" , high ( > 50) strong

54 strong 1.0 nil < 40 * * 9(I very strong 1.5708 reverse, low to

moderate equatorial ( < 30)

* Values from Croll (1875) and Milankovitch (1930). ** Despite the lack of climatic zonation for e = 54 °, the very hot summers likely would prevent glaciation in high latitudes.

(3 ( L E . W I L L I A M S

r~igh latitude Low latitude I~ glaciation ~ glaciation

!a i / E

~; I 2 / I

0 CL 10 , •

osi / ~. : i

: I . 1 -- 04 / [I

/ 0 10 20 30 40 50 6(] 70 80 90

Obliquity (degrees)

80

60

40

• 20

~ o

-40

6(]

80

b ] ,' / / !

,' J .2 it ',

£ = 90 75 60

' / 2 3 4

Re la t i ve m e a n a n n u a l i nso la t ion

Fig. 2. (a) Relation between the obliquity of the ecliptic E and the ratio of annual insolation at either pole to that at the equator (solid line); the dashed line at • = 54 ° separates the fields of potential low-latitude and high-latitude glaciation. After Williams (1975a). (b) Latitudinal variation of relative mean annual inso- lation of a planet for various values of obliquity (e, in degrees); solid line for e = 90% long-dashed line for

= 75 °, short-dashed line for • = 60 °. Adapted from Van Hemelrijck (1982). The plots in (a) and (b) to- gether illustrate that for • > 54 °, glaciation would occur preferentially in low to equatorial latitudes.

critical value of 54 ° was confirmed by Ward (1974).

If an Earth with e > 54 ° were to enter a glacial interval through some independent cause such as decline in atmospheric CO 2 partial pressures or modera te decrease in solar luminosi ty--a large obliquity per se is not a cause of glaciation--low to equatorial latitudes ( ~ 30 °) would be glaciated prefer- entially. In high latitudes the cold, arid win- ter atmosphere would allow only limited snowfall which would melt entirely during the very hot summer. Permanent ice could, however, form in low to equatorial latitudes; that zone, as well as receiving minimal solar radiation annually, would experience the ad- ditional cooling effect of frigid winds during each solstice and no extreme summer tem- peratures. The increased albedo resulting from a snow cover in low to equatorial lati- tudes would further reduce effective insola-

tion in that zone and allow the accumulation of permanent ice.

The principle of potential glaciation in low to equatorial latitudes for a large obliquity is applicable to other planets. Ward (1974) ob- served that if Mars had an obliquity similar to that of Uranus ( ~ 98°), the Martian de- posits of permanent CO 2 ice would be at the equator and not at the poles. Fur thermore, Jakosky and Carr (1985) suggested that when the obliquity of Mars periodically was as high as 45 ° early in that planet's history, ice could have accumulated in low latitudes by subli- mation of ice from the polar caps and trans- port of the water vapour equatorward; they concluded that polar ice may have formed only for minimum obliquities.

As noted by Williams (1975a), the area of a low-latitude zone symmetrical about the equator is 4rrRE 2 sin,~, and the total area of two equal polar caps is 4n-RE2(1-s in ,D, where R E is the Earth 's radius and ,~ the limiting latitude. Hence, 64% of the Earth 's surface area occurs between +40 ° latitude, whereas a total of only 23% of the Earth 's surface area occurs poleward of _+50 ° lati- tude. The area of potential glaciation there- fore is much larger for e > 54 ° than for e -- 23 ° . If continents moved through low lati- tudes of potential glaciation when • > 54 °, a misleading impression of global glaciation (albeit non-synchronous) could be gained from the stratigraphic record.

(c) The directions of zonal surface winds such as the tropical easterlies and mid-lati- tude westerlies would reverse for • > 54 ° as the circulation in "Hadley cells" reversed direction (Hunt, 1982). Westerly zonal sur- face winds would occur in low latitudes, which would receive much less precipitation than present low latitudes, and easterly zonal winds in mid-latitudes.

(d) Climatic zonation would be weakened. The stability of la t i tude-dependent climates therefore would be lessened, and any Mi- lankovitch-band fluctuations in insolation due to orbital variations might cause large or abrupt changes of climate over wide areas.

HIS'FORY OF 'l'Hff E A R T H ' S ( )BLIQUITY 7

Such climate changes might be recorded by the stratigraphic proximity of cold- and warm-climate indicators.

2.2 Decrease in obliquity (E < 23 °)

The effects of a reduced obliquity on inso- lation and climate have been investigated by Hunt (1982) and Barron (1984). Decrease in obliquity (e < 23 °) causes an increase in mean annual insolation at low latitudes and a de- crease at high latitudes, thus steepening the equator-to-pole gradient of mean annual in- solation. Cooler polar temperatures and a reduction in amplitude of the seasonal cycle would be expected.

3. EVIDENCE FOR OBLIQUITY IN THE GEO- LOGICAL PAST

3.1 Phanerozoic

The distribution of Phanerozoic palaeocli- mate indicators such as glacial deposits, evaporites and coral reefs with respect to palaeolatitudes (McElhinny, 1973; Drewry et al., 1974; Frakes, 1979; Merrill and McE1- hinny, 1983) and the frequency distribution of palaeomagnetic inclination angles for the Phanerozoic (Evans, 1976) together strongly support the geocentric axial dipole model of the Earth's magnetic field and imply that normal climatic zonation has prevailed since Precambrian time. Normal climatic zonation during the Palaeozoic and Mesozoic is indi- cated also by the prevalence of predicted normal zonal palaeowind directions deter- mined from aeolian sandstones (Runcorn, 1964a; Parrish and Peterson, 1988). It follows that the obliquity of the ecliptic has been less than the critical value of 54 ° (above which value reverse climatic zonation and direc- tions of zonal surface winds prevail) through- out the Phanerozoic.

A long-standing, controversial hypothesis in palaeobotany postulates that a former re- duced obliquity (e < 23 °) may explain the

occurrence of apparent evergreen floras, in- cluding broad-leaved forms, in high latitudes --subsequently shown to be high palaeolati- tudes - -dur ing Mesozoic-early Cenozoic time (e.g. Belt, 1874; Warring, 1885; Allard, 1948; Wolfe, 1980). It was argued that such floras are dependent on annual equability of light, whatever the temperature, and that only by a reduction in the Earth's obliquity could the required equability of light for- merly have prevailed in high latitudes. How- ever, a smaller obliquity and consequent cooler poles conflict with the evidence for warmer polar temperatures in Mesozoic and early Cenozoic time (Barton, 1984). Alterna- tively, the floras may have adapted to a po- lar-light regime, given ambient temperatures much higher than those in such regions today (Creber and Chaloner, 1984). The presence of tree-rings in high palaeolatitude Mesozoic floras confirms the occurrence of seasonal changes (Jefferson, 1982). Hence the palaeobotanical evidence may not demon- strate a Mesozoic-early Cenozoic obliquity much different from the Quaternary value.

The diurnal inequality of the tides (that is, the unequal amplitude of successive semidi- urnal tidal cycles), which is attributable largely to the obliquity of the ecliptic, can produce tidal laminae or cross-strata display- ing distinct thick-thin alternations (De Boer et al., 1989). Such alternations are displayed by tidal deposits of Cenozoic, Mesozoic and Palaeozoic age (e.g. De Boer et al., 1989; Nio and Yang, 1989; Williams, 1989c) and by tidal increments of a Late Cretaceous mol- lusc bivalve (Pannella, 1976). The evidence of a clear diurnal inequality in an ancient deposit or fossil indicates that the orbital plane of the Moon was inclined to the Earth's equatorial plane. Since the inclination of the lunar orbital plane to the ecliptic plane dur- ing most of Earth history probably was little different from its present value of only 5.15 ° (Goldreich, 1966; Mignard, 1982), the palae- otidal data imply at least a moderate (al- though unquantifiable) palaeo-obliquity dur- ing the Phanerozoic.

G.E. W I L L I A M S

A quantitative estimate of the obliquity in Late Ordovician-Early Silurian time, when the Earth was experiencing circum-polar glaciation (Hambrey and Harland, 1981), can be made from Milankovitch-band periodicity in bedded halite deposits of the Canning Basin, northwestern Australia (Williams, 1991b). Drill core of a 477-m stratigraphic interval of the Late Ordovician-Early Sil- urian Mallowa Salt, the largest halite deposit in Australia, provided detailed geochemical (Br, KzO, MgO, Na20) stratigraphic series in which strong periods (wavelengths) are revealed by Fourier spectral analysis (Fig. 3). The relative frequencies, amplitudes and structure of spectral peaks suggest climatic oscillations forced by orbital cycles. If the strongest spectral peak at 113 m is taken to represent the relatively stable eccentricity period of 100 ka and a constant net rate of accretion assumed for long sections, the other main periods recorded by the Mallowa Salt as exemplified by the Br spectrum (Fig. 3) would be 31.3 + 3.0 ka, 19.6+ 1.1 ka and 17.4 + 1.1 ka (error estimates +1o'). These figures are consistent with predicted Late Ordovician-Early Silurian periods for obliq- uity (30.5 ka) and precession (19.3 and 16.4 ka) based on evolutionary change in the Earth-Moon system (Table 3), assuming the

1 0 113

>,

g .~ 22.1

o_ 05 354 197 u~

o ~ EL

O0 I ooo o.os Frequency (cyc/m) o.lo

100 50 3r0 2'0 ~5 110

Period or waveJength (metres)

Fig. 3. Fast Fourier transform smoothed spectrum of the bromine geochemical stratigraphic series for the Late Ordovician-Early Silurian Mallowa Salt, Western Australia. Sample interval = 1 m, 477 points read; spectrum normalised to unity for the strongest peak and with linear frequency scale. The periods (wave- lengths) are expressed as stratigraphic thicknesses in metres. Peaks that are significant at the 95% level of confidence are labelled in bold type (sec Table 3). After Williams (1991b).

obliquity maintains a constant value of 23.4 ° (see Berger et al., 1989a). Hence, the appar- ent good agreement between predicted and observed precessional periods for 430 Ma may imply that the mean obliquity at 430 Ma was similar to that of today.

This apparent close agreement of preces- sional periods may, however, be partly fortu- itous. Berger et al. (1989a), in calculating

TABLE 3

Observed and postulated periodicities obtained from the fast Fourier transform spectrum of Br values for the Late Ordovician-Early Silurian Mallowa Salt (Fig. 3), compared with Milankovitch orbital periods predicted for 430 Ma (Early Silurian) and the present orbital periods. Values for the Mallowa Salt that are significant at the 95% level of confidence are shown in italics; error estimates are _+ l~r. Adapted from Williams (1991b)

Orbital element

Eccentricity Obliquity Precession

Stratigraphic wavelengths for the Mallowa Salt (m) 113 + 13

Postulated climatic periods for the Mallowa Salt (ka) 100 + 12

Predicted orbital periods for 430 Ma (Berger et al., 1989a) (ka) 100

Revised predicted precessional periods for 430 Ma (see text) (ka)

Present main orbital periods (ka) 100

35.4 ± 3.0 22.1 +_ 1.2 19.7 _+ 1.2

31.3 + 3.0 19.6 +% 1.1 17.4 + 1.1

30.5 19.3 16.4

2 1 . 3 ~ 17 .8

41 23 19

H I S T O R Y O F T H E E A R T H ' S O B L I Q U I T Y

TABLE 4

Late Proterozoic (~ 650 Ma) and modern tidal and rotational values

Parameter Late Proterozoic

Lambeck (1978, 1988) * (a) (b)

Rhythmites * *

Modern

solar days/lunar month lunar months/year lunar apsides cycle (years) lunar nodal cycle (years) solar days/year length of solar day (hours) mean Earth-Moon distance

in earth radii (R E )

30.7 30.2 14.4 13.2

~ 440 ~ 400

30.5 +_ 0.5 29.53 13.1 ± 0.1 12.37 9.7 _+ (I.1 8.85

19.5 ± 0,5 18.61 400 _+ 7 365.24

21.9 + 0.4 24.00

58.28 +_ 0.30 60.27

* Values taken from plots in Lambeck (1978, 1988) based on Phanerozoic palaeontological data. (a) average equivalent phase lag = 6 ° (the present value); (b) average equivalent phase lag = 3 °. Lambeck's plots assume that tidal friction is the only phenomenon responsible for secular changes in the Earth's rotation rate and the period of the Moon's revolution. ** Values indicated by tidal rhythmites of the Late Proterozoic Elatina Formation and Reynella Siltstone Member, South Australia (Williams, 1988, 1989a-c, 1990, 1991a; Deubner, 1990). The rhythmite data also display strong semi-annual and annual periods (see Figs. 7a and 8).

orbital periods back to Early Silurian time (taken here as 430 Ma 1) for an evolving E a r t h - M o o n system, used E a r t h - M o o n dis- tances de termined from palaeontological geochronometr ic data. They took 399 solar d a y s / y e a r and a relative mean E a r t h - M o o n distance (a/a o) of 0.966 for 380 Ma (Middle Devonian), values virtually the same as the 400 + 7 solar d ays / yea r and a/a o = 0.968 _+ 0.007 indicated for ~ 650 Ma by the palaeotidal data of the Elatina Format ion (Williams, 1989c, 1990; Deubner , 1990; see Tables 4 and 5). As concluded by Pannella (1975) and Scrutton (1978) and reviewed by Williams (1989c), the palaeontological data must be regarded as approximate only; in particular, the suggested number of days per year for the early and middle Palaeozoic may be too large. In contrast, Deubne r (1990) and Williams (1990) showed that the high degree of internal consistency among three indepen-

The age of the Late Ordovician-Early Silurian is here rounded-off to 430 Ma, based on the Ordovician- Silurian boundary age of 434 Ma given by Young and Claoud-Long (1991), which is supported by the latest zircon U-Pb SHRIMP data.

dent estimates of mean E a r t h - M o o n dis- tance at ~ 650 Ma (Table 5) strongly en- dorses the accuracy of the Late Proterozoic tidal and rotational values. Two possible in- terpretat ions of the geochronometr ic data therefore are:

(a) Virtually no decelerat ion of the Earth 's rotation occurred during an interval of ~ 270 Ma between ~ 650 and 380 Ma, and the orbital periods predicted by Berger et al. (1989a) for 430 Ma are accurate.

(b) The estimate of 399 solar days /yea r at 380 Ma is too large, and the early to middle Palaeozoic orbital periods predicted by Berger et al. (1989a) require revision. It should be noted that the value of 399 solar days /yea r for the Middle Devonian used by Scrutton (1964, 1970) was not based on coral data but was, in fact, an estimate of days /yea r for that time obtained by extrapo- lating the modern rate of decelerat ion of the Earth 's rotation.

As it is difficult to accept that the tidal evolution of the E a r t h - M o o n system was halted for an interval of ~ 270 Ma, a revi- sion of Berger et al.'s (1989a) predicted or- bital periods for 380 Ma seems required.

10 (;.E. WILLIAMS

Adjusting the time-scale of the plot of pre- cessional period against time (Berger et al., 1989b), so that their 380 Ma = 650 Ma, gives revised predicted precessional periods for 430 Ma of ~21.3 ka and ~17.8 ka. It is these revised predictions that should be compared with the precessional periods of 19.6 _+ 1.1 ka and 17.4 ± 1.1 ka suggested for ~ 430 Ma by periodicities in the Mallowa Salt (Table 3). The dominant observed precessional period of 19.6 ± 1.1 ka, which alone is significant at the 95% level of confidence, is signifi- cantly different from the revised prediction of ~ 21.3 ka. This difference may be ex- plained by the mean obliquity of the ecliptic at 430 Ma being larger than the value of 9 o ,,3.4 used by Berger et al. (1989a). As the rate of lunisolar precession ,Q varies as sin 2e (Woolard and Clemence, 1966), the palaeo- obliquity e~ at 430 Ma is given by

e~ = 0.5 arc sin (Pp,/P,)(sin 2El (1)

where P~ is the observed precessional period of 19.6 ± 1.1 ka at 430 Ma, Pp is the revised predicted precessional period of ~ 21.3 ka at 430 Ma, and E = 23.4 ° . The data indicate E~ = 26.4 ± 2.1 ° at 430 Ma, a value signifi- cantly larger than the assumed palaeo-ob- liquity of 23.4 °. The difference is increased when the effect of tidal friction on the obliq- uity is included; taking the rate of increase of obliquity due to tidal friction as 0.0006"/cy (seconds of arc per century) for the Phanero- zoic (see Section 5.1), the obliquity at 430

Ma would be 23.4 ° - 0.7 °= 22.7 ° in the ab- sence of other effects. Overall, the predic- tions of Berger et al. (1989a,b) and data from the Elatina Formation and Mallowa Salt to- gether suggest that the Earth's mean obliq- uity at 430 Ma was ~ 26.4_+ 2.1 ° , which is ~ 3.7 _+ 2.1 ° larger than the expected value.

In summary, palaeoclimate data indicate normal climatic zonation and by inference an obliquity less than 54 ° throughout the Phanerozoic. Indeed, the geological record for most of that eon provides no evidence for significant departures of obliquity beyond the Quaternary limits of 21.5-24.5 ° , although the obliquity may have been slightly larger than the present value in early Palaeozoic time. The latter suggestion is contrary to models of a slowly increasing obliquity due to tidal fric- tion (MacDonald, 1964; Goldreich, 1966; Mignard, 1982), implying that previous stud- ies on the evolution of the Earth's obliquity may be incomplete.

3.2 Late Proterozoic (~ 800-600 Ma)

3.2.1 The paradoxical Late Proterozoic glacial climate

Late Proterozoic glaciation, which af- fected all continents (with the possible ex- ception of Antarctica) between about 800 and 600 Ma, presents a major climatic enigma. As reviewed by Embleton and Williams (1986), early palaeomagnetic stud-

T A B L E 5

Mean E a r t h - M o o n distance at ~ 650 Ma and mean rate of lunar re t reat for the past ~ 651J Ma indicated by tidal rhythmites of the Elat ina Format ion and Reynel la Sil tstone M e m b e r (from Williams, 1989a,c, 1990; Deubner , 1990)

T i d a l / r o t a t i o n a l Relat ive mean E a r t h - Mean E a r t h - M o o n Mcan rate of lunar value Moon dis tance (a/a o) distance (R E) re t rea t ( c m / y e a r ) *

19.5 + 0.5 years ( lunar nodal per iod) 0.969 _+ 0.017 58.40 + 1.02 1.83 _+ 1.00

13.1 +O.1 lunar m o n t h s / y e a r 0.967 + 0.005 58.28 + 0.311 1.95 _+ 0.29

400 +_ 7 solar d a y s / y e a r 0.968 _+ 0.007 * * 58.34 + 0.42 1.89 + 1/.41

* The present rate of lunar re t rea t is 3.7 + 0.2 c m / y e a r , de t e rmined by lunar laser ranging (Dickey et al., 1990). ** Makes allowance for the solar t ides ' cont r ibut ion to the loss of angular m o m e n t u m of the Ear th ' s ro ta t ion (Deubner , 1990).

H I S T O R Y O F T H E E A R T H ' S ( ) B L I Q U F r Y 1 l

ies of Late Proterozoic glaciogenic rocks in Norway, Greenland, Scotland and Canada in general suggested low palaeolatitudes of glaciation, although some of the data are equivocal or contentious. Since 1980, how- ever, new palaeomagnetic studies of Late Proterozoic glaciogenic rocks and contiguous strata in Australia, South Africa, West Africa and China have consistently indicated low to equatorial palaeolat i tudes of glaciation (Kr6ner et al., 1980; McWilliams and McEI- hinny, 1980; Zhang and Zhang, 1985; Emble- ton and Williams, 1986; Sumner et al., 1987; Perrin et al., 1988; Chumakov and Elston, 1989; Li et al., 1991 and Schmidt et al., 1991 ). Virtually all these recent studies, which include rocks from the two major glaciations of the Late Proterozoic, indicate glaciation between 0 ° and 12 ° palaeolatitude. Unequiv- ocal evidence for high-palaeolatitude glacia- tion on any continent during the Late Pro- terozoic is lacking, and attempts to relate Late Proterozoic glaciation to movement of continents through polar regions (e.g. Craw- ford and Daily, 1971) have been unsuccess- ful. Late Proterozoic glaciation in Australia occurred between 0 ° and 30 ° palaeolatitude (McWilliams and McElhinny, 1980), not the 45-60 ° palaeolatitude incorrectly shown by Chumakov and Elston (1989). Furthermore, the North-China block occupied high palaeo- latitudes (57-62 °) during the Late Protero- zoic (800-700 Ma) yet affords no evidence of glaciation, whereas the Yangzi block experi- enced glaciation in low palaeolatitudes (0- 20 °) during the same time interval (Zhang and Zhang, 1985).

