43
SPATIAL AND TEMPORAL PERIODICITY IN THE PACIFIC TSUNAMI
OCCURRENCE
E.V. SASSOROVA & B.W. LEVIN
Shirshov Institute of Oceanology, Russian Academy of Sciences
Nakhimovsky prospekt 36, Moscow 117851 Russia
Abstract
Recent studies of the latitude distribution of earthquake numbers and energy have
shown that the region seismic activity depends on the geographic latitude of the area and it
varies with time. The time-dependent variations of seismicity suggest a 6-year-period of
activity. Such time interval is well known as a period of Chandler pole motion. To analyze
the Pacific tsunami distribution, we use the Historical Tsunami Database compiled by
V.Gusiakov looking more closely at the local seismic regions of the Pacific area. By
choosing 139 events with magnitude M>6.0 out of the Pacific zone tsunami list for the last
50 years, we subdivided these events into two groups: northern part and southern one. The
analysis showed that there is temporal regularity in the tsunami occurrence: the event series
occurred in turn for Northern Hemisphere and then for Southern one and so on. The typical
periods of the change over from one to another hemisphere were 6 and 18 years
approximately. The assessment of probability that a tsunami may occur at a given region
over the next 6 years is very important for tsunami long-term forecast. The advance of the
study gives new perspective for the tsunami warning system development and for
implementation of improved mitigation measures.
1. Introduction
The general problem of predictability and unpredictability of the earthquake and
tsunami events has been discussed before [1, 2] and remains an active area of study. Recent
research has shown that the Earth’s seismicity and probability of the earthquake occurrence
depends on the astronomical reasons: the geographical latitude of the event [3, 4], the
relative attitude of the Earth and the Moon [5], the position of the Earth on ecliptic [6, 7].
Hence the connection between the Chandler pole motion as a global process and some
geophysical phenomena is investigated. It should be mentioned that such effects as the
crust deformation induced by polar motion [8], the earthquake energy accumulation [9,10],
the shift of the Earth’s center of mass [11-12], the temporal changes in the seismic activity
and the atmospheric processes, all correlate with the Chandler wobble periods [13].
The main goal of the study is the searching of the patterns for the Pacific tsunami event
occurrence, the identification of special periods typical for the temporal distribution, and
the assessment of the possibility for improvements in the understanding of tsunami
generation process that may be useful in the solution of the tsunami prediction problem in
future.
A. C. Yalçıner, E. Pelinovsky, E. Okal, C. E. Synolakis (eds.),
Submarine Landslides and Tsunamis 43-50.
@2003 Kluwer Academic Publishers. Printed in Netherlands
44
2. Formulation of the problem
At present, sequences of tsunami events in defined areas of the Pacific have not yet been
identified. For analyzing of a spatio-temporal distribution of the Pacific tsunami events, we
used the tabulated seismic measurement data in time interval 1950-2000 given in the
History Tsunami Data Base (HTDB) compiled by V.K.Gusiakov [14]. First and foremost
we should make a separation of the Pacific whole area into several regions (lineaments),
each with similar tectonic characteristics and response to the stress and deformation of the
Earth’s crust that lead to an earthquakes. Hence for determining the boundary of each
lineament, we took into account the geological, tectonic, geophysical characteristics of
plates, blocks, and other parts of the Pacific region that should be included into the certain
lineament. Moreover, some structural peculiarities of the planet have been considered.
Basing on expert opinions, we divided the whole of the Pacific area into four lineaments
(Fig.1). The first was the north-western lineament (I) including the coast of Alaska,
Aleutian arc, Kamchatka, Kuril Islands, Japan and Taiwan with the Pacific area up to 150
W. The north-eastern lineament (II) contained the coast of the Northern America until its
intersection with the latitude of 8N and the adjacent part of the Pacific. The attitude of the
south-western lineament (III) defined its content: the Philippines Islands, Indonesia,
Australia and New Zealand with the adjacent ocean area until to the longitude 150 W. The
south-eastern lineament (IV) consists of the coast of the Southern America with the
corresponding part of the ocean.
Since the large-scale lineaments of the Pacific seismic zone have been defined, the main
goal of the study has been reduced to the finding of a temporal sequence of the tsunami
generation events or the groups of events for each lineament, determination of the statistical
validity of results, and calculation of the typical periods for this tsunami temporal
distribution.
3. Analysis of the observation data
To analyze the process of tsunami occurrence on the Pacific we selected the tectonic events
that were registered in the time interval 1950-2000 according to the HTDB [7] with
magnitude M>6.0 and the tsunami wave intensity (I) more or equal to -1. The total number
of events that was equal to 139 was distributed amongst the lineaments in the following
manner: I - 61, II - 15, III - 44, IV - 19. A fragment of the chart with an attitude of the
lineaments and the tsunami source displacement is presented in Figure 1.
