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Periodic variations in micropulsation dominant period
1969, Phys. Earth Planet. Interiors 2, 50-54, North-Holland Publishing Company, Amsterdam
PERIODIC VARIATIONS IN MICROPULSATION DOMINANT PERIOD
F. W. JONES*
Department of Mathematics, University of Exeter, Exeter, England Received 6 November 1968
Power density spectra of consecutive hourly values of the dominant period of micropulsations in the period range 10 seconds to 200 seconds have been computed in order to detect periodic variations in the dominant period. Three magnetic field variation components and three Earth current components recorded fo r
an interval of 336 hours were used. All spectra except the vertical magnetic component exhibit a peak at a 24-hour (diurnal) period. There are indications of 12, 8, 6, 4, and 3-hour periodicities, but these differ among the six components.
1. Introduction
hourly intervals. However, due to interruptions during recording, approximately 5 per cent of the magnetic field data and approximately 3 per cent of the Earth current data were lost from the 336-hour recording time. Furthermore, after the power density spectra for each hourly interval had been computed it was found that approximately 10 per cent of the hourly intervals for the X (north-south) and Y (east-west) magnetic variations could not be assigned dominant values of the period. Similarly, about 20 per cent of the Z (vertical magnetic) intervals could not be assigned values. In the Earth current variations about 13 per cent of the values for the hourly intervals were missing in each component. Since the computing program was written for equally spaced intervals, all intervals required values. The components did not always have missing values for the same intervals, and thus, although it is known that the components do not necessarily have the same dominant period at the same time (JONES et al., 1969), the missing values were calculated by taking the average value of the components which were known for that interval. By this method all except approximately 3 per cent of the hourly intervals could be assigned values. To obtain values for this last 3 per cent of the intervals it was assumed that the period changes continuously and the missing values were calculated by linear interpolation between adjacent values. It is known that the dominant period does not necessarily vary continuously and abrupt changes occur (JONES et al., 1969). How-
The diurnal variation in the period of micropulsations has been discussed extensively since it was first investigated by HOLSIBERG (1951). Recent work by JONES et al. (1969), in which other references are given, further studied this topic. JONES et al. (1968) recorded data at a station near Montreal, Canada (geographic coordinates N 45°32 ', W 73°09'; corrected geomagnetic coordinates N 58.9°, E 359.6°) and computed on an analogue computer power density spectra for each of six components (three Earth current and three magnetic field variation components) for hourly intervals over a total recording time of 336 hours. From these computations the dominant periods for the hourly intervals were selected. The analysis did not indicate definite periodicities in the value of the dominant periods. In particular, no diurnal variation could be detected. In the present work the results of JONES et al. (1969) have been used, and power density spectra of the hourly values of the dominant period have been computed. A program written by Dr. A. W. Nichol for the Elliot 803 digital computer at the University of Exeter was used for the computations. 2. Preparation of the data
The data from the work of JONES et al. (1969) gave values of the dominant period of each component for * National Research Council of Canada Postdoctorate Research Fellow.
50
PERIODIC
VARIATIONS
1N M I C R O P U L S A T I O N
DOMINANT
PERIOD
51
14
12
Q: LU
I0 &•
0 L~J F&&
._J LLJ
•
•
•
•
•
A•
• •
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• AA
•
•
•
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I 24
0 120
I 12
I 8
I 6
I 4
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I .3
I 2
PERIOD (HRS) Fig. 1.
Power spectrum o f the hourly dominant periods o f the X (north-south magnetic) component.
ever, for these unknown values, this was considered to be the best approximation possible. In this way values were obtained for each interval of the total recording time.
3. The program and spectra
The program computed the time-delay autocorrelation function and the normatised power spectrum. The
14
12
oc i,i 0 o_
I0
8
LIJ ;) 6
5 uJ nr
4
• •
ill
II li
mm m
nil
ii •
2
i I E
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ii
it
mu
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lean
•
•
• g
ni I Mi
0
i 120
i
I
12
I 8
I 6
I 4
PERIOD
Fig. 2.
