Geophys. .I
R.
. astr. Soc. (1984) 79, 939-961
Plate motions and the geomagnetic field - 11.
Jurassic to Tertiary
R. A. Livermore and F. J. Vine School of Environmental Sciences,
University of East Anglia, Norwich NR4 7TJ
A. G .
Smith Department ofEarth Sciences, University of Camhridge,
Downing Street, Cambridge CBZ 3EQ
Received 1984 June 8; in original form 1984 February 13
Summary. The analysis of the time-averaged geomagnetic field is extended
back to 200Ma. Palaeomagnetic poles from the major plates have been
carefully selected from recent compilations of reliable results for each region.
These were returned, with their corresponding sampling sites, to their locations at the estimated dates of magnetization, in a fixed-hotspots framework.
The corrected results were then grouped into 20Ma windows at intervals of
10Ma representing the past lOOMa, and 40Ma windows at 30Ma intervals
for the more sparse 100-200Ma data. Global means and Fisher statistics
were calculated for each window having included the axial quadrupole in the
calculation. The value of this coefficient which gave the maximum value for
the Fisher precision parameter (tightest grouping of poles) was taken as
representative of each interval. The results indicate that a small axial quadrupole of the same sign as the axial dipole may have persisted throughout the
Cenozoic. Tlus is equivalent to a northward offset axial dipole field (far-sided
effect). During the late Cretaceous, this component appears to have changed
sign with respect to the dipole. Negative values seem to have obtained
throughout the Cretaceous long normal polarity interval, corresponding to a
southward offset dipole (near-sided effect). The data distribution is inadequate
for the resolution of the quadrupole at earlier times, and zero values cannot
be discounted. Little relative motion is implied between the hotspots and the
geomagnetic axis for the past 90 Ma, the global mean polar path curving
around the predicted fixed-hotspots pole at a distance of typically 5"
latitude with little sign of rapid Tertiary polar wander as implied by studies of
Pacific data alone. Between 100 and 200 Ma, however, there is a clear difference between the two reference frames, amounting to 17-19" in the Jurassic.
This may reflect motion of the mantle relative to the geomagnetic axis, but
may also include errors due to inaccurate determination of hotspot tracks
and inter-hotspot motion.
940
R. A. Livermore, F. J. Vine and A. G. Smith
1 Problems involved in data selection
A dense and uniform distribution of sampling sites is required to define the non-dipole
components of the time-averaged field for any particular interval. In addition, each study
should have adequately averaged out secular variation, have incorporated corrections for
any tectonic rotations and be free from magnetic overprinting.
As t h e sampling window is moved backwards in time, so the distribution of suitable
data becomes sparser. Conspicuous gaps exist in both time and space even for large and
otherwise well-studied plates such as Eurasia. Moreover, as age increases, so do the likely
errors in relocating sampling sites and palaeopoles. High precision is required in the dating of
magnetization of older rocks through radiometric or biostratigraphic means, especially for
fast-moving plates.
We have assembled a file of palaeomagnetic poles from the major plates from published
sources as the basis of a study of the average nature of the non-dipole field during the last
200Ma. The sources used are all recent compilations of poles thought to be reliable in the
sense of representing the original field direction unaffected by local tectonic rotations or
magnetic overprinting. Many of these were published in McElhinny & Valencio (198 1). To
these have been added more recently published results t o early 1983. All results conform to
the minimum reliability criteria set out by McElhinny (1973). In addition, we have rejected
results for which an age estimate was not available t o within + 2 0 Ma. There has been much
debate o n the subject of data selection and weighting (e.g. Harrison & Lindh 1982a), which
become critical when data are sparse. The application of stringent criteria with respect to the
number of samples or specimens studied, magnetic cleaning and dating is desirable but can
result in a dataset of vanishing proportions. We take a practical approach and accept results
deemed as valid b y expert workers for each plate or fragment. We then review the reconstructed data to detect clearly deviant results, eliminating those poles which lie outside a
OgS circle of confidence about the overall mean (see Harrison & Lindh 1982a; McFadden
1982). Results based on magnetic vector fitting of seamount anomalies are weighted equally
with the continental poles. They are derived principally from t h e compilations of Harrison
et al. (1975) and Sager (1983b). Averaged poles have been used representing four similar
poles from neighbouring seamounts in the Musicians Group (OT13-68) and four Equatorial
Group seamounts (OT13-63) t o ensure more even geographical distribution of sampling
sites. Otherwise, individual results have been employed.
We have referred all stratigraphic ages t o the time-scale of Harland et al. (1982) and
corrected radiometric ages to standardized decay constants (Steiger & Jaeger 1977). A
complete list of the poles used is given in Table 1.
2 Repositioning o f data
The sites and poles have been repositioned at the locations corresponding to the estimated
ages of magnetization, For this purpose, we have used recently-published finite rotations
derived mainly from magnetic anomaly correlations, linearly interpolating for ages between
the times of identified anomalies.
Few reconstructions can be made without some areas of contention but we have made
what appear to us to be the most reasonable choices of rotation parameters in a global
context. Africa is composed o f Nubia and Somalia, which are fitted at 25 Ma, along With
Arabia, using the model suggested by Cochran (1981, 1982, 1983). Recent identification of
M-series anomalies in the Somali and Mozambique Basins has allowed much more accurate
relocation of Madagascar relative to East Africa (Segoufin & Patriat 1981), while the recent
Geomagneticfield since the Jurassic
Table 1. Palaeomagnetic data (north poles) for the interval
0-200 Ma.
Hock 1Jnit
P?Cl€IC
Kiekie Volcanlcs. Niihau
21.9 199.8
Koloa Volcanics. Kauai
22.0 200.6
s o c i e t y Islands
-17.0 209.0
Ko31au Volcanlcs, M u
21.5 201.9
mwallan Lavas
20.5 202.5
Nirhau Islard h v a s
22.0 200.0
Sanoan Volcanics
-14.0 188.0
Norfolk and P h i l i p Is. Lavas -29.1 167.9
WaiaMe Volcanics, Oahu
21.5 201.9
T r i p 3 SeanDUnt R
21.0 247.4
Nihoa Island Ldvas
23.1 202.0
Kauai Volcanlcs
22.0 200.5
Midway A t o l l Lavas
28.2 182.0
39131 S m u n t
39.0 229.0
Stanley Seannunt
8.2 198.1
wlllou3hby searrount
7.9 198.1
C h a p m Semmt
3.4 199.9
Clarke S m u n t
- 3 . 3 202.0
Abtwtt Searrount
31.8 174.3
Mconless S m u n t
31.9 218.2
Paumkua S e m u n t t112
24.9 202.9
LlNlamed SeanDUnt H I 1
26.5 182.2
uyeda Searrount
-7.5 208.5
Equatorial seamxnt ~ r o u p
8.0 182.0
Kona 4 Semmt
17.3 205.8
17.1 205.8
K ~ n a5 SeanDUnt
Chataqua Searmunt
22.2 197.4
Ryofu Searrount
38.0 146.0
Siscev Searrount
40.9 144.9
17.9 207.3
smw Sealmunt
12.0 194.2
Kapsitotwa S e m m t
30.5 197.0
Musicians SeanDUnt Group
12.5 193.0
Nagata Searmmt
31.8 195.0
Mahler SeanDunt
29.0 197.7
L i s z t SBam3unt
18.3 198.2
tD1 Seamunt
21.7 161.9
Mlami Searmunt
2 4 / 3 Semmt
55.9
42.1
355.2
38.7
58.0
33.1
313.0
236.3
34.8
93.4
329.2
23.4
11.4
23.0
356.5
14.6
37.7
20.4
4.6
41.3
1.8
8.9
345.6
355.1
352.8
1.5
359.0
352.0
359.0
350.1
333.5
339.1
4.0
342.6
333.8
342.0
341.5
0.5
1.4
1.9
2.3
2.6
2.6
2.6
2.8
3.1
3.1
3.5
4.6
27.0
35.5
41.9
41.9
42.0
42.0
42.5
42.8
70.0
74.0
75.0
m.7
80.7
82.1
e0.7
81.0
81.0
81.3
84.0
85.0
85.6
87.5
87.5
612-203
611-375
141568
14/69
815
14/47
612-82
14/75
14/70
613-32
14/72
13/17
14/103
613-38
583a
583a
583a
583a
583a
613-34
583b
5e3b
583b
613-63
613-13
613-14
613-15
613-20
613-19
613-9
613-69
613-68
5rn82
583b
583b
90.1
613-70
613-55
53.0 3162.0
63.7 331.3
93.8
94.0
613-53
-78.0
-77.4
-84.0
-84.0
-@40.
