Tectonophysics
- Elsevier
Printed in The Netherlands
Publishing
Company,
Amsterdam
GLOBAL EXPANSION AND PALEOMAGNETIC DATA
D. VAN HILTEN
Department
(Received
of Mining,
April
Technological
University,
Delft (The Netherlands)
19, 1967)
SUMMARY
The method for detecting changes in the earth’s radius from paleomagnetic data, as originally proposed by Ward (1963) is reviewed and, slightly
modified, applied to the available observations. The method enables us to
calculate the paleomagnetic pole positions for different radii of the earth:
the earth’s radius for which the coeval poles of one continent show the
least scatter is considered the best estimate of the radius during that geological period.
A number of paleomagnetic observations appear to be suitable. They
suggest that the Permian radius of the earth was about 0.8 of the present
one. In Cretaceous time this ratio had increased to 0.9’7-0.98.
For the rest of the paleomagnetic observations the method does not
work, as they indicate neither a changing nor a constant earth’s radius. It
is probable that these latter observations lack the accuracy required for this
kind of investigation.
INTRODUCTION
Several attempts have been made to estimate the radius of the earth
in the geological past by using paleomagnetic data. There is general agreement that these data can produce such information; the methods used, however, differ greatly, and so do their results. Allmethods start from some indispensable assumptions:
(a) A dipole configuration of the ancient geomagnetic field.
(b) The average direction of magnetization of the investigated rocks
of certain age parallel to the contemporary geomagnetic field.
(c) The constancy of area of the continents during the supposed contraction or expansion of the earth.
The first two assumptions are generally accepted in most studies of
rock magnetism; the third one is based on geological considerations that
regard the continents as relatively rigid slabs as compared to the oceanic
crust and the earth’s mantle. This implies that distances measured at
present between two points on a continent were the same through geological
time, regardless of changes in earth’s radius. Of course, the geocentric
angle 0 between these points will change as pa = Op. &/Rp
where R represents the radius of the earth and the subscripts a and p refer to ancient
and present respectively. In first approximation this third assumption
Tectonophysics,
5 (3) (1968) 191-210
191
seems justified; it will be discussed more deeply in another part of this
paper.
In order to detect a change in radius of the earth we require coeval
paleomagnetic observations from at least two localities that are far apart
on the same continent. For each of these localities we can calculate or construct the position of the ancient magnetic pole. In both cases we use the
fact that the distance between sampling site and pole is known by the geocentric angle ic/ that is given by:
cot $ = 5 tan I
where I is the inclination of the direction of magnetization. The further calculations to detect a change in earth’s radius seem relatively simple when
two sampling localities are situated (nearly) on the same paleo-meridian,
i.e., when the sites and their poles are on one and the same great circle.
Egyed (1960) and Cox and Doe11 (1961) were the first to present a solution
for this case: any discrepancy between their paleomagnetic poles might be
attributed to a change in the earth’s radius since the time of magnetization
of the investigated rocks. The paleomagnetic poles of these two sites can
be made to coincide precisely and then the ancient radius of the earth is
found from (Cox and Doell, 1961):
R, =d/[cot-l
(1 tar-ill) - cot-l (5 tan12)]
where II and12 are the inclinations measured at the two sites, andd is the
distance between the sites, measured along the earth’s surface. Cox and
Doe11 applied this to the only set of data that seems suitable for their purpose, some Permian sampling localities in Europe and Siberia that appear
to be situated on a Permian paleo-meridian. The poles belonging to these
two groups of sampling sites almost coincide, so Cox and Doe11 concluded
that no appreciable change in earth radius had occurred since the Permian.
Egyed (1961) introduced a more general method to calculate the ancient
earth’s radius from paleomagnetic observations from any two sampling
sites on the same continent. As compared to the method proposed later by
Ward (1963), Egyed’s calculations carry some disadvantages: (a) all sites
of one continent are to be dealt with pair-wise; (b) comparatively small
errors in the paleomagnetic data tend to produce highly aberrant values for
Ra ; and (c), in general, the two sites under consideration will never produce
fully coinciding paleomagnetic poles, so some averaging procedure has to
be applied.
The graphical method that I proposed (Van Hilten, 1963) can be regarded as only a rough procedure compared to the mathematical calculations mentioned below. It even produced erroneous results in those cases
where the sampling sites are situated close to the paleo-equator.
Thanks to Ward (1963), we now have a method that offers many advantages over those just mentioned; besides having a sounder statistical approach
(Ward, 1963, p.218) it may easily be modified so that it takes into account
the possible deformations of the continent, which are due to occur when it
adapts itself to a changing global curvature. This latter point was overlooked by the other authors.
In the next part of this paper the calculations as proposed by Ward will
be shown again; it will be seen that some discrepancies between his and my
formulae exist, discounting the misprints that were corrected by his later
192
Tectonophysics, 5 (3) (1968) 191-210
paper (Ward, 1966) and that did not play any part in his calculations. Furthermore, Ward’s way of determining the continental center is not followed by
me. Where possible, Ward’s symbols have been used throughout this paper.