I 3
(HRSI
As fig. 1 for the Y (east-west magnetic) component.
52
F.W.
JONES
14
12
nLtJ C) (1.
I0
8
•
LLI I--
6
5 n,-
000 4
•
•
000
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ee e
I
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I
I
I
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12
8
6
4
3
2
PERIOD (HRS) Fig. 3.
As fig. 1 for the Z (vertical magnetic) component.
dominant period values, the autocorrelation function and power density function were calculated for both 30 shifts and 60 shifts. The 30-shift spectra are more accurate, but the 60-shift spectra give more fine structure. Since the 30-shift and the 60-shift spectra were similar except for the better detail of the 60-shift, the
method of computation is described by SWINNERTONDYER (1963), SOUTHWORTH(1960) and BLACKMANand TUKEY (1958). For all the spectra computed it was assumed that there was no trend or secular component, and so all series were considered as stationary time series. There was no prewhitening. For the data for the 14
12
n,I.IJ
I0
3 0 n
u.I ;> I--
A
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PERIOD (HRS~ N-S Fig. 4.
As fig. 1 for the N-S (north-south Earth current) component.
•A i 2
PERIODIC
VARIATIONS
IN M 1 C R O P U L S A T I O N
DOMINANT
53
PERIOD
14
12
I0 c~ I.iJ 0 13..
8
i,1 ;) 6 < .J i,i er
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l
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PERIOD ( H R S ) E-W Fig. 5.
A s fig. 1 for the E - W (east-west Earth current) c o m p o n e n t .
hour from 1/(2m) cycles to 1/2 cycle per hour.) In terms of period, this is from a period of 120 hours to a period of 2 hours. Also, the point just above zero cycles per observation was printed and is represented by the point on the ordinate of each graph.
60-shift spectra are shown in figs. 1-6 for the six components. The smoothed spectra were printed from the program at intervals of 1/(2m) cycles per observation (where m is the number of shifts) from 1/(2m) cycles to 1/2 cycle per observation. (That is, 1/(2m) cycles per 14
12
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00
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PERIOD ( H R S ) VERT Fig. 6.
A s fig. 1 for the V E R T (vertical E a r t h current) c o m p o n e n t .
00
00 00
I
2
54
F. W. l
To establish whether or not a 24-hour periodicity exists in the Z component a longer recording period would be necessary. From fig. 7 it is seen that the K,, index does not have
l
6-
a 24-hour (diurnal) variation. This is to be expected since K,, is a measure of worldwide geomagnetic activity. There is an indication of longer period changes in K,, but this is not reflected to any great extent in the
5E
3 0
a
4-
various
w f 4 2-
I20
24
12
PERIOD
8
6
(HRS
KP Fig.
7.
Power
spectrum
of
the
3-hour
range
index
K,,.
A similar calculation was done on the 3-hour planetary range index Kp to detect periodicities in the worldwide geomagnetic activity during the duration of the recording. Since K, is a 3-hour index, 3-hour intervals were used. The number of 3-hour intervals was 112, and the number of shifts taken was 20. The power spectrum of K, is shown in fig. 7. It was printed at intervals of 1/(2m) cycles per observation (where m is the number of shifts) from 1/(2m) cycles to l/2 cycle per observation. This is from a period of 120 hours to a period of 6 hours. Again, the point just above zero cycles per observation is represented by the point on the ordinate. 4. Discussion
micropulsation
components.