-84.0
45.0
77.5
69.5
73.5
310.0
161.0
161.6
165.0
165.0
165.0
165.0
86.2 123.7
86.6 205.5
84.8 67.6
81.0 41.0
56.5 12.0
58.0 38.0
45.0 39.0
59.0 41.0
54.2 40.2
44.1 51.5
53.8 42.6
1.0
1.0
26.6
32.5
171.9
172.0
172.0
172.0
189.0
189.0
189.0
14/32
14/25
14/130
8/10
14/239
2/27
6/36
18/70
15/223
15/221
15/222
-64.0
-65.0
-64.0
-64.0
-75.4
-73.5
302.0
296.0
296.0
298.0
290.2
296.5
83.0
86.0
76.0
86.0
70.8
87.0
294.0
178.0
147.0
298.0
15.4
49.5
14.9
55.5
68.9
98.0
106.0
1G9.6
12/36
7/19
574
w 7 9
K80
16/107
-38.3
-30.3
-28.2
-27.0
-31.7
-38.0
-32.0
-36.0
143.5
150.3
153.0
152.0
150.2
145.5
151.4
150.0
86.6
78.5
74.2
78.0
71.1
63.0
70.5
56.0
266.3
264.3
294.8
266.0
275.5
320.0
305.6
333.0
2.3
18.0
22.6
23.0
34.6
51.5
52.9
95.2
13/11
11/20
14/111
8/29
11/22
7/14
11/27
7/23
27.1 148.7
29.5 153.5
marw seannunt
81.7
84.9
87.7
85.2
84.0
85.2
84.0
75.0
84.1
87.0
86.6
83.6
75.0
78.0
75.5
78.2
15.7
80.0
75.5
79.4
67.7
68.0
68.5
66.7
64.6
49.8
60.0
50.0
56.0
56.5
47.5
59.7
61.6
56.0
59.2
52.0
51.7
89.1
613-25
EAST ANT?+RCPlCA
Marion 6 Q-ozet I s l a n d s
Amsterdam Island
Kerguelen I s l a n d
Heard Island
mfek InMsives
Ferrar Dolecites,
Ferrar m l e r i t e s ,
F e r r a r mlerites,
Q.Alexandra Range
Storm Peak Lavas
Mt.Falla Lava5
WEST
46.7
-37.8
49.0
-53.0
-82.6
Ferrar
Wright
Rearhre
Intrusives
mrAKcpIcA
James Ross Is. Lavas
O r v i l l e Cmst I n t m s i v e s
Andean I n t r u s i v e s
Cape Spring
Orville Cmst Intmsives
L a s s i t e r C m s t Igneous
AUSTRALIA
N M r Victoria Volcanics
Volcam
Nanmeed h Main Range voics.
Queenslam3 Lavas 6 Dykes
L i v e q x w l Volcano
Old V o l c a n i c s V i c t o r i a
Barrington V o l c a t w
Mt.Dronedary fgne~usCplx.
94 1
942
R. A . Livermore, F. J. Vine and A . G.Smith
Table 1
~
continued
Rock U n i t
Age
Reference*
(Ma)
Bunbury B a s a l t
w e t U k a l i n e Ccmpler
Bendigo Dykes
Kangarm Island B a s a l t
T a s m i a n mlerite
I n t r u s i v e s N.S.W.
Garravnlla L Nanbi Igneous
-33.4
43.2
-37.0
-35.6
42.0
-33.7
-31.e
115.6
147.1
144.3
137.5
147.5
150.4
150.0
49.0
50.0
47.0
39.0
50.7
51.0
46.1
341.0
338.0
315.0
3.0
354.5
6.1
355.1
97.8
1ffi.6
154.1
170.0
174.5
178.5
197.4
15/35
6/31
15/62
15/67
16/118
15/70
15/72
33.1
32.8
30.2
30.1
23.0
17.8
22.5
18.0
18.0
18.0
21.5
24.1
30.2
72.4
73.0
68.2
66.6
82.'0
73.8
73.5
75.0
75.0
75.0
70.5
87.6
68.2
85.0
72.1
55.5
52.5
37.0
34.0
39.2
44.0
32.5
29.5
37.1
9.3
2.0
34.0
248.7
303.5
298.5
285.9
284.0
285.6
281.5
277.5
298.5
282.4
294.7
308.0
9.0
14.9
51.5
59.9
61.5
62.6
63.6
65.0
65.0
65.0
65.7
102.5
175.5
KR47
14/104
KR40
KR39
141160
13/22
14/159
KR37
KR36
KR35
14/185
KR24-27
KFC3
Is. -37.3 346.5
83.6
85.1
85.6
83.7
84.7
75.0
84.0
87.9
86.4
82.9
84.0
82.6
86.1
81.9
88.0
75.9
83.0
78.4
73.3
88.0
85.2
79.7
82.8
63.5
69.0
83.5
81.8
61.0
69.3
75.0
48.3
CG.0
62.5
58.6
344.1
121.8
126.0
128.4
119.4
162.0
169.0
63.8
199.4
131.9
190.2
128.4
152.4
114.4
125.0
119.7
212.0
196.1
254.3
154.0
136.6
122.8
0.5
0.6
0.9
1.0
1.0
1.0
1.3
1.3
2.2
2.6
2.6
3.6
3.6
3.7
4.3
6.1
7.7
13.3
14.9
14.9
14.9
18.4
24.6
26.7
46.4
46.5
72.0
9a.0
93.0
94.3
121.9
124.9
163.8
168.0
8/2
INIXA
Siwaliks, Normal P o l a r i t y
L.Siwalik Red S h a l e s
Saniam L m s t o n e
Brewery I . r n S t 0 n e
b n h a t 51 11
k c a n Traps, W . G h a t s
M t Pavayargh Traps
k c m
Traps, Upper Normal
Traps, Lcwer Reversed
Traps,
M
Louer Normal
M t . G l m a r Volcanrcs
R a m 1 Traps
raralai Lunestone
&Can
~
C
AIWCA
h i s t a n and InaccessLble
cdmroun Volcanics
Rniouan Cmmres Is.
Canary Is. Madiera V o l c s .
Nigerian B a s a l t s
cape verde IS.
4.5
-12.2
38.0
10.5
15.0
liar"] -sad Volcs. L i b p
27.8
Azores VOlCS.
39.4
sao lhne VOICS.
0.0
i
n
e
d
28.1
canary IS. B a s a l t 3 m
-12.8
Mayotte Carores Is.
C a n a r y I s . & Madiera V o l e s .
38.0
Jebel Nefousa Volcs. Libya
32.0
Canary Is. 6 Madiera V o l c s .
38.0
32.0
Garian Volcs. Libya
Canary Is. L M z a r m e
29.0
MorcEm Volcs.
35.0
Jebel
V o l c s . Libya
28.7
Adigrat Traps E t h i o p i a
14.0
Cavallo Massif A l g e r i a
32.0
Cape Verde Is. wan
16.5
A n n O h VOlCs.
-1.0
P r i c i p e Volcs.
1.5
Abu Zaabal L o a t r a n i &salts 30.2
Wadi Abu T e r e i f i y a
30.0
m a r i a Irm O r e s
27.5
Nubian Sandstones Egypt
25.0
Kimberlites South A f r i c a
-29.0
Wadi Natash Eyypt
24.5
Moroccan SaCdstmes
31.7
Kaoka l a v a 5 South A f r i c a
-20.0
Mlmje bassif s y e r u t r Malawi -16.0
9.0
I n t r u a i v e s Niyerra
Mateke Hills Ccnplex
-21.8
9.5
44.4
344.0
12.3
335.6
17.3
328.8
6.5
345.5
45.2
344.0
13.4
344.0
13.0
346.5
357.0
15.6
39.0
5.0
336.0
5.5
7.5
31.2
32.1
29.0
33.0
27.0
34.5
353.1
14.0
35.6
8.6
31.2
IlachaMs i a v a s
Sahara b l e r z t e S i l l s
Marawudzi Caoplex
Freetom Ignwue m l e x
DLabase I n u u s i v e s L i b e r i a
North Mauritania Hank
S o u t h Mauritania I l 0 ; m
Draa Valley S i l l s mrFom Zguid Wke, M o r c c o
-24.0
28.0
-22.1
8.4
6.5
23.0
16.0
29.5
30.5
357.5
30.7
346.8
349.5
352.0
352.0
353.5
353.5
-0.3
0.0
5.1
36.1
36.0
36.0
m 1 PlArE
K l f t Valley Lavas. Kenya
E A f r l c a n Volcdnics
Shungwa h 1Jsm F D m t l o n S N
18.0
96.6
79.6
189.0
133.6
223.0
224.0
258.0
227.0
266.6
262.0
241.6
259.7
14/21
14/23
14/39
16/11
18/14
14/52
10/4
14/46
16/17
14/49
14/64
14/135
14/90
14/74
8/16
14/84
14/83
15/25
11/19
18/32
14/93
14/129
14/127
HsS79
Stis81
SHS31
m 0
SHS31
14/224
14/226
9/40
16/120
8/63
61.9 251.9
170.9
14/25@
72.0
70.2
80.9
68.5
69.4
71.4
65.5
58.0
261.0
285.1
224.6
242.4
232.0
240.2
230.5
259.0
173.7
183.2
183.7
186.8
187.0
187.0
187.0
188.8
14/249
l0/77
13/40
14/24
77.0 2L17.0
8R.4 353.8
85.1 162.5
1.0
1.2
2.3
SOAJBUBY)
sCWBB80
13/36
13/35
8/6
15/12
16/15
Geomagnetic field since the Jurassic
Table 1 - continued
Rock Unlt
Age
Reference*
(Ma)
5.1
Shun3wa & USM Formations R
Nprm40ro Caldera, T a m a n l a -3.2
E.Afric.3~V o l c a n i c s
0.0
0.0
E.African Volcanics
-1.5
K a p i t l Phcnolite, Kmya
Nalrobl Lavas
-1.3
Ethiopian Traps
9.5
0.5
mkam h v a s , Kenya
s . P l a t e a u V o l c s . , Ethiopia
9.1
B a s a l t tykes, Ethiopra
9.0
0.7
Tororo Ring Corplex, Uganda
-16.7
Lupata Rlk.Volcs., irbzamb.
