Intensity of the Earth's magnetic field over the last 10 000 years

96

Physics of the Earth and Planetary Interiors, 20 (1979) 96-110 © Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands

INTENSITY OF THE EARTH'S MAGNETIC FIELD OVER THE LAST 10 000 YEARS C.E. BARTON l , , R.T. MERRILL l , and M. BARBETTI 2 1 Research School of Earth Science, Australian National University, P.O. Box 4, Canberra 2600 (Australia) 2 Physics Department, University of Adelaide, G.P.O. Box 498, Adelaide 5001 (Australia)

(Accepted for publication in revised form April 9, 1979)

Barton, C.E., Merrill, R.T. and Barbetti, M., 1979. Intensity of the Earth's magnetic field over the last 10 000 years. Phys. Earth Planet. Inter., 20: 96-110. Analyses of over 600 archaeomagnetic data compiled by Burlatskaya and Nachasova (1977) illustrate that our knowledge of the intensity of the Earth's magnetic field is much poorer than generally believed. The data exhibit high scatter and the distribution of sampling localities is extremely limited. Rock magnetic and experimental contributions to the scatter'are probably significant, although it is impossible to determine uniquely the sources of scatter without a substantial increase in the data base and without making additional assumptions about the past magnetic field behaviour. Nevertheless, when averaged in 1000 year intervals, the archaeomagnetic intensity data for the past 5000 years can be simply, but non-uniquely, interpreted in terms of a change in the intensity of the dipole field. This interpretation is broadly consistent with independent evidence from radiocarbon data. Because of inconsistencies in radiocarbon data prior to 8000 years B.P. and because of inadequacies in the archaeomagnetic data, the previously alleged sinusoidal variation of the dipole field intensity with a period of 8000-9000 years should be regarded as highly tentative.

1. Introduction Much work has gone into characterizing the geomagnetic field and its secular variation using directional data from palaeomagnetic studies (see reviews by Cox, 1975; McElhinny and Merrill, 1975; MerriU and McElhinny, 1977). These reviews point out that the time-averaged palaeomagnetic field is axially symmetric in the first order approximation. Departures from a geocentric axial dipole field are small but significant. Unfortunately these departures must be represented by ratios of dipole to nondipole terms in a spherical harmonic expansion. The actual magnitudes of the dipole field and nondipole fields cannot

* Present addresses: C.E. Barton, Department of Geophysics, University of Edinburgh, Edinburgh, Great Britain; R.T. Merrill, Department of Oceanography, University of Washington, Seattle, WA 98195, U.S.A.

be uniquely resolved, nor can the source of scatter in magnetic directions be uniquely separated into dipole and nondipole contributions, because of the lack of suitable palaeointensity data for the past few millions o f years. Although palaeointensity data would greatly enhance the picture, reliable estimates are far more difficult to obtain than for palaeo-directions. Beyond 10 000 years B-P. the spatial and temporal distributions of intensity data are too sparse to provide detailed information about the field. Thereafter, a greater body of data exisis based largely on results from baked archaeological materials. Analyses o f these intensity data (e.g., Bucha, !967, 1969; Cox, 1968) suggest that the variation in strength of the geomagnetic dipole resembles a sine wave of period between 8000 and 9000 years with a maximum and a minimum which are respectively about 1.5 and 0.5 times the present dipole intensity. These results have been used for a variety of purposes including (i) statistical modeling of reversals

97 ¸ of the geomagnetic field (Cox, 1969), (ii) arguing that large changes in the magnetic field energy o f the core have occurred (Verosub and Cox, 1971), (iii) explaining, and even correcting for, variations in 14C production in the upper atmosphere (Bucha, 1969; Lingenfelter and Ramaty, 1970; Damon, 1970) and (iv) isolating the behavior of the nondipole field in Hawaii (Coe et al., 1978) Recently Burlatskaya and Nachasova (1977) published a comprehensive catalogue o f archaeomaguetic data and it is worthwhile investigating whether the simple dipole oscillation model and its numerous consequences are sustained by the larger data set. We also attempt to distinguish between the factors contributing to scatter in the intensity data, namely rock magnetic and experimental uncertainties, secular variation of the nondipole field, and variation of the dipole field. Our ability to distinguish between scatter

arising from the first o f these factors and the remainder has proved to be a key step in analyzing past geomagnetic secular variation (see review by McElhinny and Merrill, 1975).

2. Equivalent dipole moments Comparison o f data from different geographical locations is complicated by the dependence on magnetic latitude o f the field due to a geocentric dipole as well as by the irregular perturbation of the nondipole field, Smith (1967a, b) reviews the methods which have been used in the past. Little can be done to reduce the scatter in intensities arising from nondipole variations, but by a suitable choice of dipole model, the moment of an imaginary geocentric dipole responsible for the observed ancient field intensity

TABLE I Various methods for expressing and comparing the intensity of the Earth's magnetic field in the past Dipole moment

Assumption

Method of calculation

Comments

(a)

Virtual dipole moment (VDM)

The dipole axis corresponds to that determined by the ancient inclination (/a) at the site.

VDM = M(~,a) where ~a is the ancient magnetic latitude given by tan Ia = 2 tan ka

(1) The uncertainty in la arising from rock-magnetic, experimental and nondipole field effects is present in addition to that in F a. (2) Because intensity data have often been published without corresponding inclinations (e.g. for unoriented samples), VDMs cannot always be calculated. (3) Dipole wobble does not introduce a scatter in VDMs.

(b)

Reduced dipole moment (RDM)

The dipole axis is that of the present day geocentric dipole, inclined at ~111° to the rotation axis.

RDM = M(~p), where ;~p is the present day magnetic latitude at the site.

(c)

Virtual axial dipole moment (VADM)

The dipole axis coincides with the geegraphic axis.

VADM ffiM(ks) where ks is the geegraphic latitude at the site.

(1) No knowledge of the ancient inclination is required. (2) The ancient geomagnetic axis will not generally coincide with the present day axis as assumed. (3) For the last few hundred years this choice may well be better than the geogIaphic axis, but some scatter in RDMs will still arise from dipole wobble. (1) An error will occur if the dipole is not along the rotation axis, as for the present field configuration. (2) Scatter will arise from dipole wobble. (3) No knowledge of the ancient inclination is required.