METHOD
OF CALCULATION
On one continent we select for a certain geologic period the n sets of
site data which look suitable for our purpose. We made use of the site data
as given in the literature. These data consist of the polar coordinates of the
sampling site cp, the longitude E of Greenwich, and A, the latitude, further,
the declination D and the inclination I of the direction of magnetization. For
each set we used either normal or reversed polarities, as the ancient reversals of the geomagnetic field are of no importance for this investigation.
Instead of X we are going to use also 0, the north polar distance, where
0 = 90°-X These sampling sites lie not dispersed over the continent but appear to be situated in a number, sayp, of grbups of nearby localities
(P = 2, 3, 4).
Fig.1. Stereographic presentation of the relation between the various
parameters used in this paper. N = North Pole. S = sampling site (q i, X i).
P = paleomagnetic pole. C = position of the continental center ( (po, 0,). In
this point, C, the positive n’ direction of a new geocentric coordinate system (I’, m’, n’) intersects with the global surface.
Then we select a central point C (Fig.1) on that continent (longitude
qo, north polar distance 0,). Next we replace the paleomagnetic site data
(vi,OiyDi;i = 192, 3, ..* n) of the n sites by a new set of data (cp’i, B'i,0; )
that refer to point C instead of to the North Pole:
Tectonophysics,
5 (3) (1968)
191-210
193
cos 9; = sin0 0
COSXi
COS(Cpi-'po)+
COS
sin hi
00
(@‘- 6’; zs 180°)
tan cpi =
cos + sin(qi-+O)
cos
cos Xi cos((p~-i~7~) - sin
e.
e o
sin Ai
(O” < cpi < 180° if numerator > 0
180° < ‘pi < 360° if numerator < 0
q; = O” if numerator = 0, and if denominator > 0
cp; = 180’ if numerator = 0, and if denominator < 0)
tan(D’-D) =
cos e
sin
o cos hi-
(O” < (D’-D)
180° < (D’-D)
e.
sin(cpi-cpg)
sin 0 o sin Xi cos(qpi --PO)
< 180° if numerator > 0
< 360°
if numerator < 0
(D’-D)
= O” if numerator = 0 and if denominator > 0
(D’-D)
= 180° if numerator
= 0 and if denominator < 0)
For the calculation we need still the angular distance ei, between
sampling site and paleomagnetic pole position:
tan I&i = 2 Cot Ii
(O” ‘q/i
P 180°)
The reason for my choosing point C in the center of the continent will
be clear when we realize what deformational effect on the continental slab
can be expected from the global contraction or expansion. During expansion,
for instance, the curvature of the globe, and consequently of the continent,
is decreased. The central part of the continent will hardly be deformed; near
its rims, however, we might suppose that radial tension faults develop
(“orange-peel
effect”, Van Hilten, 1963). Sampling sites on the continent
will keep the same longitude (cpi ) with respect to the center of the continent
C, but its present polar distance (0 i ) was - before the change in radius equal to 0; /p , where p is the ratio Ra/Rp
My method of choosing the position of point C in the center of the continent is different from that practiced by Ward (1963, p.219), who determined
it by taking the mean of the rock-unit positions; that procedure will give
another position that may differ considerably from mine.
Now we are able to calculate the position (with respect to the new coordinates around C) of the paleomagnetic pole for each site of the continent
for any earth’s radius by simply substituting e’i/p for the polar distance of
the site; the other site data (cpi_,0;’ and q/i) are not influenced by the change
in radius. This is the other advantage of having performed the transformation of coordinates, since it keeps the repetitive part of the calculation, as
will be seen later on, as short and simple as feasible.
For the further procedures it is preferable to have the pole position
presented as a unit vector, defined by its direction cosines 1;) m’i, n’i along
thk three principal axes of the coordinate system around C (Fig.1):
194
Tectonophysics,
5 (3) (1968)
191-210
1; J sin(B’i/p)coscpjcos
~~“~osD~cos(~~/~~cos(p~ sin&sinDf sin401 sin J/i
m’; = sin (61 fp)sin&
cos i&i-cos
Dg cos( @p&in
& sin Qe t
sinDi cos vi sin +i
ni =
cos (@/p)~os.
It/i + cos
Dk sin( 0; /p)sin &
The next step is to attribute equal weight to each of the groups of
sampling sites. This is achieved by muItiplying each of the obtained direction cosines by a factor so that:
lz=li
.n,/n&, ,m”$=m’;*+/ng
,ny
=ni ~n,/ng
Here 1~~is the number of sites of a reference group - usually that with
most of the sampiing localities - and ng is the number of sites of the group
under treatment.