m
C
A
36.0
35.6
36.0
36.0
37.5
36.8
38.7
36.0
41.0
39.0
34.2
34.2
83.8 140.6
81.0 62.0
86.5 147.6
86.5 186.6
80.8 117.7
82.0 139.0
80.8 167.7
84.6 163.3
75.1 170.3
86.4 202.8
75.8 195.5
62.0 259.0
2.3
2.5
4.5
12.3
13.3
13.3
14.9
17.4
21.5
24.1
24.6
110.6
16/16
13/9
15/16
15/20
14/97
8/24
12/46
15/21
14/112
141113
14/1117
7/21
-12.1
-21.1
-21.0
-16.5
-20.3
-20.3
-21.0
-19.0
-16.4
49.2
55.5
55.5
47.6
57.5
57.5
47.3
44.9
47.2
82.5
86.0
86.5
81.8
78.1
85.5
63.5
69.1
77.0
199.5
282.3
170.4
249.9
217.0
257.2
219.6
240.0
268.0
0.5
1.0
2.1
2.6
2.8
6.8
75.0
90.0
176.0
1513
14/27
14/48
15/8
11/11
11/13
15/50
15/51
WP76
-37.0
-50.5
-20.5
-3.8
-37.0
-33.0
-21.9
-29.9
290.0
287.3
330.7
327.6
290.0
295.0
313.4
289.1
85.0
83.4
85.6
87.7
87.0
70.0
80.7
77.0
75.0
226.2
185.3
126.5
132.a
225.0
52.8
14.a
1.2
1.8
2.7
9.7
12.0
76.0
76.9
77.0
-8.4 325.0
-29.9 289.1
-32.2 295.9
-34.0 296.0
-6.4 312.6
-34.0 296.0
-29.0 310.0
-29.9 289.1
-26.0 307.0
-32.2 295.8
-31.8 295.5
-6.4 312.6
4 7 . 8 292.2
6.8 287.0
9.0 291.8
88.0
82.0
84.2
88.0
83.6
83.0
84.6
81.0
78.0
72.0
78.0
85.3
85.0
87.8
70.5
135.0
72.E
270.6
326.0
261.0
196.0
295.4
345.0
234.0
205.0
193.0
82.5
17.0
96.8
120.7
92.0
101.0
108.3
109.3
120.0
121.4
121.9
125.0
126.0
127.0
142.8
1M.0
172.0
197.4
197.9
87.7
80.0
85.6
79.7
84.7
80.7
84.1
87.0
80.7
81.7
88.0
78.0
84.0
W.4
86.2
78.4
83.0
87.0
84.3
80.5
84.8
88.5
222.3
132.0
170.6
124.2
356.4
81.4
118.7
235.5
142.0
144.7
97.0
1m.0
29.0
44.6
334.2
121.9
163.0
219.0
177.7
130.6
173.7
119.8
0.7
1.0
1.0
1.4
1.6
1.7
2.4
2.6
2.6
2.6
2.6
2.9
3.6
3.7
3.8
3.8
6.0
6.0
7.6
9.4
12.3
12.3
R
M t . m e VOlCanlCS
ReUnlCn IS. Lavas
Reunion Is. Lavas
canbined Volcanics
b u n t i u s Volcanrcs
MaurltiLs V o l c a u c s
conblned V O l c a n l C S
C a n b i n d Volcanics
ISalo Ill
m AMERICA
Argentina B a s a l t
Cerm d e l F r a i l e , Rrgentirra
Trlndade Is. R a s a l t s
Fernando cb Nor&
Iqnmus
irrgentma Fasalts
San 1 . ~ 1h~ ordab3
P m v s de Caldas C m p l a x
Ouebrada Marquesa Fo-tim
C a b de S t . A g o s t i h o
V i n i t a Formatian
Sierra d e 10s Condares
Runipalla
Maranha0 % s i n
Cerro Colorado
Serra Geral B a s a l t s
Arqueros Formation
S e r r a Geral
E l Sat0 Almafuerta Lavas
Rio de 10s Fblinos t y k e s
MKanhao Basin
chon Rike Formation
Pesadem Porphry, Venezuela
G u a m y a s Volcanics
-
OT11-254
14/44
15/17
9/34
11/15
s41<l(i
OTlld-193
W18
W15
W l 9
15/59
W 4
w 9
S4fG
15/60
W17
6/35
16/96
14/227
w 2
14/241
14/273
141272
W.EUFOPE
Iceland V O l c a n i C S
P l a t e a u du Velay B a s a l t s
T e r c e i r a I s l a n d Lavas
Iceland Volcanics
J o k u l d a l u r Layas, I c e l a n d
P l a t e a u du Deves Basalts
Seneze volcanics
Ladek Zdmz volcanics
Post Orogenic B a s a l t , Czech.
B a l a t m Basalts. H q a q
B a s a l t s , Hungary
Chdm des P q s Lavas
I c e l a n d Volcanics
Iceland Volcanics
Iceland Volcamcs
I c e l a d vo1calNcs
Gattingen V o l c a n i c s
Gottiwen Volcanics
s . W . ~ e m y Volcanics
Iceland V O l C a n i C S
ReydarfJordur Wkes. Iceland
Reydarfpnlur lnvas, Iceland
65.0
45.0
38.7
65.0
66.2
45.1
45.0
50.3
48.5
46.9
47.5
44.6
65.2
64.9
64.9
65.0
51.4
51.3
48.0
65.0
65.0
65.0
342.0
3.8
332.8
342.0
344.8
3.6
4.0
16.9
19.0
17.4
18.7
3.6
345.0
344.9
344.9
342.0
9.8
9.4
9.0
345.5
346.2
346.2
13/7
11/12
14/17
1318
14/40
14/45
14/66-7
OT11-325
OT11-218
12/21
12/22
12/17
13/16
16/22
16/21
13/13
717
7/8
14/92
16/27
16/31
16/32
943
944
R. A . Livermore, F. J. Vine and A . G. Smith
Table 1 - continued
Rock Unit
%me Pasalts
Coirm
Ardeche
Mezenc M S s l f F l W
W e r Silesian Dasalts
Lava5
Mezenc MSSIf Fl-
Czech Iqnpla3us P r o v i n c e
W m r ?ndesite Wkes
NOrdllnger Paes Suevites
Kaiserstuhl Volcarucs
Central G e m y Igneous
Bohenlan Volcanics
busitz Volcanics
Parkstein Easalt
N.Bavarla Volcanics
Vaternish Eyke Swarm
N.Ireland Lavas
Skye Lavas
T e r t i a r y Dykes. Scotland
Tertiary Dykes, Smtland
S.W.Ge-y
Lundy Island tykes
w e Dykes, Noml
Skye Dykes, Reversed
Dallen W c t StrUcture
Kragem Dykes, Norway
Fishnish Dykes, m l l
S.W.Getnnny Volcanics
Mull Lykes
Clevelard Amattwaite myke
Antrim Rasalts
Rrran tykes
M u l l Lavas
Limestones, S . G e m y
Limstones, S . G e m y
Site
mie
Lat.
Lm.
rat. Lm.