When peaks at other periods are considered it is seen that the Z component and all three Earth current com-
3-O
E
JONES
ponents have a peak near a 12-hour period, whereas the X (north-south) and Y (east-west) magnetic components do not. Fig. 7 indicates that the K,, index has a slight peak near 12 hours, and one between 12 and 24 hours. Furthermore, the X and Y components have peaks at 8 hours, and the Z component and the three Earth current components do not. All components have peaks near 6 hours except the Z and N-S (north-south Earth current) in which there is a peak between 6 and 8 hours. The spectra show more peaks at shorter periods near 3 and 4 hours, but a comparison among the components does not reveal definite similarities. From the overall spectra it is seen that the Earth current spectra appear to be more similar than the magnetic field variation spectra. This is to be expected from the previous results obtained by JONES et al. (1969), and possible reasons for such similarities are mentioned in that work. Acknowledgements The author wishes to thank Professor A. T. Price for his helpful comments on the manuscript, and the National Research Council of Canada for financial assistance in the form of a postdoctorate research fellowship.
of results
From the power spectra of the dominant hourly periods (figs. l-6) it is seen that all components except the vertical magnetic (Z) component have a 24-hour periodicity in the dominant periods of the micropulsations. This indicates a diurnal variation in the periods, but it does not give an indication of the actual form of this variation. Although the Z component indicates a periodicity of approximately 40 hours and not a 24hour period, it must be remembered that 20 per cent of the original data was missing for that component.
References BLACKMAN, R. B. and J. W. TUKEY (1958), The Measurement of Power Spectra (Dover Publications Inc.). HOLMBERG, E. R. R. (1951), Ph.D. Thesis, University of London, and (1953), Monthly Notices of R.A.S., Geophys. Suppl. 6, 467. JONES, F. W., C. C. Ku and L. P. GELDART (1969), Geophys. J. Roy. Astronom. Sot. 17, 15-38. SOUTHWORTH, R. W. (1960), Autocorrelation and Spectral Analysis. In: A. Ralston and H. S. Wilf, eds., MathemaYical Methods for Digital Computers (John Wiley) 213. SWINNERTON-DYER, H. P. F. (1963), Computer J. 5, 16.
PERIODIC VARIATIONS IN MICROPULSATION DOMINANT PERIOD
F. W. JONES*
Department of Mathematics, University of Exeter, Exeter, England Received 6 November 1968
Power density spectra of consecutive hourly values of the dominant period of micropulsations in the period range 10 seconds to 200 seconds have been computed in order to detect periodic variations in the dominant period. Three magnetic field variation components and three Earth current components recorded fo r
an interval of 336 hours were used. All spectra except the vertical magnetic component exhibit a peak at a 24-hour (diurnal) period. There are indications of 12, 8, 6, 4, and 3-hour periodicities, but these differ among the six components.
1. Introduction
hourly intervals. However, due to interruptions during recording, approximately 5 per cent of the magnetic field data and approximately 3 per cent of the Earth current data were lost from the 336-hour recording time. Furthermore, after the power density spectra for each hourly interval had been computed it was found that approximately 10 per cent of the hourly intervals for the X (north-south) and Y (east-west) magnetic variations could not be assigned dominant values of the period. Similarly, about 20 per cent of the Z (vertical magnetic) intervals could not be assigned values. In the Earth current variations about 13 per cent of the values for the hourly intervals were missing in each component. Since the computing program was written for equally spaced intervals, all intervals required values. The components did not always have missing values for the same intervals, and thus, although it is known that the components do not necessarily have the same dominant period at the same time (JONES et al., 1969), the missing values were calculated by taking the average value of the components which were known for that interval. By this method all except approximately 3 per cent of the hourly intervals could be assigned values. To obtain values for this last 3 per cent of the intervals it was assumed that the period changes continuously and the missing values were calculated by linear interpolation between adjacent values. It is known that the dominant period does not necessarily vary continuously and abrupt changes occur (JONES et al., 1969). How-
The diurnal variation in the period of micropulsations has been discussed extensively since it was first investigated by HOLSIBERG (1951). Recent work by JONES et al. (1969), in which other references are given, further studied this topic. JONES et al. (1968) recorded data at a station near Montreal, Canada (geographic coordinates N 45°32 ', W 73°09'; corrected geomagnetic coordinates N 58.9°, E 359.6°) and computed on an analogue computer power density spectra for each of six components (three Earth current and three magnetic field variation components) for hourly intervals over a total recording time of 336 hours. From these computations the dominant periods for the hourly intervals were selected. The analysis did not indicate definite periodicities in the value of the dominant periods. In particular, no diurnal variation could be detected. In the present work the results of JONES et al. (1969) have been used, and power density spectra of the hourly values of the dominant period have been computed. A program written by Dr. A. W. Nichol for the Elliot 803 digital computer at the University of Exeter was used for the computations. 2. Preparation of the data
The data from the work of JONES et al. (1969) gave values of the dominant period of each component for * National Research Council of Canada Postdoctorate Research Fellow.