98

can be used for comparative purposes. The three prin. cipal models are summarized in Table I. The function, M(X) = Fr3(4 - 3 cos 2 X) -v2

Each of these three options in Table I represents a compromise. Smith (1967b) converted all intensity data to virtual dipole moments~ VDM's, or reduced dipole moments, RDM's, depending on whether inclination values were available (see def'mitions given in Table I). In view of our ignorance of the exact behaviour of the geomagnetic axis beyond the range

(1)

is used to obtain the moment of the geocentric dipole, M(X), responsible for a field strength F at radial distance r and magnetic latitude X. REL.VADM o

1

OARS EVERY 1000 YR BP

2

o

1

2

-'-.

=

F= i'ol

J

,~t..~. _ L

J'~

liT

T

•

.

i"

t

!

,o ..._

•

(b)

Ca) T

"0 ,I.

"e"

-

" - 4

.m.

T

.

..

_~_

•

•

(c)

(d)

Fig. 1. Intensity data from Burlatskaya and Nachasova's (1977) compilation plotted in terms of virtual axial dipole m o m e n t s (VADM) in units o f 1022 A m 2, for (a) the world, and for longitude zones (b) 330 ° to 60°E - "Europe and Western Asia", (c) 60 ° to 150°E - "Eastern Asia", essentially Japan, and (d) 220 ° to 330°E - "America". VADMs beyond the c u t o f f o f 16 X 1022 A m 2 are plotted at that value. The present-day dipole moment is close to 8.0 × 1022 A m 2. The data are confined almost entirely (>98%) to the northern hemisphere, hence the nomenclature chosen for the longitude zones.

99 of observatory records (but bearing in mind the recent changes suggested in the review by Barbetti, 1977), we have converted all data to virtual axial dipole moments, rather than to RDM's for comparative purposes. This choice is further supported by the fact that roughly one third of the data in Burlatskaya and Nachasova's catalogue (mostly the older results) do not have associated inclination values and so could not be reduced to VDM's. As one extends the palaeointensity estimates back in time, the virtual axial dipole moment, VADM, will probably serve as the best moment to use for comparisons because over long time intervals the magnetic field is essentially axially symmetric (Merrill and McElhinny, 1977).

3. The intensity data Virtual axial dipole moments corresponding to the intensity data compiled by Buflatskaya and Nachasova (1977) are plotted in Fig. 1 for both the whole world and for three separate longitude zones. The names given in Fig. 1 refer to these zones rather than literal geographical regions. Ages are those catalogued, and are a mixture of conventional radiocarbon, corrected radiocarbon and historical dates; in some of the original papers this distinction is not explicit. A high scatter in the data is apparent (relative to a smoothed curve such as given in Fig. 2), which cannot be accommodated within the quoted error limits. The scatter seems to be mainly due to the variation in intensity (i.e., VADM) values and not to dating uncertainties, though the latter must certainly be a contributing factor. Table II summarizes the means and standard deviations per 1000 year class interval for both VADM's (for all the data), and for VDM's (for data with associated inclination values). The standard deviations for VDM's are only slightly less than those for VADM's which means that either there is little contribution from dipole wobble or that the additional scatter introduced into the VDM's by the use of palaeoinclinations is similar to that arising from dipole wobble in the case of VADM's. We consider the second alternative to be more probable, for reasons given in Section 5. World averages of VADM's in 1000 year blocks (Fig. 2) exhibit the simple sinusoidal trend found

REL • VADM

eARS EVERY

•

I000 YR BP

(o)

" (b)

Fig. 2. Means of consecutive 1000 year intervals (circles)and 500 year intervals (squares) for the virtual axial dipole moments given in Fig. 1(a).

previously in smaller data sets and interpreted as a change in intensity of the main dipole field (e.g., Bucha, 1967, 1969, 1971; Cox, 1968). If the averaging is performed over 500-year intervals (Fig. 2), the pattern is not so smooth. It is noted that "world" averages are dominated by the European data. The very restricted spatial coverage of the present intensity data is illustrated by Table III. Only Europe

100 TABLE II 1000 year means of VADMs (for all the data) and VDMs (for data with associated palaeoinclinations) together with the corresponding standard deviations (SD). N is the number of points in each interval; dipole moments are in units of 102: A m 2 ; figures in parentheses are the standard deviations expressed as percentages of the dipole moment concerned Virtual axial dipole moments Median interval age (B.P.) 500 1500 2500 3500 4500 5500 6500 7500 8500 9500

VADM

9.08 10.92 10.29 8.88 6.61 5.62 6.04 8.93 9.84 6.20

Virtual dipole moments

N"

SD

VDM

N

SD

335 157 50 13 14 13 6 9 6 1

1.54 (16.9%) 2.12 (19.4%) 2.51 (24.4%) 2.33 (26.2%) 0.96 (14.5%) 2.47 (44.0%) 1.16 (19.2%) 1.93 (21.6%) 1.74 (17.7%)

9.01 11.61 11.91

278 90 9 0 2 1 0 0 0 0

1.50 (16.6%) 2.22 (19.1%) 2.06 (17.3%)

is adequately represented, while most of the remaining data are from Japan. Inclusion of results omitted from the catalogue (e.g., Shaw, 1974) and updating will not drastically change this situation. A number of reliable determinations now exist for Australia (Barbetti et al., 1977; Barbetti and Flude, in preparation) and, as with the Eastern Asian data, the variations are not identical to those evident in the European data. Moreover, there are virtually no data from the whole of the southern hemisphere used to obtain Fig. 2, and we should be wary about taking the variation shown in Fig. 2 as a proper world average. It is clear from the very restricted distribution of sampling localities that without additional constraints a wide variety of interpretations of the data in Figs. 1 and 2 could be made. For example, the sinusoidal trend in Fig. 2 could be due to the variation in (say) an axial quadrupole field during a time of constant dipole intensity, although this interpretation will not be favored for reasons given later. Thus, it is important to assess the possible reasons for real and apparent variations in intensity.