(%)
(OE)
(ON)
4 e
Reference'
(Ma)
(9)
50.5 10.0
44.8 4.5
45.R 4.0
51.0 16.0
45.0
4.0
48.5
18.8
49.5 20.5
49.9 10.5
48.1 7.7
50.5
7.5
50.0 13.3
51.0 14.7
49.7 12.2
50.1 11.4
57.6 353.4
55.1 353.9
57.4 353.7
53.5 358.5
55.0 355.6
49.7
8.7
51.2 355.3
57.1 354.1
57.1 354.1
61.9 16.5
58.9 9.3
56.5 354.2
48.0 9.0
56.6 353.8
54.5 358.0
55.1 353.6
55.6 354.8
56.4 353.9
49.0 11.0
49.0 11.0
83.0 197.0
m.4 142.9
80.8 134.9
82.0 194.0
84.8 130.g
8 3 . 5 122.3
79.M 54.0
78.0 143.0
67.8 172.1
70.0 108.0
86.2 157.4
75.0 123.0
72.0 199.0
78.0 140.0
75.9 160.1
69.6 162.9
71.5 165.2
77.0 211.0
73.4 196.8
79.6 142.9
82.6 155.0
84.0 165.8
82.2 155.6
68.0 165.0
79.0 147.0
74.0 139.8
Bp1.6 135.9
78.0 187.0
75.0 240.0
70.9 125.8
81.7 179.8
72.2 168.3
62.0 122.0
68.0 130.0
42.0
2.5
38.8 350.8
37.3 351.5
38.8 350.5
81.0
72.5
73.0
76.5
35.9 253.5
19.0 261.0
53.0 188.0
32.5 249.5
32.5 249.5
35.2 248.4
19.6 261.0
20.8 256.1
19.5 260.8
51.5 238.8
51.8 238.2
19.5 260.8
46.0 240.0
43.0 245.0
19.5 260.8
44.5 240.4
35.5 246.6
41.5 237.0
39.8 253.3
38.5 245.0
19.5 260.8
38.0 253.0
24.0 255.0
38.5 247.0
29.3 256.7
39.0 244.0
53.0 228.0
55.9 296.6
49.3 238.5
45.0 247.0
83.0
84.1
88.0
78.4
85.5
87.8
13.3
13.3
13.3
13.3
13.3
13.3
14.9
15.2
17.4
19.0
19.5
21.5
24.4
29.3
46.4
46.4
46.4
46.4
46.7
49.5
50.8
51.5
51.5
51.5
51.5
53.3
53.3
53.8
59.9
60.2
62.6
63.6
153.0
159.0
14/81
12/30
14/78
11/16
14/77
18/24
11/21
8/30
OT11-496
6/11-13
OT11-264
18/35
14/128
16/34
14/14
12/49
14/145
11/28
8/33
611-693
15/30
wHcB2
-2
OT11-656
611-675
16/47
14/150
14/143
14/163
14/211
16/56
16/59
H78
H78
IB
E
m
GBrOM VOlCanlCS
L i a w Volcanics
Monchique syenite
Sintn Granite
204.0
197.0
165.5
174.0
1.0
46.4
58.5
82.0
83.0
49.8
197.8
38.4
28.5
101.1
88.8 34.3
80.3 158.8
86.8 258.9
84.9 213.3
84.0 219.7
88.4 315.3
85.0 245.0
89.0 316.0
82.7 138.0
86.0 26.0
84.1 34.4
85.5 208.5
81.6 131.0
88.5 120.5
88.7 65.4
85.0 114.0
70.7 157.1
74.7 290.9
81.0 89.0
82.3 150.5
70.0 206.0
85.5 117.7
87.7 208.1
76.7 203.7
0.9
1.0
1.0
2.6
2.6
3.4
7.0
7.3
9.0
12.3
12.3
12.8
13.3
10/5
13/19
11/29
11/32
NORM AMERICA
Valles Caldera Volcanics
Valley of Mexim Volcanics
Aleutian Islands Volcanics
Curtis Ranch, Reversed
Curtis Ranch, Noml
New Mexia Lavaa h Bake3 Sed.
Iztaccihuatl Volcanics
R i a Grande de Santiaw Volcs.
Upper sierra Group Volcanics
Gabbm Pluqs, Canada
C a r i b Plateau &salts
b,s2r sierra Group Volcs.
Ellensbuq Formatron
Payette Formation
GuadeluFe Group Volcanics
mlunbia Plateau Rasalts
Peach Springs Tuff 6 Lavas
Grotto h snapaline Bath's.
Colorado Basalt Flows
Ash FlOd Sheets, Nevada
Xochitepec Group Volcs.
San Juan Volcanics
hlranq VOlcaniCS
Needles Range m m t i o n
Buck Hill Volcanics
Ash F l w Sheets, Nevada,Utah
Younger P l u t o n s , Q.Charlotte
Mistatln Lake Volcanics
Hope Ccnplex, British Col.
Beaverhead Valley Volcanics
13.3
15.0
15.0
17.3
21.3
23.4
24.4
24.6
26.9
28.2
30.5
32.1
33.3
33.3
38.0
39.0
39.5
1118
14/33
14/35
14/59
14/58
9/13
OT11-362
13/15
OTll-707
11/16
11/17
OTll-709
3/15
3/14
OTll-708
8/28
i4/inn
14/109
OTll-361
OT11-442
611-718
16/42
15/27
14/121
12/45
14/122
16/39
11/44
15/29
f177
Geomagnetic field since the Jurassic
945
Table 1 - continued
Rock Unit
spsh
peaks Dyke s
w
a
m
r
3 a t t l e s m k e H i l l s . wyoning
Absakora B a s a l t , y c r m n g
Intrusions, Virginia
H i g h K d i+3untams, MontaM
I n t r u s i v e 6 Baked, Colorado
B e a r p w Wuntairrs, Eontam
Cape Dfer Lwas, B a f f i n Is.
N a c m i e n t o Formation
Gringo Gulch Volcmics
Alkalic Intmsicms, M a n t a ~
G i l l e s S SearrOmt
V O l C a n l C S 6 SedS., mntana
Elkhorn MD~ntalnsVolcanics
Mesaver& Group SedUnentS
Nmbrara Fomtim,
S i e r r a Nevada P l u m n s
Isachsen Diabase
Magnet Cove
Monteregian H i l l s
Y t Ascutney Gabbro
Ruck’s Batholith
Topley Intrusions, C a n a d a
Canelo H i l l s Volcmiics
S t q FOnMtlCn
IJpper i.f3rrLSon Formation
m e r EorrIson Formation
37.4
42.8
44.5
38.4
47.5
40.0
48.0
66.6
36.6
31.5
47.5
35.6
46.0
46.0
41.0
40.0
38.0
78.7
34.5
45.5
43.4
39.9
54.0
31.5
43.0
38.1
38.1
255.2
252.7
250.0
280.4
250.0
254.7
250.0
298.7
252.1
249.2
251.0
301.4
248.0
248.0
251.0
255.0
240.0
256.3
267.2
286.0
287.5
238.7
235.0
249.5
249.0
251.8
251.8
81.0
79.4
83.5
87.6
81.2
68.0
80.5
83.0
75.9
77.0
80.5
65.2
71.0
69.0
65.0
64.5
68.8
69.0
65.1
72.4
64.0
57.6
70.0
62.2
70.1
61.4
67.5
211.0
146.2
177.4
45.9
167.3
189.0
198.4
305.0
147.7
201.0
185.1
178.8
204.0
189.0
198.0
174.8
195.2
180.0
186.7
191.0
187.0
194.8
128.6
130.3
166.8
142.2
161.8
39.8
45.0
47.6
48.3
51.1
51.5
52.1
59.5
59.9
62.6
64.0
69.0
75.0
80.0
81.3
81.3
S3.6
100.0
1W.4
120.0
133.1
138.8
142.3
149.0
151.0
151.0
151.0
sumnerv~liem m t m
Kelvm Group S-unts
Newark Gmup
P a l i s a d e s S ~ l l Ne*
,
.Jersey
ComieCtiCut Valley Igneous
Diabase Dykes, Anticosta
Appalachtm Wkes 6 S i l l s
PennsylvanLan D~abase
38.8 248.9
38.3 297.4
40.1 285.1
41.0 286.g
41.5 287.3
49.8 296.8
40.0 286.0
40.2 283.7
67.0
71.8
63.0
74.0
65.U
75.7
68.6
62.0
109.8
103.2
108.0
98.0
87.0
84.7
100.9
104.5
166.0
170.0
194.4
191.0
196.0
197.0
197.0
199.0
.
