Analysis of geomagnetic secular variations 10 000 to 30 000 years bp, Lac du Bouchet, France

Physics of the Earth and Planetary Interiors, 44 (1986) 1—14

Elsevier Science Publishers B.V., Amsterdam

—

1

Printed in The Netherlands

Analysis of geomagnetic secular variations 10000 to 30000 years bp, Lac du Bouchet, France G. Smith and K.M. Creer Department of Geophysics, University of Edinburgh, Kings Buildings, Edinburgh, EH9 3JZ (Gt. Britain)

Smith, G. and Creer, K.M., 1986. Analysis of geomagnetic secular variations 10000 to 30000 years bp, Lac du Bouchet, France. Phys. Earth Planet. Inter., 44: 1—14. Cores of the bottom sediments from Lac du Bouchet, in the Haute Loire, France (44.90 N, 3.8°E) have been taken using Mackereth type pneumatic piston corers. The sediments have been dated by palynological control back to 15000 years bp (years before present), and by radiocarbon age determinations using both conventional and accelerator methods. The depth/ time transform provisionally used here dates the sequence from 10 000 to 30000 years bp. The stacked records of demagnetised remanent magnetisation from eight cores have been examined. Fourier and maximum entropy method spectral analyses show good agreement. Inclination and declination spectra are different in that the dominant inclination periods tend to fall in the negative part of the complex spectrum, while the dominant declination periods tend to fall in the positive part. The VGP path traced out by the remanent magnetisation vector shows predominantly clockwise looping, consistent with essentially westward drifting geomagnetic sources. The detailed form of the VGP path is affected by the degree of smoothing, but clockwise looping always predominates averaging — 67% over the whole time interval investigated. A band of frequencies between — 0.9 and — 0.3 cycles per thousand years is associated with the strongest bias towards clockwise rotation (— 80% to 90%) while a band between — 0.3 and 0.1 cycles per thousand years is associated with only — 50% clockwise rotation. Individual core records show some negative inclinations at horizons where inclination minima occur suggesting that ‘excursions’ should be regarded as extreme values of secular variation rather than aborted polarity reversals of the main field.

1. Introduction Lac du Bouchet is a small rnaar (crater) lake situated in the Massif Central, France (44.9°N, 3.8°E).The work reported here is part of a cornprehensive study of the lakes of the Haute Loire region and the palaeomagnetic results are part of a much broader investigation (for an initial multidisciplinary report, see Bonifay et al., 1987). The region comprises a plateau of Quaternary volcanics and is characterised by many cinder cones associated with the strombolian type volcanoes typical of the area. The lake itself is small 800 m diameter), almost perfectly circular, with a flat bottom at a depth of 26 m. Cores have been extracted from the bottom sediments using Mackereth type pneumatic piston (—

—

0031-9201/86/$03.50

© 1986 Elsevier Science Publishers B.V.

corers during three field campaigns. A single piece corer (Mackereth, 1958) was first used, then a two piece 12 m corer, which failed to obtain cores of length greater than 6 m, and then a single piece 9 m corer with which the results described here were obtained. Since then a single piece 12 m corer has been built and used to obtain cores of up to 11.5 rn in length [Smith, 1985].

2. Sampling and measurement Each core taken for palaeomagnetic investigation was opened by splitting the PVC coring tube carefully along diametrically opposite sides. One half was then sub-sampled by pressing cubic sampie boxes made of plastic into the sediment. Spe-

2

cial care was taken to align each box parallel to the edge of the core tube and to locate it centrally within the sediment. Each sample box had a hole in the top face to allow the air trapped above the sampled sediment to escape with minimal dis— turbance of the sediment. The depth of each sampie box was measured and they were then numbered sequentially and carefully extracted, cleaned and sealed On arnval in the laboratory, they were stored within Helmholtz coils in a ‘zero’ magnetic field environment The length of storage time varied between 1 day and several months and so the results quoted here as natural remanent magnetisation (NRM) are stored remanent magnet! sation values For a full descnption of the meth ods and techniques see Creer et al (1983) Remanent magnetisations were measured using a two axis CCL superconducting SQUID magne tometer controlled by a Sirius microcomputer Each result is the average of measurements in four positions 900 apart each measurement consists of the average of 2048 digital conversions of the analogue output from the SQUID sensors. Susceptibilities were measured using a Bartington bridge meter. 3.

Results

3.1. NRM Results The results obtained from the set of (nominal) 6 m cores collected during our first field campaign are given in Thouveny et al. (1985) and in Creer et al. (1986). In the present paper, results from (nominal) 9 m cores collected during our third field campaign are described. Figure 1 illustrates the results for core B49, the longest of these cores, Strong intensity values are apparent below 2 m (— 500 mA m’) and the patterns of declination and inclination, particularly of the latter, are well defined. The stability of the remanence has been investigated by step-wise alternating field (AF) demagnetisation of pilot samples. The median destructive field (MDF) varied between 15 and 27 mT, but averaged around 18 mT. At least 90% of the original remanence was removed by a peak

L©~~ouohe~Core B49

DEC

INC 500 300

- ~

I

900 I I

I

I

TNT

0

6~ 0

!~LH~ SUSC

15

C

0

in

I

~1

2

:

‘:~..