The Elatina Formation, of the Late Pro- terozoic ( ~ 650 Ma) Marinoan glacial suc- cession in South Australia, possesses a high- temperature, stable remanent magnetisation that indicates a palaeomagnetic latitude of

5 ° (inclination < 10 °) (Embleton and Williams, 1986; Schmidt et al., 1991). Positive fold tests on soft-sediment slump folds in the Elatina Formation confirm that the rema- nence was acquired very soon after deposi- tion, prior to soft-sediment folding (Sumner

et al., 1987; Schmidt et al., 1991). The Elatina palaeomagnetic data satisfy six of the seven reliability criteria of Van der Voo (1990); the only criterion not fulfilled is the presence of reversals because of the brief time-interval sampled (60-70 years). Although represent- ing a virtual geomagnetic pole (an instanta- neous sample of the geomagnetic field, which is generally subject to secular variation), the pole position for the Elatina Formation is in close proximity to other Late Proterozoic poles for Australia, indicating that the low inclination for the Elatina data is not a record of a geomagnetic excursion or reversal. The proximity to other Late Proterozoic pole po- sitions also is evidence that inclination error is not significant. Hence the Elatina palaeo- magnetic data do indeed indicate deposition in low palaeolatitudes. The Elatina data and palaeomagnetic data for contiguous forma- tions in the Adelaide Geosyncline together indicate a mean palaeolatitude of ~ 12°N for Late Proterozoic glaciation in South Aus- tralia (Embleton and Williams, 1986; Schmidt et al., 1991).

Glacial pavements occur below Late Pro- terozoic tillites in Western Australia, north Africa, southern Africa, Scandinavia, Spits- bergen, Normandy, South America and China (see Williams, 1975a; Hambrey and Harland, 1981; Guan et al., 1986). The excel- lently preserved Late Proterozoic glacial pavements in Western Australia indicate grounded ice-sheets close to the edge of ma- rine basins, with transgression accompanying glacial retreat (Plumb, 1981).

Structures interpreted as periglacial ice- and sand-wedges that formed by seasonal

contraction-expansion, occur in partly ma- rine Late Proterozoic basins in South Aus- tralia, Mauritania, Scotland 2, northern and southern Norway, and Spitsbergen (see re- view by Williams, 1986) and East Greenland

2 The origin of sand wedges in the Port Askaig Forma- tion in Scotland is contentious (sec Spencer, 1985; Eyles and Clark, 1985).

12 ¢;.E. WILLIAMS

(Spencer, 1985). A fossil permafrost horizon displaying numerous periglacial features, in- cluding excellently preserved sand wedges with near-vertical diverging lamination (Fig. 4), formed near sea level on the cratonic Stuart Shelf bordering the Adelaide Geosyn- cline during the Marinoan Glaciation (Wil- liams and Tonkin, 1985); the Stuart Shelf subsequently was submerged by the Mari- noah post-glacial marine transgression (Pre- iss, 1987). Identical sand wedges are forming today in arid periglacial regions such as the Arctic and the dry valleys of Antarctica (P6w6, 1959; Washburn, 1980; Karte, 1983); the permafrost contracts and cracks vertically during severe winters and the cracks fill with windblown sand, and lateral pressure during

summer expansion causes upturning of per- mafrost adjacent to wedges.

Periglacial features, particularly ice- and sand-wedge structures, can provide quantita- tive palaeoclimatological information such as mean annual air temperature, seasonal tem- perature range and mean annual precipita- tion (Washburn, 1980; Karte, 1983). Indeed, periglacial structures are perhaps the most reliable of palaeoclimate indicators, because they formed through processes of physical weathering and their interpretation thus avoids such uncertainties as the former na- ture of the atmosphere and biosphere and s u b s e q u e n t d i agene t i c mod i f i c a t i on . Periglacial wedge structures indicate a strongly seasonal palaeoclimate, as only the

Fig. 4. Vertical exposure of a Late Proterozoic (~ 650 Ma) periglacial sand wedge 3 m deep (2) in brecciated mid-Proterozoic quartzite at the Cattle Grid copper mine, South Australia. A near-vertical, diverging lamination that parallels the wedge margins is discernible within the wedge. Deformed sand wedges of an earlier generation (1) occur within the breccia and a third-generation wedge (3) occurs within overlying Late Proterozoic aeolian sandstone (Whyalla Sandstone) and the uppermost part of the large wedge. Bedding in breccia and sandstone is turned upward adjacent to the wedges. Numerous such sand wedges formed near sea level in the area bordering the Adelaide Geosyncline during the Marinoan Glaciation at ~ 650 Ma. Identical sand wedges are forming today in the periglacial dry valleys of Antarctica and in the Arctic. The structures indicate a very cold, arid. strongly seasonal climate.

H1S ' [ ' ( )RY O F TH['2 1 2 A R T H ' S ( ) B L I Q U 1 T Y l 3

seasonal temperature cycle, coupled with rapid drops of temperature, can produce the required contraction cracking. The presence of primary sand wedges within Late Protero- zoic partly-marine basins, best exemplified by the sand wedges on the Stuart Shelf, South Australia (Fig. 4), indicates that (a) mean annual air temperatures near sea level were then as low as - 12 ° to -20°C or lower, (b) strongly seasonal palaeoclimates pre- vailed, with mean monthly temperature ranges as great as ~ 40°C or more (mean monthly temperatures from < - 3 5 ° C in midwinter to < +4°C in midsummer) and (c) climates were arid (< 100 mm mean an- nual precipitation) and windy (see Karte, 1983; Williams and Tonkin, 1985; Williams, 1986). In South Australia this harsh palaeo- climate occurred in a coastal region.

The presence of a powerful annual signal in rhythmites of tidal-climatic origin from the Marinoan glacial succession in South Aus- tralia, attributable to a large seasonal oscilla- tion of sea level (see Section 3.2.6), is consis- tent with strong seasonality. The occurrence of varve-like laminites with dropstones in certain Late Proterozoic glaciogenic se- quences (e.g. Spencer, 1971) also accords with a strongly seasonal glacial climate. However,

well-developed lacustrine varves may not be common, since many Late Proterozoic glaciogenic sequences are largely of marine origin (e.g. Preiss, 1987). Overall, strong sea- sonality is an important feature of the Late Proterozoic glacial climate and cannot be ignored.

Arid, windy, Late Proterozoic glacial cli- mates also are indicated by the presence of widespread periglacial-aeolian sandstones (Williams and Tonkin, 1985; Deynoux et al., 1989; Williams, 1993) and glacial Ioessites (Edwards, 1979). Curiously, dominant palae- owinds indicated by cross-bedding in the periglacial (Marinoan) Whyalla Sandstone in South Australia were westerlies relative to contemporary low (~ 12°N) palaeolatitudes (Williams, 1993), whereas expected zonal surface winds in such latitudes would be easterlies to northeasterlies.

Another interesting feature of Late Pro- terozoic glaciogenic sequences is the strati- graphic proximity of cold- and warm-climate indicators. The presence of micritic, appar- ently primary dolostones capping Late Pro- terozoic glaciogenic sequences in Australia (Williams, 1979) and immediately underlying such sequences in Spitsbergen (Fairchild and Hambrey, 1984) is consistent with relatively

TABLE 6

The Late Proterozoic Iow-palaeolatitude climate near sea level indicated by periglacial sand-wedge structures in fossil permafrost horizons, compared with low-latitude climates modelled for possible arrangement of Late Proterozoic continents and for Palaeozoic supercontinents (assuming an obliquity of the ecliptic the same as that of today), and with the modern surface climate in low latitudes

Agc, and Mean surface Seasonal temperature basis for temperature in low range in low latitudes palaeoclimate latitudes ( < 8-10 ° lat.) < 8-10 ° lat.) estimates (°C) (°C)

Reference(s)

Late Proterozoic < - 12 to < - 20 > 40 (periglacial structures)

Late Proterozoic + 23.5 (modelled)

Carboniferous Gondwana + 22 (modelled)

Late Permian Pangaea + 25 to + 30 _< 5 (modelled)

Modern + 26.3 1.8

Karte (1983), Williams (1986)

Worsley and Kidder (1991)

Crowley et al. (1991)

Crowley et al. (1989)

Oort (1983)

14 G.E. WII.LIAMS

abrupt changes of mean temperature (al- though detrital carbonates interbedded with Late Proterozoic tillites are not of palaeocli- matic importance; Fairchild et al., 1989). Sig- nificant changes of mean annual surface temperature in low palaeolatitudes (fluctua- tions perhaps as great as 20°C or more, rang- ing from as low as -20°C to >0°C) on a 103-year time-scale during Late Proterozoic glaciation are supported by the presence of at least four generations of periglacial sand- wedge structures in South Australia (Wil- liams and Tonkin, 1985; Williams, 1992). The implied temperature fluctuations greatly ex- ceed the changes of only 1-2°C in mean surface temperature experienced in low lati- tudes between the last glacial maximum at 18 ka and the present day (Crowley and North, 1991).

As shown in Table 6, the Late Proterozoic low-palaeolatitude climate near sea level in- dicated by periglacial sand-wedge structures in fossil permafrost horizons contrasts markedly, in regard to mean surface temper- ature and seasonal temperature range, with the modern climate in low latitudes and with modelled low-latitude climates for Palaeo- zoic supercontinents and for possible ar- rangement of Late Proterozoic continents (climate modelling tacitly assuming an obliq- uity the same as that of today). In present low latitudes (0 + 10°), the mean annual air tem- perature near sea level is 26.3°C and the mean monthly temperature range is only 1.8°C (Oort, 1983). Mean annual air temper- atures near sea level < -20°C and seasonal temperature ranges > 40°C, which occurred in low palaeolatitudes during the Late Pro- terozoic, are found today only in high lati- tudes. Climate modelling for a possible Late Proterozoic arrangement of continents at in- termediate to low latitudes gives a mean annual surface temperature in tropical re- gions (< 8 ° latitude) of +23.5°C (Worsley and Kidder, 1991). This mean value is only a few °C lower than mean surface tempera- tures in present low latitudes, but is up to 40°C or more higher than mean annual tern-

peratures near sea level in low palaeolati- tudes during Late Proterozoic glaciation (Ta- ble 6).The model of Worsley and Kidder (1991) permits glaciation at > 46 ° latitude, whereas available palaeomagnetic data indi- cate that Late Proterozoic glaciation oc- curred mainly at 5 12 ° palaeolatitude. Moreover, climate modelling for Gondwana during Carboniferous glaciation indicates a mean surface tropical temperature only ~ 4°C lower than that of today caused by a presumed lower solar luminosity (Crowley et al., 1991). Climate modelling also shows that Pangaea experienced an annual temperature range < 5°C in low latitudes during the Per- mian, whereas annual temperature ranges > 40°C were confined to middle and high southern latitudes (Crowley et al., 1989). Clearly, climates modelled for Palaeozoic and possible Late Proterozoic arrangements of continents, assuming a mean obliquity of 23 °, do not duplicate the enigmatic Late Protero- zoic glacial climate.

Overall, palaeomagnetic and palaeocli- mate data thus present the enigma of frigid, strongly seasonal climates, with permafrost and grounded ice-sheets near sea lecel apparently in preferred low to equatorial palaeolatitudes, during the Late Proterozoic. This climate is all the more extraordinary because the faster rotation of the Earth in the past would have reduced poleward transport of heat, causing warmer low latitudes and colder high lati- tudes (see Hunt, 1979). The Late Proterozoic glacial climate is a major paradox in contem- porary Earth science, challenging conven- tional views on the nature of the geomag- netic field, climatic zonation and the Earth's orbital dynamics in Late Proterozoic time.

Four hypotheses have been advanced to explain glaciation near sea level in low to equatorial palaeolatitudes during the Late Proterozoic:

(a) Glaciation extended over all latitudes during global refrigeration and severe ice ages (Harland 1964a,b).

(b) The Earth then possessed an equato- rial ice-ring system that shielded low lati-

FtlS'I'()R~ ()|: I H E EARTH'S OBIAQUITY 15

tudes from solar radiation and induced low- latitude glaciation (Sheldon, 1984).

(c) The geocentric axial dipole model for the Earth's magnetic field does not hold for the Late Proterozoic (Emble ton and Williams, 1986).

(d) Reverse climatic zonation and marked global scasonality prevailed because of a large obliquity of the ecliptic (E > 54 °) (Williams, 1975a: Embleton and Williams, 1986).

3,2.2 Global refrigeration Since low palaeolatitudes experienced

mean annual air temperatures as low as -20°C or lower near sea level in coastal areas, as much as 45°C or more lower than the mean annual air temperature near sea level in present low latitudes, an average global surface temperature less than - 1.9°C (the freezing point of seawater; Frakes, 1979) and global freezing during the Late Protero- zoic are implied by the hypothesis of glacia- tion over all latitudes. However, the North China block occupied high palaeolatitudes during the Late Proterozoic yet apparently was not glaciated, while the Yangzi block experienced glaciation in low palaeolatitudes (Zhang and Zhang, 1985). The Chinese data appear inconsistent with the concept of global glaciation and show that the lack of evidence for high-palaeolatitude glaciation is not ade- quately explained by an alleged absence of continents in high palaeolatitudes during global refrigeration.

Crowell (1983, p. 254) noted that signifi- cantly greater iciness of the Earth accompa- nying world-wide glaciation would have caused drastically lowered sea level. How- ever, detailed palaeogeographic reconstruc- tions for Late Proterozoic South Australia (Preiss, 1987) do not reveal any drastic lower- ing of sea level during the major glaciations of the Late Proterozoic.

Climate modelling demonstrates addi- tional difficulties with the concept of global refrigeration. Importantly, Sellers (1990) found there is little seasonal t'ariation with global refrigeration because the very low tern-

peratures inhibit precipitation and sublima- tion. Hence the large seasonal mean-monthly temperature range (as much as - 4 0 ° C or more) in low to equatorial palaeolatitudes indicated by Late Proterozoic periglacial sand-wedge structures (Fig. 4) argues strongly against the global-refrigeration hypothesis.

Furthermore, even with a 30% reduction in solar luminosity more than half of the Earth's land area between +20 ° latitude re- mains snow-free (Sellers, 199(/); hence, global refrigeration would not lead to preferential low-latitude glaciation for the present Earth. Indeed, a frozen-over Earth may be very difficult to unfreeze; solar radiation is so efficiently reflected by ice and snow that solar luminosity has to increase by ~ 35% above its present value to remove the ice and snow that covers a frozen-over Earth (North et al., 1981). Such an unlikely increase in solar luminosity would exceed the total in- crease in luminosity expericnced by the Sun in its 4700-Ma history (see Gough, 1981; Endal and Schatten, 1982).

The survival of long-evolved organisms, in- cluding metazoans (Runnegar, 1991a) and other shallow-water biota, through Late Pro- terozoic time may present a further objection to the concept of global refrigeration. All known organisms require liquid water during at least some stage of their life cycles (Kast- ing, 1989), a requirement that would not be met in paralic settings and all other shallow and surface waters during thc implied global freezing.

For numerous reasons, therefore, the hy- pothesis of global refrigeration and glacia- tion over all latitudes during the Late Pro- terozoic is difficult to support. Use of the term Cryogenian, implying global glaciation, for the interval 850-650 Ma (Harland et al., 1990, p. 17) appears premature.

3.2.3 Equatorial ice-ring system The hypothesis of' an equatorial ice-ring

system in Late Proterozoic time also encoun- ters major difficulties. Ice rings probably

1 6 ( i .E . W I I . L I A M S

4 2

4.0

~ ' 3 8

>, r~ 3 6

c 3 4

~ z cq ~ 3 2

~30 o N 2.8

._o 2.6

m 24 _c

_~22

2O

18

out rings

w t h n ~ / ~

0 20 30 40 50 60 70 80 90 Lat i tude (degrees)

Fig. 5. Latitudinal variation of the mean annual daily insolation for Saturn. The equator-to-pole insolation gradient is modified by the shadows of Saturn's rings for most latitudes <45 ° , but is not inverted, and insolation at the equator is unaltered. After Brinkman and McGregor (1979).

could not exist so close to the Sun, even for a younger Sun of slightly lower luminosity. More importantly, mean annual daily insola- tion at the top of the atmosphere of Saturn, a planet with a well developed equatorial ring system and an obliquity (26.7 ° ) similar to the Earth's, is maximum at the equator and minimum at the poles (Fig. 5; Brinkman and McGregor, 1979), Saturn's equator-to-pole insolation gradient is modified by the ring shadows for most latitudes less than 45 ° , but is not inverted, and insolation at the equator is unaltered. High latitudes of an Earth with an equatorial ring system, not low to equato- rial latitudes, would be glaciated preferen- tially.

3.2.4 Geomagnetic field non-axial The validity of the geocentric axial dipole

model for the Earth's magnetic field in the geological past can be tested by comparing palaeomagnetic data with independent indi- cators of past latitude. As discussed in Sec- tion 3.1, the distribution of Phanerozoic palaeoclimate indicators and the frequency distribution of palaeomagnetic inclination

angles together strongly support the geocen- tric axial dipole model for the Phanerozoic, and hence the model remains basic to palaeomagnetic interpretation. Embleton and Williams (1986) noted that any deviation from this model for the Late Proterozoic could not have been short-lived, because of the group- ing of Australian poles for the quasi-static interval from ~ 800 Ma to Middle Cambrian time (see also Schmidt et al., 1991). They concluded that invalidation of the geocentric axial dipole model for such a long interval would raise strong doubts concerning other Precambrian palaeomagnetic data unsup- ported by independent evidence of past lati- tude.

The Earth, Jupiter and Saturn exhibit only small dipole tilts with respect to spin axes (11.4 °, 9.6 ° and 0 °, respectively; R~idler and Ness, 1990) as well as relatively small quadrupole contributions (< 10% of the dipole; Ness et al., 1989). The Voyager 2 spacecraft discovered that the magnetic fields of both Uranus and Neptune are, by con- trast, tilted at surprisingly large angles (58.6 ° and 46.9 °, respectively) to the spin axes and that quadrupole moments are comparable to dipole (Connerney et al., 1987, 1991; Ness et al., 1989). The observation that the magnetic fields of two planets are of such configura- tion virtually rules out the possibility that they are undergoing transient excursions or reversals, and indicates that non-axial dipole-quadrupole planetary magnetic fields are indeed possible. However, R~idler and Ness (1990) concluded that simply reorient- ing an Earthlike or Jupiterlike magnetic field cannot produce the Uranian magnetic field. The magnetic fields of Uranus and Neptune may result from the unique interior composi- tion and state of those planets (Connerney et al., 1987, 1991; Ness et al., 1989).

Idnurm and Giddings (1988) and Idnurm (1990) suggested that the near-linear plots of accumulated polar wander angle versus time for 0-3500 Ma, and the low scatter of data points, may indicate that the geocentric axial dipole model has been a reasonably good

H I S T O R Y O F T H E E A R T H ' S O B l i Q U I T Y 17

approximation over that long interval; how- ever, such plots are based on the arguable assumption that Precambrian polar wander paths as presently known are substantially complete (P.W. Schmidt, pers. commun., 1991). The tendency for local palaeomag- netic intensity to increase with distance from the palaeomagnetic equator avoids such un- certainty and suggests that the palaeomag- netic field may indeed be approximated by a geocentric dipole model as far back as 2500 Ma (Schwarz and Symons, 1969). The distri- bution of Precambrian palaeomagnetic incli- nation angles also accords with a geocentric dipole model for the interval 600-3000 Ma (Piper and Grant, 1989). Embleton and Williams (1986) noted, moreover, that the hypothesis of a non-axial dipole field does not predict an unusually large area of glacia- tion.