11/25
Ss80
16/48
14/146
DWl80
10/46
DWieG
13/20
16/64
m 0
mm80
61349
610-50
14/214
11/35
W10-216
8/48
7/25
11/37
Fs79
8/52
9/43
141232
m m 2
SV83
15/65
15/66
16/121
01’1345
5/34
1676
18/88
14/247
15/75
14/285
*Codes refer to lists published in the Geophysical Journal
(see Livermore et al. 1983 for refcrences), except codes
prefixed by ‘OT’ which refer to the Ottawa Catalogues, ‘KR’
which refer t o the summary of Indian data by Klootwijk &
Radharkrishnamurty (1981) and ‘SA’ which refer to the South
American summary by Vilas (1981) and Valencio, Vilas &
Pacca (1983); other codes as follows: S83a - Sager (1983a);
S83b - Sager (1983b); SDKP82 - Sager et d.(1982); S74
Scharnberger (1974); VMV79
Valencio, Mendia & Vilas
(1979); K80 - Kellogg (1980); HSS79 - Hussain, Schult &
Soffel (1979); SHS81 - Schult, Hussain & Soffel (1981);
H 0 8 0 - Hargreaves & Onstott (1980); SOAJBB80 - Sichler
et al. (1980); MEDP76 - McElhinny et al. (1976); WHD82 Wilson, Hall & Dagley (1982); H78 - Heller (1978); H77 -.
Hanna 0 9 7 7 ) ; SS80 - Sheriff & Shive (1980); DBBH80 -Diehl et al. (1980); BB80 - Barnes & Butler (1980);
JBDH80 - Jacobson et al. (1980); FS79 - Foster & Symons
(1979); KBHSD82 - Kluth et al. (1982); SV83 - Schwarz &
Van der Voo (1983); RS76 - Rigotti & Schmidt (1976).
~
-
work of Fisher & Sclater (1983), together with earlier work by Norton & Sclater (1979),
forms the basis of our model of Indian Ocean evolution.
We have modified these rotations so that the separation of East and West Gondwanaland
from Smith & Hallam’s (1970) fit takes place at about 165 Ma and the opening of the Somali
Basin is completed by MO time ( 1 19 Ma), when Antarctica begins to separate from India.
Separation of India from Madagascar occurs just before anomaly 34 time (83 Ma).
946
R. A . Livermore, F. J. Vine and A . G. Smith
Compromises had t o be made in the North Atlantic where the rotations of Kristoffersen &
Talwani (1977) and Kristoffersen (1978) were used for North America and West Eurasia;
the final fit being that of LeFort & Van der Voo (1982). Greenland and its data were
omitted from this study because of doubts about its location relative to the other North
Atlantic continents. On the other hand, the history of the Central Atlantic now seems t o be
quite well-known: we have followed the recent work o f Klitgord & Schouten (1982); while
in the South Atlantic, the widely-used models of Ladd (1976) and Rabinowitz & La Brecque
( 1 979) have been adopted.
Each plate, together with its data, was retui-ned to its former position with respect to
Africa (Nubian plate) and then transformed t o fixed-hotspots coordinates using the model of
Morgan (1983) given in Table 2, except for Pacific data which were returned directly t o the
hotspots frame using dated tracks on that plate. Anomalies d o exist about the PacificAntarctic ridge allowing the Pacific plate to be linked to the hotspots through Antarctica
and Africa, but there is a suspicion that a further plate boundary was active either in the
Pacific or Antarctica until mid-Tertiary times (Gordon & Cox 1980). For the late Tertiary,
the differences between the two methods are negligible (Livermore, Vine & Smith 1983).
The position of the Pacific plate relative t o the hotspots is problematical and we have
employed two alternative models for comparison.
Table 2. Africa-hotspots
rotations from Morgan
(1983).
Age
(Ma)
10
20
30
40
50
bW
70
80
90
100
110
120
130
140
150
160
170
188
190
200
Angle*
Rotation Pole
Lat.
Lon.
(ON)
(OE)
(Oacw)
513.4
50.4
49.2
48.8
46.8
44.2
413.4
35.4
31.9
29.0
27.3
25.9
25.5
23.7
20.6
17.0
11.9
5.5
-5.5
-17.6
-2.70
-5.40
-8.00
-10.40
-12.30
-14.60
-17.50
-21.70
-24.70
-27.90
-31.00
-34.213
-34.60
-34.00
-31.60
-29.40
-26.30
-23.80
-21.90
-22.70
323.1
323.1
324.3
322.2
318.6
311.4
303.4
301.6
308.4
313.4
315.7
317.5
316.5
314.0
310.2
306.0
300.0
292.9
283.9
266.7
*Positive angle represents
anticlockwise
rotation
viewed from outside the
Earth.
Several studies (McDougall & Duncan 1980; Turner, Jarrard & Forbes 1980) have shown
that the trends of seamount chains can be well-approximated for the last 43 Ma by a single
rotation pole with at least one variation in the angular rate of rotation about it. ‘Model A’
is that given by Gordon (1983) and is based on the Turner et al. rotation pole since 43 Ma,
with an increase in the rate of rotation at 25 Ma (Table 3 ) . These parameters are very similar
to those obtained by McDougall & Duncan (1980) from a comparable study of various
suspected Pacific hotspot tracks. For the period 43-71 Ma, corresponding t o the formation
of the Emperor seamount chain, the pole o f Clague & Jarrard (1973a) is used with another
change in rate in order to bring Suiko seamount to the latitude of Hawaii at 65 Ma. Earlier
Geomagnetic field since the Jurassic
947
Table 3. Pacific-hotspots rotations.
Aye
Rotation Pole
(Ma)
Angle
Lat.
Idon.
(ON)
IoE)
(Oacw)
711.0
70.0
55.1
50.5
48.1
265.0
265.0
266.4
266.7
276.1
24.00
35.00
44.72
49.49
72.56
Refareilce
Model-A*
25
43
65
71
97
Turner e t al. ( 1 9 8 0 )
..
..
..
..
..
..
C l a y u e h J a r r a r d 11973)
Epp ( 1 9 7 8 )
Rates a r e t h o s e g i v e n by
( 19A3).
cordon
Mode 1- B
1
16
za
43
67
140
36.0
67.0
69.5
66.3
47.9
42.1
204.0
279.9
274.3
294.4
279.8
285.9
0.90
14.26
17.75
33.48
45.67
99.81
Epp and T u t h i l l ( i n p r e p . )
..
..
..
..
..
..
..
..
..
..
*These rotations were obtained by addition of the incremental poles given by the authors.
motions are described by a pole obtained by Epp (1978) and a rate determined by
henderson & Gordon (in preparation).
The second model, 'model B', is one derived recently by Epp & Tuthill (in preparation)
from a detailed fit of several Pacific seamount chains. This model differs from model A
mainly in the position o f the rotation pole since 43 Ma, which is moved in order t o fit the
observe tracks better (Table 3). It gives a total 0-43 Ma pole much closer to the rotation
pole estimated earlier by Clague & Jarrard (1973b) at 69"N, 68"W. The choice of this pole is
important for positioning all the Pacific data, since finite rotations for earlier times are based
on the addition of younger poles. For example, the finite pole given in Table 3 for 71 Ma
using model A is computed b y the addition of 0-43 Ma and 43-71 Ma poles, after first
rotating the latter t o its 43 Ma position. A constant rate is adopted for the Emperor chain
with a somewhat younger age of 67 Ma for the northern bend.
3 Analysis
With good data coverage, spherical harmonics have proved successful in analysis of the global
field from palaeomagnetic data, satisfactory results having been obtained for coefficients to
third degree for Quaternary and latest Tertiary times (Merrill & McElhinny 1977; Coupland
& Van der Voo 1980; Livermore et al. 1983). These show that most of the non-zonal
components average out while the zonal quadrupole and possibly octupole components
persist.
However, the distribution of data for Miocene and earlier times is very uneven, parliculady between northern and southern hemispheres. This precludes accurate determination of
third- and higher-degree components (Livermore et al. 1983, hereinafter referred to as
paper 1). (Schmidt quasi-normalized coefficients are used throughout this work.) Values
may certainly be obtained for components such as g ! , but, if these are due t o inaccurate
relocation or data errors at a few southern hemisphere sites rather than geomagnetic sources,
these estimates will be invalid. Moreover, the inclusion o f higher terms may seriously affect
the values obtained for gi by aliasing. We note further that recently-published Tertiary
palaeomagnetic inclinations from DSDP leg 7 3 sediments (Tauxe, Besse & La Brecque 1983)
'on the African plate indicate far-sidedness at palaeolatitudes around 30"s o f similar magnitude to northern hemisphere poles. This suggests a quadrupole rather than octupole nondipole field as invoked by Coupland & Van der Voo (1980) and Lee & McElhinny (in
R. A . Livermore, F. J . Vine and A . G. Smith
948
preparation). Each pole is rotated with its sampling site to its position at the estimated time
o f magnetization, then transformed into equivalent angles of inclination and declination at
the repositioned site. We have made the assumptions that longitudinal drift has been
effective in averaging out the non-zonal components and that the persistent non-dipole field
can be represented b y the zonal quadrupole coefficient g: alone. A full spherical harmonic
analysis o f the Late Tertiary and Quaternary global field (Livermore et al. 1983) gave values
for the non-zonal coefficients generally close to zero. supporting this assumption.