The TR4 electronic digital computer of the Technological University
at Delft was programed in this way to calculate the desired pole positions
from the coeval site data of a continent, repeating the calculations for different values of p. For each p the n sites produce ft pole positions. The
Iength of their resultant vector Rp is given by:
._
I2f 6~: m”i12
42=[$1 1’3
z1
nqfi121
i=n
+ (qzl
Herein each group of sampfing sites has equal weight, Rp is a measure for
the precision of the cluster of the poles. For easier comparison with other
values of Rp, as obtained from other continents and other geological periods
with different numbers of sites, preference is given to the use of Rp/N,
where N = P.n,. Also the value of k, the best estimate of the precision
parameter K f is easily found now:
The values for p were varied from 0.64 up to 1.12, increasing by steps of
0.02. Graphs of the calculated values for RpIN are shown in the FigJI-7.
The values for RQ~~/N, R1,12 /Nand extreme values for Q/N
- if any are tabulated in Table I, When the curve representing the vafue of RJN
reaches a maximum, the corresponding p gives the radius P of the earth
for which the paleomagnetic data produce pole positions with the least
scatter, i.e., they satisfy best the configuration of a dipole field. The value
of P is, in other words, the best estimate of the ancient radius of the earth
for the geological period under consideration.
I have tried to take alf data into account which might produce sufficiently great variations in the value R/N. Therefore their sampling sites
should lie far apart on the same continent. The site data of the observations
used are given in the Appendix, arranged according to their age and continent, The available observations were judged first on their reliability;
some were discarded on such grounds as: (a) unreliable magnetization according to the criteria proposed by Irving (1964, p.102); (b) uncertain age
of the magnetization; or (c) doubtful structural environment. This latter
point was overlooked by other workers in this field when they used the
Permian data of the Esterel rocks in southern France, which have probably
Tectonaphysics,
5 (3) (1968) 191-210
195
i
I
of calculations
Cretaceous
Carboniferous
Carboniferous
Carboniferous
Permo-Carboniferous
Permo-Carboniferous
Permo-Carboniferous
Permo-Carboniferous
Permo-Carboniferous
Carboniferous
+
Permo-Carboniferous
Permian
Permian
Permian
Permian
Permian
Triassic
Triassic
Triassic
Jurassic
Cretaceous
Age
Summary
TABLE
SO
25
15
25
95
95
25
90
S
t
4
4
4
4
4
5
5
5
6
7
7
Siberia
Europe (selected)
Europe (selected)
Europe (all)
North America
North America
South Africa
Siberia
Antarctica
North America
(3 sites)
North America
(4 sites)
r
g
P
0
k
1
m
n
60
85
95
85
so
so
95
85
95
America
America
America
America
America
America
America
America
America
95 w
95 w
E
E
E
E
w
w
E
E
W
w
w
w
w
w
w
w
w
~~~ PO
2
2
2
3
3
3
3
3
3
Center
North
North
North
North
North
North
North
North
North
Graph
Figure
Continent
0.98019
40
42.1
>103
182.7
164.9
85.1
29.2
17.9
33.2
12.9
62.0
50.2
0.98443
0.98305
0.98280
0.98167
0.98002
0.97864
0.97749
0.97031
0.99951
0.99544
0.99495
0.98867
0.97007
0.94727
0.97158
0.92911
0.98656
0.98505
k 0.64
30
35
35
30
45
45
80
30
180
40
64/n’
62.6
57.8
53.1
54.5
51.1
46.9
43.9
41.7
32.2
0
0.98562
30
37
45
30
35
40
45
45
45
e
0
R
0.99605
0.99647
0.99502
0.99510
0.99351
0.97389
0.94999
0.97440
0.91522
0.99590
0.99766
0.98420
0.98442
0.98462
0.97768
0.97796
0.97827
0.97849
0.97866
0.97158
R 1.12/A’
57.0
57.8
58.5
42.0
42.5
43.2
43.6
43.9
33.6
1.12
212.8
326.2
167.4
169.9
148.6
33.5
16.9
36.9
10.8
203.0
320.8
k
lJ.99716
0.99660
0.99372
1.00000
0.99603
0.99584
0.94452
-
R’*‘rmax
k
111 ax,
0.9880
0.9820
0.9810
0.9800
I
I
064
0.76
A
I
cJ.88
I
l.OO
I
1.12
P
Fig.2. Graphs of R/H against p (ratio of ancient to present radius) for
the Carboniferous data from North America. Curves are shown for three
different positions of the continental center C (see Table I). The value of p
for which R/N reaches a maximum is indicated by the triangle.