~:.

6

—

1111111

11111

I

III

IiIiilIIlIiiIi

tI-ti

II

Fig. 1. Logs of natural remanent magnetisation (NRM) for core B49. Declinations (DEC) and inclinations (INC) are measured in degrees, intensities (INT) in mA m~ susceptibilities 1. (SUSC) S.I.against units and the Q-ratios (Q)in inmetres. mA m Each loginis i0~ plotted the downcore depth

field of 50 mT suggesting that magnetite is the predominant carrier of the remanence. Figure 2 consists of (1) step by step plots of the component of RM (a) in the horizontal plane and (b) in the vertical/north—south plane, revealing the presence of a weak viscous component which is removed by peak fields greater than 7.5 mT and a stable primary component; (2) a stereographic plot of direction—after an initial shift of a few degrees on removal of the viscous component, directions remain stable to within about 2°;and (3) a plot of RM intensity versus AF field. Sub-samples from each core were subjected to bulk demagnetisation in peak fields of 10 mT. The resulting plots are shown in Fig. 3. A comparison of Figs. 1 and 3 shows that the intensity values are reduced by 25% on AF demagnetisation and that the patterns of the declination and inclination are not noticeably improved by ‘cleaning’. —

3

3.2. Averaging of the results

uP

north

Ii.! west

(.,~

east

south

II I1~III

First, rather coarse correlations were made using the sediment stratigraphy and magnetic susc~ptibility logs. Although finer-scale details cannot be identified using these parameters, the importance of using them is that they offer independent evidence that the oscillations of the NRM vector are primarily due to the geomagnetic field and not a result of the form of sedimentation as controlled, for example, by climatic variations. These correlations were then ‘fine tuned’ using the inclination log patterns, any ambiguities which arose being resolved by reference to the declination and inten-

north II I~ II ~

down

N MD F

~9-4 ml

05

0

I

I

0

20

I

I

I

I

~

I~~I~I I

I

40 60 AF demag field ml)

Fig. 2. Demagnetisation diagrams of a typical pilot sample (141) from core B49, including normalised plots in the horizontal plane and in the vertical/north—south plane, normalised step demagnetisation of intensity and stereographic projection of directions. There are ten points for each diagram representing the step demagnetisation in peak fields of 0, 2.5, 5, 10, 15, 20, 30, 40, 50 and 60 mT. Note that the zero of declination is arbitrary.

Lao du Boucheh Core B49

.

sity vanation patterns. Figure 4 shows plots of each core on the transformed depth scale, that of core B49. The major, larger amplitude features are clearly well correlated as are many subsidiary features, but the deeper (older) smaller amplitude variations are not so clearly resolved than the younger ones.

lAP cleaned)

(a) DECLINATIONS

‘ rn’111111111’ 05

590

DEC

590300

111111111

INC

TNT too o

o

—t———I———I———1’——l—

—I——I——I——I——f

SUS[

15

i+-44.1444+14—f

o

C

100

1111111111

i~fr

-~

a

‘--

‘~

-

~

512

f-44’++I-I-i-

±50 1

BiS

042

B46

B47

•j~~

//

3/’~’ ~

0

~.

3

~.

.‘~

‘‘.~

5

~ 0 - -

-

‘:.,

~c

:~

~ 24.

•~1~

.-.~

6

6

.

~

~‘

+—I--l--I-+

-f-I--f—+--f

I+4+H+H44+

i-I-H-I-f-H-

Fig. 3. Logs of the remanent magnetisation for core B49 after demagnetisation in a peak field of 10 mT. The units are identical to Fig. i. Note that the intensities have been reduced but the declinations and inclinations are very stable,

-‘

IF;:

3 ~s$ 5 ~

* I

~

~: ~.

1’ •

‘t,, ~

?

*#~)

1 111111111

~

~

I

‘I

949

-I-H-H~+-+-;;-I-I-H4-I-I-i;+H-I-I-i-I-I;4-4-I-I-,-I-,l-I-l-I-f+#1-

‘0

2

~°

field

• *

~ ~ ~

0~ ~

~

‘2

) 9 -1+1-I-H-H :4-H-I-I-I-H

4-I-I-H-I-I-

FH+l-l-I-I-: -I-H-I-H-I-I :4-I-I-I-I-I-H

I-I-I-I-I-H-

l4-I-H-I-I+,

Fig. 4. Logs of eight cores; B5, B7, B12, B15, B42, B46, B47 and B49 after transformation to a common depth scale, that of core B49: (a) declinations, (b) inclinations, (c) intensities, (d) susceptibilities, (e) Q-ratios. The units are identical to Fig. 1.

4 (c)INTCNSITIES (b) INCLINATIONS

fieLd

B5 H

57

I-H—t~4 -4-4—I—H 0

012

uS

-I—I—H-+

H—I—I—I

00*o:~~

~

542 4--H—H

B46

047

Bios

-I--I--I---I-+

H—I--I--I

4—I--I--H

04

3 ‘~ Jf

‘~p

•~• ~

0

~*0

‘~

S

Ft 6

E

~

4-

•*~,0

~

?