4. Scatter due to dipole wobble Directional changes in the dipole field as well as intensity changes will affect VADM's. The present

10.12 11.84

geocentric dipole is inclined to the axis of rotation at about 11.5%, but when averaged over the past 5 million years it coincides with the earth's rotation axis (Merrill and McElhinny, 1977). We consider two idealized extreme ways in which this averaging can occur: (i) the dipole axis can precess about the axis of rotation at a constant angle (precessionmodel), or (ii) the dipole axis can oscillate to and fro through the axis of rotation in a random manner (pendulum model). The term dipole wobble is often used to describe combined latitudinal and longitudinal motions o f the dipole (e.g., Cox, 1975). The scatter resulting from any dipole wobble would be bracketed by the scatter calculated for the precession and pendulum models. One cannot distinguish uniquely between contributions to the angular standard deviation in virtual geomagnetic poles due to changes in the dipole and nondipole fields. However, a contribution of 10 ° to the angular standard deviation is a reasonable estimate for scatter produced by dipole variations (McElhinny and Merrill, 1975). Accordingly, an angular offset of 10 ° for the precession model, and one of 20 ° amplitude for the pendulum model (i.e., mean offset = 10 °) gives a total range (not standard deviation) of VADM variations o f 24%--43% at 20 ° latitude and 21%-39% at 45 ° latitude, respectively. Because these models describe opposite extremes

I01 of possible dipole movements, scatter in intensity values are expected to lie within the above limits for a paleointensity data set in which the time-averaged field approaches that of a geocentric axial dipole. Most of the intensity data centers about a latitude of 45°N (Table III), so that variations of the order of 21-43% over long time periods are expected solely from dipole wobble! It is important also to note that the errors in VADM's due to tilting of the dipole axis will tend to cancel when VADM's from widely separated geographical regions are averaged over short periods of time. Mean VADM's calculated in this way should therefore not differ,significantly from mean VDM's, but the standard deviation of the latter should be less if dipole wobble has occurred.

5. Scatter due to nondipole field variations A dominant feature of the nondipole field over the last few hundred years has been its westward drift at approximately 0.2 ° per year (Bullard et al., 1950), although a substantial part of the secular variation of the nondipole field cannot be explained in this manner. Yukutake and Tachinaka (1969) have argued that roughly half of the nondipole field can be ascribed to a standing field of constant or slowly varying amplitude on which is superimposed the remaining drifting part. This explanation does, however, leave unexplained large changes in the axisymmetric components of the field, such as exhibited by the axial quadrupole during the past 150 years (James, 1971,1974). It is not possible to determine from palaeosecular variation studies whether the nondipole-to-dipole field ratio averaged over the Earth's surface has changed significantly in time. We can only assume that the present-day value is characteristic of the past, i.e. the nondipole field accounts for about 10% of the total field at the Earth's surface. If the 1965.0 International Geomagnetic Reference Field (IAGA Commission 2, Working Group 4, 1969) is sampled at 10° intervals about circles of latitude (equivalent to sampling as a function of time with the field pattern drifting westwards), intensities expressed in terms of VADM's show standard deviations which are typically 15% (Table IV). Of course, this scatter is due to con-

tributions from the dipole (which is tilted with respect to the axis of rotation) and nondipole fields. This is equivalent to saying that 5% of the grid points sampled are expected to give moments outside +30% of the mean for a normal distribution. For VDM's the corresponding figure is -+22% (Table IV). The other entries in Table IV demonstrate that (i) the magnitudes of the mean VADM's and VDM's are not significantly different, (ii) the present-day nondipole field variation has an approximately equal effect on VADM's and VDM's and (iii) the standard deviation for VDM's is not very much less than that for VADM's. Point (i) is not surprising because it is to be expected that errors in individual VADM's, arising from both the tilt in the dipole axis and the local nondipole field, will tend to cancel when values from widely-separated geographical regions are averaged to obtain a mean. Points (ii) and (iii) together mean that the absence of a dipole wobble contribution in VDM's is to some extent offset by nondipole perturbation of the inclinations which are substituted in the calculation. It is not possible to separate uniquely the nondipole from dipole contributions to the standard deviation. Even the last values given in each column in Table IV assume that the present field is representative of the past field and that the nondipole and dipole fields rotate in unison. The last part of this assumption has not been satisfied during the last 150 years, a time in which the nondipole field has clearly drifted westward faster than the dipole field. Nevertheless, if the variations due to the nondipole field are assumed to be independent of those due to dipole field, then the standard deviation of VADM's that arises from the nondipole field is roughly 10%. This value is probably a reasonable estimate of the relative contribution to the standard deviation arising from the nondipole field in the past providing the present field division into nondipole and dipole parts is characteristic of the past.

6. Scatter due to rock-magnetic and experimental limitations "Reliable" palaeointensity techniques have builtin consistency checks based on various assumptions. For example, versions of Thellier's method (Thellier

102 TABLE III Geographical distribution of the data plotted in Fig. I. Entries denote the number of points within 10° X 10° blocks centered on the specified latitude (positive -- north, negative = south) and longitude (east) Latitude Longitude (degrees north) (degrees east) 225

235

245

255

265

275

285

295

305

315

325

335

345

355

5

15

25

85 75 65 55 45 35 25 15 5 -5 -15 -25 -35 -45 -55 -65 -75 -85

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 1 0 2 1 12 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 1 3 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 1 0 0 7 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0

0 0 0 4 5 1 0 0 1 0 0 0 0 0 0 0 0 0

0 0 0 14 20 2 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 16 53 0 0 0 0 0 0 0 0 0 0 0 0 0

Sum

0

0

10

16

1

0

4

8

0

0

0

0

0

3

11

36

69

and Thellier, 1959) assume that any secondary magnetization acquired by a sample will not change the primary remanence by a constant percentage throughout the blocking temperature spectrum. Shaw's technique (Shaw, 1974) makes a parallel assumption

TABLE IV Mean values and mean standard deviations for vktual axial dipole moments and virtual dipole moments for the 1965 IGRF. Intensities of the field (dipole, nondipole or total) were taken at 10° intervals around ckcles of latitude, convetted to the relevant dipole moment and averaged. The means given are averages of the dipole moment means and standard deviations for the 17 circles of latitude 80°N, 70°N, .... 0 ° ... 80°S

Dipole field Nondipole field Total field

Mean VADM ±1 SD (1022 A m 2)

Mean VDM ±1 SD (1022 A m 2)

7.97 ± 0.52 (7%) 1.66 ± 0.68

7.98 + 0.00 1.88 -+0.66

8.07 -+ 1.19 (15%)