Tecton~physics, 5 (3)(1368)191-210
197
0.9850
I
I
I
I
I
09640
0.9620
0.9810
09eco
0 9790
0 9760
h
0.9770
09720
0.9710
0 9700
I
I
I
I
0.64
0.76
0.0b3
100
I
1.12
P
Fig.3. Graphs of R/N against p for the Permo-Ckrboniferous
data
(d-h) and a combination of Carboniferous with Permo-Carboniferous
data
(i) from North America. The dependence of R/N on the choice of the five
positions of the continental center C (see Table I) shows clearly,
198
Tectonophysics,
5 (3) (1968) 191-210
R/N
o.QQQo
aQQm
a9970
aEG60
0.9950
a9940
0.9740
a9930
0.9730
0.9920
0.9710
o.gSto
0.9700
0.64
a-&3
a86
1.12
P
Fig.4. Graphs for the Permian data from Siberia (j), Europe {selected
data = k and E; all data = m), and North America (n). The curves k and 1 are
not essentially altered by a variation of the crustal deformation pattern
(Le., the choice of the position of C).
Tectonophyrsics,5 (3)(1968)191-210
199
0.9500
09300
09290
0.9280
09270
0.9260
0.9750
0.9250
0.9740
0.9240
09730
09230
0.9720
09220
0.9710
0.9210
09200
09700
064
076
088
I.00
112
?
Fig.5. R/N against p for the Triassic data from ,North America
Siberia (q) and the Triassic-Jurassic
data from South Africa (p).
200
Tectonophysics,
(cv),
5 (3) (1968) 191-210
0.0890
0.9870
0.9EEo
I
I
I
0.64
0.76
0.66
I
1.00
I
1.12
P
Fig.6.
R/N against p for the Jurassic
Tectonophysics,
5 (3)(1968)191-210
data from Antarctica.
201
1.000
I
I
I
I
I
1.00
1.12
%
0.9990
O.QSSO
0.9Q70
0.9960
0.9950
CL9940
,
0.9930
,
0.9920
0
0.9910
I,
0.9900
I
0.64
Yl
0.76
I
0.66
m
I
I
P
Fig.?. R/N against p for the Cretaceous data from North America.
In curve t one more - unreliable - site has been used than in curve s
(see Appendix).
202
Tectonophysics, 5 (3)(1968)191-210
been influenced by Alpine erogenic mavements (Van Hilten, 1964). The
same argument withheld me from considering pre-Carboniferous
data which
might also have suffered from the Hercynian erogenic movements.
CONTROLOF
THE COMPUTER'SRESULTS
Much attention was dedicated to a thorough checking of the computeis
results. The principal control applied was the recalculation by the computer
from the values of li, mi, and ni into a pole position with polar coordinates
referring again to the original coordinate system, producing a longitude E
of Greenwich, qip, and a latitude A Q,, where:
(12cos 60 + ni sin 0O)sin ‘p0 + rni cos ‘pf-~
tan ‘Pip
=
sin hip =
(1; cos
O. + ni
n; COS 6 0 -
sin 0 0)cos cp0 -
rn;
sin ‘p.
Iisin 0 0
This utterly complicated system allows us to check easily the correctness
of the computing procedure, as in the p = 1.00 step of the program qip and
Q are to produce exactly the polar coordinates of the pole position given
in the literature, calculated along more conventional lines. For other values
of p, CQ and Xip give pole positions that can be checked in the stereographic
projection with an accuracy of about lo. Furthermore, numerous hand
checks were made on the values R/N and k, and on other parts of the program.
INTERPRETATIONOFTHEGRAPHS
The results of most of the calculations are compiled in Fig. 2-7 and
in Table I. The graphs are plots of R/N against p; they are all on the same
vertical and horizontal scales, tofacilitate comparison of their curvature
and their steepness. Fig.6 presents a survey over the graphs, visualizing
their relative positions on the R/N and k scales. We may distinguish three
types ,of graphs:
(1) The graph has no maximum or minimum value in the interval
between p = 0.64 andp = 1.12, which are thought “reasonable”limits
(e.g.,
Fig.2, graphs a and c; Fig.3, graphs d, e,f, h and i). The graphs of this type
do not allow estimation of the ancient radius of the earth according to the
criteria mentioned above.
(2) The graphs show a clear maximum in the interval investigated
(Fig.4, graphs j , k, 1 and m; Fig.7). An estimate of the earth’s radius P for
that geological period can be made, and it is mentioned in Table I, final
column. From Fig.6 it is readily seen that these/graphs are characterized
by the highest values for R/N and k found in this’ investigation.
(3) The graphs show a faint maximum or minimum (Fig.2, graph b;
Fig.3, graph g). It is likely that these extremes have no significance, because
of the small influence of the variation of p on the R/N value, and by the fact
that these graphs - together with those of type (1) - have generally lower
R/N and k values in Fig.8. The low significance of these extremes follows
also from an experiment made with the computer. It should be realized that
Tectonophysics, 5 (3)(1968)191-210
203
600
i
t
5
l
l
t .
k 1.00
k.1 .
I-
m
.*
100
a-c
60
d-h
40I
20-
P .
l*
l
.
”
CJ .
q
.