,~

—

~,,

‘

ft

*

5i.*o~~

“*~

a~’°

44* ‘

IF

4

1 ,$

/

11:11

11111

Id) SUSCEPTIBILITIES B5 B7 512 IlllIlIll:Il

11111111,11

l~I,l

,::I;

v

,II,

515

4

—

~ffiH-

...~

6

0

•c’

~ ,•

k

~2~’’:~ ~,

~ c,

\‘j1

?-‘

~

ç ~

f’:

I’

11l11

11111

11111

f,*~

I~Ill

0 RATIOS

I field

(e)

85

87

512

015

~IIlI

-

‘i’,

~,•

‘It

.o,’~:

II~II

11,11

~#‘

I

I

ito 100 mA/rn I 842

046

547

049

:I:,-lI::

~

:.

‘ ~

~.t’ /,~, c...

:~~ ~~

1

0~, ‘~•‘~

i~

,~‘

~..

:II:,II~

~

~‘

‘~

.i~

~ e’.

~

0*

*

~•

~

~a.

~

:~

0

“~•~

r ~ ‘.r”.’

‘~

:,~

~

t~

~

~

6

~

~

~

~,

‘7

~(

~ •‘~

.t j,’.

)C. ‘l~

0

~

9

•~

“~

‘~

,

~,

‘*,•

8

~

~

,

1*,,,

1~40 I~’

,~.

o~’

( ~ ~(k C k ~

,

~

(

4

~

~

I11~l

‘

5

3

~ o~

0?

B49 ,.lll

5’

,~.

•‘

6

•?

847 i,,,1

•(i 0

I field~0 to 150 1O~SII 542 546 547 549

+1H-~ H-H-1+

2

11,11

~.°;.

~. ~

-

546 ,.,,.

~

l~

•~~O

‘

Ilill

,~•

842

515

_____ H-~f-+ :1:::

I

•

‘:.•‘

•~

,~

a

______ 1,111

33 ~

~ •)•“~.&•~“s

0

9

1 2

)f

~,

512

-H-H~ *

~

•*

q

—

1”

f~

J.0~ 0

4

B7

_____

‘I

(

~

(fielditotiirnA/m)

30 to 900)

4/

;~

E~

i%

0’

:~ 9 1+111111111 *4144-4414

14411+4+

41I4~444 I~4IIII+I+ 41+~I+ 4+41+4441144

~

9 ::

,::Illll:

~

:11111,11

H+1~: :,I,l,,:

:

::IIll:II~

5

3.3. Stacking the common depth data -

Having transformed the depth scale of each demagnetised core to the depth scale of core B49, we note that several approaches are possible to transform the records into the time domain. One such approach would be to transform each core individually and examine the results for common trends; a second approach would be to transform each core to the time scale and then to stack the results; a third one would be to stack the cornmon-depth scale data and then to transform to the time scale. Each approach has been examined systematically and the resulting stacks have been found to be essentially identical. The last of these approaches was deemed to be most appropriate, as the most reliable correlations are known on the depth scale and the presentation of results is made more convenient. Also, the results can be more easily updated when improved time-scales are constructed, Figure 5 shows the result of stacking the eight 50 U C If E T

-50

EC 0

S 7 AC INC

50 30

90

0

151

600

0

SIJSC

I II

--

15

0

100

~i”~ -‘

1 -~

2

-~

cores. Prior to stacking, the data for each core were evenly spaced (at 3 cm intervals) with linear interpolation between points and then the average of all the cores contributing at each level was calculated. The linear interpolation and the effects of stacking smooth the original data and damp the amplitudes of the variations. The declination and inclination may be averaged either as separate parameters or together by treating declination—incination pairs as unit vectors. This approach means that the ~ confidence limits attached to the mean declination at a particular level will depend on the value of inclination at that level. Clearly, as the inclination approaches ±90°the declinations become indeterminable, leading to very large error bounds. For this reason, Fig. 5 shows the Gaussian means of declination and inclination treated separately in the same way as the other three parameters, intensity, susceptibility and Q ratio. The error bands plotted correspond to the standard deviation of the mean (standard error) of the measurements used. For spectral analysis, however, the individual cores were stacked treating each declination—inclination pair as a unit vector. Alternatively the results from the different cores may be combined by merging the data points after transformation to a common depth scale into a single file, without interpolating them to equal depth increments. Curves may then be constructed through the merged data points using cubic splines (Creer and Tucholka, 1983). 4. Conversion to time scale Transformation of the demagnetised NRM di-

t

5

6

______ -

O

-c

9

t t

-

111111111

,~ 1

,‘,I

I

‘‘‘“‘‘‘‘

Fig. -5. A stack of the eight cores shown .in Fig. 4 after equal spacing at 3 cm intervals. The error bars indicate the standard deviation of the mean of the measurements contributing at each stacking level. The units are identical to Fig. 1.

rections from a depth scale to a time scale necessitates dating the cores at different depths. Given the limited allocation of samples for dating, it was decided to concentrate the work on specific cores and to date these cores as accurately as possible. Core B5 was selected from the (nominal) 6 m cores collected during the first field campaign and core B49 was selected from the (nominal) 9 m cores with which this paper is concerned. Time scales were attached to the other cores by correlat.

rng their depth scales with these two dated cores as described in section 3.