8.03 -+0.88 (11%)

throughout the coercive force spectrum determined by alternating field demagnetization. Such assumptions appear reasonable on the basis of a variety of rock-magnetic studies, although the extent to which secondary magnetizations alter the shapes o f thermal and AF demagnetization curves is yet to be adequately determined. Examplesexist when apparently good palaeointensity data give completely (more than 200%) erroneous results (e.g., U . S . - J a p a n Paleomagnetic Cooperation Program in Micronesia, 1975). Most workers test their particular technique on samples formed recently in places where the field intensity is well determined. Obtaining a correct estimate o f the field is~a necessary condition for the palaeointensity technique to work, but not a sufficient condition, as is often assumed. For example, a demonstrably " b a d " method may pass the above test simply because the sample contains a purely thermal remanent magnetization (TRM), yet be quite unable to cope with older rocks which have undergone partial alteration. No palaeointensity technique has yet been proved to give the correct value for samples

103

35

45

55

65

75

85

95

105

115

125

135

145

155

165

0 0 0 0 0 0 126 27 18 93 12 0 0 0 0 0 0 0,,. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 40 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 1 24 4 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 16 0 1 1 0 0 0 0 0 0 0 0 0 0

0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 53 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

156120

9

40

29

0

0

18

10

0

53

10

0

0

which have suffered substantial post-TRM chemical alteration (see Merrill, 1975, for further discussion). Inevitably, the data compiled b y Buflatskaya and N~chasova (1977) have been derived from a variety o f different experimental techniques and span a wide range in quality (a warning to this effect is appended to the catalogue). An example o f this is the East Asian data for samples older than 7000 years, which give lower palaeointensity values than those from Europe (Fig. 1). This East Asian data comes-from the work o f Kitazawa (1970), who used a reasonable palaeointensity technique (a modified Thellier technique) and divided his results into groups A, B, and C o f decreasing reliability. Although Burlatskaya and Nachasova's compilation distinguishes broadly between techniques, the distinctions are insufficient to separate the three groups o f Kitazawa, all o f which appear to have been used to obtain averages. Most workers would accept values from Kitazawa's group A, but might be reluctant to accept those from groups B and C. A further uncertainty arises from the fact that

Sum 0 0 0 190 224 131 27 19 2 3 7 0 0 0 0 0 0 0

some intensity data were originally reported as a ratio o f the ancient to modern values at the field site. In cases where the latter was not quoted b y the authors, Burlatskaya and Nachasova have adopted the 1965 value at the site in question in order to calculate the ancient intensity. There can be little doubt that some o f the scatter in Fig. 1 stems from poor intensity data. Probably, that part o f the scatter which arises from the use o f low quality results far exceeds that part which originates from the occasional occurrence o f erroneous results from a good palaeointensity technique in which consistency checks are satisfied.

7. Interpretation of the arehaeomagnetic data It is clear that a unique interpretation o f the data given in Figs. 1 and 2 is not possible. One can only attempt to construct plausible models if some additional assumptions are introduced, such as made here

104 that the behaviour of the field during the past 9000 years has not differed markedly from that observed during recent times. In particular, we assume that the fraction of the magnetic field that is nondipole (roughly 10% today) has not changed significantly in the past 9000 years. The magnetic field of internal origin can be described in terms of a potential (qo given by oo

qt = a ~

1 (~)1+1 ~

lw-1 m=O

+ h~n sin m~)

etm(cos 0)(g~n cos mS (2)

where we use spherical coordinates (r, 0, ~b),a is the Earth's mean radius,P~t are the Schmidt polynomials, and g~t and h~ are the Gauss coefficients. The field is obtained by taking the negative gradient of q~. In principle, the increased intensity between 1000 and 2000 B.P., apparent in (essentially) three different regions in the northern hemisphere, could be explained by an increased strength of the geocentric axial quadrupole field (characterized by the gO term in equation (2)). However, this explanation would be inconsistent with the assumption given above. The spherical harmonic expansion given by equation (2) for the present field rapidly converges at the Earth's surface for low order terms out to l = 6 to 8 (Vestine, 1967; Cain, 1975). Although coefficients out to l = 23 have, on occasions, been calculated, coefficients greater than I = 12 are believed to have significant contributions from crustal remanence sources (Kolesova and Kropachev, 1973; Cain, 1975). The A / g ° ratio (axial quadrupole to axial dipole) for the present field is 0.06 (IAGA division I study group, 1975), which is slightly larger than that for the timeaveraged normal polarity field (Merrill and McElhinny, 1977). Thus, to explain the higher intensity by changes in the quadrupole field or fields represented by higher order harmonics would require that a very different field existed in the past than either the present or the time-averaged field. For example, if the higher intensity 1500 years ago were due solely to a change in the intensity of the axial quadrupole field, then that quadrupole field would have to be an order of magnitude larger than at present. In general, one would expect to see large changes in palaeo-directions associated with such large nondipole fields, but such changes have not been reported. We conclude that the

intensity variation over the 5000 years shown in Fig. 2 is most simply explained by changes in intensity of the dipole field. This interpretation is broadly consistent with the radiocarbon data discussed in the next section. The lack of coherence between the European and East Asian data prior to 5000 B.P. (Fig. 1) could be interpreted as a tilt of the dipole axis towards Europe or as evidence of nondipole field changes, or as some combination of dipole and nondipole effects. As noted in the next section, the 14C data do not help to resolve this ambiguity. More reliable palaeo-direction data for this time period would be valuable. It is difficult to assess precisely the origin of the large scatter in VADM estimates in Fig. 1. The scatter is significantly larger than expected from changes in a nondipole field similar to that of today (Table IV), and persists even if the dipole wobble contribution is suppressed by taking VDM's (Table II). It seems likely that a large part of the scatter is of rock-magnetic or experimental origin. For example, if one assumes that the dipole, nondipole and rock-magnetic and experimental contributions to the scatter are independent factors, and if the first two have standard deviations each of 10% (see McElhinny and Merrill, 1975), then the standard deviation arising from the rock magnetic and experimental factor (including dating errors) would be of the order of 15% (13.5% for the data of Table II). That is, this factor would be one of the largest sources of the scatter. This is unfortunate because it probably precludes the use of statistical procedures analogous to those used in palaeosecular variation direction studies (McElhinny and Merrill, 1975), unless it is possible to greatly improve the quality of the data set. It is doubtful that the westward drift of the nondipole field can be resolved in these data, as has been previously claimed (Bucha et al., 1970). Additional evidence about the contribution of the non-dipole field comes from the recent palaeointensity estimates from Hawaiian basalts by Coe et al. (1978), who report consistently high values for rocks with 14C ages between 2000 and 5000 B.P. Their values for rocks of these ages are nearly twice that of the "mean" field intensity expected in Hawaii, if the variations shown in Fig. 2 for the past 5000 years are mainly due to variations in the dipole field intensity. The associated scatter in palaeomagnetic directions is