I
0.92
I
0.94
I
I
I
I
0.98
0.96
RI_OO/fq
I
I
100
-
Fig.8. The relative positions of the curves of Fig.2-7 is illustrated by
their k and R/N values, as calculated for the present radius of the earth
(p = 1.00). The observations with the least scatter (highest k-values), represented by the curves j, k, 1, m, s, and t, appear to produce positive results. The other data, with lower k-values, seem to miss the required
accuracy.
is very hard to define the center of a continent with an accuracy of, say,
5” or 1V. In general, a number of positions will do, depending on the geologic
reasoning behind it. Now a number of calculations were repeated for other
positions of C (cp 0, 8 o), and they show us that the curvature of the R/N
value against p is in many cases largely dependent on this position of C.
This may be seen from the curvesof Fig.2 and Fig.3,d-h,
which differ
greatly in sense and degree of slope. The significance of the weak extremes
of this type (3), occurring only for special positions of C, seems therefore
doubtful. The curves of type (2) (clear maximum) are not essentially altered
when the position of C is varied. I should add here that this conclusion is
based on more calculations than shown in this paper.
The central point, C, of a continent was introduced in order to take
into account the deformation of the continental crust during changes in the
earth’s radius. Another choice of the position of this continental center
means, in fact, an alteration of the deformation pattern over the entire continent. Judging from the graphs just mentioned, the deformation provoked
it
204
Tectonophysics,
5 (3) (1968)
191-210
by changes in the earth’s size are not negligible - at any rate, not in such
questions as concern the present study. Studies in this field which ignore
these deformations must, therefore; have a limited value. This goes also
for those calculations in which the distance between any two points (sampling
sites) on a continent - usually referred to as d - is kept constant.
According to the model of deformation proposed in this paper, that
distance remains constant only when the points are in line with the continental center. For the two mean Permo-Carboniferous
sampling sites of North
America, I determined the difference in distance before and after a hypothetical expansion (RJR,
= 0.80) on 31 km, that is about 1% of the total distance
between those two sites. It is hardly to be expected that an increase so relatively small in length could be traced in the field, as much of it will be
consumed, for instance, by the formation of joints.
Finally, I want to call attention for the remarkable fact that there are
graphs (type (1)) without any extreme values within - or near to - the
“reasonable” interval between p = 0.64 and p = 1.12. In the line of reasoning
of this paper these graphs fail to demonstrate a change in earth’s radius as
well as its constancy! This inconsistency might find its explanation in the
incorrectness
of the earlier-mentioned
assumptions: a non-dipole configuration of the ancient geomagnetic field, deviation of the direction of magnetization
from this field, later remagnetization, or unknown relative movements of the sampling sites. Analternative explanation is less rigorous: from Fig.8 it is clearly
seen that the graphs of this type are typified by lower values for R/N and k
than those of type (2) (clear maxima). This greater scattering of data suggests that the individual observations lack the accuracy required for this
kind of calculation.
DISCUSSIONAND RESULTS
The method for detecting changes in the earth’s radius, as proposed
originally by Ward (1963) has been modified at several points. It thus
becomes more suitable than other methods which disregard crustal deformations accompanying such changes in radius and which carry statistical
disadvantages or have a limited applicability. The present method makes
allowance for the probable deformation pattern of the crust, and most of
the calculations presented in this paper appear to be highly dependent on
this pattern.
TABLE II
Estimates of the radius of the earth in the past
Age
Permian
Permian
Permian
Cretaceous
Continent of sampling
Ratio of ancient to present radius
Siberia
Europe (1)
Europe (2)
North Amkrica
0.76
0.78-0.83
1.00
0.97-0.98
The results differ from Ward’s (1963). Estimates can be made of the
earth’s radius in the geological past, as shown in Table II.
Tectonophysics,
5 (3) (1968) 191-210
205
There exists an inconsistency in the Permian data of Europe. The
result labeled “Europe (1)” is derived from the six most reliable investigations - through alternating magnetic field demagnetization - made in
Western Europe (see Appendix). The result marked “Europe (2)” is based
upon all available European data, inclusive of those from Russia. In order
to account for the discrepancy between the European results, one might
invoke relative displacements of the East European sampling sites with
respect to those of Western Europe. A possible remnant of such movements
might be the Polish-German depression. Similar tectonic events have been
advanced (Van Hilten, 1963) in order to explain the Permian results obtained
by Cox and Doe11 (1961).
The remaining calculations fail to produce convincing evidence for
either a change in earth’s radius or a constant one. Besides, these latter
observations have lower &values (Fig.8), so it is safe to assume that their
accuracy is too low for the present purpose. There remains, of course, the
possibility that these data are unreliable because the assumptions regarding
rock magnetism are invalid. One might think of rocks having acquired a magnetization not parallel to the ancient magnetic field, or of a later remagnetization.