Hence, global palaeomagnetic data and the widespread occurrence of Late Protero- zoic glaciation together argue against a non- axial, non-dipole geomagnetic field during the Late Proterozoic.

3.2.5 Large obliquity (e > 54 °) Of the four hypotheses, the climatic ef-

fects of a large obliquity (e > 54°; see Section 2.1) may best account for the enigmatic fea- tures of the Late Proterozoic glacial climate (assuming the Late Proterozoic geomagnetic field was a geocentric axial dipole) because:

(a) Glaciation and periglacial climates would occur preferentially in low to equato- rial latitudes, which accords with available palaeoclimatic and palaeomagnetic data for the Late Proterozoic.

(b) The global seasonal cycle would be greatly amplified, and low to equatorial lati- tudes would experience marked seasonal changes of temperature. Strong seasonality in low to equatorial palaeolatitudes is indeed an important feature of the Late Proterozoic glacial climate. Furthermore, the occurrence of extensive glacial loessites and periglacial aeolian sandstones of Late Proterozoic age is consistent with the predictions of frigid sol-

stitial winds and reduced precipitation in low to equatorial latitudes.

(c) The directions of zonal surface winds would be reversed. The dominant palae- owinds indicated by the Late Proterozoic periglacial-aeolian Whyalla Sandstone in South Australia were indeed westerlies rela- tive to contemporary low palaeolatitudes, rather than the expected easterlies to north- easterlies.

(d) Climatic zonation would be weakened, and any medium-term Milankovitch-type variations of insolation might cause large or abrupt changes of climate over wide areas. Large changes of mean temperature on a 103-year time-scale in low palaeolatitudes during the Late Proterozoic are indeed indi- cated by the formation of at least four gener- ations of periglacial sand-wedge structures in South Australia. The stratigraphic proximity of cold- and warm-climate indicators also is consistent with abrupt changes of mean tem- perature.

Considering all the above points, the hy- pothesis of an obliquity greater than 54 ° (to- gether with a geocentric axial dipolar mag- netic field) in explanation of the Late Pro- terozoic paradox--frigid, strongly seasonal climates, with permafrost and grounded ice- sheets near sea level apparently in preferred low to equatorial palaeolat i tudes--must be given serious consideration. The complex na- ture and distribution of the Late Proterozoic glacial climate is not adequately explained by a simple global refrigeration or icehouse ef- fect alone, whatever the former arrangement of continents.

3.2.6 Discrimination between hypotheses Palaeomagnet ic and geochronological

studies of Late Proterozoic glaciogenic rocks may discriminate between the hypotheses of global refrigeration (synchronous low-lati- tude glaciation) and a large obliquity. As discussed by Williams (1975a), diachronism of glaciation could result from movement of continents across low latitudes when E > 54°; hence Late Proterozoic glaciogenic se-

[~ (;.E. WILLIAMS

quences, despite their low palaeolatitudes of deposition, may not be synchronous and cor- relative over wide areas. Isotopic age deter- minations and palaeomagnetic studies of Late Proterozoic glaciogenic rocks therefore might distinguish between (a) global refrigeration, which predicts synchronous glaciation in low palaeolatitudes, and (b) glaciation preferen- tially in low palaeolatitudes for a large obliq- uity, which could be either synchronous or diachronous. As noted by Li et al. (1991), if all continents were static in low latitudes one could not distinguish on palaeomagnetic evi- dence between glaciation during global re- frigeration and for a large obliquity. Kr6ner (1977) indeed concluded that the apparent diachronism of Late Proterozoic glaciations in Africa supports the large-obliquity model, and Deynoux et al. (1978) presented much

geochronological data supporting diachro- nism of Late Proterozoic glaciogenic se- quences in Central and West Africa. Preiss (1987) argued, however, that Kr6ner's (1977) geochronological data are insufficiently pre- cise to demonstrate the diachronism he pro- posed,

Discrimination between the hypotheses of a non-axial geocentric dipole model of the Earth's magnetic field, and a large obliquity, requires palaeogeophysical data that are in- dependent of palaeomagnetism. Such data are provided by rhythmites of tidal-climatic origin from the Late Proterozoic Marinoan glacial sequence in South Australia (Fig. 6; Williams, 1988, 1989a-c, 1990, 1991a). The ~ 60-year long, unsurpassed palaeotidal record of mixed/synodic type from the Elatina Formation, and palaeotidal data also

Fig. 6. Late Proterozoic (~ 650 Ma) tidal rhythmites, South Australia. Muddy material appears darker than sandy to silty layers. Scale bar 1 cm for both photographs. (a) Elatina Formation from Pichi Richi Pass, showing four fortnightly lamina-cycles each comprising ~ 12 + 2 graded (upward-fining), diurnal laminae of very fine-grained sandstone and siltstone. Dark bands delineating lamina-cycles are mud-drapes deposited at neaps. The lamina-cycles typically are abbreviated by the absence of several clastic laminae near neaps. (b) Reynella Siltstone Member from Hallett Cove, showing a thick, fortnightly lamina-cycle that contains 14 diurnal laminae of fine-grained sandstone each with a muddy top. Arrows indicate thinner, muddy laminae deposited at neaps. Most diurnal laminae in (b) comprise two semidlurnal sublaminae of unequal thickness, which record the diurnal inequality of the tides.

H I S T O R Y O F l'Hft~ L A R T H ' S O B I A Q U I T Y 19

of mixed/synodic type from the Reynella Siltstone Member of the same formation, contain features that together are consistent with a substantial obliquity in Late Protero- zoic time and a low latitude of deposition. The features are a clear diurnal inequality of the tides, strong semi-annual and annual sig- nals and marked abbreviation of fortnightly tidal cycles at equinoctial neaps.

The diurnal inequality (see Section 3.1), best displayed by the Reynella rhythmites (Fig. 6b) and recorded also by the Elatina rhythmites (Williams, 1991a), indicates at least a moderate palaeo-obliquity. Although the tidal forcing for the diurnal inequality vanishes at the equator and the poles (de Boer et al., 1989), the arrangement of conti- nents allows the inequality to occur over all latitudes. Hence this palaeotidal feature is not lati tude-dependent.

The semi-annual tidal period of solar de- clination (the angular distance of the Sun north or south of the celestial equator) is conspicuous in the fast Fourier transform (FFT) spectrum of the Elatina palaeotidal data (Fig. 7a). The very strong annual signal in the same spectrum is attributable to a large seasonal oscillation of sea level. Today, the dominant seasonal oscillation of sea level, and the less-important solar annual tidal constituent (S,) due to the eccentricity of the Earth's orbit, both attain their maximum de- velopment in low latitudes (Pariwono et al., 1986; and unpublished data from the Na- tional Tidal Facility, Flinders University). Hence the presence of a very strong annual signal in the Elatina data accords with the indicated low palaeolatitude of deposition of the Elatina Formation.

An idea of the relative power of the semi- annual and annual signals in the Elatina rhythmite data may be gained by comparing FFT spectra for the Elatina data and for modern tidal data from Townsville, Queens- land (Fig. 7). Comparing these spectra ap- pears justified because each tidal record is of mixed/synodic type and is from low latitudes (Townsville is at 19°16'S). The two spectra in

10 ~

05

O0 £o

*d

O_

261 a

13,1 215

j 87 66

k _J I i5 3. o.oo o'.1o o'.~c, o'.3o 0'40 o'.so

Frequency (1/cycles)

1'o ; ~: ~

1.0- b

0.5-

o.o

Period or wavelength (lamina-cycles) 2,15

125

000 O. 10 020 030 0~40 050 Frequency (1/cycles)

Period (lunar fortnightly cycles)

Fig. 7. Fast Fourier transform smoothed spectra of palaeotidal and tidal data, with power spectral densi- ties normalised to unity for the strongest peak in each spectrum and with linear frequency scales. (a) Spec- trum for the Late Proterozoic Elatina tidal-rhythmite sequence of 1580 fortnightly lamina-cycle thickness measurements ( ~ 60-year record). The very strong peak at 26.1 lamina-cycles represents an annual signal, with harmonics at 13.1 (semi-annual), 8.7, 6.6 and 5.3 lam- ina-cycles. The peak near :2 lamina-cycles (the Nyquist frequency) reflects the monthly inequality of alternate thick and thin fortnightly lamina-cycles, due to the eccentric palaeo-lunar orbit. (b) Spectrum for the max- imum heights of 495 spring tides between January 1, 1966 and December 31, 1985, for Townsville, Queens- land. The periods of 24.4 and 12.5 fortnightly cycles represent annual and semi-annual signals. The peak near 2 fortnightly cycles (the Nyquist frequency) re- flects the monthly inequality of alternate high and low spring tides, due to the eccentric lunar orbit. Tidal data for Townsville supplied by the National Tidal Facility, Flinders University.

Fig. 7 are for similar, long sequences (~ 20- 60 years) of fortnightly data and show an- nual, semi-annual and monthly peaks. Nor- malising the power spectral densities against the monthly peak for each spectrum shows that the annual and semi-annual signals in the Elatina spectrum (Fig. 7a) have ~ 15

20 G.E. WILl JAMS

times and ~ 4 times more power, relative to the related monthly peak, than do the annual and semi-annual signals in the Townsville spectrum (Fig. 7b). A further difference be- tween the two spectra is the presence, only in the Elatina spectrum, of a sequence of higher harmonics of the annual and semi-an- nual signals (peaks at 8.7, 6.6 and 5.3 fort- nightly cycles). These higher harmonics are attributable to beating among the annual and semi-annual signals and their combination tones. It would seem that the Late Protero- zoic annual and semi-annual oscillations of sea level in the Adelaide Geosyncline had sufficient power to generate a sequence of higher harmonics in sea-level height and /o r tidal range, which was recorded by the Elatina rhythmites. Although differences in geographic settings may account for some of the distinctions between these ancient and modern tidal records, the important point is that annual and semi-annual signals are very strongly developed in the Late Proterozoic data.

The common abbreviation (absence of sev- eral diurnal laminae) near the neap part of fortnightly lamina-cycles in the Elatina rhythmites (Fig. 6a) is attributable to small neap-tidal ranges (Williams, 1988, 1989a-c, 1990, 1991a). The number of diurnal laminae deposited per lamina-cycle, and by inference the range of palaeo-neap tides, were strongly modulated by the semi-annual tidal period. As shown by Williams (1991a), the abbrevia- tion of fortnightly lamina-cycles was very marked at and near equinoxes, when deposi- tion of diurnal laminae ceased for up to 6-8 lunar days (Fig. 8). The palaeotidal pattern indicated by the Elatina rhythmites--ex- tended intervals of very small neap-tidal ranges at and around equinoxes--also is consistent with a large obliquity in Late Pro- terozoic time. The amplitude of fluctuations, and range, of the semidiurnal part of the lunar equilibrium tide (the principal tidal constituent, M 2) vary as cos2d, where d is the Moon's declination (Pillsbury, 1940); and maximum declination dma x = • ± i , where i is

-,~-~sola year--~- lamina thickness

. SS AE WS VE SS 1"~ r ~,15 1.0

m ~ ~ ' ~ J ~ ' I

laminae per lamina-cycle

25 50 75 100

Lamina cycles

Fig. 8. The number of diurnal clastic laminae per fortnightly lamina-cycle counted between lamina thick- ness minima (neaps), for 110 lamina-cycles from the Elatina tidal rhythmites (see Fig. 6a); lamina-cycle number increases up-sequence. The unbroken curve (smoothed by 5-point weighted filter) reveals a strong modulation of lamina counts by a semi-annual signal of ~ 13 lamina-cycles; maximum abbreviation of lamina- cycles occurred near equinoxes. The dashed curve shows lamina thickness for the same stratigraphic in- terval (smoothed by 111-point filter). The shaded bands mark the stratigraphic positions of essentially unabbre- viated lamina-cycles, which were deposited at solstices. V E = vernal equinox, A E = autumnal equinox, S S =

summer solstice, W S = winter solstice. Adapted from Williams (1991a).

the inclination of the lunar orbital plane to the ecliptic plane of 5.15 ° . Hence, tidal ranges at and around equinoctial neaps, when lunar declination is maximal, would be much re- duced for e >> 23.5 °. The average equinoc- tial neap-tidal range of the M 2 constituent for e = 5 4 ° would be ~41% that of today, for • = 60 ° only ~ 30%, and for • = 65 ° only ~ 21% that of today. Extended intervals of very small neap-tidal ranges thus would oc- cur at and near equinoxes for • > 54 °.

It is thus significant that the independent palaeogeophysical data provided by the Elatina and Reynella tidal rhythmites accord with a substantial obliquity of the ecliptic and a low palaeolatitude of deposition dur- ing Late Proterozoic glaciation.

Vanyo and Awramik (1982, 1985) sug- gested, from the apparent sinuosity of one sample of an inclined columnar stromatolite from central Australia, that the obliquity was 26.5 ° at ~ 850 Ma. However, in most in- stances the causes of inclination of columnar

HISTORY OF "I'HE EARTH'S OBt,IQUITY 2 [

stromatolites are unknown or only tentatively inferred. Current direction (Walter, 1976) and prevailing wind direction (Playford and Cockbain, 1976) appear to strongly influence such inclination. Moreover, Chivas et al. (1990) queried the use of stromatolites as possible indicators of heliotropism because of the very high rates of stromatolite growth (up to ~ 10 cm/year) assumed by Vanyo and Awramik (1982, 1985). Indeed, it seems unlikely that columnar stromatolites could faithfully track the Sun throughout the year for large values of obliquity. That would re- quire symmetrical growth, partly by sediment trapping, on submerged algal columns tilted 45 ° or more (taking account of the refraction of light at the seawater surface), whose con- vex algal surfaces would range from near- horizontal to near-vertical. Since a near- horizontal algal surface would trap settling sediment more efficiently than would a steeply inclined surface, columnar stromato- lites probably have maintained a very strong vertical component of growth throughout the year, whatever the obliquity. The apparent sinuosity of a few specimens thus could lead to large underes t imates of palaeo-obliquity. Any annual sinuosi~ in the ,-, 850-Ma stro- matolites may reflect the annual oscillation of sea level, which strongly influenced the Late Proterozoic paralic environment in South Australia and left a clear imprint on the Elatina tidal rhythmites (Fig. 7a). Until a valid basis for interpreting stromatolite growth patterns is widely accepted, the sug- gestion of Vanyo and Awramik (1982, 1985) must be viewed as unsubstantiated.

3.3 Prior to ~ 800 Ma

Interpretation of Precambrian palaeocli- mates requires reliable palaeomagnetic data, based on the tenet that the geomagnetic field was then a geocentric axial dipole (see Sec- tion 3.2.4). Importantly, Idnurm and Gid- dings (1988, p. 81), in reviewing Australian Precambrian palaeomagnetic data back to 3500 Ma, concluded that overall " the Aus-

tralian Precambrian palaeolatitudes do not fit uniformitarian concepts of palaeoclimate". Instances of non-uniformitarian palaeocli- mates mentioned by them, in addition to the low palaeolatitudes of Late Proterozoic glaciogenic deposits discussed here (Section 3.2), include an apparent glaciogenic drop- stone facies deposited at ~ 1400 Ma when Australia occupied low palaeolatitudes; the palaeogeography is uncertain, but Idnurm and Giddings (1988, p. 80) stated that "a general low latitude glaciation cannot be ruled out".

Early Proterozoic (--, 2300 Ma) glaciogenic rocks occur in North America, South Africa, Australia and several other continents (see De Villiers and Visser, 1977; Hambrey and Harland, 1981), but palaeomagnetic data are available only for the Gowganda Formation (Coleman Member) and Chibougamau For- mation of the Huronian Supergroup in Canada. The Gowganda Formation is partly of glaciomarine origin and overlies striated basement rocks (Young, 1981). Morris (1977) found that most specimens from the Gow- ganda and Chibougamau formations carried either an A or a B remanence direction. Specimens carrying the A direction were from sites showing little sign of metamorphism and contained no secondary overgrowths on detrital magnetite; fold tests of remanence were positive and the A direction thus pre- dates folding of the Huronian Supergroup. By contrast, sites giving the B direction show metamorphic grades from lowest to upper- most greenschist and specimens contained secondary euhedral overgrowths on mag- netite grains; fold tests for the B direction were negative, indicating remagnetisation that postdates folding. As noted by Morris (1977), Symons' (1975) remanence directions indicate such secondary (reset) magnetisa- tion. The A direction, which Morris (1977) implied was acquired at the time of deposi- tion of the rocks, consistently gave an incli- nation of 54 ° for the dip-corrected direction for all three areas sampled. Hence, the glacial sediments may be assigned a palaeolatitude

-)~ G.E, WII.LIAMS

of ~ 35°; Young (1981), in discussing the data of Morris (1977), evidently mistook in- clination for palaeolatitude. Furthermore, Kalam-Aldin (1983) showed that the matrix of glaciogenic conglomerate from the Gow- ganda Formation has a remanent magnetisa- tion, interpreted by him as a primary compo- nent, that indicates a palaeolatitude of depo- sition of 26 ° (inclination = 44.3°). A palaeo- latitude of 26-35 ° for the Huronian glacio- genic rocks is supported by the magnetisa- tion of the Firstbrook Member of the Gow- ganda Formation (immediately overlying the glaciogenic Coleman Member), which Roy and Lapointe (1976) concluded was acquired early and which indicates a palaeolatitude of 34 °. New palaeomagnetic data for the 2217- Ma Nipissing diabase in the Gowganda area in Canada give a palaeolatitude of 28 ° (mean inclination = 47 °) for igneous intrusion (Buchan, 1991), which accords with a moder- ately low palaeolatitude for the Gowganda area during the Early Proterozoic.

A palaeolatitude of 26-35 ° for Huronian glaciation near sea level is intriguing. Indeed, Donaldson et al. (1973, p. 11) had noted previously "the somewhat puzzling anomaly" and Irving (1979) the "paradox" of a possible low to moderately low palaeolatitude for Huronian glacial deposition. Although the Pleistocene continental ice sheet in the North American interior at times expanded far be- yond its usual areas in high latitudes to ~ 37-40°N latitude (Frakes, 1979), glaciation near sea level would be expected preferen- tially in high latitudes for the Early Protero- zoic because the faster rotation of the Earth at that time would have increased the equa- tor-to-pole surface temperature gradient and caused warmer low latitudes and colder high latitudes (see Hunt, 1979). Importantly, the Huronian glaciogenic deposits contain struc- tures regarded as sandstone casts after periglacial ice-wedges (Young and Long, 1976); the structures, if interpreted correctly, would indicate a very strongly seasonal palaeoclimate (seasonal mean-monthly tem- perature range > 35°C to > 60°C) and a

mean annual air temperature < - 4 ° C to < - 8 ° C (see Karte, 1983; Williams, 1986). The presence of laminated argillites with abundant dropstones in the Huronian de- posits, interpreted as or compared to glacial varves (e.g. Lindsey, 1969; Long, 1974; Young, 1981; Mustard and Donaldson, 1987), may provide supporting evidence for a strongly seasonal glacial climate. Another feature of the Huronian deposits is the puz- zling association of glaciogenic formations with aluminous quartzites that are suggestive of intense chemical weathering under warm- climate conditions; the same facies associa- tion occurs in Early Proterozoic rocks in South Africa (Young, 1973), The evidence of grounded ice sheets near sea level in moder- ately low palaeolatitudes under a cold, ap- parently very strongly seasonal climate, to- gether with the stratigraphic proximity of cold- and warm-climate indicators, suggest non-uniformitarian glacial conditions compa- rable to those of the Late Proterozoic.