105 slightly, but not significantly, larger than expected at that latitude (McElhinny and Merrill, 1975), and no evidence of these larger intensity values is recorded in Japan or North and Central America (Fig. 1). Coe et al. (1978) attribute the large deviations from the expected dipole value to the nondipole field. If this is so, the terms in the spherical harmonic expansion (eq. 2) that describe this nondipole field must be of order l = 4 or greater. This suggests that a relatively complex field exists in the core, since these nondipole terms would be amplified by a factor of roughly 2 (l+l) by downward continuation to the core-mantle interface. However, this complex field had to exist for 2000 years or so, with a direction in Hawaii not significantly different from that of the local dipole field. Nevertheless, this interpretation is consistent with the findings of Yukutake and Tachinaka (1969) who point out that the superposition of standing and drifting components of the nondipole field can account for some very rapid local changes in the magnetic field, such as the "standing" Mongolian anomaly where the intensity has increased at an average rate of 50 nT per year over the last 400 years.

8. Radiocarbon and the strength of the Earth's magnetic field The isotope ~4C is one of several species of radionuclide produced by the interaction of cosmic rays with the Earth's atmosphere. ~4C is produced mainly in the stratosphere by the (n, p) reaction with ~4N, and it forms ~4CO2 which is rapidly and thoroughly mixed with ordinary carbon dioxide (riCO2 and ~3CO2) in the atmosphere. Carbon dioxide is continually exchanged between the atmosphere and the oceans. The oceans contain about 95% of the inventory of exchangeable carbon, and the mean residence time is of the order of 1000 years. Exchange between the Oceanic and the atmospheric reservoirs regulates the carbon dioxide content of the latter, and has an important influence on the isotopic composition of atmospheric carbon dioxide. Carbon-14 dating is based on the fact that atmospheric CO2, with its trace level of radiogenic '4C, is absorbed and incorporated by living materials. After

incorporation, the level of '4C gradually diminishes with time, through radioactive decay with a half-life of about 5730 years. Measurement of the residual 14C concentration of old organic materials thus allows an estimate to be made for the date of its formation, provided that one also knows the original concentration. By convention, all 14C dates are estimated on the assumption that the atmospheric concentration in the past was constant (Libby, 1952), and equal to that of an agreed international standard (0.95 times the concentration in NBS Oxalic Acid). This standard value was originally chosen because it approximated the actual atmospheric concentration in 1890 A.D. It is also conventional practice to continue using an earlier estimate of the half-life (5568 years; sometimes called the Libby half-life) and to express dates in years before the present, i.e. 1950 A.D. Numerous 14C measurements have been made on samples of known age in order to define the errors which inevitably occur in the radiocarbon time-scale because of the assumption of a constant atmospheric concentration of '4C in the past. The results from various radiocarbon-dendrochronologic age comparisons have been conveniently combined by Clark (1975). We have taken Clark's Table 8, which contains estimates of the true age (Tt) corresponding to radiocarbon ages (Tc) at intervals from 50 to 6500 B.P. and calculated relative atmospheric 14C concentrations (CA) using the expression CA = exp {(57-~0

5T68)ln 2}

The results are illustrated in Fig. 3, together with estimates for earlier times derived from the radiocarbonvarve age comparisons of Tauber (1970) and Stuiver (1971). The main features of Fig. 3 are the period of higher ~4C concentration from about 7000 to 4500 B.P., the fairly steady decrease from 4500 to 2500 B.P. to a value close to 1 and the shorter-term (500 years or less) fluctuations prominent since then. The marked decrease for the last 100 years is generally attributed to dilution by CO2 from the burning of fossil fuels (the Suess effect). There is a serious discrepancy between the results from Tauber (1970) and Stuiver (1971) for the period before 8000 B.P., but the reasons for this disagreement are not yet

106

DIPOLE MOMENT 6.5 1

7.0 I

7.5 I

8.0 I

8.5 I

I000 2000 n" co

3000

u-~ 4000 n,,cE bJ >- 5000

z

6000 rr, r,.." G: 3000 EEl

o 8000 rr rr" _j

9000

E~ Z I0000

11000

g

12000 13000 14000 15000 1.15

CLRR~ (1975) m

STUIVER (19?1)

m

TIMBER119"701 I 1.10

I

1.05

I 1.00

.95

ATMOSPHERIC C-14 CONCENTRATION Fig. 3. Atmospheric 14C concentration as a function of time in radiocarbon years B.P. Values of concentration are relative to the agreed international standard (0.95 times the concentration of NBS Oxalic Acid), and are calculated from pubfished data as indicated. Standard errors are shown when given by the original author. An equivalent horizontal scale is shown for the radiocarbon dipole moment (RCDM) in units of 1022 A m 2 (i.e. the geomagnetic dipole moment based on the assumptions that 14C concentration variation is due solely to geomagnetic variation and that production and decay of 14C are instantaneously balanced at any time).

fully understood (M. Stuiver, personal communication, 1979). Causes of change in the atmospheric ~ac concentration, apart from recent artificial perturbations, e.g. fossil fuel and atomic bomb effects, can be divided broadly into two categories: (a) Reservoir changes (for example, changes in ocean temperature, sea-level or circulation patterns) and fluctuations in the exchange rates between reser-

voirs. It has been argued that these might produce 14C variations as large as those observed since 7000 B.P. (Lal and Venkatavaradan, 1970), but Damon (1970) predicts only a very small effect. Unfortunately, these types of changes are not yet documented in sufficient detail to permit an accurate assessment of their contribution to the observed 4C variation. (b) Changes in the production rate of 14C due to changes in the intensity and composition of galactic cosmic rays, changes in the interplanetary and in the Earth's magnetic fields, and changes in the highenergy particle flux from the sun. Fluctuations in the production rate with timescales shorter than several half-lives of radiocarbon produce fluctuations of reduced amplitude in the atmospheric ~4C concentration. The attenuation becomes more severe as the period of the fluctuations becomes shorter; it is approximately a factor of 100 for periods of about 10 years (Houtermans, 1966). Observed variations in atmospheric ~*C concentration on time-scales less than about 500 years are generally attributed to solar activity. Following the work of Stuiver (1961), such variation is expected because the cosmic ray flux reaching the Earth's atmosphere varies inversely with sunspot activity, because of changes in the interplanetary magnetic field carried by plasma streaming out from the Sun. Lingenfelter and Ramaty (1970) calculate a + 12% variation in the ~4C production rate over the last three solar cycles. The effec~ may be partly balanced by increases in the high-energy particle flux from solar flares when the sun is most active. Measurements of ~4C concentration in annual tree-rings by Damon et al. (1973) and Stuiver (1978) present convincing evidence for an 11-year cycle in ~4C production that is correlated with the sunspot cycle. However, the amplitude of this 11-year variation is very small. Moreover, variations at this frequency would not be evident in Fig. 3 because many of the 14C analyses were made on samples covering ten annual growth rings (e.g., Ferguson, 1970) and Clark's (1975) calibration curve incorporates further smoothing. The attenuation is less severe, and of the order of a factor of 10, for variations in solar activity on timescales of 100-200 years (Houtermans, 1966). Eddy (1976) has recently documented a 70-year period