REFERENCES
Beck, M.E., 1965. Paleomagnetic
and geological
implications of magnetic properties
of the Triassic
diabase of southeastern Pennsylvania. J. Geophys. Res.,
70(12) : 2845-2856.
Birkenmajer,
K. and Nairn, A.E.M., 1964. Paiaeomagnetic
studies of Polish rocks.
1. The Permian igneous rocks of the Krak6w district and some results from
the Hoiy Cross Mountains. Ann. Sot. GBoi. Pologne, 34(1/2): 225-244.
Black, R.F., 1964. Palaeomagnetic
support of the theory of rotation of the western
part of the Island of Newfoundland. Nature, 202(4936): 945-948.
Collinson, D. W. and Runcorn, S.K., 1960. Polar wandering and continental drift:
evidence from palaeomagnetic
observations
in the. United States. Bull. Geol.
Sot. Am., 71: 915-958.
Cox, A. and Doell, R.R., 1960. Review of paleomagnetism.
Bull. Geol. Sot. Am.,
71(6): 645-768.
Cox, A. and Doell, R.R., 1961. Paiaeomagnetic
evidence relevant to a change in the
earth’s radius. Nature, 189(4758): 4547.
De Magnee, 1. et Nairn, A.E.M., 1962. La methode paleomagnetique.
Application au
Poudingue de Maimedy. Bull. Sot. Belge Geol., 71(3): 551-565.
Doell, R.R., 1955. Palaeomagnetic
study of rocks from the Grand Canyon of the
Colorado River. Nature, 176: 1167.
Egyed, L., 1960. Some remarks on continental drift. Geofis. Pura Appl., 45: 115-116
Egyed, L., 1961. Palaeomagnetism
and the ancient radii of the earth. Nature,
190(4781): 1097-1098.
Gough, D.I. and Brock, A., 1964. The paleomagnetism
of the Shawa ijoiite. J. Geophys.
Res., 69(12): 2489-2493.
Gough, D.I., Brock, A., Jones, D.L. and Opdyke, N.D., 1964. The paleomagnetism
of
the ring complex at Marangudzi and the Mateke Hills. J. Geophys. Res.,
69(12): 2499-2507.
Graham, K.W.T., Helsley, C.E. and Hales, A.L., 1964. Determination
of the relative
positions of continents from paleomagnetic
data. J. Geophys. Res., 69(18):
3895-3900.
Helsley, C.E., 1965. Paleomagnetic
results from the Lower Permian Dunkard Series
of West Virginia. J. Geophys. Res., 70(2): 413-424.
206
Tectonophysics,
5 (3) (1968) 191-210
Irving, E., 1964. Paieomsgnetism and its application to geological and geophysical
problems. Wiley, New York, 399 pp.
Khramov, A.H. and Andreyeva, O.L., 1964. Application of the determination of a
compensating field for finding the direction of the primary magnetization of
rocks. Bufl. Aead Sci. U.S.S.R., Geophys. Ser., 1964(4): 329-331 (English
transl.),
Kruseman, G.Y., 1962. Etude pai&omagn&ique et sedimentoiogique du Bassin Permien
de Led&e, Herault, France. Thesis, University of Utrecht, Geol. Ultraiectina,
9: 66 pp.
Nairn, A.E.M., 1960. Paleomagnetic resuIts from Europe. J. Geoi., 68(3): 285-306.
Nairn, A.E.M., 1964. Evidence of latitude from Permian palaeomagnetic data. In:
A.E,M. Nairn {Editor), Problems in PaiaeoclimatoIogy. Wiley, London, pp.550-558.
Nijenhuis, G.H.W., 1961. A palaeomagnetic study of the Permian volcanics in the
Nshe region (SW Germany). Geol. Mijnbouw, 40(l): 26-38.
Opdyke, N.D., 1964. The paleomagnetism of some Triassic red beds from Northern
Rhodesia. J. Geophys. Res., 89(12): 2495-2497.
Picard, MD., 1964. Paieomagnetic correfations of unite within Chugwater (Triassic)
formation, west-central Wyoming. Bull. Am. Assoc. Petrol. Geologists,
48(3): 269-291.
Roche, A., Saucier, II. et Lacaze, J., 1962. Etude paleomagnetique des roches volcaniques Permiennes de la region Nideck-Donon. Bull. Serv. Carte Geol.
Alsace-Lorraine,
X(2): 59-68,
Roy, J.L., 1963. Paiaeomagnetism of Prince Edward Island. Geophys. J., S(2): 226230
Van Hiften, D., 1963. Paiaeomagnetic indications of an increase in the earth’s radius.
Nature, 200(4913): 1277-1279,
Van Hi&en, D., 1964. Evaluation of some geotectonic hypotheses by paieomagnetism.
Tectonophysics, l(1): 3-71.
Vfasov, A.Ya. and Nikoiaichik, N.V,, 1964. Paieomagnetic investigations of the Mesozoic deposits of Taimir and the central part of the Erasnoyarsk territory. Buil.