Early Proterozoic banded iron-formations (BIFs) on several continents, best exempli- fied by the ~ 2500-Ma BIFs of the Hamers- ley Group, Hamersley Basin, Western Aus- tralia (Trendall, 1983), typically show regu- lar, laterally persistent microband couplets of silica and iron oxide. The couplets usually are interpreted as annual varves (e.g. Tren- dall, 1972, 1973a, 1983; Ewers and Morris, 1981); locally cyclic, very thin banding (Trendall, 1973b) may record subdivisions of yearly microbands (Williams, 1989c, 1990). An annual origin of the BIF microbands implies a strong seasonal influence on basi- nal sedimentation. Palaeomagnetic data (Clark and Schmidt, 1986) show that the BIFs of the Hamersley Group possess a con- sistent, pre-folding magnetisation that indi- cates near-equatorial palaeolatitudes (< 5 °) of deposition. A strong seasonal influence on BIF deposition near the palaeo-equator im- plies a large amplitude of the global seasonal cycle (see also Trendall, 1972).

A mixtite containing striated and faceted boulders occurs in the Early Proterozoic

}tlST()RY OF I'Ht5 EARTH'S OBLIQUITY 23

Turee Creek Formation, which conformably overlies the Hamersley Group in the Hamer- sley Basin (Trendall, 1976). As discussed by Trendall, the mixtite may record an Early Proterozoic glaciation in Western Australia that was broadly coeval with the Huronian Glaciation in Canada. It is noteworthy that the apparent polar wander path for Australia spanning the interval from ~ 1800 Ma to > 2860 Ma (Clark and Schmidt, 1986), which includes primary poles for the Hamersley Basin, suggests that northwestern Australia occupied low palaeolatitudes at ~ 2300 Ma. Palaeomagnetic study of the Turee Creek Formation is required to ascertain whether glacial deposition occurred near the palaeo- equator.

No palaeomagnetic data are available for the Early Proterozoic glaciogenic Mak- ganyene Formation in South Africa. Accord- ing to Piper et al. (1973), Upper Ventersdorp volcanics (2300 + 100 Ma) gave a palaeolati- tude of ~ 40 ° and volcanics of the Cox Group (~ 2250 Ma), which overlie the Makganyene Formation with regional unconformity (Kent, 1980), a high palaeolatitude. The Gaberones granite (2340 +_ 50 Ma) in Botswana gave a palaeolatitude of 3-7 ° (McElhinny et al., 1968). Further palaeomagnetic studies clearly are required.

Since the direction of zonal surface winds such as the trade winds and mid-latitude westerlies would be reversed for • > 54 °, palaeowind directions indicated by Protero- zoic aeolian deposits also may provide infor- mation on palaeo-obliquity. As mentioned in Section 3.2.5, the dominant direction of palaeowinds indicated by the Late Protero- zoic periglacial Whyalla Sandstone in South

o N Australia (mean palaeolatitude ~ 12 ; Em- bleton and Williams, 1986; Schmidt et al., 1991) is opposite to that expected for zonal surface winds in such latitudes (Williams, 1993). In addition, the mean direction of palaeowinds for the Keweenawan (1000-1200 Ma) Copper Harbor Formation (palaeolati- tude = 21 °) in Michigan is perpendicular to the expected direction of palaeo-trade winds

(Taylor and Middleton, 1990). More palae- owind and related palaeomagnetic data are required for the Proterozoic to establish whether non-uniformitarian palaeowind di- rections are typical for that con.

Surface temperatures as high as 50-80°C during the Precambrian (~ 1300-3800 Ma) and Phanerozoic surface temperatures of ~ 15-45 ° have been estimated from ~SO values for sedimentary cherts and phos- phates (Knauth and Epstein, 1976; Knauth and Lowe, 1978; Karhu and Epstein, 1986). Such proposed palaeotemperatures are sus- pect as absolute temperatures because of possible diagenetic modification of 3lSo val- ues. However, the good correlation of a ~ 150-Ma periodicity in the Phanerozoic palaeotemperature data (Karhu and Epstein, 1986) with the apparent near periodicity of ~ 150 Ma for major glaciations since the Late Proterozoic (Williams, 1975b; Frakes and Francis, 1988) gives confidence that the 3mO values can be expressed as relatic'e palaeotemperatures. One possible explana- tion of apparent relatively high surface tem- peratures during the Precambrian is that they reflect high summer temperatures resulting from a strongly seasonal global climate.

The above review discusses some impor- tant palaeoclimate indicators and events for pre-Sinian time. Although more sedimento- logical and palaeomagnetic studies are of course required, an image seems to be form- ing of a strangely zoned and strongly sea- sonal non-uniformitarian Precambrian world. At different times the pre-Sinian environ- ment was marked by seasonal deposition of banded iron-formations near the palaeo- equator, grounded ice-sheets and glaciation near sea level in moderately low palaeolati- tudes under a cold, evidently very strongly seasonal climate, and the interbedding of cold- and warm-climate indicators in moder- ately low palaeolatitudes. The apparent re- verse climatic zonation (despite the climatic effects of a faster-rotating Earth), very strong seasonality and abrupt changes of climate in moderately low palaeolatitudes are consis-

-34 G.E. W I I J I J A M S

tent with a large obliquity (e > 54 °) during Precambrian time.

4. ORIGIN AND LIMITS OF THE PRIMORDIAL EARTH'S OBLIQUITY

It has long been suggested that the pri- mordial Earth acquired its obliquity by im- pact with a large body (e.g. Safronov and Zvjagina, 1969; Cameron, 1973; Singer, 1977). This view is strongly supported by the now widely-accepted single-giant-impact hypothe- sis of lunar origin (Hartmann and Davis, 1975; Cameron and Ward, 1976; Cameron, 1986; Hartmann, 1986; Taylor, 1987; New- sore and Taylor, 1989), which has become the "current consensus theory" of the Moon's formation (Melosh, 1990). This hypothesis holds that at ~ 4500 Ma the Protoearth, when close to its present size, experienced one very large glancing impact with a differ- entiated body about the size of Mars or slightly larger (the requisite mass of the im- pactor depends on its velocity); material from the impactor's a n d / o r the Protoearth's man-

tle then went into orbit about the Earth as the primordial Moon. The wide appeal of the single-giant-impact hypothesis arises from its apparent explanation of the angular momen- tum and orbital characteristics of the Ear th -Moon system and the distinctive lunar composition. The obliquity of the primordial Earth also is attributed to this single giant impact.

Hartmann and Vail (1986) showed that a given impactor can produce a wide range of results, depending on the impact parameters. The impact-induced obliquity of the target planet can range from 0 ° to ~ 180 °, the most likely value depending on the impac tor / ta r - get-planet mass ratio and the velocity of ap- proach. Importantly, Hartmann and Vail (1986) demonstrated that a most common post-impact obliquity of up to - 70 ° for the primordial Earth could result from approach velocities of 20-30 k m / s and mass ratios of ~ 0.05-0.10 (Fig. 9a); the most likely obliq- uity increases with impactor mass and also tends to increase with increasing approach velocity. An obliquity of ~ 70-80 ° also could

7O

~ " 60

~ 50

"5 4 0

o 30

E E 2O g ~ 10 o

0

• o ~ i ~ I i • ~ ~ I

a APPROACH VELOCITY O

• 30 km/s • O 20 km/s • 10 km/s • O x 5 km/s

O •

• O •

0 0 • 0

~) • • x x x * x

o ~ x ~ x ~ o

• ×

I ~ i I r i J J i r I 0 0.05 0.10

Planetesimal mass / target planet mass

180

150

~ 120

~ 90

~ 60

30

0

0 0.05 0 1 0

Planetesimal mass / target planet mass

Fig. 9. (a) Impact-induced obliquity of a target planet for a range of approach velocities and impactor/target-planet mass ratios. The target planet has physical parameters of the Earth, with pre-impact obliquity of 0 ° and pre-impact rotation period of 10 hours. Each point plotted is the most frequent value in a run of 500 impacts at specified impactor mass. Results applicable to any planet, but assume the Earth's specific density and coefficient of angular momentum. Adapted from Hartmann and Vail (1986). (b) Variation in obliquity occurring when the impactor approaches the Earth at 5 kin/s, with pre-impact obliquity of 0 ° and pre-impact rotation period of 10 hours. The plot, which is smoothed, represents the results of 500-impact runs at intervals of 0.01 mass ratio. Shaded zone includes two-thirds of the values, centred on the most frequent values (dashed line). The outer envelope includes 99.8% of the values. Adapted from Hartmann and Vail (1986).

H I S T O R Y O F T H E E A R F H ' S O B L I Q U I T Y 25

readily be produced by an approach velocity as low as 5 k m / s and mass ratios of 0.08-0.11 (Fig. 9b). Approach velocities ranging from 5 to 20 k m / s and mass ratios from 0.08 to 0.14 have indeed been suggested for the Moon- producing impact (e.g. Cameron, 1986; Hart- mann, 1986; Taylor, 1987; Newsom and Tay- lor, 1989), and hence a large (~ 70 °) impact- induced obliquity must be considered very possible to likely. Such impact parameters give a post-impact rotation period for the Earth in the range of ~ 3-10 hours (Hart- mann and Vail, 1986).

The large obliquity ( ~ 98 °) of Uranus has been attributed to an early impact with a single large body of mass ratio ~ 0.07-0.14 (Hartmann and Vail, 1986; Taylor, 1987; Ko- rycansky et al., 1990). According to Goldre- ich and Peale (1970), the rapid rotation of Uranus, the negligible mass of its moons, and its great distance from the Sun imply that tidal friction has not appreciably altered its primordial spin. The negligible tidal and pre- cessional torques acting on Uranus may im- ply that its large obliquity also is essentially primordial. As discussed below, the Earth, by contrast, has been subjected to substantial luni-solar tidal and precessional torques throughout its history, providing mechanisms for secular change not only in rotation rate but also obliquity.

5. MECHANISMS FOR SECULAR CHANGE IN THE EARTH'S OBLIQUITY

Collisions between the Earth and im- pactors since the formation of the Moon are most unlikely to have caused significant change in the Earth's obliquity. Dachille (1963) calculated that an impactor 32 km in diameter (about three times the diameter of the envisaged K/T-boundary bolide), for ex- ample, with a density of 3.5 g / c m 3 and trav- elling at the very high velocity of 72 k m / s would alter the obliquity by only 0°00'02 " under optimum conditions of impact. He also showed that an impactor 320 km in diameter and with the same density and conditions of

impact would produce a maximum shift of axis of only 0°32'. Furthermore, the dynami- cal effects of terrestrial impact over time would have been random and would not have led to cumulative change in obliquity. Slow change in obliquity, however, could have re- suited from the action of luni-solar tidal and precessional torques during Earth history.

5.1 Tidal friction

The effect of lunar tidal friction on the obliquity of the ecliptic is discussed by Mac- Donald (1964, 1966). Because the Earth is not perfectly elastic, the tidal bulge raised by the Moon lags behind the tide-raising force and so is carried forward by the Earth's rotation (Fig. 10). The angle between the Ear th -Moon axis and the tidal bulge is termed the phase lag. The lunar attraction on the tidal bulge facing the Moon exceeds that on the more distant bulge, because tidal force decreases with distance. Consequently the Moon exerts a net torque acting about the Earth's spin axis that tends to retard the Earth's rotation, and the tidal bulge exerts a reciprocal torque that tends to accelerate the Moon's orbital motion. By this mechanism, angular momentum is transferred from the Earth's rotation to the lunar orbital motion.

Because of the Earth's obliquity of 23.5 ° and the inclination of the lunar orbital plane

Tidal bulge

Fig. 10. Tidal bulge for the present case where the ratc of the Earth's rotation exceeds the rate of the Moon's revolution. The tidal bulge raised by the Moon is carried forward by the Earth's rotation; 'F represents the phase lag angle. The Moon exerts a net torque on the tidal bulge that acts about the Earth's spin axis and tends to retard the Earth's rotation, and a reciprocal torque tends to accelerate the Moon's orbital motion. Adapted from MacDonald (1964).

2 ( 3 ( ; . E . W I L I . I A M S

to the ecliptic plane of 5.15 ° , the Moon does not revolve in the equatorial plane of the Earth. The Earth's rotation therefore carries the tidal bulge out of the Moon's orbital plane. The net effect of lunar torques acting on the tidal bulge tends to decrease the component of angular momentum of the Earth that is perpendicular to the lunar or- bital plane and conserve the component in the orbital plane. The Earth's obliquity thus tends to increase and, conversely, a torque tends to decrease the Moon's orbital inclina- tion.

Employing the lunar tidal torque indicated by modern observations, MacDonald (1964; Fig. 1 la) calculated that the Earth's obliquity was 20 ° at 1000 Ma. Based on MacDonald's expressions for the lunar tidal torque, Gol- dreich (1966; Fig. l lb) illustrated a slow de- crease in obliquity going back in Earth his- tory (time expressed as Ear th-Moon dis- tance), with a mean obliquity of ~ 10 ° for an Ear th-Moon distance < 10 R E (earth radii). More recently, Mignard (1982; Fig. 1 lc), pro- jecting the rate of tidal dissipation deduced from Palaeozoic coral data (which are of dubious reliability and give a rate of tidal dissipation similar to the modern rate; see Section 3.1 and Williams, 1989c) back to 1300 Ma and using a smaller value before that time, calculated that the obliquity was

13 ° when the lunar distance was ~ 10 R p MacDonald's (1964) curve of obliquity-

change (Fig. l la) indicates an average rate of increase in obliquity due to lunar tidal fric- tion ( ( i t ) ) of 0.0012"/cy (brackets ( ) indi- cate time-average) since 1000 Ma; this value is based on the assumption that the phase lag remained equal to its present value. The curve of Mignard (1982; Fig. llc) implies a similar value of ( i t ) since 1300 Ma. The curves of Goldreich (Fig. l lb) and Mignard further indicate that i~ has steadily increased with time; ( i , ) for early Earth history (Earth-Moon dis tance=20-35 RE: Lam- beck and Pullan, 1980; Webb, 1982) is only about half the value of ( i t) since the Late Proterozoic (~ 58-60 RE: Williams, 1989a,

30

s- 2s

~,~- 2o > ,

"5

Z15 0

10

50

" ~ ' 4 0

~o ~-2o o-

~1o

24

2 o

a)

~ 1 2

8

4

0

a

I

I ~_ J

15100 10100 500 0 Age (Ma)

x- t t i i i i k _ _ i i

10 20 30 40 50 60 70 Distance (Earth radii)

i i i i - ~ - - 1 ~ -

C o b l i q u i t y ~ . . ~

i n c l i n ~ t i o n . . . . . . . . . . . .

z i £ • 1 @ 20 ~0 40 50 60

D i s t a n c e ( E a r t h r a d i i )

Fig. l l . Variation in the obliquity of the ecliptic due to tidal friction plotted againsl age or Ear th-Moon dis- tance. (a) Adapted from MacDonald (1964), showing the obliquity back to 1600 Ma for a mean phase lag equal to the present value. (b) Adapted from Goldre- ich (1966). (c) Adapted from Mignard (1982).

1990; Deubner, 1990), that is, only about 0.0006"/cy.

These computed values for ( i , ) of ~ 0.0006-0.0012"/cy are at odds, however, with recently acquired geochronometric data. The palaeotidal record provided by the Late Proterozoic Elatina Formation and Reynella Siltstone Member in South Australia (Wil- liams, 1989a-c, 1990, 1991a) indicates an av- erage equivalent phase lag since ~ 650 Ma that is only half the present value (Table 4). The palaeotidal data also indicate a mean rate of lunar retreat of 1.83-1.95 cm/year since ~ 650 Ma (Table 5), only about half the value of 3.7 _+ 0.2 cm/year determined by lunar laser ranging (Dickey et al., 1990). Tentative palaeotidal data for ~ 2500 Ma suggest that tidal dissipation during the Pro-

H I S T O R Y O F T H E E A R T H ' S O B I _ I Q U I T Y 27

terozoic was even smaller (Williams, 1990). These findings are consistent with increasing oceanic tidal dissipation as the Earth's rota- tion slows (Hansen, 1982; Webb, 1982). Geo- logical observations therefore imply that the rate of increase in obliquity during Earth history due to tidal friction was only about half that calculated by MacDonald (1964), Goldreich (1966) and Mignard (1982); rea- sonable estimates are (~t) ~ 0.0006"/cy since the Late Proterozoic and ( i t )--- 0.0003"/cy in earlier time. The total increase in obliquity during Earth history attributable to tidal friction is thus < 7.5 °.

5.2 Dissipati~e core-mantle torques

As discussed by Munk and MacDonald (1960), changes in attitude of the Earth's rotation axis in space result largely from the gravitational pull of the Moon and Sun on the Earth's equatorial bulge. The equatorial plane and the lunar orbital plane are in- clined at 23.5 ° and 5.15 ° to the ecliptic, re- spectively, and if the Earth did not rotate the action of the Moon and Sun would pull these planes into coincidence. Because of the gyro- scopic effect of the Earth's spin, however, the obliquity of the ecliptic remains near 23.5 ° and the celestial pole describes a circle about the pole of the ecliptic in 25.5 ka relative to the fixed perihelion (Fig. 12). This motion is termed the astronomical preces- sion of the equinoxes as distinct from cli- matic precession relative to the moving peri- helion, which has main periods of 23 ka and 19 ka (Berger, 1984). The precessional torque is about four million times greater than the tidal torque but acts solely in the ecliptic plane (Hipkin, 1975).

Because the mean density of the core is much greater than that of the mantle, the dynamic ellipticity of the core is only 3 /4 the corresponding value for the mantle (Malkus, 1968; Lambeck, 1980). If the core and mantle were uncoupled, the core would thus precess at 3 /4 the rate of mantle precession. The

Pe

I / \ Pc\.. /

Fig. 12. The precessing Earth, showing the obliquity of the ecliptic e = 23.5 ° and the circle described about the pole of the ecliptic Pc by the celestial pole P,. (the extension of the Earth 's spin axis on the celestial sphere) as a result of the astronomical precession. RE, R l and R 2 are the radii of the Earth, the outer core and the inner core~ respectively. Adaptcd from Malkus (1968).

core and mantle are, however, essentially coupled and precess at virtually the same rate, although there may be a small non- alignment of their figure axes. The mechani- cal couples or torques at the core-mantle boundary (CMB) most commonly discussed in regard to the transfer of angular momen- tum between core and mantle (see Lambeck, 1980; Merrill and McElhinny, 1983; Rochester, 1984; Hide, 1989) are:

(a) t~iscous coupling~ a function of the vis- cous friction in either a laminar or turbulent boundary layer at the CMB, and dependent on either the kinematic or effective viscosity of the outer core;

(b) electromagnetic coupling, a function of magnetic field strengths and electrical con- ductivity in the core and mantle; and

2~ (i.E. WILI.IAMS

(c) topographic coupling, in which "bumps" or depressions at the CMB modify the flow of fluid past the boundary and the pressure distribution on the mantle.

Hide and Dickey (1991, p. 632) noted that limited knowledge of the motions, viscosity and electrical conductivity of the core, the electrical conductivity and magnetic field of the lower mantle, and the topography of the core-mant le interface "make it impossible to determine the torque acting at the CMB with much certainty." Nonetheless, as discussed below, each of the above three mechanisms has been advanced as a cause of substantial core-mant le torques.