107 from 1645 to 1715 A.D. in which there were very few sunspots (the Maunder Minimum), and has suggested a second earlier minimum (the Sp6rer MinimuM, 1460-1550 A.D.). Stuiver and Quay (1978) have recently suggested that new radiocarbon data indicate that four such minima have occurred in the last 1000 years. The observed long term variation in ~4C concentration over the last seven millenia is generally attributed to variation in the geomagnetic dipole moment. However, Bucha et al. (1970) have pointed out that the variations in the nondipole part of the Earth's magnetic field might also affect the production rate of 14C. We wish to emphasize this possibility, although we realize that it will be many years before archaeomagnetic measurements are made with an accuracy and global coverage sufficient to permit proper evaluation of the hypothesis. Because of both observational difficulties and difficulties in modeling the nondipole effects, only changes in the dipole field will be considered further here. Elsasser et al. (1956) derived a simple expression for the dependence of ~4C production on geomagnetic moment (proportional to M -°'s 2 where M is the magnetic moment), and made approximate calculations of the 14C variation which might arise. Following the archaeomagnetic work of Bucha et al. (see review, 1970), it has been usual to perform model calculations of the ~4C variation using a sinusoidal variation of the geomagnetic field with maxima and minima about 1.5 and 0.5 times the present-day value (Lal and Venkatavaradan, 1970; Damon, 1970; Suess, 1970; Yang and Fairhall, 1972). In these studies, it has been assumed for mathematical convenience that the geomagnetic variation was sinusoidal and, in consequence, that ~4C production varied cyclically for an indefinite period prior to about 8000 B.P. There are minor differences in the numerical values used for the geomagnetic period, the dependence of ~'C production on geomagnetic moment (an approximation to the Elsasser et al. (1956) expression is usual), and various reservoir parameters. In general, however, the theoretical predictions are in reasonable quantitative agreement with the observed variations in ~4C concentration. Lingenfelter and Ramaty (1970) reassessed the dependence of ~4C production on geomagnetic moment and found that it varies approximately as

M -°'s only whenM is close to the present-day value of 8 X 1022 A m2; the relationship is quite different for much smaller and much larger values of M. Lingenfelter and Ramaty also calculated the 14C concentration variation, using the 500-year average values of dipole moment listed by Cox (1.968) for the last 10 000 years. In their method, the need for arbitrary assumptions about 14C production in the more remote past is avoided by introducing a parameter Ro (equal to the present ratio between production and decay) and integrating backwards in time. Lingenfelter and Ramaty found that the measured ~4C concentrations are reasonably well bracketed by curves calculated for 1.0 < R 0 < 1.05 and concluded that the gross features of ~4C variations can be understood in terms of the variations in geomagnetic moment. In all the aforementioned studies the published archaeomagnetic data have been taken as a staring point, and only Damon (1970) has previously pointed to possible misinterpretations that could arise from doing this. It is not difficult to see the historical reasons for this approach, particularly since the archaeomagnetic data was often published first. That position has now changed somewhat and, for the last 7000 years at least, the ~4C variation is known much more accurately than the geomagnetic variation. Let us therefore consider the problem from the other direction and start by taking the Clark (1975) curve as an accurate measure of the global atmospheric 14C concentration. To deduce the geomagnetic intensity we shall assume that 14C variations are solely of geomagnetic origin, and that the production and decay of ~4C are instantaneously balanced so that the atmospheric concentration varies linearly with production. The latter assumption is only strictly valid if all variations in ~4C concentration occur on time-scales of several ~4C half-lives or more. However, its use enables 14C concentrations to be simply converted to dipole moments (referred to herein as a Radiocarbon Dipole Moment, RCDM) using the relationship between production rate and dipole moment given by Lingenfelter and Ramaty (1970). The calculated RCDM scale is shown in Fig. 3. Two features are immediately obvious when the results are compared with those of Fig. 1 : the predicted amplitude (minimum ~6.8 at around 6000

108 B.P.; maximum ~8.2 between ~2000 and ~ 1000 B.P.) is too small, and the median value is too low. Because of various non-uniqueness problems associated with accurately assessing all the errors, it is difficult to assess how significant these differences really are. However, it would seem reasonable to attribute the small amplitude to attenuation effects because the time-scale of the main variation is ~10 000 years. The low median value also has a simple explanation. 14C concentration has tended to increase since " 2 0 0 0 B.P. and probably lags behind a more substantial increase in the production rate; the value of unity for concentration at 0 B.P. therefore reflects a slightly earlier value (>8.0) for the dipole moment. It is not possible to derive a unique value for the attenuation effect and hence correct the dipole moment scale in Fig. 3, as it is well known that attenuation varies rapidly with time-scale and we have no justification for assuming that only one time-scale is present. Nor is it possible to determine precisely the scale adjustments (both time and moment) necessitated by the lag between the change in production rate and the change in atmospheric concentration over the last 2000 years. Coe et al. (1978) have attempted to do this with a sinusoidal fit to the ~4C variation but the exercise has, as those authors admit, no quantitative significance. Nevertheless, we may make some qualitative predictions about long-term geomagnetic dipole changes. Firstly, the ~4C concentration minimum between 2000 and 1000 B.P. (Fig. 3) implies a broad maximum in dipole moment between about 3000 and 1500 B.P. (assuming a theoretical lag time of ~ 1000 years; Houtermans, 1966) which is a little earlier than the corresponding peak in the archaeomagnetic data (Fig. 2). This point has already been made by Damon (1970), Sternberg, and Damon (1976) and Damon and Sternberg (1978). Secondly, the steady but high t4C concentration between about 6500 and 4500 B.P. implies a broad minimum in dipole moment from ~7500 to 5500 B.P.; the corresponding minimum in the archaeomagnetic data, however, does not appear until 5500 B.P. Thirdly, Stuiver's (1971) data imply a low value of dipole moment between ~10 000 and "~7500 B_P., while the data of Tauber (1970) suggest a dipole moment higher than 8.0 X 1022 A m 2 between ~13 000 and ~10 000 B.P.; this last suggestion should still be regarded with some