6 35

TABLEI

I

I I

B~

Radiocarbon dates on core B49 obtained from the High Energy Mass Spectrometer at Oxford Depth (m)

Date (years bp)

Label (Fig. 6)

1.75—1.80 3.00—3.05 4.20—4.25 5.00—5.04 6.00—6.06 6.61—6.66 7.10—7.15 8.12—8.i7

9700± 200 12900± 180 14300± 250 19200± 300 23100 ± 600 27300± 900 28 500± 900 30600±1300

Hi H2 H3 fl4 H5 H6 H7 H8

/

I

H8 30

07

-

-

A

Hi 25

-

H5

2!

-

-

1H4 ~ 05

Age determinations, made directly by the conventional radiocarbon method and indirectly by palynological studies on core B5 have already been described (Bonifay et al., 1986; Creer et al., 1986). Additional datings (see Table I) have been carried out on the longer core B49 using the High Energy Mass Spectrometer (HEMS) facility at Oxford (Hedges (1983), also see Smith (1985)) for a detailed description of the method and results. All the individual age estimates for both cores (B5 and B49) are shown in Fig. 6. Dating control over the Holocene sediments is good but there are important discrepancies in the different ages obtamed for the Late Glacial sediments in that the two HEMS radiocarbon ages, H2 and H3 measured on core B49 are substantially younger than ages for the same depths given by our first transform described in Creer et al. (1986) and shown by the line of slope 2.41 labelled ‘A’ in Fig. 6. We are quite sure that this is not due to mis-correlation of core B49 with core B5. Considering the lack of firmly based criteria with which to accept or discard a date, and given the substantial number of dates available, it seemed to us that the most appropriate approach at the present stage of the work was to construct a new time—depth transfer function consisting of two straight lines fitted by minimisation of least squares. These lines were found to intersect at the Holocene—Late Glacial boundary (Smith, 1985). The resulting transfer function for the time prior to 10000 years bp with which we are principally concerned in this paper (line labelled ‘B’ in —

is

~

134

-

H3 02 10

-

-

/ ~

/

~

Hi 03

H.

accelerator rid bc orion

0.

conventional r ad, o c or ion

-

/

~

.

02 ~ 131

-

©

0

0 0

-

I 1 e n

10 -

core 849 depth (ml Fig. 6. Age control over the stacked data. Pollen ages (co) and conventoonal radoocarbon ages (•) measured along core B5 are those described in Creer et al. (1986). The High Energy Mass -

Spectrometer facility at Oxford was used to measure radiocarbon ages along core B49 (•). Where error bars are not shown, they are shorter than the diameter of the symbols used to plot- them. Line ‘A’ represents - transform function previously used on Creer et al. (1986) and line B represents that used in this paper.

,

F’ 6~ ig. ~ is = 2.92d + 6.03 where t represents the age in thousands of years bp and d is the depth in m on the core B49 depth scale. This transform was applied both to the stacked and to the merged data points. Representative curves for each parameter have been constructed by smoothing both in the time domain using cubic

7 DEC 0

I

INC

1111111

12

14

A

1ST

so’ no’

0’

5~0

90°

I I I I

I

t

so

~

0050

o

too o I

P

2

0

I

15

-

100

0 111111111

before making any drastic modification to the transfer function originally used (Creer et al. (1986)

ç

and line ‘A’ in Fig. 6). Pollen studies and ‘accelerator’ radiocarbon age determinations are currently being carried out on these 9 m cores and also on longer 12 m cores which have since been collected.

M

N

4

18 —

0

20

6

22

we preferred to await confirmation (or otherwise) of the oldest ages (H6, H7 and H8) and to look further into the dating of the Late Glacial deposits

~

5. Spectral analysis of the stack

24 P 0

26

0

28

0

30

III

11111

I

I

I

III

I

111111

Fig. 7. Cubic spline curves fitted with 50 equally spaced knots to the merged records of declination, inclination, intensity, susceptibility and Q ratio after transformation to the time scale. The record runs from 10000 to 30000 years bp. The labels are those used in Creer et al. (1986) and are mainly for descriptive purposes. The units are as in Fig. 1.

splines, and in the frequency domain by filtering out the higher frequencies. Figure 7 illustrates the curves smoothed by fitting cubic splines with 50 equally spaced knots to the merged data files; the labels used to identify the various features characterising the patterns of variations are the same as those used previously (Creer et al., 1986). The family of curves obtained by filtering out frequencies higher than 1 cycle per thousand years (equivalent to T= 1000 years) is virtually identical to the curves of Fig. 7. The practical effect on the dating of the maxima and minima of our SV curves by using the time scale preferred here (line ‘B’ in Fig. 6) rather than the first time scale (line ‘A’ in Fig. 6) will be noticed if Fig. 7 is compared with Fig. 6 of Creer et al. (1986). This type of transform function inherently assumes constant rates of sedimentation. Clearly this is not true on a short time scale due to periods of slumping or severe climatic conditions, but it is likely to be valid over longer periods of time. It would have been possible to construct a more sophisticated transfer function with the dating controls presently available, but for the time being -