Since the available data are so sparse, we have adopted the following method for finding
the best-fitting dipole plus quadrupole field. The overall mean and Fisher statistics for
20 Ma windows have been calculated for a range of model fields in which g: was varied in
0.01 g': increments, while all coefficients other t h a n z ? andg: were set to zero. This involves
the use o f the modified relation between magnetic inclination and colatitude given in paper
1. The value of gy for which K , the dispersion parameter, is maximized was taken as representative of the interval. We could, equivalently, have minimized the value of A , , without
affecting our results.
The dispersion parameter, K , has been estimated for each mean using the robust estimate
described b y Fisher (1982) t o minimize the effects of outliers:
K
=
I/
c
I.jC({],
i
Table 4. Results of dipole plus quadrupole field analysis.
W F
GADF
Age*
N
(Ma)
A
B
M e a n Pole
K
9;
Mean P o l e
Lat.
LO".
__
1.at.
Lon.
('%)
(OE)
:Y
(ON)
(OE)
K
Model A
10
6 . 3 119
20
56
17.7
30
28.4
28
40
41.8
28
50
49.9
38
33
60
58.0
56.7
27
40s
70
68.8
24
70.7
17
705'
80
81.0
29
90
87.1
29
100 98.5
19
120 1 1 7 . 1
19
150 154.5
17
186 182.0
36
87.3
85.4
85.1
83.7
84.1
84.9
85.2
84.0
85.5
84.6
86.1
81.8
75.7
77.4
71.1
140.4
146.2
144.7
155.1
159.5
200.8
172.5
229.0
189.8
186.2
210.3
307.8
302.0
290.1
311.1
144
96
Y2
83
85
78
95
50
54
61
53
60
78
45
65
0.06
0.05
0.03
0.10
0.10
0.13
0.08
0.05
-0.10
-0.14
-0.09
-0.08
-0.03
-0.07
-0.07
88.2
86.3
85.4
84.6
85.9
87.1
86.8
84.3
83.6
83.7
86.9
83.1
76.7
79.2
72.3
121.5
140.4
148.9
175.1
167.6
222.7
184.5
238.8
163.2
146.5
177.1
302.9
299.6
281.2
304.4
162
102
95
97
103
87.3
85.5
85.3
84.6
84.6
83.3
85.4
84.1
84.0
80.t1
141.4
146.6
146.8
167.9
168.5
235.7
206.9
228.1
253.3
3n6.4
145
96
93
88
89
55
58
76
h0
57
0.06
0.05
0.03
0.09
0.09
0.04
-0.10
-0.11
-0.B8
-0.67
88.2
86.3
85.6
84.9
86.1
83.6
H4.1
86.1
85.9
81.4
123.0
140.8
151.3
189.5
180.0
242.9
174.9
200.2
250.4
302.6
162
102
95
101
105
56
65
90
64
59
1B5
106
52
60
72
57
64
78
46
68
Model B
10
20
316
40
50
7(1
7'd$
80
90
100
6.3
17.7
28.4
41.8
49.9
68.8
70.7
81.0
87.1
98.5
119
56
28
28
38
24
17
29
29
19
*Column A is the nominal age, column B the mean age
of poles.
5 Excluding results from Deccan Traps.
N H , Values ofg; which lead to maximum values for K arc
given; K is the estimate of the precision parameter given
by Fisher (1982); N is the number of poles included;
GADF = geocentric axial dipole field; DQF = dipole plus
quadrupole field. No values are given for model B for
60 Ma as no Pacific data are included in this window and
results are thercfore identical to model A
Geomagnetic field since the Jurassic
949
where
Li = 1/12 -2il ( n 2 ( n+ I ) )
and
c ( ~=) I
cos O,!,
O f being the colatitude of sample i with respect t o the mean. these values having been
ordered so that c(1) < . . . < c ( ~ ) .
Prior t o 100Ma, there are insufficient poles t o make a 2 0 M a window practicable. We
have therefore used 40 Ma windows centred on 120. 150 and 180 Ma.
4 Results of dipole plus quadrupole analysis
A similar pattern may be discerned in the results incorporating either of the two alternative
models of Pacific plate motion (Table 4). A small quadrupole component appears to have
persisted for the last 30 Ma, as concluded in paper I . During the early Tertiary and latest
Cretaceous, the (normalized) quadrupole seems have assumed larger positive values, while
earlier still, during the Cretaceous, negative values are found.
Examination of the polar path shows a sudden shift in the mean pole latitude for the
60 and 70 Ma datasets. (Note that the 6 0 Ma results for models A and B are identical as no
Pacific poles are available for this time window.) This is largely a result o f the inclusion in
these intervals of the poles from the Deccan Traps, dated at 60&65Ma, which at-e clearly
at odds with the other poles (Fig. 1). We have found that the Indian mean agrees better with
the other fragment means and with the hotspots model when an age of about 70-80Ma is
assumed for the Traps. Although a radiometric age similar to this has been published
(Kaneoka 1980), the younger age is based on several reliable K-Ar determinations and is
generally accepted. The problem is compounded by the rapid rate of northward motion o f
India during this time, although the position of India is constrained by the identification o f
58-78 Ma
68-80 Ma
a
b
Figure 1. (a) Mean poles and A,, circles of confidence for India, including results from the Deccan Traps
dated at 60-65 Ma (solid squares), and rest of the world (solid circle) for the interval centred on 60 Ma.
No Pacific data are available for thir interval so that models A and B do not apply. Stereographic projection. (b) A\ above for 70 Ma interval. Open circle is global mean using model A for Pacific data, solid
circle is for model B.
R. A. Livermore, F. J. Vine and A. G. Smith
9.50
anomaly 28 (about 63 Ma) in the Indian Ocean. Slightly younger results from the Sanjawi
and Brewery limestones give poles in better agreement with the hotspots. This discrepancy
was also noted by Briden, Hurley & Smith (1981).
On deleting the Deccari Traps poles, a much smaller value ofgi was obtained in the case
of the 60 Ma window (Table 4), but a change of sign was observed at 70 Ma. The mean poles
n o w agreed better with the trend of polar wander and the dispersions were slightly improved.
On this evidence, we prefer t o leave the Deccan Traps poles aside for the time being. Even
without these poles, there appears to be a period of rapid polar wander for the dipole plus
quadiupole solution between 60 and 7 0 M a (Fig. 2); however, the revised 70Ma set contains
only 17 poles and has a low dispersion, so that the values obtained fromgi for this interval
are considered unreliable
Model-A
a
Figure 2. ( a ) Global mcan pole positions for 20 Ma windows at 10 Ma intervals representing 0--110Ma.
Fixed-hotspots coordinates are used, and results for both centred axial dipole (solid circles) and dipole
plus quadrupole (open circles) models are shown. Model A is used for Pacific motions. Note that all poles
from 90 Ma lie within 7" of the position indicated by the hotspots. Ages marked correspond to mean ages
o f data in 10 and l 0 0 M a windows as given in Table 4 . Stereographic projection. (b) As (a) but using
model H for Pacific motions.
Geomagnetic field since the Jurassic
95 1
Model-6
b
Figure 2
-
continued
Results for g; and K excluding the Deccan Traps poles are illustrated in Fig. 3, from
which it is apparent that an axial quadrupole component has persisted in the field throughout the Cenozoic with similar magnitude and constant sign.
The intervals centred on 80, 90 and l00Ma give results suggesting a large southward
offset of the dipole field (Fig. 3). Data are sparse and poorly distributed for these intervals
and K values are somewhat poorer than for the past 60 Ma. Thus the actual values obtained
for g i prior t o latest Cretaceous time should be regarded as tentative. We have, however,
checked that the negative &/g: values are not due t o relative motion between the Pacific
and African hotspots by repeating the analyses of 80 and 90Ma groups without the Pacific
poles. In both cases, the quadrupole coefficient retained its sign.
Model B gives higher values of K for most intervals prior to 10Ma (Fig. 3), g i being
generally slightly smaller. This lack of agreement between models casts some doubt o n the
ages assigned to certain Pacific tracks dnd/or their hotspot origin. The agreement between
hotspots in the Atlantic and Indian Oceans is similarly imperfect (Duncan 1981; Morgan
1983).