caution because the 14C record prior to 7500 B.P. may be dominated by late Pleistocene trends (Barbetti and Flude, 1979) and reservoir changes associated with the transition from glacial to post-glacial climate. Finally, it is interesting to note that if some of the shorter-term ~4C fluctuations are due to geomagnetic variation, then changes of up to about -+1 X 1022 A m 2 in the effective dipole moment on time-scales of a few centuries would be required. The possible existence of such rapid variations in the globally-averaged geomagnetic record should not be excluded. We emphasize that all these predictions are based on the assumption that the observed ~4C variations are due entirely to geomagnetic variation, and could be largely invalidated if it can be demonstrated that long-term changes in solar activity, the galactic cosmic ray flux or reservoir parameters have occurred over the last 10 000 years.

9. Conclusions The palaeointensity data compiled by Burlatskaya and Nachasova (1977) spanning the last 9500 years show a high degree of scatter which cannot be uniquely resolved into the components arising from variations in the dipole and nondipole fields and from experimental and dating uncertainties. Assuming the recent behavior of the geomagnetic field to be characteristic of-the past, we can expect standard deviations in virtual axial dipole moments of about 10% arising from each of the dipole and nondipole variations, which implies that the rock-magnetic, experimental plus dating errors have an associated standard deviation that is roughly 15%. The simplest model suggests that the dipole intensity increased from about 5000 B.P. to 2000 B.P. and then subsequently decreased to the present-day value. This model is roughly consistent with both the archaeomagnetic and radiocarbon data, which exhibit similar variations. Archaeomagnetic data between 5000 and 10 000 B~P. comes mainly from Japanand Europe and differences between these data are not readily explained solely by a change in the dipole field strength. Due to the sparsity in archaeointensity data, due to conflicting radiocarbon results beyond 8000 B.P., and due to the fact that both the radio-

109

carbon and magnetic results cannot be uniquely interpreted, the alleged sinusoidal variation of the dipole field with a period of 8000-9000 years must be regarded as highly tentative. In addition, some data, such as that of Coe e t al. (1978) strongly suggest that nondipole field variations have on occasion contributed significantly to the magnetic field intensity at some localities in the past 8000 years. There is an obvious need to concentrate future effort on periods prior to 5000 B.P., and in regions other than Europe and Japan, particularly the southern hemisphere. A more selective treatment of the present data would also be well worthwhile.

Acknowledgements We thank Dr. Burlatskaya for sending us copies of his catalogue so that many of the analyses given in this paper could be undertaken. Reviews by, and discussions with, Dr. R. Coe and Dr. M. Stuiver were very helpful. Numerous discussions with Dr. M. McE1hinny have helped shape our views of the Earth's magnetic field. R.T.M. acknowledges financial support from the U.S.A. National Science Foundation and from the Research School of Earth Sciences of the Australian National University. M.B. acknowledges support from the Australian Research Grants Committee.

References Barbetti, M., 1977. Measurements of Recent geomagnetic secular variation in southeastern Australia and the question of dipole wobble. Earth Planet. Sci. Lett., 36: 2 0 7 218. Barbetti, M. and Flude, K., 1979. Geomagnetic variation during the Late Pleistocene period and changes in the radiocarbon time-scale. Nature (London), 278: 153-156. Barbetti, M.F., McElhinny, M.W., Edwards, D.J. and Schmidt, P.W., 1977. Weathering processes in baked sediments and their effects on archaeomagnetic field-intensity measurements. Phys. Earth Planet. Inter., 13: 346-354. Bucha, V., 1967. Intensity of the Earth's magnetic field during archaeological times in Czechoslovakia. Archaeometry, 10: 12-22. Bucha, V., 1969. Changes of the Earth's magnetic moment and radiocarbon dating. Nature (London), 224: 681-683. Bucha, V., 1971. Archaeomagnetic dating. In: H.M. Michael

and E.K. Ralph (Editors), Dating Techniques for the Archaeologist. MIT Press, Cambridge, Mass. Bucha, V., Taylor, R.E., Berger, R. and Haury, E.W., 1970. Geomagnetic intensity: changes during the past 3000 yrs in the Western Hemisphere. Science, 168:111-114. Bullard, E.C., Freedman, C., Gellman, H. and Nixon, J., 1950. The westward drift of the Earth's magnetic field. Philos. Trans. R. Soc. London, Set. A, 243: 67-92. Burlatskaya, S.P. and Nachasova, I.Ye. (compilers), 1977. Archaeomagnetic determinations of geomagnetic field elements. Mater. Mirov. Tsentra Dannykh B., Soy. Geophys. Comm. Acad. Sci. U.S.S.R., Moscow, 112 pp. Cain, J.C., 1975. Structure and secular changes of the geomagnetic field. Rev. Geophys. Space Phys., 13: 203-208. Clark, R.M,, 1975. A calibration curve for radiocarbon dates. Antiquity, 4 9 : 2 5 1 - 2 6 6 (and comments by Suess, and reply, Antiquity, 5 0 : 6 1 - 6 3 ) . Coe, R.S., Gromme, S. and Mankinen, E.A., 1978. Geomagnetic palaeointensities from radiocarbon-dated flows on Hawaii and the question of the Pacific nondipole low. J. Geophys. Res., 83: 1740-1756. Cox, A., 1968. Lengths of geomagnetic polarity intervals. J. Geophys. Res., 73: 3247-3260. Cox, A., 1969. Geomagnetic reversals. Science, 163: 2 3 7 245. Cox, A., 1975. The frequency of geomagnetic reversals and the symmetry of the nondipole field. Philos. Trans. R. Soc. London, Ser. A, 243: 67-92. Damon, P.E., 1970. Climatic vs. magnetic perturbation of the carbon-14 reservoir. In: LU. Olsson (Editor), Radiocarbon Variations and Absolute Chronology. Almqvist and Wiksell, Stockholm, pp. 571-593. Damon, P.E. and Sternberg, R.S., 1978. The use of radiocarbon as a boundary condition for geomagnetic field models. EOS, 59: 1057. Damon, P.E., Long, A. and Wallick, E.I., 1973. On the magnitude of the I 1 year radiocarbon cycle. Earth Planet. Sei. Lett., 20: 300-306. Eddy, J.A., 1976. The Mauder Minimum. Science, 192: 1189-1202. Elsasser, W., Ney, E.P. and Winckler, J.R., 1956. Cosmic ray intensity and geomagnetism. Nature (London), 178: 1226-1227. Ferguson, C.W., 1970. Dendrochronology of bristlecone pine, Pinus aristata;establishment of a 7484-year chronology in the White Mountains of eastern-central California, U.S.A. In: I.U. Olsson (Editor), Radiocarbon Variations and Absolute Chronology. Almqvist and Wiksell, Stockholm, pp. 237-245. Houtermans, J., 1966. On the quantitative relationships between geophysical parameters and the natural 14 C inventory. Z. Phys., 193: 1-12. IAGA Commission 2, Working Group 4, 1969. International Geomagnetic Reference Field 1965.0. J. Geophys. Res., 74: 4407-4408. IAGA Division 1, Study Group, 1975. International Geomagnetic Reference Field 1975. J. Geomagn. Geoelectr., 27: 437-440.