- -

The rate of sedimentation in Lac du Bouchet through Holocene time was very low (— 1 m in 10000 years) and therefore the palaeomagnetic secular variation (SV) record lacks detail since each sub-sample represents nearly 300 years. Moreover, the SV record for the last 2000—3000 years is lost on coring due to disturbance of the topmost sediments which consist of a very wet slurry. Also we suspect that sediment deposition may not have been continuous during the Bolling, Older Dryas, Allerod and Younger Dryas zones of the Late Glacial (Creer et al., 1986). We therefore decided, in this paper, to concentrate on analysing the d~tacovering the period before 12000 bp (on our time scale) for which the Bouchet record is very good and makes a new and original contribution to the SV data bank. A preliminary inspection of the declination and inclination data plotted on this time scale (Fig. 7) shows that the peaks of the inclination oscillations are separated by about 1000 years between 12000 and 16000 years bp. Those features before about 17000 years bp back to 30000 years bp (our present preferred estimate of the start of our record) have half-periods of between 750 and 1500 years and the feature T has a half-period of more than 2000 years. In the declinations, there seem to be two dominant half-periods of 1800 to 2000 years (e.g., between 13000 and 18000 years bp) and a much longer — 4000 year variation upon which the former appears to be superimposed. Less subjective methods of spectral analysis are abundant. The two methods chosen here are Fourier analysis and maximum entropy method (MEM) analysis. —

8

Certain assumptions are implicit in Fourier analysis, the most important being that the time series analysed is stationary and infinitely repeating. It is immediately apparent that these assumptions are not true for the short period variations (<2000 years) that can be observed within our record, although it is possible that the longer period variations may be more continuous. The solution of our problem is thus restricted by the short length of our data set which may contain no more than two or three full periods. MEM has been proposed as a suitable ‘predictive’ analysis tool which does not need the infinite repetition condition and can work on short data sets. However, to choose the correct order of the autoregressive process used to model the data one needs to make certain subjective conclusions about the results of the analysis. The approach we have used to minimise this subjectivity is to perform a DFT of the data and then choose the lowest order that maximises the power at the frequencies ‘picked’ by the DFT. Any other frequencies then apparent will be extra resolution available from the MEM analysis. No order outside the ranges specified by Berryman (1978) and Ulrych and Bishop (1975) have been used to minimise the possibility that the spectral peaks observed are the result of peak splitting due to the MEM algorithm.

random noise), i.e., a 1000: 1 signal to noise ratio. The power spectrum obtained for the declination and inclinations (shown in Fig. 8a) tends to a power of 2 dB for frequencies greater than 2 cycles per thousand years (500 year period), mdicating that variations measured below these penods are probably just noise from depositional, sampling and measurement errors and show the limit of resolution of this method for this lake and sampling frequency. The length of the data set (18000 years) and the sampling frequency (100 years) limits the frequency resolution. Periods of the order of the data set length would be expected and cannot be accepted as real until a longer time sequence is —

[a) F ou r i e r

~,o

0 3600

I

I

I

-

-

.

5.1. Fourier analysis

-

2000

o

~0’ 5

-

1500 1280 ~

0

0

I

I

I

1

2

f (cy/kyr) The merged and time transformed data were evenly spaced by interpolation at intervals of 100 years. Applications of a half-cosine bell to the first and last 10% of the data points was found to have little effect on the -position of the principal periods but had a small effect on the power at a particular frequency. The Fast Fourier transform algorithms used performs a multivariate complex Fourier transform on any number of points factorisable by primes (Singleton, 1968). This reduces leakage due to the padding of the data with zeros required by more rapid, shorter algorithms (e.g., Cooley and Tukey, 1965). Analysis of artificial data using the programs have shown that a power of 2 dB was obtained for random noise and a power of 34 dB for a signal included within the noise (signal +

6000

I

I

I

I

I I

OEC w -

~o-5 -

-

1640 950 1280 ~

0

I

0

780 4

1

2 f (c y/ k y r)

9

(3)

M

EM

analysed. The dominant frequency found here will have at least four full wavelengths and these can

11050

1-0

________________________________ I I

-

3820

r

I

be accepted as satisfying the Fourier analysis assumptions. The spectra are illustrated in Fig. 8a.

I

tNC

5.2. MEM analysis

~0-5

data Thewere evenly detrended spaced,bytime removal transformed of a firstmerged order

/~l360 2160

a

/

L

380

~860

0

00

0

1

f

(c -

y/

2 k yr)

I

tion of the vector (Denham, 1975). In this case the negative frequency half of the spectrum is asym-

I

measure metrical can be considered to of the the positive degree to of part be rotation the and sense the ofdifference the of vector driftthis isof in features the tion complex is such of the plane. that non-dipole positive For palaeomagnetic field. (negative) Our sign frequency work convenisa associated (clockwise) precession ofwith the counter-clockwise magnetic vector when viewed from its south seeking end to its north seeking end. The algorithm used to compute the MEM power spectra for a complex data set is based

6660

1-0

I—I

E

~3o75o6L

0

I

I

0

I

I

1 142~ I

I

2

f

1-0-

would polynomial. introduce NoIndividual tapering spuriouswas frequencies performed as this the power spectra. analyses of the into declination and inclination results were performed using the algorithm due to Burg (1967). Treating the declination and inclination as a single complex number enables the an~alysisof the sense of rota-

(cy/kyr)

-

I

COMPLEX 3010 3680(5850

upon that due to Smylie et al. (1973). The programs have been adapted from those used by Barton (1983). The results of the spectral analyses performed on the merged data are shown in Fig. 8b and the locations of the spectral peaks listed in Table H. Three time windows have been examined: 12000—30000 years bp, 12000—21000 years bp

~ 0-5

and 21000—30000 years bp.