Any precession-induced differential mo- tion between a fluid core and a non-aligned rigid mantle causes dissipation of rotational energy at the CMB. Since the precessional torque acts only in the ecliptic plane, the component of spin angular momentum in that plane is reduced by core-mant le dissi- pation and the component perpendicular to the orbital plane is conserved (Peale, 1976). Dissipation at the CMB thus tends to drive the obliquity toward 0 ° for • < 90 ° and to- ward 180 ° for • > 911 °. Deceleration of the Earth's rotation accompanying decrease in obliquity by core-mant le coupling involves no exchange of angular momentum between the Earth and the Moon, and may be small compared to the tidally-produced decelera- tion. Aoki and Kakuta (1971) obtained (o/w = - - 5 . 8 X l O - 1 4 " / c y due to core-mant le coupling (where to is the rate of the Earth's rotation) for a rate of obliquity-decrease of 11.0254"/cy, as against the observed rota- tional deceleration of - 1 0 - s " / c y . Accord- ing to Rochester (1976), the rate at which rotational kinetic energy is dissipated by the axial component of core-mant le coupling currently is < 10 ~' W, which is negligible compared with the total rate of tidal energy dissipation of 4.5 × 10 j2 W (Lambeck, 1980).

Secular change in planetary obliquity through t,iscous core-mantle coupling has been proposed for the Earth (Aoki, 1969; Aoki and Kakuta, 1971), Venus (Goldreich

and Peale, 1970; Lago and Cazenave, 1979) and Mercury (Peale, 1976). Bills (1990a) also recognised the potential importance of dissi- pative core-mant le viscous and electromag- netic coupling to the long-term obliquity his- tories of the Earth and Mars. In addition, Vanyo (1991) argued that viscous core-man- tle coupling may dominate over electromag- netic and topographic coupling, causing some sizeable portion of the Earth's secular despin (presumably with concomitant secular de- crease in obliquity).

Aoki (1969) proposed that the rate of de- crease in the Earth's obliquity (~p) caused by viscous core-mant le dissipation = - 0 . 3 2 " / cy (the minus sign indicates decreasing obliq- uity). Rochester (1976), however, argued that core-mant le coupling is provided largely by inertial torques (a view disputed by Vanyo, 1991) and that ~p is <; -0 .0004"/cy. In de- riving his figure for ~p, Rochester (1976) observed that the most uncertain parameter is the kinematic viscosity of the Earth's outer core (u). He showed that ~v varies as u ~/2 for large values of u (/> 105 cm2/s), and took an upper limit for u of 105 cm2/s (from Toomre, 1974). Rochester (19761 acknowl- edged that core-mant le coupling would be important in the dynamical evolution of the Ear th -Moon system if u approaches 105

S c m - / k .

The kinematic viscosity of the Earth's outer core is, however, "one of the least known physical parameters of the Earth" (Jacobs, 1987, p. 55), postulated values dif- fering by many orders of magnitude and ranging from 10 -~ to 10 ~ cm2/s. High val- ues for ~, of 10 9 to 1011 cm2/s (which may be regarded as far upper limits) have been sug- gested from seismological observations (e.g. Sato and Espinosa, 1967, 1968; Suzuki and Sato, 1970). Inferred upper limits are < 105 cm2/s from the phase of the Earth's forced nutation (Toomre, 1974), < 106 cm2/s from the amplitudes of the forced nutation (Molodenskiy, 1981), < 10 7 cm2/s from tidal variations in the Earth's rotation rate (Moiodenskiy, 1981) and < 106 cm2/s from

HISTORY O F T H E [-AR I'H'S OIaII.1QUITY 29

the estimated amplitude of topography at the CMB (Hide, 1971). The lowest values for v of 10 3 to > 10 ° cm2/s are theoretical esti- mates based on the behavior of liquid metals at high temperatures and pressures (e.g. Gans, 1972; Bukowinski and Knopoff, 1976; Poirier, 1988). Workers in geomagnetism usually have assumed v -- 10 -2 cm2/s as for liquid metals (Gans, 1972). Theoretical esti- mates of v were challenged by Officer (1986), who presented a model of core dynamics and the Earth's magnetic field using v = 2 × 107 cm2/s. Officer's model predicts the correct order of magnitude for the external magnetic field and the westward drift of the non-di- pole field. Toomre's (1974) upper limit for v has been regarded as the best estimate yet (e.g. Rochester, 1976), but the value of 1, remains uncertain.

Further uncertainty regarding the viscosity of the core arises from the suggestion that, through consideration of the core's likely temperature limits, the outer core may be a slurry comprising up to 60% or more of solid particles suspended in an iron-sulphur melt (Jeanloz, 1990; Williams and Jeanloz, 1990). The viscosity of a suspension of solid parti- cles increases rapidly with increase in the volume fraction of suspended solids above 0.4-0.5 (Roscoe, 1952; Jeffrey and Acrivos, 1976). Tonks and Melosh (1990) showed that the viscosity V~ur, ~ of a mechanical suspen- sion of solid crystals in a high-temperature melt may be expressed as

/)slurry' = 12 l i q u i d 10 re,t, (2)

w h e r e /"liquid is the viscosity of the liquid component and • the fraction of solids. High concentrations of suspended solids would greatly increase the viscosity of the outer core compared with that of an iron-rich liq- uid; using eq. 2, theoretical estimates of Vuqu~ d of 10 3 to > 10 ° cm2/s give /"slurry = 103 to > 10" cm2/s for ~ = 0.6. Gubbins (1976, p. 39) likewise concluded that the viscosity of the core "may be drastically affected if the

concentration of solid particles is very high". Hence the presence of a core slurry may permit the viscosity to be much larger than theoretical estimates, although any shear flow in the outer core could reduce the slurry viscosity by "shear thinning" (see Jeffrey and Acrivos, 1976).

Importantly, turbulent flow in the fluid core may greatly increase its effective viscos- ity and the drag on the mantle. The occur- rence of turbulent flow in a fluid gives rise to an "eddy" or "turbulence" viscosity that may be up to several thousand times the "molecu- lar" or "absolute" viscosity (Hinze, 1975; Massey, 1979); the turbulence viscosity is not a constant for a given fluid but is primarily a function of the fluid turbulence. Melchior (1986, pp. 216, 224) has applied this principle to the Earth's outer core, observing that to- pography at the CMB may produce turbu- lence in the fluid core and a turbulence viscosity "several orders of magnitude higher than v" which could increase viscous torques at the CMB by "several powers". If the ef- fective viscosity of the outer core resulting from turbulent flow were ~ 105 cm2/s dur- ing the geological past, then viscous dissipa- tion at the CMB would indeed have played an important role in the evolution of the Earth's obliquity.

The magnitude of electromagnetic core- mantle coupling depends on the assumed in- tensity of the magnetic field at the core- mantle interface and the assumed electrical conductivity of the lower mantle (Hide and Dickey, 1991). Such coupling commonly is viewed as the most likely mechanism causing decade fluctuations in the length of day (e.g. Roden, 1963; Yukutake, 1972; Lambeck, 1980; Merrill and McElhinny, 1983). Indeed, Stix and Roberts (1984) concluded that the average electromagnetic couple exceeds that required for length of day fluctuations, and so must be balanced by an equally important electromagnetic couple of opposite sense. Variations in electromagnetic core-mantle coupling also have been associated with changes in the geomagnetic dipole moment

3() G.E. WILl JAMS

with periods of ~ 1 0 2 - 1 0 4 years (Watanabe and Yukutake, 1975). Secular change in the Earth's obliquity by dissipative electromag- netic core-mant le torques has been pro- posed by Aoki and Kakuta (1971), who found i p = - 0 . 0 2 5 4 " / c y (employing the value of the electromagnetic torque between core and mantle given by Rochester, 1968), and by Kakuta and Aoki (1972), who found ip = - O. l " / c y .

Topographic core-mantle coupling requires bumps no more than 1 km in vertical ampli- tude at the CMB, but such irregularities can- not yet be resolved by seismology (Bloxham and Jackson, 1991). Hide (1969, 1989) has suggested that topographic coupling may be comparable to or even more effective than electromagnetic coupling. Indeed, topogra- phy at the CMB of a few hundred metres or more may lead to a torque that is orders of magnitude larger than the torques inferred from irregularities in the length of day fluc- tuations, implying that such fluctuations may be caused by changes of flow in the core with respect to a stable flow-configuration (Hinderer et al., 199{/; Jault and Le Mou61, 1990; Le Mou61 et al., 1992). Furthermore, core-mant le topography and possible density heterogeneities in the lower mantle may give rise also to a gravity torque which could be of similar magnitude to the topographic torque (Jault and Le MouEl, 1989). Topo- graphic core-mant le coupling may greatly affect the value of ip; Aoki and Kakuta (1971) suggested that their figure of -0 .0254" /cy for i~, caused by electromag- netic core-mant le coupling may be amplified by up to two orders of magnitude if topo- graphic coupling at the CMB is taken into consideration.

Important changes in core-mant le cou- pling may occur on geological time-scales. Thermal perturbations at the CMB may cause electromagnetic core-mant le coupling to vary significantly on time-scales of the order of IIIs years and have expression in long-term variations in the geomagnetic field (Merrill and McElhinny, 1983; McFadden and Mer-

rill, 1984). Changes in core-mant le coupling might arise also from chemical reactions be- tween the silicate mantle and the liquid iron alloy of the Earth's core, which may cause the electrical conductivity of the 200-300 km-thick D" layer at the base of the mantle to vary spatially (and also temporally?) by up to eight orders of magnitude (see Knittle and Jeanloz, 1991). Furthermore, the topography of the CMB may change with time through reactions between the outer core and mantle and changes in subduction or mantle convec- tion (Jacobs, 1972; Gubbins and Richards, 1986); such topographic changes could affect the turbulence viscosity of the outer core and cause temporal variations in topographic and viscous torques at the CMB.

In summary, the present and past values of ip resulting from the combined effects of viscous, electromagnetic and topographic torques at the CMB cannot be accurately determined because of uncertainties in esti- mating, at present and for the geological past, the effective viscosity of the outer core, the nature of magnetic fields at the CMB and within the lower mantle, and the topog- raphy of the CMB. The above review indi- cates, however, that several potential mecha- nisms for substantial core-mant le dissipation do indeed exist; if flow in the core were turbulent and hydromagnetic, large drag on the mantle could result even for a core fluid of low molecular viscosity. Importantly, esti- mates of iv by Aoki and Kakuta (1971) and Kakuta and Aoki (1972) are two to three orders of magnitude greater than the mean rate of increase in obliquity ( i t) of

0.0003-0.0006"/cy attributable to lunar tidal friction, and the upper limit for ip of 0.0004"/cy proposed by Rochester (1976) employing u = 105 cm2/s (which may under- estimate the effective or turbulence viscosity of the core now and in the geological past) approximates the likely value of ( i t ) during Earth history. Given the range of uncertain- ties and the likelihood that conditions at the CMB have varied with time, dissipative torques at the CMB may indeed have been

H I S I O R Y O F I H I L A I < ' I ' H ' S ( ) B H Q U I T Y 31

of great importance in the evolution of the Earth's obliquity.

6. A P R O P O S E D OBLIQUITY HISTORY

Since dissipative torques at the CMB could be substantial and may have varied in the geological past, the evolution of the Earth's obliquity must be critically reviewed. The commonly held views that the obliquity has slowly increased during Earth history under the sole influence of tidal friction and that the obliquity of the primordial Earth was < 10-15 ° are open to question. Indeed, as discussed in Section 4 and shown in Fig. 9, the primordial Earth's obliquity could have been as great as 70 ° or more.

Accordingly, a proposed curve of obliquity against time, based on the normal climatic zonation during the Phanerozoic, the para- doxical Late Proterozoic glacial climate, the seeming reverse climatic zonation of the Pre- cambrian in general, and the single giant impact hypothesis for the origin of the Moon, is shown in Fig. 13. The curve has four control points:

(1) At 4500 Ma, when the primordial Earth acquired a large obliquity (54°< e < 90 °) by a single giant impact with a Mars-sized body that produced the Moon. As noted earlier, an obliquity < 90 ° is required for dissipative core-mantle torques to drive the obliquity toward 0 °. A mean obliquity (g) of 70 ° arbitrarily chosen at 4500 Ma could have been induced by an impact velocity of 5-20 km/s and an impactor/Earth mass-ratio of 0.08-0.14 (Fig. 9).

(2) At 650 (+_ 30) Ma, the time of the last major glaciation of the Late Proterozoic. The preferred low palaeolatitudes of glaciation and the large amplitude of the seasonal cycle in low palaeolatitudes imply that e > 54 ° (see Section 3.2.5), and g = 60 ° is taken as a mini- mum value at 650 Ma (some alternative cal- culations are made in Section 7 also for g = 65 ° at 650 Ma). Milankovitch-band oscil- lations of obliquity about the mean value may have influenced the advance and retreat of ice sheets.

(3) At 430 Ma (Irate Ordovician-Early Silurian). Palaeo-orbital and palaeotidal data

80

Q

60

.~ r 40

o

g ~ 20

I I I I

1

I I L I [ T-

80

45"

4 uOI w

I Precambrian-Cambrian boundary ~ ' ~ l

I I I I I I t

2500 1500 500 0 Age (Ma)

60

40

20

0 I I I I 0 4500 3500

Fig. 13. Proposed curve of mean obliquity of the ecliptic g against time, consistent with the single giant impact hypothesis for the Moon ' s origin and interpreta t ion of the geological record. The curve's four control points are: (1)

= 70 ° at 4500 Ma; (2) g = 60 ° at 650 Ma; (3) g = 26 ° at 430 Ma; and (4) ~ = 23 ° at 0 Ma. These data indicate that ~: = 45 ° (when gp is maximum) at ~ 550 Ma, which is taken as the P recambr ian-Cambr ian boundary.

32 (~.[:,. WILI,IAMS

for the Mallowa Salt and Elatina Formation suggest that g: = 26 ° is a best estimate (see Section 3.11.

(4) A t 0 M a , f = 2 3 ° . An important feature of the curve is the

overall decline in obliquity during Earth his- tory, reflecting a postulated dominant influ- ence of dissipative core-mantle coupling. Furthermore, the curve has a strong inflec- tion and thus is divisible into three distinct parts:

(a) Very slow decrease in mean obliquity, from g = 7 0 ° at 4500 Ma to g = 6 0 ° at 650 Ma, giving a mean rate of obliquity-change (~) of -0.0009"/cy: ( ~ p ) = ( g ) - ( e t ) = -0.0012"/cy. The time of commencement of decrease in obliquity from the primordial large value, by means of dissipative torques at the CMB, is dependent on the time of formation of the fluid outer core. The origin of the core is reviewed by Jacobs (19871; a commonly held view is that core formation was essentially coeval with, or occurred shortly after, the accretion of the Earth, al- though it has also been suggested that core growth took place over much of Earth his- tory or is still continuing (e.g. Runcorn, 1964b), The single giant impact hypothesis for the origin of the Moon assumes that the Earth at the time of impact had an iron core (e.g. Taylor, 1987; Newsom and Taylor, 1989). Any subsequent growth of the outer core would increase core-mantle dissipation and ¢}p.

(b) Relatively rapid decrease in mean obliquity, from g = 60 ° at 650 Ma to g = 26 ° at 430 Ma; ( ~ ) = -0 .0556"/cy and (~v) -0.(1562"/cy. This postulated decrease in g actually is very slow; the required value of (~) is three orders of magnitude less than the present rate of obliquity oscillation (~ 47"/cy) and is below the level of de- tectability by current astronomical observa- tions.

(c) Very slow reduction in mean obliquity, from g = 2 6 ° at 430 Ma to g = 2 3 ° at 0 Ma; (~) = -0 .0025"/cy and (Ep) ~ -0.0031"/ cy.

The postulated relatively rapid decrease in mean obliquity from g = 60 ° at 650 Ma to g = 26 ° at 430 Ma may partly reflect special conditions at the CMB which caused signifi- cant increase in dissipative core-mantle torques at that time. The palaeomagnetic record may provide independent evidence of possible change in conditions at the CMB between 650 and 430 Ma. Studies of palaeo- magnetic field intensity back to ~ 2700 Ma suggest that the mean virtual dipole moment was abnormally low during the Late Protero- zoic and early Palaeozoic, with an apparent minimum < 10% of the present value at ~ 500 Ma (Carmichael, 1967, 1970; Smith, 1967, 1970; McEIhinny, 1973; Stacey, 1977; Merrill and McElhinny, 1983, Pal, 1991). As noted by McElhinny (1973), the weak palae- ofield seems to be a real effect because the mean virtual dipole moment from - 1000- 2700 Ma was similar to the present value. Stacey (1977, p. 274) stated that this pro- longed interval of very weak field "may imply a special condition in the Earth's interior at that time", and McElhinny (19791 concluded that long-term change in the geomagnetic field would most likely be accomplished by a change in the conditions at the CMB. In view of the apparent connection between recent changes in the geomagnetic field and in elec- tromagnetic core-mantle coupling (see Sec- tion 5.2), major change in electromagnetic torques at the CMB may have occurred dur- ing the Late Proterozoic and early Palaeo- zoic. As discussed in Section 5.2, electromag- netic core-mantle coupling may indeed vary significantly on time-scales of ~ l0 s years and be expressed as long-term variations in the geomagnetic field. Changes in the topog- raphy of the CMB and consequently in tur- bulent flow and effective viscosity of the outer core also could greatly affect core-mantle dissipation and the nature of the geomag- netic field.

The inflection in the proposed curve of g versus time at g = 45 + 15 ° also may partly reflect feedback effects arising from an in- creased precessional rate and the value of

H I S T O R Y O F T H E E A R T H ' S O B L I Q U I T Y 33

the obliquity itself. A first-order approxima- tion of ~p in terms of the Earth's motions is

~p cc (~2/~o)(sin 2e) (3)

where fZ is the precessional rate of the mantle and w the rate of the Earth's rotation (from equations in Aoki, 1969, and Rochester, 1976). The function ~2 in eq. 3 finds support in experiments with precessing and spinning liquid-filled spheroidal cavities (Vanyo, 1984), which imply that energy dissi- pation rates at the CMB vary as precessional rates squared. The function sin 2e provides the required change of sign for ~p at e = 90 °. Since f~ varies as sin 2e, ft is maximum when E = 45 °, and eq. 3 shows that ~p also is maximum when e = 45 °.

From eq. 3, the combined effect of em- ploying estimated increased values of ~ (see Berger et al., 1992), w (see Table 4) and e for the latest Proterozoic increases ~p by a factor of up to ~ 4 relative to ~p determined from present-day values. Furthermore, ex- periments with a rotating and precessing liq- uid-filled spheroidal cavity (Malkus, 1968) showed that turbulence produced in the pre- cessing fluid increased with increase in pre- cessional rate, abruptly jumping to a "satura- tion" value at a critical rate. Malkus (1968, p. 262) concluded that "the core was very un- stable in the past when the moon was closer to the earth than it is today." His findings raise the possibility of increased turbulence in the core, and consequent increase in ef- fective (turbulence) viscosity and dissipative core-mantle torques, as the obliquity ap- proached the value of 45 ° at which the pre- cessional rate is maximal. Dynamical effects therefore may have significantly increased the magnitude of ~p in latest Proterozoic time.

The secular deceleration of the Earth's rotation may have contributed to instability of the obliquity at ~ 530 Ma. Toomre (1974) showed that when the day was ~ 22.3 h (~ 0.93 of the present day), the core's free nutation (periodic motion of the spin-axis in

space) would have resonated precisely with the Earth's retrograde annual nutation caused by solar torques. This annual reso- nance would have caused nutation of the mantle (obliquity oscillation) with an ampli- tude of up to ~ 75", several orders of magni- tude greater than the present upper limit of any free nutation (see Rochester et al., 1974) and as much as an order of magnitude greater than the observed 18.6-year principal nuta- tion. Intriguingly, palaeorotational data for ~ 650 Ma (Table 4) imply that the resonance would have occurred at ~ 530 Ma, about the time when the postulated value of ~p was maximal (see Section 7).

The occurrence of glaciation preferentially in low to equatorial palaeolatitudes during the Late Proterozoic (see Section 3.2) would have moved polar ocean water to equatorial ice sheets and thus altered the mass distribu- tion of the Earth. The added mass of ice at the equator would have increased slightly the Earth's rate of precession, which may have led in turn to further, small increase in ~p in Late Proterozoic time.