Acad. Sci. U.S.S.R., Geophys. Ser., 1964(11): 10261027 (English transl.).
Ward, MA., 1963. On detecting changes in the earth’s radius. Geophys. J.,
8(2): 217-225.
Ward, MA., 1966. Comments on detecting changes in the eartbh”s radius. Geophys.
J., lO(4): 445-447.
APPENDIX
List of data used in this paper, Unless otherwise stated, reference is made to the
“list of paleomagnetic resulb+ compiled by Irving (1964, pp.294-362)
Group
Long.
(degr.)
Lat.
(degr.)
Carboniferous, North
1
66.0 w
66.0 W
66.0 w
59.0 w
66.0 w
2
113.0 w
111.5 w
99.0 w
Tectonophysics,
America
47.5 N
48.0 N
45.0 N
48.0 N
46.5 N
36.0 N
34.5 N
31.0 N
Direction of
magnetization
R(degr.)
Hdegr.)
162.5
+15.5
t13.0
+33.5
123.5
t30.5
- 3.5
+16.0
- 5.0
166.0
161.5
174.5
161.5
149.5
125.0
322.0
5 (3) (1968) 191-210
Reference
Black
Black
Black
Bfack
Biack
6.64
6.65
6.63
(1964)
(1964)
(1964)
(1964)
(1964)
207
~._~____.
Group
Long.
(degr.)
Lat.
(degr.)
__~~~
.-. _~
Direction of
magnetization
D(degr.)
Reference
I(degr.)
_
Permo-Carboniferous,
1
105.5 w
112.0 w
109.0 w
112.0 w
112.0 w
110.5 w
111.3 w
112.0 w
2
64.0 W
63.5 W
63.0 W
63.5 W
North America
35.5 N
175.5
35.0 N
141.U
35.5 N
164.0
36.0 N
146.0
36.0 N
132.5
34.0 N
159.0
35.0 N
143.5
35.0 N
161.0
46.5 N
170.0
46.0 N
171.0
46.0 N
177.0
46.0 N
174.5
+30.5
i lb.0
* 3.0
* ;;.o
+23.0
+ 2.0
+ 9.5
+lU.O
i- 3.5
+ 7.0
r 5.5
+ 1.0
7.52
Collinson and Runcorn
Collinson and Runcorn
Doe11 (1955)
Cox and Doe11 (1960; E
Cox and Doe11 (1960; E
Cox and Doe11 (1960; E
Collinson and Runcorn
Black (1964)
Black (1964)
Black (1964)
Roy (1963)
Permian,
1
2
Siberia
102.0 E
91.0 E
72.0 N
53.0 N
-68.0
-64.5
7.39
7.57*1
Permian,
1
Europe (selected
3.0 E
43.5
3.0 E
43.5
10.5 E
60.0
8.0 E
50.0
8.0 E
50.0
7.5 E
48.5
-
Kruseman (1962)
Kruseman (1962)
7.13
Nijenhuis (1961)
Nijenhuis (1961)
Roche et al. (1962)
__-
2
3
Permian.
1
2
208
data)*Z
N
193.0
N
184.0
204.0
N
N
193.0
198.0
N
192.0
N
-
Eurone (all data)
60.0 N
10.5 E
50.5 N
6.0 E
49.5 N
7.0 E
49.0 N
7.0 E
49.0 N
7.5 E
49.0 N
8.U E
50.0 N
8.0 E
50.0 N
8.0 E
50.0 N
20.0 E
50.5 N
16.0 E
48.5 N
7.5 E
43.5 N
3.0 E
43.5 N
3.0 E
48.5 N
7.5 E
58.0 N
56.0 E
61.0 N
46.0 E
59.0 N
51.0 E
53.0 N
52.0 E
54.0 N
52.0 E
61.0 N
45.0 E
57.0 N
54.0 E
57.0 N
55.0 E
56.0 N
55.0 E
48.0 N
38.0 E
55.0 N
53.0 E
57.5 N
55.0 E
For footnotes
295.0
255.5
204.0
193.5
181.0
183.0
186.0
182.0
193.0
198.0
205.0
205.0
193.0
193.0
184.0
192.0
221.0
222.0
222.0
226.0
222.0
220.0
226.0
229.0
228.0
225.0
220.0
222.0
6.5
+ 4.0
-36.5
-18.0
- 9.0
-13.0
-
-36.5
-14.5
- 9. 0
- 5.0
+ 4.0
- 7.0
-18.0
- $1.0
-19.5
- 9.0
- 7.0
- 6.5
+ 4.0
-13.0
-40.0
-48.0
-4x.0
-46.0
-39.0
-35.0
-44.0
-44.0
-40.0
- 9.0
-37.0
-42.0
(1960)
(1960)
46)
41)
39)
(1960)
7.13
De Magnee and Nairn (1962)
7.08
Nairn (1960)
Nairn (1960)
Nairn (1960)
Nijenhuis (1961)
Nijenhuis (1961)
Birkenmajer
and Nairn (1964)
mentioned in Nairn (1964)
7.07
Kruseman (1962)
Kruseman (1962)
Roche et al. (1962)
7.35
7.22
7.23
7.24
7.26
7.27
7.28
7.33
7.36
7.38
Khrambv and Andreyeva (1964)
7.32
see p.210
Tectonophysics
5 (3) (1968) 191- 210
(continued)
APPENDIX
Group
Permian,
1
2
Triassic,
1
2
Long.