R. A . Livermore, F. J. Vine and A . G. Smith
952
-
BEST F I T T ING QUAORUPO!LE
0.10
0.05
Model A
Model €3
s:Q
-0.05
-0.10
20
40
60
80
KTQ-M
100
120
K-N
140
160
180
Ma
160
180
Ma
JK-M
160
120
K
80
40
20
40
60
80
100
120
140
Figure 3. Computed values of normalized zonal quadrupole coefficient g: relative to the axial dipole
coefficient g:, assuming two alternative models of Pacific plate motion as discussed in the text. Poles from
the Deccan Traps are omitted. The lower plot shows the highest values of the 1;isher precision parameter
achieved by including the quadrupole. Centre section shows the polarity superchrons as given in Harland
et ~ l (1982).
.
The trend of mean poles calculated using model B is smoother for both centred and offset
dipole models (Fig. 2b), which, together with the generally higher K values and smaller
quadrupoles inclines us toward this model.
5 Resolution and errors
The precision parameter, K , used t o define g!, may also be viewed as the invariance in the
data. Thus an F-test could be used to decide whether the derived dipole plus quadrupole
fields give a significant improvement in K at 95 or 99 per cent confidence levels. This test
is too stringent, however, as the small values obtained for g!/gy d o not increase K sufficiently. As in paper 1 , therefore, we have employed the method o f Wells (1973) to gauge
the likely errors in our estimates of g!. In the present case, artificial datasets were synthesized from a field model in which gy = - 1 .O and g: = -0.05. Ten such datasets were
created for each interval using the reconstructed sampling sites, with the addition of random
errors to the synthetic palaeopoles, drawn from a Fisherian distribution with a precision
parameter comparable to that observed. Sites corresponding to model B were used for
Pacific pseudopoles. though of course this choice makes very little difference.
Geomagnetic field since the Jurassic
953
These were analysed as were the real data, and the rms deviation of the resulting estimates
of go2 about the true value calculated as a guide to the errors in our results. Naturally, reconstruction errors for palaeomagnetically important plates such as North America or Europe
will impose bias o n o u r solutions and so increase the errors. On the other hand, t h e high
values of K obtained in the original analysis, especially during the Cenozoic, leads us to
believe that no drastic errors have been made in our reconstructions.
The results of this procedure are given in Table 5. Data distributions for all intervals in
the range 10-90Ma appear adequate for the resolution of &!, assuming random crrors.
Earlier intervals give rise to greater scatter in the values obtained for the quadrupole, and the
values given for them in Table 4 are probably not significant. This is because o f t h e very
limited distributions in these groups, with a strong bias toward southern palaeolatitudes.
There is a striking correspondence between the mean values obtained for g: from the
model fields and the results in Table 4 for all intervals younger than 7 0 M a . This suggests
that the fluctuations observed in the quadrupole may be the result of changes in the
distribution and magnitude o f errors in the data as much as geomagnetic causes. If so, t h e
quadrupole may well have retained a value close to O.OSg:, as observed for well-distributed
Quaternary and late Tertiary data (paper 1), for the entire Cenozoic. The Mesozoic/Cenozoic
boundary might then mark a fundamental change in the character of the average geomagnetic field, including a possible change in sign of the non-transient quadrupole. However.
the mean values of go2 derived for the 100 Ma and older datasets are all substantially lower
Table 5. Results of analysis o f
10 tcst fields with random
errors for each interval. Pacif'ic
sites used are based on model
B rotations and no Deccan
Traps results are included.
10
150
0.07
20
100
100
100
0.06
0.06
0.118
0.02
0.02
0.02
0.05
103
114
117
50
60
10U
9.08
0.87
0.04
8.04
123
131
70
811
90
100
50
50
50
544
0.07
0.@5
0.04
0.07
0.03
0.02
16.05
62
67
57
120
50
1511
50
50
30
40
180
100
0.02
0.01
0.01
B.0#
0.08
0.87
0.117
154
70
63
69
57
K , is thc precision parameter
of the 1,'isher distribution from
which random errors arc
drawn, RO, is the mcan value of
the axial quadrupole obtained
from analysis of the 10 artificial fields, K M S is the root
mean square deviation of the
calculated values from the true
value of O.OSg:, and K , IS the
mean value of the precision
parameter in these solutions.
954
R. A , Livermore, F. 1. Vine and A . G. Smith
than the model value and so the calculated coefficients may again be at least partly due to
deficiencies in global coverage and data scatter.
This bias is a result of t h e progressively more limited longitudinal distribution o f sampling
sites as t h e plates return t o their locations within Pangaea, leaving a substantial unsampled
oceanic area, the crust of which has since been subducted. This causes a dipole plus quadrupole field to be disguised as a dipole tilted away from the sampled region, so reducing the
computed values o f g:.
The small but distinct bias toward larger g! values in the youngest groups, we interpret
as an effect of the clustering of sampling sites. When the scatter in palaeopoles for a group o f
data from well-represented regions such as Western Europe exceeds that of the sampling sites
themselves. one may always improve K b y increasingg!. This is because the addition of this
term causes the computed pole position t o move along a great circle passing through the
GADF pole and the sampling site, a positive value o f g;/gy giving rise to a near-sided pole
compared to the GADF position. If many sampling sites are concentrated in a small region,
therefore, the variance of t h e mean pole position will consequently be reduced.
To correct this, we averaged the data in the 10 Ma window over 10" x 10" areas of the
globe. The averaged directions were analysed as before t o give a revised estimate of g; of
O.O4g:, with a mean pole at 88.6"N, 164.3"E. The mean and rnis deviation of g: from 10
test fields were now 0.05 and 0.0 I for this interval, showing that the bias has been corrected.
The older results are scarcely affected b y averaging and are not shown.
On t h e strength of Table 5 , one would expect the 80 and YO Ma intervals to give reliable
results even with their larger errors. indicating that, barring serious errors in repositioning,
the negative values forg; at these times are significant.
6 True polar wander
True polar wander has been invoked b y several workers o n the basis of comparisons of
palaeomagnetic and other 'absolute' frames of reference, most recently b y Gordon (1983).
This conclusion depends upon the disagreement of polar estimates from seamount magnetic
anomalies and palaeomagnetic inclinations from deep-sea cores from the Pacific plate with the
positions predicted b y rotations based o n fixed Pacific hotspots. Sager (1983a), using
model B for Pacific motions, and paper 1, using global data including those from the Pacific,
concluded that little or n o true polar wander has occurred since Eocene times (30-35 Ma).
The present work, in common with that of Harrison & Lindh (1982b), which did not
consider data from the Pacific plate, suggests that the hotspots may provide a reasonable
estimate (to within about 5") of the palaeorotation axis for the last 90Ma.
The disagreement of certain Pacific data, notably that from Suiko seamount, with this
model may point t o dating errors. For example, the rate of Pacific rotation 43--70Ma has
t o be varied in order to bring Suiko to the latitude of Hawaii at 6SMa (Gordon 1983).
Alternatively, failure to sample secular variation adequately may be the cause of the
discrepancy, though this seems unlikely given the large number of flows sampled at DSDP
site 433 o n Suiko seamount.
On the other hand, the disagreement may result from a short-lived excursion of the
geomagnetic axis at about 6 5 Ma, such that its effect is lost amongst other data within the
20 Ma window. Such an excursion would explain the apparent correspondence between the
palaeocolatitude of Suiko seamount and the mean pole for t h e Deccan Traps, of similar age
and high quality, when plate motions are taken into account (Gordon & Cox 1980). It might
also contribute t o the low precision found at 70Ma. A similar phenomenon appears t o exist
for Eocene data: the substantial swings in sign and magnitude of magnetic inclination
Geomagnetic field since the Jurassic
955
anomalies from Pacific piston cores on a time-scale of 5-10Ma are not reflected in analyses
of palaeomagnetic poles from seamounts (Epp er al. 1983).
Finally, it map reflect the presence of a persistent non-dipole field. A field such as that
derived here for 70 Ma (excluding the Deccan Traps poles) would explain the palaeolatitude
observed for Suiko b y a combination of 5-6" true polar wander plus a global near-sidedness
of up to 4".
Fig. 4 shows the angular difference between the two reference frames (using model B)
compared to the results obtained from an earlier analysis b y Harrison & Lindh ( 1 987-b). Our
model shows a distinct change in the orientation of the geomagnetic field at about 90Ma.
Since that time, the global mean pole has been within 7" of that predicted by the hotspots,
with no clear evidence of the gradual polar wander suggested (Gordon & Cape 1981) on the
basis of Pacific data.