Special conditions at the CMB and dy- namical effects on ~p therefore may explain the inflection in the curve of obliquity versus time, centred on g = 45 °, during the Late Proterozoic-early Palaeozoic. Interestingly, Lago and Cazenave (1979), in modelling the evolution of the obliquity of Venus under the influence of dissipative core-mantle viscous coupling and tidal torques, showed a sharp inflection in the curve of obliquity versus time for several cases where the obliquity moved from 90 ° to 180 ° .

Since the rate at which rotational kinetic energy is dissipated by the axial component of core-mantle coupling varies as ~O2~p tan e (Rochester, 1976), the hypothesis presented here may imply that a sizeable portion of the Earth's secular deceleration during the Pre- cambrian was caused by core-mantle dissi- pation; this possibility accords with Vanyo's (1991) model of viscous core-mantle cou- pling. Palaeotidal data suggest, however, that tidal friction has been the principal cause of

34 (u- . WILLIAMS

the Earth's deceleration during the Phanero- zoic (see Williams, 1989c, 1990, 1991a; Deub- net, 1990).

7. T H E P R O T E R O Z O I C - P H A N E R O Z O I C T R A N - SITION

An important implication of Fig. 13 is that the interval of largest and most rapid de- crease in mean obliquity, from g = 60 ° at 650 Ma to g = 26 ° at 430 Ma, spans the Protero- zoic-Phanerozoic transition. Such decrease in g, although actually very slow on a short time-scale, may have caused relatively abrupt transitions between different climate states; Crowley and North (1988) have shown that transitions between climate states at "critical points" can be rather sudden and can be caused by small changes in forcing.

Profound changes in global climate state may have occurred at two such "critical points" while g decreased from 60 ° to 26°:

(a) A change from reverse to normal cli- matic zonation would have occurred as decreased past the critical value of 54 ° . Lin- ear interpolation between the points g = 60 ° at 650 Ma and g = 26 ° at 430 Ma places this "flip-over" at ~ 610 Ma (taking g = 65 ° at 650 Ma puts the flip-over at ~ 590 Ma).

(b) Decrease in amplitude of the seasonal cycle between 650 and 430 Ma, which changed a global climate state of intense seasonality to a state more like that of today, would have been most rapid at g: = 45 + 5 ° when the rate of decrease of obliquity was maximal. The time of this critical point is placed by linear interpolation at ~ 550 __% 30 Ma (or ~ 540 _+ 30 Ma, taking ~: = 65 ° at 650 Ma). This age-range is of particular impor- tance because it includes the Precambr ian- Cambrian boundary, variously placed at 530 to 570 Ma (Gale, 1982; Odin et al., 1983, 1985; Conway Morris, 1988; Harland et al., 1990).

It is most significant, therefore, that the interval of postulated rapid and marked cli- matic and seasonal amelioration spans the two most spectacular radiation bio-events in

Earth history: the widespread appearance of soft-bodied metazoans in latest Proterozoic time at - 6 2 0 - 5 9 0 Ma and the Cambrian explosion of biota commencing at around 550 ± 20 Ma. These radiations during the Proterozoic-Phanerozoic transition signal "a major change in the earth system" (Valen- tine, 1989, p. 145).

The postulated flip-over of climatic zona- tion at ~ 610 (or ~590) Ma would have occurred near the start of the Ediacaran epoch that spans the interval between the last major glaciation of the Proterozoic and earliest Cambrian time; the age limits of the Ediacaran have been given as ~ 590-540 Ma (Jenkins, 1984), 590-570 Ma (Harland et al., 1990) and ~ 620-530 Ma (Conway Morris, 1988, 1990). The widespread appearance of Ediacaran soft-bodied metazoans (Hofmann, 1987; Conway Morris, 1990) may in part re- flect their spreading out from Late Protero- zoic equatorial havens of least stressful cli- mate and their proliferation in response to the proposed change to normal climatic zonation and accompanying reduction in sea- sonality.

The "Cambrian explosion" of faunas has been described as "a biological event of pro- found significance in the history of life" (Harland and Rudwick, 1964, p. 36) and "an evolutionary burst that was unprecedented and which has been unsurpassed" (Valen- tine, 1989, p. 145). This fundamental event in the biotic record took place during the postu- lated time of most rapid decrease in obliq- uity centred at ~ 550 (or ~ 540) Ma and hence the most rapid reduction of global seasonality. The substantial amelioration of the environment through reduction in sea- sonal temperature stresses during that inter- val would have been a major catalyst to evo- lution; it also would have enabled faunas to spread out over most of the Earth, including the vast vacant habitats of middle and high latitudes where former seasonal tempera- ture-ranges had been too large to permit advanced forms of life. Furthermore, neap- tidal ranges would have become more uni-

HISTORY OF THIz F2ARTH'S OBLIQUITY 35

form throughout the year and the long inter- vals of small neap-tidal ranges at and near equinoxes would have contracted as the obliquity decreased (see Section 3.2.6). Hence, during the Proterozoic-Phanerozoic transition, paralic tidal environments would have become more hospitable to benthonic fauna dependent on a continual oscillation of the tides.

A causal connection has been suggested between deglaciation in latest Proterozoic time and the subsequent appearance of the Ediacaran metazoans (e.g. Runnegar, 1982; Sokoiov and Fedonkin, 1986) and the Cam- brian fauna (e.g. Rudwick, 1964; Harland and Rudwick, 1964). Such suggestions, how- ever, do not adequately explain how deglaciation at ~ 620-600 Ma alone could have triggered profound biotic events over the succeeding ~ 50-100 Ma. Data from molecular biology suggest that metazoans first appeared prior to 1000 Ma (Conway Morris, 1990). Indeed, burrow-like structures of apparent metazoan origin occur in 800- 850 Ma sandstones stratigraphically below the two main glaciogenic sequences (equiv- alents of the Sturtian and Marinoan glacial deposits in South Australia) of the Late Pro- terozoic in central Australia (Lindsay, 1991), and rare Ediacaran remains occur between the two Late Proterozoic glaciogenic hori- zons in Canada (Hofmann et al., 1990; Aitken, 1991). Hence it may be asked why the disappearance of the earlier (Sturtian) ice sheets, which had occupied low palaeolat- itudes, and the advent of interglacial warm climates and transgressive seas at ~ 750 Ma (see Preiss, 1987), did not then trigger major biotic events. Evidently the evolutionary trig- ger was not deglaciation per se.

Another suggestion is that a significant increase in atmospheric oxygen at the end of the Proterozoic and the beginning of the Phanerozoic caused the appearance and rapid development of the Metazoa (Knoll, 1991), although Runnegar (1991b) concluded that Late Proterozoic-early Palaeozoic oxy- gen levels are uncertain. Since atmospheric

oxygen is almost entirely the product of pho- tosynthesis by green plants, any rapid in- crease in atmospheric oxygen during the Pro- terozoic-Phanerozoic transition may have been a consequence of improt,ing era,iron- mental conditions which permitted the prolif- eration of photosynthesising biota. An in- crease in atmospheric oxygen at that time could have provided a positive feedback that assisted the coeval development of the Meta- z o a .

It is postulated here that the first-order cause of the abrupt evolution and radiation of the Metazoa after more than three billion years of life on Earth was not deglaciation, rapid increase in atmospheric oxygen, tecton- ism, or changes in oceanic circulation, but the transition from an inhospitable global state of reverse climatic zonation and ex- treme seasonality to a benign state of normal climatic zonation, moderate seasonality and more habitable tidal environments. These changes occurred during the key interval bounded by terminal Late Proterozoic low- latitude glaciation at ~ 600 Ma and the start of Late Ordovician circum-polar glaciation at ~ 450 Ma.

8. DISCUSSION AND POSSIBLE TESTS

Secular decrease in obliquity during Earth history is envisaged as a progressive change in global state which had spectacular geologi- cal expression only at the Proterozoic- Phanerozoic transition. The progressive change has been punctuated by other events of independent origin such as icehouse and greenhouse conditions and mass extinctions.

The hypothesis of a large obliquity during the Precambrian-- the Earth's prolonged "Uranian" obliquity s tate--requires rigorous testing. Palaeomagnetic and geochronologi- cal studies of Late Proterozoic glaciogenic rocks in several continents may discriminate between glaciation during global refrigera- tion and low-latitude glaciation for a large

3('t (; .E, W I I J . I A M S

obliquity. Age determinations of the glacial deposits, preferably by zircon U - P b dating of coeval volcanics, may show whether glacia- tion was synchronous or diachronous; the demonstration of diachronous glaciation in low palaeolatitudes would favour the large- obliquity hypothesis (although the converse does not hold). The hypothesis presented here predicts ice sheets and periglacial cli- mates preferentially in low to equatorial palaeolatitudes for all pre-Ediacaran glacia- tions. Hence, palaeomagnetic studies of Early Proterozoic glaciogenic rocks in South Africa, Australia and Europe are required to ascer- tain palaeolatitudes of glacial and periglacial deposition.

Evidence for the predicted large ampli- tude of the global seasonal cycle during the Precambrian could be sought by the detailed study of varve-like deposits, rhythmites of tidal-climatic origin, and periglacial wedge- structures attributed to seasonal contraction and expansion, together with palaeomagnetic determinations of their palaeolatitudes of formation. The hypothesis presented here predicts that during the Precambrian high latitudes were subjected to extreme seasonal- ity, with very hot summers and severe win- ters; hence the search for and study of Pre- cambrian high-palaeolatitude deposi ts--such as the Late Proterozoic carbonates and shales of the North China block (Zhang and Zhang, 1985)--should be major objectives. Further- more, much palaeowind data that can be related to apparent polar wander paths for the Precambrian are required to test the prediction of non-uniformitarian palaeowind directions such as low-latitude westerlies and mid-latitude easterlies.

Geophysical investigations also are re- quired into the viability of the geocentric axial dipole model of the Earth's magnetic field during Precambrian time. In addition, the role of core-mant le dissipation in the dynamical history of the Earth requires criti- cal review, particularly for the vital interval spanning the Proterozoic-Phanerozoic tran- sition.

9. CONCLUSIONS

Study of the Earth's palaeoclimate record indicates that Phanerozoic conditions were essentially uniformitarian with regard to cli- matic zonation, whereas Precambrian envi- ronments in general appear to have been non-uniformitarian in this regard. Most no- tably, strongly seasonal glacial and periglacial Late Proterozoic climates occurred near sea level evidently in preferred low to equatorial palaeolatitudes, implying reverse climatic zonation and a Late Proterozoic obliquity greater than 54 ° (assuming a geocentric axial dipolar magnetic field). Palaeotidal data are consistent with a substantial obliquity during the Late Proterozoic.

It is postulated here that the primordial Earth acquired a large obliquity (54°< E < 90 °) from a single giant impact with a Mars- sized impactor at ~ 4500 Ma, which is widely believed to have produced the Moon. Since ~ 4500 M a the obliquity has slowly de- creased under the dominant influence of dis- sipative core-mant le torques. Some 3900 Ma after the formation of the Ear th -Moon sys- tem an increase in core-mant le dissipation, apparently related to changes in conditions at the core-mant le boundary and other dy- namical effects, caused an interval of rela- tively rapid decrease in obliquity. This "ob- liquity revolution" caused a profound change of global state recognised as the Protero- zoic-Phanerozoic transition. Before the obliquity revolution the Precambrian Earth endured a "Uranian" obliquity state (g: > 54 °) with reverse climatic zonation and a strongly seasonal global climate, and was subject to episodic glaciation preferentially in low to equatorial latitudes. Subsequent to the revo- lution the obliquity has been similar to that of the Quaternary, resulting in a less-stress- ful global state marked by normal climatic zonation, episodic circum-polar glaciation, and a much-reduced amplitude of the global seasonal cycle. The obliquity revolution trig- gered the two most spectacular radiation bio-events recognised: the widespread ap-

| t lST( )RY Of-: FHI: [:AI~/FH'S ( )BLIQUrl 'Y 37

pearance of the Ediacaran metazoans at ~ 610-590 Ma when climatic zonation flipped from reverse to normal at g = 54 °, and the "Cambrian explosion" of biota com- mencing at 550 +_ 20 Ma when the rates of obliquity-decrease and amelioration of global seasonality were maximal at g = 45 °.

This obliquity history of the Earth from a geological viewpoint implies that the terres- trial palaeoclimate record may provide vital information concerning the early dynamics and evolution of the Ear th -Moon system and dissipative processes at the core-mant le interface. Physicists are indeed considering the role of dissipative core-mant le coupling in the obliquity history of the Earth (e.g. Bills, 1990a), and the present study aims to stimulate such work.

Overall, the hypothesis presented here of an obliquity that has slowly decreased during Earth history from a primordial large value (54°< • < 90 °) accords with the widely ac- cepted single giant impact hypothesis for the origin of the Moon, employs a plausible geo- physical mechanism (dissipative core-mant le coupling) for obliquity-change, is consistent with much geological and geophysical evi- dence, can explain paradoxes and major events in the climatic and biotic records, and is readily testable. The concept of an evolv- ing obliquity therefore is soundly based and offers new perspectives on the history of the Earth.

ACKNOWLEDGMENTS

! thank Brian Embleton and Phil Schmidt of the CSIRO Division of Exploration Geo- science for fruitful collaborative research on the palaeolatitude of Late Proterozoic glaciation; Larry Frakes, Richard Jenkins and Stuart Williams of the University of Ade- laide, Jozef Syktus of the CSIRO Division of Atmospheric Research, Bill Mitchell of the National Tidal Facility, Flinders University, and Wolfgang Preiss of the South Australian

Geological Survey for helpful discussions; and Sherry Proferes for drafting. Comments by several referees led to an improved manuscript. The work is supported by the Australian Research Council.

10. REFERENCES

Aitken, J.D., 1991. Two Late Proterozoic glaciations, Mackenzie Mountains, northwestern Canada. Geol- ogy, 19: 445-448.

Allard, H.A., 1948. Length of day in the climates of past geological eras and its possible effects upon changes in plant life. In: A.E. Murncck and R.O. Whyte (Editors), Vernalization and Photoperi- odism. Chronica Botanica, Waltham, Mass., pp. 101-119.

Aoki, S., 1969. Friction between mantlc and core of the Earth as a cause of the secular change in obliquity. Astron. J., 74: 284-291.

Aoki, S. and Kakuta, C., 1971. The excess secular change in the obliquity of the ecliptic and its rela- tion to the internal motion of the Earth. Celestial Mech., 4: 171-181.

Barton, E.J., 1984. Climatic implications of the vari- able obliquity explanation of Cretaceous-Paleogene high-latitude floras. Geology, 12: 595-598.

Belt, T., 1874. An examination of the theories that have been proposed to account for the climate of the glacial period. Q.J. Geol. Soc. London, 4 (N.S.): 421-464.

Bergcr, A., 1984. Accuracy and frequency stability of the Earth's orbital elements during the Quaternary. In: A. Berger, J. Imbrie, J. Hays, G. Kukla and B. Saltzman (Editors), Milankovitch and Climate. Rei- del, Dordrecht, pp. 3-39.

Berger, A., lmbrie, J., Hays, J., Kukla, G. and Saltz- man, B. (Editors), 1984. Milankovitch and Climate. Reidel, Dordrecht, Parls 1 and 2. 895 pp.

Berger, A., Loutre, M.F. and Dehant, V., 1989a. Influ- ence of the changing lunar orbit on the astronomi- cal frequencies of pre-Quaternary insolation pat- terns. Paleoceanography, 4: 555-564.

Berger, A., Loutre. M.F. and Dchant, V., 1989b. Pre- Quaternary Milankovitch frequencies. Nature, 342: 133.

Berger, A., Loutre, M.F. and Laskar, J., 1992. Stability of the astronomical frequencies over the Earth's history for paleoclimate studies. Science, 255: 560- 566.

Bills, B.G., 1990a. Obliquity histories of Earth and Mars: influence of inertial and dissipative core- mantle coupling. XXI Lunar Planet. Sci. Conf., Houston, Abstr., pp. 81-82.

38 G,E. WILLIAMS

Bills, B.G., 1990b. The rigid body obliquity history of Mars. J. Geophys. Res., 95: 14,137-14,153.

Bloxham, J. and Jackson, A., 1991. Fluid flow near the surface of Earth's outcr core. Rev. Geophys., 29: 97-12(/.

Brinkman, A.W. and McGregor, J., 1979. The effect of the ring system on the solar radiation reaching the top of Saturn's atmosphere: direct radiation. Icarus, 38: 479-482.

Buchan, K.I,., 1991. Baked contact test demonstrates primary nature of dominant (NI) magnetisation of Nipissing intrusions in the Southern Province, Canadian Shield. Earth Planet. Sci. Lctt., 105: 492- 499.

Bukowinski, M.S.T. and Knopoff, L., 1976. Electronic structure of iron and models of the Earth's core. Geophys. Res. Lett., 3: 45-48.

Cameron, A.G.W., 1973. History of the solar system. Earth-Sci. Rev., 9: 125-137.

Cameron, A.G.W., 1986. The impact theory for origin of the Moon. In: W.K. Hartmann, R.J. Phillips and G.J. Taylor (Editors), Origin of the Moon. Lunar and Planctary Institute, Houston, pp. 609-616.

Cameron, A.G.W. and Ward, W.R., 1976. The origin of the Moon. Lunar Planet. Sci., VII: 120-122.

Carmichacl. C.M., 1967. An outline of the intensity of thc paleomagnetic field of the Earth. Earth Planet. Sci. Lett., 3: 351-354.

Carmichael, C.M., 1970. The intensity of the Earth's paleomagnetic field from 2.5× 109 years ago to the prcsent. In: S.K. Runcorn (Editor), Palaeogeo- physics. Academic, London, pp. 73-77.

Chivas, A.R., Torgersen, T. and Polach, H.A., 1990. Growth rates and Holoccne development of stroma- tolites from Shark Bay, Western Australia. Aust. J. Earth Sci., 37: 113-121.

Chumakov, N.M. and Elston, D.P., 1989. The paradox of Irate Proterozoic glaciations at low latitudes. Episodes, 12: 115-12{).

Clark, D.A. and Schmidt. P.W., 1986. Magnetic prop- erties of the banded iron-formations of the Hamers- Icy Group, W.A.. CS1RO Inst. Energy Earth Re- sour. Restricted Investigation Rep. 1638R, 33 pp. (unpubl.).

Connerncy, J.E.P., Acufia, M.H. and Ness, N.F., 1987. Thc magnetic field of Uranus. J. Geophys. Res., 92: 15,329-15,336.

Connerney, J.E.P., Acufia, M.H. and Ness, N.F., 1991. The magnetic field of Neptune. J. Geophys. Res., 96:19,023-19,042.

Conway Morris, S., 1988. Radiometric dating of the Precambrian-Cambrian boundary in the Avalon Zone. In: E, Landing, G.M. Narbonne and P. My- row (Editors), Trace Fossils, Small Shelly Fossils and the Precambrian-Cambrian Boundary. N.Y. State Mus. Bull., 463: 53-58.

Conway Morris, S., 1990. Late Precambrian and Cam- brian soft-bodied faunas. Annu. Rev. Earth Planet. Sci., 18: 101-122.

Crawford, A.R. and Daily, B., 1971. Probable non-syn- chroneity of Late Precambrian glaciations. Nature, 230: 111-112.

Creber, G.T. and Chaloner, W.G., 1984. Influence of environmental factors on the wood structure of liv- ing and fossil trees. Bot. Rev., 50: 357-448.

Croll, J., 1875. Climate and Time. Daldy, Isbister and Co., London, 577 pp.

Crowell, J.C., 1983. Ice ages recorded on Gondwanan continents. Trans. Geol. Soc. S. Africa, 86: 238-261.

Crowley, T.J., Baum, S.K. and Hyde, W.T., 1991. Cli- mate model comparison of Gondwanan and Lau- rentide glaciations. J. Geophys. Res., 96: 9217-9226.