1480 530

950

[H

~

1530

7

a

630

5.3. Discussion of results -

675

E

—2

0

2 f {c y/ yr)

Fig. 8. Power ipectral estimates for the Lac du Bouchet declination and inclination records, stacked at 180 levels spaced by 100 years running from 12000 to 30000 years bp: (a) the Fourier transform spectra, inclination above declination; (b)

Inspection 8a, band indicates good agreement between of theFig. Fourier MEM spectra. the MEM spectra at order 61, inclination (top), declination (middle) and complex spectrum (bottom). The frequency ranges from 0 to 2.0 cycles per thousand years equivalent to periods down to 500 years. Power has been normalised to the largest peak value.

10 TABLE II

Summary of the dominant periods found using Fourier and MEM analysis Age range (thousands of years)

Mean periods (years) about which power is concentrated

declination 12—21 21—30 12—30 12—21 21—30 12—30 12—21 21—30 12—30 12—21 21—30 12—30

6660 7650 6600 inclination 11050

3110 2620 3100 3820

2160 2210 2160

—

3820 complex positive 5850 7650 5850 complex negative 5850

3015 2690 3000 3010

—

—

—

3680

Turning to the MEM spectra, an inspection of Table II shows that peaks in the inclination spectrum (Fig. 8b, top) can be identified with peaks in the negative part of the complex spectrum (Fig. 8b, bottom), while the peaks in the declination spectrum (Fig. 8b, middle) appear to be located in the positive part of the complex spectrum. It will be interesting to test whether this rather surprising relationship is a general one or whether it is a peculiar property of this particular data set. However, it appears to hold for all three time windows inspected (Table I~ The numerical values of the periods (wavelengths) of the spectral peaks clearly depend on the accuracy of the adopted time scale. It has already been noted (section 4), that the time scale used for the present study (line ‘B’ in Fig. 6) should be regarded as tentative. But any future modification of the time scale will not alter the observed relationship between the spectra separately obtained for declination and inclination so that the peculiar property that the inclination variations appear to be associated with westward drifting sources while declination variations appear to be associated with eastward drifting sources will remain, We have divided our data set into two parts

—

(2310) (2200)

1530 1400 1530

950 950 950

750 740 750

1365 (1215) (1360)

(985) (860) (980)

(73)

1530 (1440) 1530

930 950 930*

(750) (750)

1530 1440* 1480*

930 950* 950*

625 650 625

535 — —

600 (730) 540

750

(635) (650) 635

(750) 725 740

(635) 625 675

540

— —

— —

running (1) from 12000 to 21000 years bp and (2) from 21000 to 30000 years bp. The spectra obtamed from these two subsets show some similarities and some differences. The latter are to be expected, first because it is probable that the geomagnetic SV spectrum is not stationary; second, because our time scale is calibrated in radiocarbon, not calendar years; third, because of uncertainties in our currently preferred time scale.

6. Rotation of the geomagnetic vector

If virtual geomagnetic pole (VGP) positions are calculated from declination—inclination pairs at a succession of time intervals, the poles will trace out a path around the axial dipole position. The shape of this path depends upon the way in which the non-dipole field components change with time. A clockwise (counter-clockwise) looping path (with ages getting younger) indicates a westward (eastward) drifting source, although this interpretation is not unique. A linear path can be obtained from a single stationary source of varying intensity. A full description of these effects is given in Creer (1983). -

11

~ l2000bp

16000 12000 p 100005p

I

,

80° hI

—__________

/

/

80°

Ii)

___________

°~-.

____________

__________

T 161101

.

t 20000 —

200bhp ‘

-

70° S0011bp (

24000 bp

—s.

I

\

______ -~

270CC 27000

—

—

—

80°

80°

Is)

If I 70°

BOO

ch e t sta c k

70° 50k not

c ub I c spline

V0 P

‘S

Fig. 9. Polar stereographic plots of VGP paths corresponding to declination—inclination pairs along the curves of Fig. 7. (a) 10000—12 000 years bp, (b) 12000—16 000 years bp, (c) 16000—20000 years bp, (d) 20000—24000 years bp, (e) 24000—27000 years bp and (0 27000-30000 years bp. The north pole is at the centre of each projection, the 0° meridian is at ‘six o’clock’ and the 90° east meridian is at ‘three o’clock’. The positions of the 800 and 70° latitude circles are indicated,

Figure 9 shows the VGP path computed for the merged demagnetised data after smoothing by fitting cubic splines with 50 equally spaced knots (i.e., from the declination and inclination curves of Fig. 7). The period of time covered (10000—30000 years bp) has been divided into six windows of lengths 3000 or 4000 years to facilitate the ohservation of the movement of the VGP position. The motion of the path is 67% clockwise over—

.