Nevertheless, the global mean pole does migrate around the fixed-hotspots pole in a
manner generally similar t o that described by Morgan (1982), but at a much smaller angular
distance of about 5". This distance would appear to be statistically significant, as the global
A9, circles d o not include the predicted hotspots pole (Fig. 5 ) . Prior t o 100Ma the mean
poles lie between 13" and 19" from the hotspots pole (Fig. 4), the distance increasing with
age. There are at least three possible explanations for this: the first is that wander of the
hotspots has taken place during the earlier interval 200-100Ma: the second is that the
hotspot tracks have been misidentified prior t o l 0 0 M a ; while the third is that the result
reflects data errors.
The fixed-hotspots frame used (Morgan 1983) is based upon the identification of hotspot
tracks in the Atlantic for the last 100 Ma which are generally clear and well-dated. Earlier
tracks are identified only on the African continent and are more diffuse. Thus it would seem
that the likelihood of error is greater prior t o 100 Ma (Duncan 1981) and that at least some
DEVIATION BETWEEN HOTSPOTS AND PALAEOMAGNETIC FRAMES
L"
c-0
15:
-
8
s2
9
Dipole plus quadrupole
GADF
Harrlson and Lindh (1982b)
10-
5 -
20
40
60
80
100
120
140
160
180
20
Figure 4. AngulaI deviation between fixed-hotspots pole and global mean pole for both centred axial
dipole and dipole plus quadrupole field models, compared to results of Harrison & Lindh using different
data and plate reconstruction parameters.
956
R. A . Livermore, F. J. Vine and A . G. Smith
o f the observed difference may disappear when improved estimates of the ages and
directions of hotspots tracks are available.
Our preferred model of global polar wander in the fixed hotspots frame of reference is
shown in Fig. 5: model B is used for Pacific data and Deccan Traps poles are omitted.
7 Geomagnetic implications
A physical explanation is required for the persistence o f the quadrupole component o f the
geomagnetic field. The simplest explanation is a standing non-dipole field due to the
north-south displacement of the core currents responsible for field generation. Problems
with this hypothesis include the requirement for a north-south hemispherical asymmetry
o f the core-mantle boundary and evidence from Hawaiian volcanics (Cox 1975) which
reveals no apparent standing component in the secular variation record at that latitude.
Cox showed that a non-random distribution of positive and negative features o f the nondipole field could lead t o a time-averaged field in which the even zonal field harmonics
G l o b a l m e a n p o l e s : f i x e d hotspots
Figure 5 . Global mean pc'lez and A,,, circlcs of confidcnre for dipolc plus quadrupole field model utingthe
rotations of Cpp & l'utliill ( ~ n o d c H)
l for Pacific poles. Ages corrcspond t o t h e mean ages given in Table 4.
957
Geomagnetic field since the Jurassic
persist. The latitudinal distribution of inclination anomalies predicted b y this model was
examined b y Harrison & Watkins (1979), who preferred, on the basis o f averaged results
from Icelandic lavas, a simple offset dipole solution. Additionally, it was found in paper 1
that while g: retained a value close to that of the present field for the last 5 Ma. g: was
substantially reduced in the palaeofield. Thus Cox's model requires modification to produce
a dominantly gy +g: field. Other possible explanations have been discussed by Merrill &
McElhinny ( I 977) and Coupland & Van der Voo ( 1 980).
Cox (1975, 1981) has also suggested that motions in the fluid core and lower mantle may
be coupled, with lateral variations in physical conditions in the latter influencing the pattern
of core motions. Changes in mantle convection would then affect the core-mantle boundary
conditions and so produce measurable changes in long-term field behaviour. As well as the
non-dipole field, the frequency of reversals and the polarity bias (taken here as percentage
o f time in reversed polarity) would be affected, so that a correlation might be expected
between these phenomena.
In Fig. 6 are plotted the reversal frequency and polarity bias o f the geomagnetic field as
represented b y the polarity time scale of Harland et al. (1982), sampled in the same 2 0 or
4 0 M a windows as used here. Our results for the ratio g:/g? are also shown for comparison.
COX (1981), using an earlier version of the polarity scale. pointed out that reversal frequency
changes occur with a shorter period than polarity bias and suggested that they represent
fluctuations on different time-scales: reversal frequency reflecting local shifts in t h e location
of individual lower mantle convection cells, while polarity bias changes in response to
changes in the overall pattern o f mantle convection.
Using the newer polarity time-scale and the present windows. we get a much smoother
variation in reversal frequency than Cox, and the discontinuity at 45 Ma does not appear.
This was also noted b y Lowrie & K e n t (1983). There is only a superficial correlation withg:
inasmuch as negative values of the latter are seen during the Cretaceous long normal polarity
,60
- 50
ACf
(03 )
Figure 6 . Comparison of computed values of quadrupole coefficient (using model 13) with polarity bias
and reversal frequency of geomagnetic field averaged over same windows. The polarity time-scale used is
that of Harland eral. (1982). + - ~ : / g : ;,\ - reversal frcquency; ',' polarity bias.
~
958
R. A . Livermore, F. J. Vine and A . G. Smith
interval. The correlation with polarity bias is much more pronounced, the change in sign of
g: corresponding t o a rapid increase in the percentage o f reversed polarity between 80 and
60 Ma, with fairly constant values for each during the Cenozoic. It appears that a pattern o f
convection favourable to stable normal polarity also tends t o give rise t o a persistent quadrupole opposite in sign t o t h e axial dipole, in other words, a southward shift of the main
dipole, while a pattern such as that experienced in the Cenozoic. with frequent reversals and
about equal duration o f normal and reversed polarity, corresponds to a small positive axial
quadrupole.
By neglecting g!, we have ignored possible asymmetries between the northern and
southern hemispheres, and, b y combining results from both normally and reversely magnetized rocks, have assumed no differences between polarities. Such asymmetries have been
postulated and discussed elsewhere (Merrill & McElhinny 1977; Merrill, McElhinny &
.Stevenson 1079), but the global data would have to be greatly improved and extended for
such studies to be undertaken for times earlier than the last 5 Ma. Even for this period, the
signs are that differences are small, for example, Merrill & McElhinny find values o f 0.017
and 0.034 respectively for g!/g': for normal and reversed polarity data: both a good deal less
than their corresponding zonal quadrupole coefficients. Evaluating contrasts of this order for
earlier times would require, in addition to densely spaced and well-dated samples, very
accurate relocation of data without the uncertainties which a t present accompany plate
reconstructions even for t h e Tertiary.
8 Conclusions
(1) The angular difference between the fixed-hotspots and palaeomagnetic reference frames
has been typically about 5" for the last 9 0 M a .
( 2 ) Before 90 Ma, the t w o frames diverge, with a difference o f 17-19' at about 180 Ma.
This may point t o wander of the hotspots frame as a whole, relative to the geomagnetic axis,
and/or inaccuracies in the identification of hotspot tracks across Africa.
(3) There appears to have been a persistent axial non-dipole component in the average
geomagnetic field which has been more o r less constant for 30 Ma, was rather larger during
the early Tertiary, and which was of opposite sign during t h e Cretaceous long normal
polarity interval.
(4) Preliminary results indicate small axial non-dipole components during Jurassic and
early Cretaceous times.
(5) Problems exist with t h e reconstruction of India at the time of eruption of the Deccan
Traps, which seem to require an older age of 70-80 Ma, rather than 60-65 Ma as generally
accepted.
(6) Experiments with test fields indicate that all results for 9 0 Ma and younger intervals
are significant but that bias is introduced by the limited distributions, to which some of the
observed fluctuations in t h e quadrupole coefficient may be attributed.
(7) There appears to be agreement between the variations in g! and other characteristics
of the geomagnetic field with time, in particular polarity bias.
Finally, we stress the importance of allowing for the presence of zonal non-dipole
components in the average field when assessing polar wander from palaeomagnetic data from
a single plate. Values of g; = (0.045 k 0.01S)g': are now rather well established for later
Tertiary time, and, while we expect that the actual values presented here for earlier intervals
will change with t h e availability o f improved data, there is evidence that the non-dipole field
may be significant for the whole of Cenozoic and late Mesozoic time.
Geomagnetic field since the Jurassic
959
Correction to Paper 1 (Liverrnore et al. 1983)
The value o f gi given in Table 4, column B, page 165, should he 0.062g': and not
-0.062 g? as printed.
Acknowledgments
We thank W. J . Morgan and R. Gordon for their valuable comments. and W. Sager for kindly
supplying a copy of his thesis on Pacific seamounts. We gratefully acknowledge helpful
discussions with C. G . A . Harrison, B. Keating. J . F. Harper. D. Gubhins and J . Shaw.
P. Perkins assisted with the preparation of the pole list. This work was funded by a NERC
studentship and grant no. GR3/4405.
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