50
PERIODIC
VARIATIONS
1N M I C R O P U L S A T I O N
DOMINANT
PERIOD
51
14
12
Q: LU
I0 &•
0 L~J F&&
._J LLJ
•
•
•
•
•
A•
• •
•
&••
• AA
•
•
•
• •
I 24
0 120
I 12
I 8
I 6
I 4
&•••
I .3
I 2
PERIOD (HRS) Fig. 1.
Power spectrum o f the hourly dominant periods o f the X (north-south magnetic) component.
ever, for these unknown values, this was considered to be the best approximation possible. In this way values were obtained for each interval of the total recording time.
3. The program and spectra
The program computed the time-delay autocorrelation function and the normatised power spectrum. The
14
12
oc i,i 0 o_
I0
8
LIJ ;) 6
5 uJ nr
4
• •
ill
II li
mm m
nil
ii •
2
i I E
•
lille
ii
it
mu
• •
lean
•
•
• g
ni I Mi
0
i 120
i
I
12
I 8
I 6
I 4
PERIOD
Fig. 2.
I 3
(HRSI
As fig. 1 for the Y (east-west magnetic) component.
52
F.W.
JONES
14
12
nLtJ C) (1.
I0
8
•
LLI I--
6
5 n,-
000 4
•
•
000
000000o 0
• O
2
0
0°0 O • • Ooo O
I
120
000 •
Ooo0
000 oO
• • • o
ee e
I
I
I
I
I
I
12
8
6
4
3
2
PERIOD (HRS) Fig. 3.
As fig. 1 for the Z (vertical magnetic) component.
dominant period values, the autocorrelation function and power density function were calculated for both 30 shifts and 60 shifts. The 30-shift spectra are more accurate, but the 60-shift spectra give more fine structure. Since the 30-shift and the 60-shift spectra were similar except for the better detail of the 60-shift, the
method of computation is described by SWINNERTONDYER (1963), SOUTHWORTH(1960) and BLACKMANand TUKEY (1958). For all the spectra computed it was assumed that there was no trend or secular component, and so all series were considered as stationary time series. There was no prewhitening. For the data for the 14
12
n,I.IJ
I0
3 0 n
u.I ;> I--
A
6~
•
5 ILl nr
AA•
• •
A&
•
&A
4 •
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• • &A&
•
• •
A• •
A•
•
2
0
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I
120
L'4
I 12
i 8
I 6
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i 4
•A&
•&&•
I 3
PERIOD (HRS~ N-S Fig. 4.
As fig. 1 for the N-S (north-south Earth current) component.
•A i 2
PERIODIC
VARIATIONS
IN M 1 C R O P U L S A T I O N
DOMINANT
53
PERIOD
14
12
I0 c~ I.iJ 0 13..
8
i,1 ;) 6 < .J i,i er
• •
l
4
•
•
•
•
• •
•
mm
mm •
mm •
•
•
mm
•
•
•
• •
•
•
•
•
i m
mI
mm m i I1!
2
mmmm
0 120
I 24
I 12
I 8
I 6
•
liilill
I 4
I 3
PERIOD ( H R S ) E-W Fig. 5.
A s fig. 1 for the E - W (east-west Earth current) c o m p o n e n t .
hour from 1/(2m) cycles to 1/2 cycle per hour.) In terms of period, this is from a period of 120 hours to a period of 2 hours. Also, the point just above zero cycles per observation was printed and is represented by the point on the ordinate of each graph.