.

0.5 cycles per thousand years, approximately equivalent to periods from 333 to 2000 years (Fig.

‘a’,

I

.

(Fig. lOa) and (2) in the frequency domain by removal the powerlessduethan to Fourier components with a of frequency a certain cut-off frequency which has been decreased from 3.0 to

IdI

70°

___________

24010— I j

I

80

Ic)

all, indicating that westward drifting sources predominate at least for this particular degree of smoothing. Most of the counter-clockwise motion occurs at the ‘hairpin’ bends between the larger clockwise loops. The variation of the sense of rotation with time is illustrated in Fig. 10 where clockwise curvatures of the VGP path are plotted to the right and counter-clockwise curvatures to the left (see Creer et a!. (1986) for definition of curvature). The de. . clinatoon—inclinatton data from which the VGP paths have been computed have been smoothed (1) in the time domain by fitting cubic splines with evenly spaced knots increasing from 10 knots to 50 knots through the 20000 year period shown

lob. The percentage of clockwise rotation (CR) throughout the whole of the time interval under consideration, 10000—30000 years bp, has been computed for varying bandwidths in the frequency domain to find out whether clockwise (counterclockwise) rotation can be identified with particular parts of the spectrum. Figure 11 shows the percentage of CR plotted against frequency for bandwidths of 0.1 and 0.3 cycles per thousand years these values being typical of the widths of .

.

the spectral peaks illustrated in Fig. 8. This figure shows that for frequencies from 2 to 1 cycles per thousand years (periods 500—1000 years) there is a slight bias to clockwise rotation with CR values between 55% and 65%. From — 1.1 to —

—

—

—

— 0.9 cycles per thousand years (periods 900—1100 years), there is a narrow band of frequencies with only — 50% CR. Then, between — 0.9 and — 0.25 to 0.3 cycles per thousand years (periods 1100—3000 years) there is a broad band with very strong CR rotation, up to 80% to 90% and a narrow band down to 0.1 cycles per thousand years (period 10000 years) is associated with only — 50% CR. The lowest frequencies, less than — 0.1 cycles per thousand years, seem to be associated with higher than average CR. —

12

V G P ia)

smoothing

CURVATURES by

VGP cubic

splines

ib)

CURVATURES

smoothing

by

FFT

filt.ers

16 --

18 --

20 --

22 --

24 -a _!x L x Y

26 --

E

28 --

aJ ol l”

30--H

Fig. 10. Plots illustrating the sense of curvature (clockwise = positive, counter clockwise = negative) of VGP plots as a function of time. Different degrees of smoothing have been achieved by using (a) cubic splines with between 2 and 50 equally spaced knots and (b) filtering out components with frequencies less than between 0.1 and 2.0 cycles per thousand years (10000 years to 500 years).

13

100

thickness from the Boiling through the Younger Dryas is so thin. While it is possible that additional new sedimentological and palynological studies currently in progress may provide some positive evidence of depositional breaks, we do not expect to find that these will constitute a I

I -

80

-

60 ~

40

100 80

I

0

1

~ ‘

f

I

( c y / k yr)

I

2

I -

b)

-

-

~

60

~

400_

1—

2 f

(c y / k y r)

Fig. 11. Percentage of clockwise rotation (VGP path curvature) from 10000 to 30000 years bp for frequency bandwidths of (a) 0.1 and (b) 0.3 cycles per thousand years.

The same general picture holds when this large time window is divided into halves in that the pronounced bias towards CR remains, but the detailed association of specific bandwidths with above or below average bias to CR changes. This could be because the geomagnetic time series is not stationary. However, deficiencies in the provisional time scale we have used is bound to have had a detrimental effect on our analyses.

7. Conclusions

(1) Our (nominal) 9 m cores of the bottom sediments of Lac du Bouchet provide records of the secular variations of the geomagnetic field direction from 10000 years bp to 30000 years bp. (2) There are some discrepancies in our age determinations on the Late Glacial deposits, particularly from the Ancient through the Younger Dryas. It seems curious to us that the sediment

serious problem, considering that the lake basin has remained isolated throughout its existence and since the water level in the lake has not changed by more than 2 m through the period covered by our records. (3) Data for eight cores have been combined by transforming the individual core data to the depth scale of a chosen ‘master’ core (B49) and then stacking them at equally spaced horizons (Fig. 5). Smoothing has been performed in both time and frequency domains. The form of the final patterns of variations is not sensitive to the method of combining or smoothing the data. (4) Although the points along the curves produced by stacking at equal depth increments may be transformed directly into the time domain (Creer and Tucholka, 1982), we have preferred here to transform the individual points of the file obtained by merging the data for all the cores and then to construct smoothed curves in the time domain, as in Fig. 7 (see Creer and Tucholka, 1983). (5) Visual inspection of the declination and inclination patterns shows them to be characterised by oscillations with ‘wavelengths’ of a few thousands of years (Fig. 7). This subjective observation is confirmed by spectral analyses carned out by both Fourier and Maximum Entropy methods (section 5). (6) The stacked records which are, of course smoothed do not show any abnormally large amplitude oscillations (‘excursions’) which might be interpreted in terms of aborted attempts at polarity reversals of the main field. Individual core records do, however, contain some negative inclination values at horizons where minima occur. We consider these negative inclinations to be part of the ordinary secular variation pattern. (7) The sense of rotation of the palaeo-vector as revealed by visual inspection of the VGP paths (Fig. 9) is predominantly clockwise (section 6). Quantitatively, the proportion of CR depends on