Crowley, T.J., Hyde, W.T. and Short, D.A., 1989. Sea- sonal cycle variations on the supercontinent of Pan- gaea. Geology, 17: 457-460.

Crowley, T.J. and North, G.R., 1988. Abrupt climate change and extinction events in earth history. Sci- ence, 240: 996-1002.

Crowley, T.J. and North, G.R., 1991. Paleoclimatology. Oxford Univ. Press, New York, 339 pp.

Dachille, F., 1963. Axis changes in the Earth from large meteorite collisions. Nature, 198: 176.

de Boer, P.L., Oost, A.P. and Visscr, M.J., 1989. The diurnal inequality of the tide as a parameter for recognizing tidal influences. J. Sediment. Petrol., 59: 912-921.

Deubner, F.-L., 1990. Discussion on late Precambrian tidal rhythmites in South Australia and the history of the Earth's rotation. J. Geol. Soc. London, 147: 1083-1084.

De Villiers, P.R. and Visser, J.N.J., 1977. The glacial beds of the Griqualand West Supergroup as re- vealed by four deep boreholes between Postmas- burg and Sishen. Trans. Geol. Soc. S. Aft., 80: 1-8.

Deynoux, M., Kocurek, G. and Proust, J.N., 1989. Late Proterozoic periglacial aeolian deposits on the West African Platform, Taoudeni Basin. western Mali. Sedimentology, 36: 531-549.

Deynoux, M., Trompette, R., Clauer, N. and Sougy, J., 1978. Upper Precambrian and lowermost Palaeo- zoic correlations in West Africa and in the western part of Central Africa. Probable diachronism of the Late Precambrian tillite. Geol. Rundsch., 67: 615- 630.

Dickey, J.O., Williams, J.G. and Newhall, X.X., 1990. The impact of lunar laser ranging on geodynamics. Eos (Trans. Am. Geophys. Union), 71: 475.

Dobrovolskis, A.R., 1989. Dynamics of Pluto and Charon. Geophys. Res. Lett., 16: 1217-1220.

Donaldson, J.A., McGlynn, J.C., Irving, E. and Park, J.K., 1973. Drift of the Canadian Shield. In: D.H. Tarling and S.K. Runcorn (Editors), Implications of

HISTORY OF THE I£ARTH'S O B I . I Q U r r Y 39

Continental Drift to the Earth Sciences, vol. 1. Academic, London, pp. 3-17.

Drcwry, G.E., Ramsay, A.T.S. and Smith, A.G., 1974. Climatically controlled sediments, the geomagnetic field, and trade wind belts in Phanerozoic time. J. Geol., 82: 531-553.

Edwards, M.B., 1979. Late Precambrian glacial locs- sites from North Norway and Svalbard. J. Sediment. Petrol., 49: 85-91.

Embleton, B.J.J. and Williams, G.E., 1986. Low palae- olatitudc of deposition for late Precambrian periglacial varvites in South Australia: implications for palaeoclimatology. Earth Planet. Sci. Lett., 79: 419-430.

Endal~ A.S. and Schatten, K.H., 1982. The faint young Sun-climate paradox: continental influcnces. J. Geophys. Res., 87: 7295-7302.

Evans, M.E., 1976. Test of the dipolar nature of the geomagnetic field throughout Phanerozoic time. Nature, 262: 676-677.

Ewers, W.E. and Morris, R.C., 1981. Studies of the Dales Gorge Member of the Brockman Iron Forma- tion, Western Australia. Econ. Geol., 76: 1929-1953.

Eyles, N. and Clark, BM., 1985. Gravity-induced soft- sediment deformation in glaciomarine sequences of the Upper Proterozoic Port Askaig Formation, Scotland. Sedimentology, 32: 789-814.

Fairchild, l.J. and Hambrey, M.J., 1984. Thc Vendian succession of northeastern Spitsbergen: petrogenc- sis of a dolomite-til l i te association. Precambrian Res., 26: 111-167.

Fairchild, I.J., Hambrey, M.J., Spiro, B. and Jefferson, T.H., 1989. Late Proterozoic glacial carbonates in northeast Spitsbergen: new insights into the carbon- ate-t i l l i te association. Geol. Mag., 126: 469-490.

Frakcs. L.A., 1979. Climates Throughout Geologic Timc. Elsevier. Amsterdam, 310 pp.

Frakcs, L.A. and Francis, J.E., 1988. A guide to Phanerozoic cold polar climates from high-latitude ice-rafting in the Cretaceous. Nature, 333: 547-549.

Gale, N.H.. 1982. Numerical dating of Caledonian times (Cambrian to Silurian). In: G.S. Odin (Editor), Nu- merical Dating in Stratigraphy. Wiley-lnterscience, Chichester, pp. 467-486.

Gans, R.F., 1972. Viscosity of the Earth's core. J. Geophys. Res., 77: 360-366.

Gold, T., 1966. Long-term stability of the Ear th-Moon system. In: B.G. Marsden and A.G.W. Cameron (Editors), The Ear th-Moon System. Plenum Press, New York, pp. 93-97.

Goldreich, P., 1966. History of the lunar orbit. Rcv. Gcophys., 4:411-439.

Goldreich, P. and Peale, S.J., 1970. The obliquity of Venus. Astron. J., 75: 273-284.

Gough, D.O., 1981. Solar interior structure and lumi- nosity wlriations. Solar Phys., 74: 21-34.

Greenberg, R., 1974. Outcomes of tidal evolution for orbits with arbitrary inclination. Icarus, 23: 51-58.

Guan Baode, Wu Ruitang, Hambrey, M.J, and Geng Wuchen, 1986. Glacial sediments and erosional pavements near the Cambrian-Precambrian bound- ary in western Henan Province, China. J. Geol. Soc. London, 143:311-323.

Gubbins, D., 1976. Observational constraints on the generation process of the Earth's magnctic field. Geophys. J.R. Astron. Soc., 47: 19-39.

Gubbins, D. and Richards, M., 1986. Coupling of the core dynamo and mantle: thcrmal or topographic'? Geophys. Res. Lett., 13: 1521-1524.

Hambrey, M.J. and Harland, W.B., 1981. Earth's Prc- Pleistocene Glacial Record. Cambridge Univ. Press, Cambridge, 101)4 pp.

Hansen, K.S., 1982. Sccular effects of oceanic tidal dissipation on the Moon's orbit and the Earth's rotation. Rev. Geophys. Space Phys., 20: 457-480.

Harland, W.B., 1964a. Evidence of Late Precambrian glaciation and its significance. In: A.E.M. Nairne (Editor), Problems in Palaeoclimatology. Inter- science, London, pp. 119-149.

Harland, W.B., 1964b. Critical evidence for a great Infra-Cambrian glaciation. Geol. Rundsch., 54: 45- 61.

Harland, W.B., Armstrong, R.L., Cox, A.V., Craig, L.E.. Smith, A.G. and Smith, D.G. (Editors), 1990. A Geologic Time Scale 1989. Cambridge Univ. Press, Cambridge, 263 pp.

Harland, W.B. and Rudwick, M.J.S., 1964. The grcat Infra-Cambrian ice age. Sci. Am., 211 (2): 28-36.

Harris, A.W. and Ward, W.R., 1982. Dynamical con- straints on the formation and evolution of planetary bodies. Annu. Rcv. Earth Planet. Sci., 10: 61-108.

Hartmann, W.K., 1986. Moon origin: the impact-tri- ggcr hypothesis. In: W.K. Hartmann, R.J. Phillips and G.J. Taylor (Editors), Origin of the Moon. Lunar and Planetary Institute, Houston, pp. 579- 608.

Hartmann, W.K. and Davis, D.R., 1975. Satellite-sized planetesimals and lunar origin. Icarus, 24:504-515.

Hartmann, W.K. and Vail, S.M., 1986. Giant im- pactors: plausible sizes and populations. In: W.K. Hartmann, R.J. Phillips and G.J. Taylor (Editors), Origin of the Moon. Lunar and Planetary Institute, Houston, pp. 551-566.

Hide, R., 1969. Interaction between the Earth's liquid core and solid mantle. Nature, 222: 1055-1056.

Hide, R., 1971. Viscosity of the Earth's core. Nature Phys. Sci., 233: 100-101.

Hide, R., 1989. Fluctuations in the Earth's rotation and the topography of the core-mantle interface. Philos. Trans. R. Soc. London, A 328: 351-363.

Hide, R. and Dickey, J.O., 1991. Earth's variable rota- tion. Science, 253: 629-637.

40 G.E. WILl JAMS

Hinderer, J., Legros, H., Jault, D. and Le Mou61, J.-L., 199(I. Core-mantle topographic torque: a spherical harmonic approach and implications for the excita- tion of the Earth's rotation by core motions. Phys. Earth Planet. Inter., 59: 329-341.

Hinzc, J.O., 1975. Turbulence (2nd edition). McGraw- Hill, New York, 790 pp.

ttipkin, R.G., 1975. Tides and the rotation of the Earth. In: G.D. Rosenberg and S.K. Runcorn (Edi- tors), Growth Rhythms and the History of the Earth's Rotation. Wilcy, London, pp. 319-336.

Hofmann, H.J., 1987. Precambrian biostratigraphy. Geosci. Can., 14: 135-154.

Hofmann, H.J., Narbonne, G.M. and Aitken, J.D., 1990. Ediacaran remains from intertillite beds in northwestern Canada. Geology, 18: 1199-1202.

Hunt, B.G., 1979. The influence of the Earth's rotation rate on the gencral circulation of the atmosphere. J. Atmos. Sci., 36: 1392-1408.

Hunt. B.G., 1982. The impact of large variations of the Earth's obliquity on the climate. J. Meteorol. Soc. Jpn., 6(1: 309-318.

Idnurm. M.. 1990. A new method of dating Australian Prccambrian rocks: accumulated polar wander. BMR Res. Newsl., 13: 6-7.

Idnurm, M. and Giddings, J.W., 1988. Australian Pre- cambrian polar wandcr: a review. Precambrian Res., 40/41 : 61-88.

Irving, E., 1979. Paleopoles and paleolatitudes of North America and speculations about displaced terrains. Can. J. Earth Sci., 16: 669-694.

Jacobs, J.A., 1972. Possible changes in the core-mantle and inner-outer core boundaries. In: P. Melchior and S. Yumi (Editors), Rotation of the Earth. Int. Astron. Union Symp. No. 48. Reidel, Dordrecht, pp. 179-181.

Jacobs, J.A., 1987. The Earth's Core (2rid ed.). Aca- demic, London, 416 pp.

Jakosky, B.M and Carr, M.H., 1985. Possible precipi- tation of ice at low latitudes of Mars during periods of high obliquity. Nature, 315: 559-561.

Jault, D. and Le Mou~l, J.-L., 1989. The topographic torque associated with a tangentially geostrophic motion at the core surface and inferences on the flow inside the core. Geophys. Astrophys. Fluid Dynamics. 48: 273-296.

Jault, D. and Le Mou61, J.-L., 1990. Core-mantle boundary shape: constraints inferred from the pres- sure torque acting between the core and the mantle. Gcophys. J. Int., 1(11: 233-241.

Jcanloz. R., 1990. The nature of the Earth's core. Annu. Rev. Earth Planet. Sci., 18: 357-386.

Jcfferson, T.H., 1982. Fossil forests from the Lower Cretaceous of Alexander Island, Antarctica. Palaeontology, 25: 681-708.

Jeffrcy, D.J. and Acrivos, A., 1976. The rheological

properties of suspensions of rigid particles. Am. Inst. Chem. Eng. J., 22: 417-432.

Jenkins, R.J.F., 1984. Ediacaran events: boundary rela- tionships and correlation of key sections, especially in 'Armorica'. Geol. Mag., 121: 635-643.

Kakuta, C. and Aoki, S., 1972. The excess secular change in the obliquity of the ecliptic and its rela- tion to the internal motion of the Earth. In: P. Melchior and S. Yumi (Editors), Rotation of the Earth. Int. Astron. Union Syrup. No. 48. Reidel, Dordrecht, pp. 192-195.

Kalam-Aldin, S., 1983. Application of the Paleomag- netic Conglomerate Test to the Huronian Gow- ganda Formation of Northeastern Ontario. MSc thesis, Univ. Windsor, Ontario, 112 pp. (unpubl.)

Karhu, J. and Epstein, S., 1986. The implication of the oxygen isotope records in coexisting cherts and phosphates. Geochim. Cosmochim. Acta, 5(1: 1745- 1756.

Karte, J., 1983. Periglacial phenomena and their signif- icance as climatic and edaphic indicators. GeoJour- hal, 7: 329-340.

Kasting, J.F., 1989. Long-term stability of the Earth's climate. Palaeogeogr., Palaeoclimatol., Palaeoecol., 75: 83-95.

Kent, L.E. (comp.), 1980. Stratigraphy of South Africa. Handb. Geol. Surv. S. Afr., 8:690 pp.

Knauth, L.P. and Epstein, S., 1976. Hydrogen and oxygen isotope ratios in nodular and bedded cherts. Geochim. Cosmochim. Acta, 40" 1095-1108.

Knauth, L.P. and Lowe, D.R., 1978. Oxygen isotope geochemistry of cherts from the Onverwacht Group (3.4 billion years), Transvaal, South Africa, with implications for secular variations in the isotopic composition of cherts. Earth Planet. Sci. Lett., 41: 209-222.

Knittle, E. and Jeanloz, R., 1991. Earth's core-mantle boundary: results of experiments at high pressures and temperatures. Science, 251: 1438-1443.

Knoll, A.H., 1991. End of the Proterozoic eon. Sci. Am., 265 (4): 42-49.

Korycansky, D.G., Bodenheimer, P., Cassen, P. and Pollack, J.B., 1990. One-dimensional calculations of a large impact on Uranus. Icarus, 84: 528-541.

Krimigis, S.M., 1992. The magnetosphere of Neptune. Planet. Rep., 12 (2): 10-113.

Kr6ner, A., 1977. Non-synchroneity of late Precam- brian glaciations in Africa. J. Geol., 85: 289-300.

Kr6ner, A., McWilliams, M.O., Germs, G.J.B., Reid, A.B. and Schalk, K.E.L., 1980. Paleomagnetism of late Precambrian to early Paleozoic mixtite-bearing formations in Namibia (South West Africa): the Nama Group and Blaubeker Formation. Am. J. Sci., 280: 942-968.

Lago, B. and Cazenave, A., 1979. Possible dynamical

HISTORY OF THE EARTH'S OBI.IQUrrY 41

evolution of the rotation of Venus since formation. The Moon and the Planets, 21: 127-154.

Lambeck, K., 1978. The Earth's palaeorotation. In: P. Brosche and J. SiJndermann (Editors), Tidal Fric- tion and the Earth's Rotation. Springer, Berlin, pp. 145-153.

Lambeck, K., 1980. The Earth's Variable Rotation: Geophysical Causes and Consequences. Cambridge Univ. Press, Cambridge, 449 pp.

Lambeck, K., 1988. Geophysical Geodesy. The Slow Deformations of the Earth. Clarendon Press, Ox- ford, 718 pp.

Lambeck, K. and Pullan, S., 1980. The lunar fossil bulge hypothesis revisited, Phys. Earth Planet. In- ter., 22: 29-35.

Lc Mou~51, J.L., Courtillot, V. and Jault, D., 1992. Changes in Earth rotation rate. Nature, 355: 26-27.

Li, Yianping, Li, Yongan, Sharps, R., McWilliams, M. and Gao, Z., 1991. Sinian paleomagnetic results from the Tarim block, western China. Precambrian Rcs., 49: 61-71.

Lindsay, J.F., 1991. New evidence for ancient meta- zoan life in the Late Proterozoic Heavitree Quartzite, Amadeus Basin, central Australia. Bur. Miner. Res. Geol. Geophys. Bull., 236: 91-95.

Lindsey, D.A., 1969. Glacial sedimentology of the Pre- cambrian Gowganda Formation, Ontario, Canada. Geol. Soc. Am. Bull., 80: 1685-1702.

Long, D.G.F., 1974. Glacial and paraglacial genesis of conglomeratic rocks of the Chibougamau Formation (Aphebian), Chibougamau, Quebec. Can. J. Earth Sci., 11: 1236-1252.

MacDonald, G.J.F., 1964. Tidal friction. Rev. Geophys., 2: 467-54l.

MacDonald, G.J.F., 1966. Origin of the Moon: dynami- cal considerations. In: B.G. Marsden and A.G.W. Cameron (Editors), The Ear th-Moon System. Plenum, New York, pp. 165-209.

Malkus, W.V.R., 1968. Precession of the earth as the cause of geomagnetism. Science, 160: 259-264.

Massey, B.S., 1979. Mechanics of Fluids (4th ed.). Van Nostrand Reinhold, New York, 543 pp.

McEIhinny, M.W., 1973. Palaeomagnetism and Plate Tectonics. Cambridge Univ. Press, Cambridge, 358 pp.

McElhinny, M.W., 1979. Palaeomagnetism and the core-mantle interface. In: M.W. McElhinny (Edi- tor), The Earth: Its Origin, Structure and Evolution. Academic, London, pp. 113-136.

McElhinny, M.W., Briden, J.C., Jones, D.L. and Brock, A., 1968. Geological and geophysical implications of paleomagnetic results from Africa. Rev. Geophys., 6: 201-238.

McFadden, P.L. and Merrill, R.T., 1984. Lower mantle convection and geomagnetism. J. Geophys. Res., 89: 3354-3362.

McWilliams, M.O. and McElhinny, M.W., 1980. Late Precambrian paleomagnetism of Australia: the Adc- laide Geosyncline. J. Geol., 88: 1-26.

Melchior, P., 1986. The Physics of the Earth's Core. Pergamon, Oxford, 256 pp.

Melosh, H.J., 1990. Giant impacts and the thermal state of thc early Earth, In: H.E. Newsom and J.H. Jones (Editors), Origin of the Earth. Lunar and Planetary Institute, Houston, pp. 69-83.

Merrill, R.T. and McElhinny, M.W., 1983. The Earth's Magnetic Field. Academic, London, 4(/1 pp.

Mignard, F., 1982. Long time integration of the Moon's orbit. In: P. Brosche and J. Siindcrmann (Editors), Tidal Friction and thc Earth's Rotation I1. Springer, Berlin, pp. 67-91.

Milankovitch, M., 19311. Mathematischc Klimalchre und Astronomische Theorie dcr Klimaschwankungcn. Handbuch der Klimatologic. GcbriJdcr Borntraegcr, Berlin, I(A), 176 pp.

Molodenskiy, S.M., 1981. Upper viscosity boundary of the Earth's core. lzv. Earth Phys., 17: 9//3-9(/9.

Morris, W.A., 1977. Paleomagnetism of the Gowganda and Chibougamau Formations: evidencc for 2,200- m.y.-old folding and rcmagnetization event of the southern province. Geology, 5: 137-140.

Munk, W.H. and MacDonald, G.J.F., 1960. The Rota- tion of the Earth. Cambridge Univ. Press, Cam- bridge, 323 pp.

Mustard, P.S. and Donaldson, J.A., 1987. Early Pro- terozoic ice-proximal glaciomarinc deposition: the lower Gowganda Formation at Cobalt, Ontario, Canada. Geol. Soc. Am. Bull., 98: 373-387.

Ness, N.F., Acufia, M.H., Burlaga, L.F., Connerney, J.E.P., Lepping, R.P. and Neubaucr, F.M., 1989. Magnetic fields at Neptune. Science, 246: 1473- 1478.

Newsom, H.E. and Taylor, S.R., 1989. Geochemical implications of the formation of the Moon by a single giant impact. Nature, 338: 29-34.

Nio, S.D. and Yang, C.S., 1989. Recognition of Tidally-lnfluenced Facies and Envimnmcnts. Inter- national Gcoservices, Lcidcrdorp, Short Course Notes Scr., 1,230 pp.

North, G.R., Cahalan, R.F. and Coaklcy, J.A., 1981. Energy balance climate models. Rev. Gcophys. Space Phys., 19: 91-12l.