60-shift spectra are shown in figs. 1-6 for the six components. The smoothed spectra were printed from the program at intervals of 1/(2m) cycles per observation (where m is the number of shifts) from 1/(2m) cycles to 1/2 cycle per observation. (That is, 1/(2m) cycles per 14
12
I0 W 0 13.
00
8
W
6 .J w
•
4
00 000
00• O
•
• •
• •
000
• OO
'
120
'
24
"
I2
i 8
i 6
•
OO •
o
00
• 00
O• •
• 0•
i 4
• i :3
PERIOD ( H R S ) VERT Fig. 6.
A s fig. 1 for the V E R T (vertical E a r t h current) c o m p o n e n t .
00
00 00
I
2
54
F. W. l
To establish whether or not a 24-hour periodicity exists in the Z component a longer recording period would be necessary. From fig. 7 it is seen that the K,, index does not have
l
6-
a 24-hour (diurnal) variation. This is to be expected since K,, is a measure of worldwide geomagnetic activity. There is an indication of longer period changes in K,, but this is not reflected to any great extent in the
5E
3 0
a
4-
various
w f 4 2-
I20
24
12
PERIOD
8
6
(HRS
KP Fig.
7.
Power
spectrum
of
the
3-hour
range
index
K,,.
A similar calculation was done on the 3-hour planetary range index Kp to detect periodicities in the worldwide geomagnetic activity during the duration of the recording. Since K, is a 3-hour index, 3-hour intervals were used. The number of 3-hour intervals was 112, and the number of shifts taken was 20. The power spectrum of K, is shown in fig. 7. It was printed at intervals of 1/(2m) cycles per observation (where m is the number of shifts) from 1/(2m) cycles to l/2 cycle per observation. This is from a period of 120 hours to a period of 6 hours. Again, the point just above zero cycles per observation is represented by the point on the ordinate. 4. Discussion
micropulsation
components.
When peaks at other periods are considered it is seen that the Z component and all three Earth current com-
3-O
E
JONES
ponents have a peak near a 12-hour period, whereas the X (north-south) and Y (east-west) magnetic components do not. Fig. 7 indicates that the K,, index has a slight peak near 12 hours, and one between 12 and 24 hours. Furthermore, the X and Y components have peaks at 8 hours, and the Z component and the three Earth current components do not. All components have peaks near 6 hours except the Z and N-S (north-south Earth current) in which there is a peak between 6 and 8 hours. The spectra show more peaks at shorter periods near 3 and 4 hours, but a comparison among the components does not reveal definite similarities. From the overall spectra it is seen that the Earth current spectra appear to be more similar than the magnetic field variation spectra. This is to be expected from the previous results obtained by JONES et al. (1969), and possible reasons for such similarities are mentioned in that work. Acknowledgements The author wishes to thank Professor A. T. Price for his helpful comments on the manuscript, and the National Research Council of Canada for financial assistance in the form of a postdoctorate research fellowship.
of results
From the power spectra of the dominant hourly periods (figs. l-6) it is seen that all components except the vertical magnetic (Z) component have a 24-hour periodicity in the dominant periods of the micropulsations. This indicates a diurnal variation in the periods, but it does not give an indication of the actual form of this variation. Although the Z component indicates a periodicity of approximately 40 hours and not a 24hour period, it must be remembered that 20 per cent of the original data was missing for that component.
References BLACKMAN, R. B. and J. W. TUKEY (1958), The Measurement of Power Spectra (Dover Publications Inc.). HOLMBERG, E. R. R. (1951), Ph.D. Thesis, University of London, and (1953), Monthly Notices of R.A.S., Geophys. Suppl. 6, 467. JONES, F. W., C. C. Ku and L. P. GELDART (1969), Geophys. J. Roy. Astronom. Sot. 17, 15-38. SOUTHWORTH, R. W. (1960), Autocorrelation and Spectral Analysis. In: A. Ralston and H. S. Wilf, eds., MathemaYical Methods for Digital Computers (John Wiley) 213. SWINNERTON-DYER, H. P. F. (1963), Computer J. 5, 16.