14

the amount of smoothing applied. Also, the extent of bias towards clockwise rotation depends on frequency. (8) The time scale used in this paper is provisional and should be much improved in the near future (section 4). Nevertheless, inaccuracies in age control and the lack of information to be able to convert to calendar years will continue to be one of the main obstacles to precise time series analysis and to the reliability of conclusions that can be inferred therefrom.

Acknowledgements We record our thanks to those organisations and individuals who gave permission for the field campaigns to take place. In particular to the Genera! Council of the Haute Loire Department and the Municipalities of Cayres and !e Bouchet. The work reported here is part of a collaborative programme of investigation in which the sedimento-. logical and palynological studies in particular are carried out by our French colleagues—see Boñifay et a!. (1987). The work is co-financed by NERC grant GR3/2238 (UK), the CNRS, DGRST and Ministere de la Research (France). Graeme Smith was in receipt of a NERC studentship.

References Barton, C.E., 1983. Analysis of palaeomagnetic time series and applications. Geophys. Surv., 5: 335—368. Berryman, J.G., 1978. Choice of operator length for Maximum Entropy Method spectral analysis. Geophysics, 43: 1384—1391. Bonifay, E., Creer, K.M., de Beaulieu, J.L., Casta, L., Dclibrias, G., Perinet, G., Pons, A., Reille, M., Servant, S., Smith, G., Thouveny, N., Truze, E. and Tucholka, P., 1987. A study of the Holocene and Late Wurmian sediments of Lac du Bouchet (Haute Loire, France): first results. In: MR. Rampino, W.S. Newman, J.E. Sanders and L.K.

Konigsson (Editors), Climate, History, Periodicity and Predictability. van Nostrand Reinhold, in press. Burg, J.P., 1967. Maximum entropy spectral analysis. 37th Ann. Int. Meeting, Soc. Explor. Geophys., Oklahoma City. Cooley, J.W. and Tukey, J.W., 1965. An algorithm for the machine calculation of complex Fourier series. Math. Comp., 19: 297—301. Creer, K.M., 1983. Computer synthesis of geomagnetic paleosecular variations. Nature, P., 304:1982. 695—699. Creer, K.M. and Tucholka, Construction of Type Curves of geomagnetic secular variation for dating lake sediments from East-central North America. Can. J. Earth Sd., 19: 1106—1115. Creer, K.M. and Tucholka, P., 1983. On the current state of lake sediment palaeomagnetic research. Geophys. J.R. Aston. Soc., 74: 223—238. Creer, K.M., Tucholka, P. and Barton, C.E. (Editor), 1983. Geomagnetism of Baked Clays and Recent Sediments. Elsevier, Amsterdam, 324 pp. Creer, KM., Smith, G., Tucholka, P., Bonifay, E., Thouveny, N. and Truze, E., 1986. A preliminary palaeomagnetic study of the Holocene and Late Wurmian sediments of Lac du Bouchet (Haute Loire, France). Geophys. J. R. Astron. Soc., 86: in press. Denham, C.R., 1975. Spectral analysis of paleomagnetic time series. J. Geophys. Res., 80: 1897—1901. Hedges, R.E.M., 1983. Radiocarbon dating of sediments. Section 2.3 (pp. 37—44). In: KM. Creer, P. Tucholka and CE. Barton (Editors), Geomagnetism of Baked Clays and Recent Sediments. Elsevier, Amsterdam, 324 pp. Mackereth, F.J.H., 1958. A portable core sampler for lake deposits. Limnol. 181—191. Singleton, R.C., 1968.Oceanogr., Algorithm3:339. An ALGOL procedure for the fast Fourier transform with arbitrary factors (C6). Communications of the ACM, 11: 776—782. Smith, G., 1985. Late Glacial Palaeomagnetic Secular Variations from France. Ph.D. Thesis, Department of Geophysics, University of Edinburgh, 308 pp. Smylie et al., 1973. Analysis of irregularities in the Earth’s rotation. In: Methods of Computational Physics. Academic Press, New York, 13: 391—340. Thouveny, N., Creer, K.M., Smith, G. and Tucholka, P., 1985. Geomagnetic oscillations and excursions and Upper Pleistocene Chronology. Episodes, 8: 180—182. Turner, G.M. and Thompson, R., 1982. Detransformation of the British secular variation record for Holocene time. Geophys. J. R. Astron. Soc., 65: 789—792. Ulrych, T.J. and Bishop, T.N., 1975. Maximum entropy spectral analysis and autoregressive decomposition. Rev. Geophys. Space Phys., 13: 183—200.