Odin, G.S., Galc, N.H., Auvray, B., Biclski, M., Dor6, F.,Lancelot, J.R. and Pastccls, P., 1983. Numerical dating of Prccambrian--Cambrian boundary. Na- ture, 301: 21-23.

Odin, G.S., Gale, N.H. and Dor6, F., 1985. Radiomct- ric dating of Late Preeambrian times. In: N.J. Snelling (Editor), The Chronology of thc Gcological Record. Gcol. Soc. London Mcm., 10: 65-72.

Officer, C.B., 1986. A conceptual model of core dy-

42 (;.1~. WILLIAMS

namics and the earth's magnetic field. J. Geophys., 59: 89-97.

Oort, A.H., 1983. Global atmospheric circulation statistics, 1958-1973. Natl. Oceanic Atmos. Adm. Prof. Pap., 14: 1-180.

Pal, P.C., 1991. The correlation of long-term trends in the palaeointensity and reversal frequency varia- lions. J. Geomagn. Gcoelectr., 43: 409-428.

Pannella, G., 1975. Palaeontological clocks and the history of the Earth's rotation. In: G.D. Rosenberg and S.K. Runcorn (Editors), Growth Rhythms and the History of the Earth's Rotation. Wiley, London, pp. 253-284.

Pannclla, G., 1976. Tidal growth patterns in recent and fossil mollusc bivalve shells: a tool for the recon- struction of paleotides. Naturwissenschaften, 63: 539-543.

Pariwono, J.l., Bye, J.A.T. and Lennon, G.W., 1986. Long-period variations of sea-level in Australasia. Geophys. J.R. Astron. Soc., 87: 43-54.

Parrish, J.T. and Peterson, F., 1988. Wind directions predicted from global circulation models and wind directions determined from eolian sandstones of the western United S ta t e s - -A comparison. Sediment. Geol., 56: 261-282.

Pcalc, S.J., 1976. Inferences from the dynamical history of Mercury's rotation. Icarus, 28: 459-467.

Perrin, M., Elston, D.P. and Moussine-Pouchkine, A., 1988. Paleomagnetism of Proterozoic and Cambrian strata, Adrar de Mauritanie, cratonic West Africa. J. Geophys. Rcs., 93: 2159-2178.

P~Sw~5, T.L., 1959, Sand-wedge polygons (tesselations) in the McMurdo Sound region, Antarc t ica- -a progress report. Am. J. Sci., 257: 545-552.

Pillsbury, G.B., 1940. Tidal Hydraulics. Corps of Engi- neers U.S. Army, Prof. Pap., 34, 283 pp.

Piper, J.D.A., Bridcn, J.('. and Lomax, K., 1973. Pre- cambrian Africa and South America as a single continent. Nature, 245: 244-248.

Piper, J.D.A. and Grant. S., 1989. A palaeomagnetic test of the axial dipole assumption and implications for continental distribution through geological time. Phys. Earth Planet. Inter., 55: 37-53.

Playford, P.E. and Cockbain, A.E., 1976. Modern algal stromatolites at Hamelin Pool, a hypersaline barred basin in Shark Bay, Western Australia. In: M.R. Walter (Editor), Stromatolites. Elsevier, Amster- dam, pp. 389-411.

Plumb. K.A., 1981. Late Proterozoic (Adelaidean) tillilcs of the Kimberley-Victoria River region, Western Australia and Northern Territory. In: M.J. Hambrey and W.B. Harland (Editors), Earth's Pre- Pleistocene Glacial Record. Cambridge Univ. Press, Cambridge, pp. 5114-514.

Poirier, J.P., 1988. Transport properties of liquid met-

als and viscosity of the Earth's core. Geophys. J., 92: 99-105.

Preiss, W.V. (Compiler), 1987. The Adelaide Geosyn- cline. Geol. Surv. S. Aust. Bull., 53, 438 pp.

R~idler, K.-H. and Ness, N.F., 1990. The symmetry properties of planetary magnetic fields. J. Geophys. Res., 95: 2311-2318.

Rochester, M.G., 1968. Perturbations in the Earth's rotation and geomagnetic core-mantle coupling. J. Geomagn. Geoelectr., 20: 387-4112.

Rochester, M.G., 1076. The secular decrease of obliq- uity duc to dissipative core-mantle coupling. Geo- phys. J.R. Astron. Soc., 46: 109-126.

Rochester, M.G., 1984. Causes of fluetualions in the rotation of the Earth. Philos. Trans. R. Soc. London A, 313: 95-105.

Rochester, M.G., Jensen, O.G. and Smylie, D.E., 1974. A search for thc Earth's 'nearly diurnal free wob- ble'. Geophys. J.R. Astron. Soc., 38: 349-363.

Roden, R.B., 1963. Electromagnetic core-mantle cou- pling. Geophys. J.R. Astron. Sot., 7: 361-374.

Roscoe, R., 1952. The viscosity of suspensions of rigid spheres. Br. J. Appl. Phys., 3: 267-269.

Roy, J i . and Lapointe, P i . , 1976. The paleomag- netism of Huronian red beds and Nipissing diabase; post-Huronian igneous events and apparent polar wander path for the interval 23110 to -1500 Ma for Laurentia. Can. J. Earth Sci.. 13: 749-773.

Rubincam, D.P., 1991). Mars: change in axial lilt duc to climate'? Science, 248: 720-721.

Rudwick, M.J.S., 1964. The Infra-Cambrian glaciation and the origin of the Cambrian fauna. In: A.E.M. Nairn (Editor), Problems in Palaeoclimatology. In- terscience, London, pp. 150-155.

Runcorn, S.K., 1964a. Palaeowind directions and palaeomagnetic latitudes. In: A.E.M. Nairn (Editor), Problems in Palaeoclimatology. lntersciencc, Lon- don, pp. 409-421.

Runcorn, S.K., 1964b. A growing core and a convecting mantle. In: H. Craig, S.L. Miller and G.J. Wasser- burg (Editors), Isotopic and Cosmic Chemistry. North-Holland, Amsterdam, pp. 321-340.

Runnegar, B., 1982. Oxygen requirements, biology and phylogenctic significance of the late Precambrian worm Dickinsonia, and the evolution of the burrow- ing habit. Alcheringa, 6: 223-230.

Runnegar, B., 1991a. Oxygen and the early cw)lution of the Metazoa. In: C. Bryant (Editor), Metazoan Life without Oxygen. Chapman and Hall, London, pp. 65-87.

Runnegar, B., 1991b. Precambrian oxygen levels esti- mated from the biochemistry and physiology of early e u k a r y o t e s . Pa l a e oge og r . , P a l a e o c l i m a t o l . , Palaeoecol., 97: 97-111.

Safronov, V.S., 1966. Sizes of the largest bodies falling

H I S T O R Y OF r i l e E A R T H ' S OI~LIQUITY 43

onto the planets during their formation. Sov. As- tron. AJ, 9: 987-991.

Safronov, V.S. and Zvjagina, E.V., 1969. Relative sizes of the largest bodies during the accumulation of planets. Icarus, 10: 109-115.

Sato, R. and Espinosa, A.F., 1967. Dissipation factor of the torsional mode c~T2 for a homogeneous-mantle Earth with a soft-solid or a viscous-liquid core. J. Geophys. Res., 72: 1761-1767.

Sato, R. and Espinosa, A.F., 1968. Reflection and transmission coefficients of SH waves at a solid- firmoviscous boundary. Ann. G~ophys., 24: 709-714.

Schmidt, P.W., Williams, G.E. and Embleton, B.J.J., 1991. Low palaeolatitude of Late Proterozoic glacia- tion: early timing of remanence in haematite of the Elatina Formation, South Australia. Earth Planet. Sci. Lett., 105: 355-367.

Schwarz, E.J. and Symons, D.T.A., 1969. Geomagnetic intensity between 1011 million and 2500 million years ago. Phys. Earth Planet. Inter., 2: 11-18.

Scrutton, C.T., 1964. Periodicity in Devonian coral growth. Palaeontology, 7: 552-558.

Scrutton, C.T., 1970. Evidence for a monthly periodic- ity in the growth of some corals. In: S.K. Runcorn (Editor), Palaeogeophysics. Academic, London, pp. 11-16.

Scrutton, C.T., 1978. Periodic growth features in fossil organisms and the length of the day and month. In: P. Brosche and J. Siindermann (Editors), Tidal Fric- tion and the Earth's Rotation. Springer, Berlin, pp. 154-196.

Sellers, W.D., 1990. The genesis of energy balance modeling and the cool sun paradox. Palaeogeogr., Palaeoclimatol., Palaeoecol., 82: 217-224.

Singer, S.F., 1977. The early history of the Earth-Moon system. Earth-Sci. Rev., 13: 171-189.

Sheldon, R.P., 1984. Ice-ring origin of the Earth's a t m o s p h e r e and hydrosphere and Late Proterozoic-Cambrian phosphogenesis. Geol. Surv. India Spcc. Publ., 17: 17-21.

Smith. P.J., 1967. The intensity of the ancient geomag- netic field: a review and analysis. Geophys. J.R. Astron. Soc., 12: 321--362.

Smith, P.J., 19711. The intensity of the ancient geomag- netic field: a summary of conclusions. In: S.K. Run- corn (Editor), Palaeogeophysics. Academic, Lon- don, pp. 79-90.

Sokolov, B.S. and Fedonkin, M.A., 1986. Global bio- logical events in the late Precambrian. In: O.H. Wa[liser (Editor), Global Bio-Events. Springer, Berlin, pp. 105-108.

Spencer, A.M., 1971. Late Pre-Cambrian glaciation in Scotland. Mere. Geol. Soc. Ixmdon, 6, 100 pp.

Spencer, A.M., 1985. Mechanisms and environments of deposition of late Precambrian geosynclinal tillites:

Scotland and East Greenland. Palaeogcogr., Palaeoclimatol., Palaeoecol., 51: 143-157.

Stacey, F.D., 1977. Physics of the Earth, 2nd edn. Wiley, Ncw York, 414 pp.

Stix, M. and Roberts, P.H, 1984. Time-dependent electromagnetic core-mantle coupling. Phys. Earth Planet. Inter., 36: 49-60.

Sumner, D.Y., Kirschvink, J.L. and Runnegar, B.N., 1987. Soft-sediment paleomagnetic field tests of late Precambrian glaciogenic sediments (abs.). Eos, 68: 1251.

Symons, D.T.A., 1975. Huronian glaciation and polar wander from the Gowganda Formatiom Ontario. Geology, 3: 304-306.

Suzuki, Y. and Sam, R., 19711. Viscosity determination in the Earth's outer core from ScS and SKS phases. J. Phys. Earth, 18: 157-170.

Taylor, I.E. and Middleton. G.V., 1990. Aeolian sand- stones in the Copper Harbor Formation, Late Pro- terozoic, Lake Superior basin. Can. J. Earth Sci., 27: 1339-1347.

Taylor, S.R., 1987. The origin of the Moon. Am. Sci., 75: 469-477.

Tonks, W.B. and Melosh, H.J., 199/). The physics of crystal settling and suspension in a turbulent magma ocean. In: H.E. Newsom and J.H. Jones (Editors), Origin of the Earth. Oxford Univ. Press, New York, pp. 151-174.

Toomrc, A., 1974. On the 'nearly diurnal wobble' of the Earth. Geophys. J.R. Astron. Soc., 38: 335-348.

Tremaine, S., 1991. On the origin of the obliquities of the outer planets. Icarus, 89: 85-92.

Trendall, A.F., 1972. Rew)lution in Earth history. J. Geol. Soc. Aust., 19: 287-311.

Trcndall, A.F., 1973a. lron-fl)rmations of the Hamers- ley Group of Western Australia: type examples of varved Precambrian cvaporites. In: Genesis of Pre- cambrian Iron and Manganese Deposits. UNESCO, Paris, Earth Sciences, 9: 257-2711.

Trendall, A.F., 1973b. Varve cycles in the Wecli Wolli Formation of the Precambrian Hamcrsley Group, Western Australia. Econ. Geol., 68: 11/89-1(t97.

Trendall, A.F., 1976. Striated and facetcd boulders from the Turcc Creek Formation--evidence for a possible Huronian Glaciation on the Australian continent. Geol. Sure. W. Aust. Annu. Rep. 1975, pp. 88-92.

Trendall, A.F., 1983. The Hamerslcy Basin. In: A.F. Trendall and R.C. Morris (Editors), Iron-Forma- tion: Facts and Problems. Elsevier, Amsterdam, pp. 69-129.

Valentine, J.W., 1989. Phanerozoic marine faunas and the stability of the Earth system. Palaeogeogr., Palaeoclimatol., Palaeoccol., 75: 137-155.

44 G.I-. WILLIAMS

Van der Voo, R., 1990. The reliability of palcomag- nctic data. Tectonophysics, 184: 1-9.

Van Hemelrijck, E., 1982. The insolation at Pluto. Icarus, 52: 560-564.

Vanyo, J.P., 1984. Earth core motions: experiments with spheroids. Geophys. J.R. Astron. Soc., 77: 173 183.

Vanyo, J.P., 1991. A geodynamo powered by luni-solar precession. Geophys. Astrophys. Fluid Dynamics, 59: 2/t9-234.

Vanyo, J.P. and Awramik, S.M., 1982. Length of day and obliquity of the ecliptic 850 Ma ago: prelimi- nary results of a stromatolite growth model. Geo- phys. Res. Lctt., 9:1125-1128.

Vanyo, J.P. and Awramik, S.M., 1985. Stromatolites and Ear th -Sun-Moon dynamics. Precambrian Res., 29: 121-142.

Walter, M.R., 1976. Hot-spring sediments in Yellow- stone Nalional Park. In: M.R. Walter (Editor), Stro- matolitcs. Elsevier, Amsterdam, pp. 489-498,

Ward, W.R., 1974. Climatic variations on Mars 1. As- tronomical theory of insolation. J. Gcophys. Res., 79: 3375-338(7.

Ward, W.R., 1975. Past orientation of the lunar spin axis. Science, 189: 377--379.

Ward, W.R., 1979. Present obliquity oscillations of Mars: fourth-order accuracy in orbital e and I. J. Gcophys. Res., 84: 237-24l.

Ward, W.R., 1982. Comments on the long-term stabil- ity of the Earth's obliquity. Icarus, 50: 444-448.

Ward, W.R., Burns, J.A. and Toon, O.B., 1979. Past obliquity oscillations of Mars: the role of the Thar- sis Uplift. J. Geophys. Res., 84: 243-259.

Warring, C.B., 1885, The uniformity of geological cli- mate in high latitudes. Trans. N.Y. Acad. Sci., 3: 84-97.

Washburn, A i . , 1980. Geocryology. A Survey of Periglacial Processes and Environments. Wiley, New York, 4(16 pp.

Watanabc, H. and Yukutake, T., 1975. Electromag- nctic corc-mantle coupling associated with changes in the geomagnetic dipole field. J. Geomagn, Gco- electr., 26: 153-173.

Webb, D.J., 1982. On the reduction in tidal dissipation produced by increases in the Earth's rotation rate and its effect on the long-term history of the Moon's orbit. In: P. Brosehe and J. Siindermann (Editors), Tidal Friction and the Earth's Rotation II. Springer, Berlin, pp. 21(/-221.

Williams, G.E., 1975a. Late Precambrian glacial cli- mate and the Earth's obliquity. Geol. Mag., 112: 441-465.

Williams, G.E., 1975b. Possible relation between peri- odic glaciation and the flexure of the Galaxy. Earth Planet. Sci. Lctt., 26: 361-369.

Williams, G.E., 1979. Sedimentology, stable-isotope geochemistry and palaeoenvironment of dolostones

capping late Precambrian glacial sequences in Aus- tralia. J. Geol. Soc. Aust., 26: 377-386.

Williams, G.E., 1986. Precambrian permafrost horizons as indicators of palaeoclimate. Precambrian Res., 32: 233-242.

Williams, G.E., 1988. Cyclicity in the late Precambrian Elatina Formation, South Australia: solar or tidal signature? Clim. Change, 13: 117-128.

Williams, G.E., 1989a. Late Prccambrian tidal rhyth- mites in South Australia and the history of the Earth's rotation. J. Geol. Soc. London, 146:97-111.

Williams, G.E., 1989b. Precambrian tidal sedimentary cycles and Earth's paleorotation. Los (Trans. Am. Geophys. Un.), 70: 33, 40-41.

Williams, G.E., 1989c. Tidal rhythmites: geochronome- ters for the ancient Earth-Moon system. Episodes, 12: 162-171.

Williams, G.E., 19911. Tidal rhythmites: key to the history of the Earth's rotation and the lunar orbit. J. Phys. Earth, 38: 475-491.

Williams, G.E., 1991a. Upper Proterozoic tidal rhyth- mites, South Australia: sedimentary features, depo- sition, and implications for the Earth's paleorota- tion. In: D.G. Smith, G.E. Reinson, B.A. Zaitlin and R.A. Rahmani (Editors), Clastic Tidal Sedi- mentology. Can. Soc. Petrol. Geol. Mere., 16: 161- 178.

Williams, G.E., 1991b. Milankovitch-band cyclicity in bedded halite deposits contemporaneous with Late Ordovician-Early Silurian glaciation, Canning Basin, Western Australia. Earth Planet. Sci. Lctt., 103: 143-155.

Williams, G.E., 1993. The enigmatic Late Proterozoic glacial climate: an Australian perspective. In: M. Deynoux, J.M.G. Miller, E.W. Domak, N. Eylcs, I.J. Fairchild and G.M. Young (Editors), Earth's Glacial Record. Cambridge Univ. Press, Cambridge (in press).

Williams, G.E. and Tonkin, D.G., 1985. Periglacial structures and palaeoclimatic significance of a late Precambrian block field in the Cattle Grid copper mine, Mount Gunson, South Australia. Aust. J. Earth Sci., 32: 287-30(I.

Williams, Q. and Jeanloz, R., 1991). Melting relations in the iron-sulfur system at ultra-high pressures: implications for the thermal state of the Earth. J. Geophys. Res., 95: 19,299--19,310.

Wolfe, J.A., 1980. Tertiary climates and floristic rela- tionships at high latitudes in the Northern Hemi- sphere. Palaeogeogr., Palaeoclimatol., Palacoecol., 30: 313-323.

Woolard, E.W. and Clemence, G.M., 1966. Spherical Astronomy. Academic, New York, 453 pp.

Worsely, T.R. and Kidder, D.L., 1991. First-order cou- pling of paleogeography and CO 2, with global sur- face temperature and its latitudinal contrast. Geol- ogy, 19: 1161-1164.

HISrORY ()F IHI~ 15AR'I'H'S ()BI.IQUI'FY 45

Young, G. and Claoud-Long, J., 1991. Age control on sedimentary sequences. BMR Res. Newsl., 15: 14- 16.

Young, G.M., 1973. Tillites and aluminous quartzites as possible time markers for middle Precambrian (Aphcbian) rocks of North America. Geol. Assoc. Can. Spec. Pap., 12: 97-127.

Young, G.M., 1981. The Early Proterozoic Gowganda Formation, Ontario, Canada. In: M.J. Hambrcy and W.B. Harland (Editors), Earth's Pre-Pleistocene Glacial Record. Cambridge Univ. Press, Cambridge, pp. 8117-812.

Young, G.M. and Long, D.G.F., 1976. lce-wedgc casts from the Huronian Ramsay Lake Formatkm ( > 2,3110 m.y. old) near Espanola, Ontario, Canada. Palaeogeogr., Palaeoclimatol., Palaeoecol., 19:191- 200,

Yukutakc, T., 1972. The effect of change in the geo- magnetic dipole moment on the rate of the Earth's rotation. J. Ocomagn. Gcoelcctr., 24: 19-47.

Zhang, H. and Zhang, W., 1985. Palaeomagnctic data, late Precambrian magnctostratigraphy and tcctonic evolution of eastern China. Prccambrian Res., 29: 65-75.