110 James, R.W., 1971. More on secular variation, comms, earth sci. Geophysics, 3: 28-29. James, R.W., 1974. The inability of latitude-dependent westward drift to account for zonal secular variation. J. Geomagn. Geoelectr., 26: 359-361. Kitazawa, K., 1970. Intensity of the geomagnetic field in Japan for the past 10,000 years. J. Geophys. Res., 75: 7403 -7411. Kolesova, J.l. and Kropachev, E.P., 1973. Spherical harmonic analysis of the geomagnetic field for the 1965 epoch up to M = 23 according to ground-based data, II, results. Geomagn. Aeron., 13: 127-131. Lal, D. and Venkatavaradan, V.S., 1970. Analysis of the causes of C-14 variations in the atmosphere. In: I.U. Olsson (Editor), Radiocarbon Variations and Absolute Chronology. Almqvist and Wiksell, Stockholm, pp. 5 4 9 569. Libby, W.F., 1952. Radiocarbon dating. University of Chicago Press, Chicago. Lingenfeiter, R.E. and Ramaty, R., 1970. Astrophysical and geophysical variations in C-14 production. In: I.U. Olsson (Editor), Radiocarbon Variations and Abse!ute Chronology. Almqvist and Wiksell, Stockholm, pp. 513-535. McElhinny, M.W. and Merrill, R.T., 1975. Geomagnetic secular variation over the past 5 m.y. Rev. Geophys. Space Phys., 13: 687-708. Merrill, R.T., 1975. Magnetic effects associated with chemical changes in igneous rocks. Geophys. Surv., 2: 277-311. Merrill, R.T. and McElhinny, M.W., 1977. Anomalies in the time-averaged paleomagnetic field and their implications for the lower mantle. Rev. Geophys. Space Phys., 15: 309-323. Shaw, J., 1974. A new method of determining the magnitude of the palaeomagnetic field. Application to five historic lavas and five archaeological samples. Geophys. J.R. Astron. Sot., 39: 133-141. Smith, P.J., 1967a. The intensity of the Tertiary geomagnetic field. Geophys. J.R. Astron. Soc., 12: 239-258. Smith, P.J., 1967b. The intensity of the ancient geomagnetic field: a review and analysis. Geophys. J.R. Astron. Soc., 12: 321-362. Sternberg, R.S. and Damon, P.E., 1976. Sensitivity of radiocarbon fluctuations and inventory to geomagnetic and reservoir parameters. Proceedings of the Ninth International Radiocarbon Conference, Los Angeles and La JoUa, in press.

Stuiver, M., 1961. Variations in radiocarbon concentration and sunspot activity. J. Geophys. Res., 66: 273-284. Stuiver, M., 1971. Evidence for the variation of atmospheric C14 content in the late Quaternary. In: K.K. Turekian (Editor), Late Cenozoic Glacial Ages. Yale Univ. Press., New Haven, CT, pp. 57-70. Stuiver, M.,"1978. Radiocarbon time-scale tested against magnetic and other dating methods. Nature (London), 273: 271-274. Stuiver, M. and Quay, P.D., 1978. Solar variability and 14C isotope stages. EOS, 59:1154. Suess, H.E., 1970. The three causes of the secular C14 fluctuations, their amplitudes and time constants. In: I.U. Olsson (Editor), Nobel Symposium 12, Radiocarbon Variations and Absolute Chronology. Almqvist and Wiksell, Stockholm, 595 pp. Tauber, H., 1970. The Scandinavian varve chronology and 14 C dating. In: I.U. Olsson (Editor), Radiocarbon Variations and Absolute Chronology. Almqvist and Wiksell, Stockholm, pp. 173-196. Thellier, E. and Thellier, O., 1959. Sur l'intensitie des champ magnetique terrestre dans le passe historique et geologique. Ann. Geophys., 15: 285-376. U.S.-Japan Paleomagnetic Cooperation Program in Micronesia, 1975. Paleosecular variation of lavas from the Marianas in the western Pacific Ocean. J. Geomagn. Geoelectr., 27: 57-66. Verosub, K.L. and Cox, A., 1971. Changes in the total magnetic energy external to the Earth's core. J. Geomagn. Geoelectr., 23: 235-242. Vestine, E.H., 1967. Main geomagnetic field. In: S. Matushita and W.H. Campbell (Editors), Physics of geomagnetic phenomena, Vol. 1, Academic Press, New York, NY, pp. 181-234. de Vries, H.L., 1958. Variation in concentration of radiocarbon with time and location on Earth. Koninkl. Ned. Wetenschap. Proc., Ser. B., 61: 94-102. Yang, A.F.C. and Fairhall, A.W., 1972. Variations of natural radiocarbon during the last 11 millenia and geophysical mechanisms for producing them. Proc. 8th Int. Radiocarbon Dating Conf., Wellington, N.Z.: A44-A57. Yukutake, T. and Tachinaka, H., 1969. Separation of the Earth's magnetic field into the drifting and standing parts. Bull. Earthquake. Res. Inst. Univ. Tokyo, 47: 65-97.