Lat.
(degr.)
(degr.)
2
3
4
Jurassic,
1
2
D(degr.)
I(degr.)
Reference
North
106.5
108.5
105.5
109.0
81.0
America
W
34.5
W
35.5
w
35.5
w
38.0
w
39.5
N
N
N
N
N
149.0
160.5
143.0
150.0
163.5
+ 8.0
+55.0
- 1.0
+20.0
+ 7.7
7.47
7.48
7.50
7.46
Helsley
North
108.0
110.5
113.0
105.0
109.5
109.5
111.5
104.0
108.5
74.9
73.0
72.5
77.5
76.5
America
W
43.0
w
38.0
w
37.5
w
35.5
w
38.5
w
38.5
w
37.0
w
35.0
w
43.0
w
40.5
w
42.0
W
42.0
w
39.5
W
40.0
N
N
N
N
N
N
N
N
N
N
N
N
N
N
334.0
338.0
338.0
16.0
156.0
160.0
17.0
16.5
331.0
358.7
12.0
10.0
334.0
359.5
+17.0
+19.0
+16.0
+ 9.0
- 7.0
-10.0
+31.0
+55.5
+39.0
+25.1
+14.0
+16.0
+4a.o
+23.0
8.30
8.31
8.32
8.37
8.38
8.39
Cox and Doe11 (1960; F 105)
Cox and Doe11 (1960; F 25)
Picard (1964)
8.42
8.43
8.44
8.41
Beck (1965)
352.0
333.5
329.0
330.0
162.0
178.0
325.0
150.6
335.3
350.3
332.0
-62.0
-60.0
-54.0
-50.0
+54.0
+66.0
-13.0
+55.0
-52.0
-55.6
-40.0
9.26
mentioned in Graham et al.(1964)*2
9.46
9.47
9.48
9.49
8.26
Gough et al. (1964)
Gough and Brock (1964)
Opdyke (1964)
9.24
Triassic-Jurassic,
1
28.5
27.0
29.3
27.8
29.3
27.8
2
27.0
30.5
32.0
3
28.7
26.0
Triassic,
1
Direction of
magnetization
E
E
E
E
E
E
E
E
E
E
E
South Africa
30.3 s
31.9 S
29.6 S
29.4 s
29.6 S
29.4 s
23.0 S
22.0 s
19.0 s
16.2 S
18.0 S
Siberia
88.0 E
88.8 E
92.0 E
101.0 E
101.0 E
101.0 E
111.0 E
111.0 E
108.0 E
114.0 E
66.0
67.0
67.0
71.0
71.0
71.0
76.0
76.0
75.0
63.0
N
N
N
N
N
N
N
N
N
N
90.0
62.0
92.0
286.0
117.0
303.0
161.0
168.0
130.0
179.0
+71.0
+76.0
+80.0
-59.0
+64.0
-64.0
+39.0
+1a.o
+68.0
+a7.0
8.16
8.17
8.18
8.22
8.23
8.24
Vlasov
Vlasov
8.21
8.19
Antarctica
161.0 E
161.6 E
165.0 E
25.0 W
78.0
77.4
84.0
80.5
S
s
s
s
255.0
250.0
244.0
64.0
-76.0
-68.0
-75.0
-68.0
9.37
9.38
9.56
9.42
For footnotes
Tectonophysics,
(1965)
and Nikolaichik
and Nikolaichik
(1964)
(1964)
see p.210
5 (3) (1968) 191- 210
209
APPENDLX
Group
Cretaceous,
1
2
3
(continlled)
Long.
(degr.)
Lat.
(degr.)
North America
71.0 w
45.5 N
73.0 w
45.5 N
103.7 w
78.7 N
110.0 w
34.0 N
Direction of
magnetization
Reference
D(degr.)
I(degr.)
157.0
151.0
284.0
164.0
-52.0
-.59.5
+x0.0
-62.0
10.12
10.11
10.17
10.13*3
*IValue of declination
and inclination computed from positions of sampling site and pole.
*%election
of the most reliable Permian data of Europe. Their rocks were cleaned
by alternating magnetic fields and/or by thermal procedures.
*3This latter, unreliable observation
was omitted from one of the calculations
(graph s in Fig.7).
210
Tectonophysics
5 (3) (1968)
191- 210