It was shown that the group of the events as well as a single event occurs either at one
lineament or at other by turn almost without intersection. The cases of the tsunami
occurrence at the different lineaments simultaneously during one year run close to 10%.
A study of the temporal behavior of the tsunami event sequence showed that the seismic
activity of the neighboring lineaments is turned on one after another. In all cases
considered, the general rule was inferred where a tsunami event group in the Northern
45
Figure 1. Four lineaments in the Pacific area (dark gray circles - the earthquake epicenters).
Hemisphere changed to the occurrence of an event series into Southern one and vice versa.
The temporal behavior of tsunami events in the Northern and the Southern Hemisphere is
presented in Figure 2. As noted previously, one can see a clearly defined periodicity.
On the Figure 2 horizontal axis is time axis and it is situated between two rectangles
(upper for the Northern Hemisphere and lower for the Southern Hemisphere). Tsunami is
presented as switching function for two Hemispheres. Every event corresponds to one
vertical line started from the time axis. If tsunami occurs in Northern Hemisphere so
correspondent vertical line directed upwards and it directed downwards for the tsunami
which occurs in the Southern Hemisphere.
Thus the time sequence of the tsunami events is now described as time series with the
significance +1 and –1. The nonparametric run test was used and the distribution-free
statistics was calculated, showing that with the probability 99.8% sequence shown is not a
purely random and it includes nonrandom component.
On the figure 2 the whole catalogue is subdivided into tree parts (time intervals: 1950 1967, 1968 - 1985, 1986 - 2000). Here, it is shown also the envelope for the observed data.
The envelope was computed for switching rectangle function with the smoothing
procedure.
46
N
1968
1986
2001
1965
1983
1967
1964
1982
1985
1963
2000
1962
1981
1996
1966
1961
1959
1980
1958
1977
1960
1957
1976
1979
1956
1975
1991
1995
1955
1974
1953
1971
1973
1952
1970
1990
1951
1969
1954
1950
1968
S
N
1984
1978
1972
S
N
1999
1998
1997
1994
1993
1992
1989
1988
1987
1986
S
Figure 2. The temporal behavior of tsunami event generation in the Northern and the Southern Hemisphere
The gain-frequency spectrum for the envelope is presented in Figure 3 and it reflected
temporal characteristics of the tsunami occurrence process. The main maximum of the
spectrum corresponds to the period of 6 years and one of the maximums is close to period
of 412-437 days. Both of the mentioned periods are well known as periods of the Chandler
pole motion [15]. The spectrums computed for the envelope as a rectangle switched
function and for the envelope line computed with the smoothing procedure show inessential
difference for the frequencies from 0.01 up to. 2.5 cycles per year.
Bold dotted line indicates the upper confidence boundary U (1- ) of the level (1- ),
equal to 0.95 (or 95%). One can see that the spectral peaks for the frequencies more than
0.5 cycle/year (period equal to 2 years) are below U (1- ), while the peaks for the
frequencies less than 0.5 cycle/year are clearly in excess of U (1- ).
47
0.2
T=6.0
years
95%
0.1
T=412437days
Frequency (cycles/year)
0.0
0.0
0.4
0.8
1.2
1.6
2.0
2.4
Figure 3. The gain-frequency spectrum of the Pacific tsunami occurrence (for the events 1950 - 2000 y).
According to the Avsjuk’s hypothesis [11, 16] the mass center of the Earth shifts
because of Earth’s inner core displacement in the ecliptic plane. The change of the Earth’s
mass center position is caused by the effect of the Sun and the Moon and it leads to the
movement of the rotation axis of the Earth. The schematic model of this process is
presented on the figure 4.
In the astronomical observations this process is treated as the Chandler pole wobble.
The typical samples of pole trajectories for the time interval 1955 - 1961 are given in
Figure 5. The temporal variations of pole trajectory radius (R - modulus of radius vector)
from 1898 to 2000 are presented in Figure 6.
Figure 4. The inner core mover and the shift of the Earth rotation axis and the shift of Earth’s pole.
48
-X
- 0,2”
1957
1958
1956
+Y
-Y
1961
1959
1960
1955
+ 0,2"
"
+ 0,6”
+X
+ 0,2"
+ 0,4
Figure 5. The Chandler pole motion from 1955 up to 1961 years.
R, sec
0.5
0.4
0.3
0.2
0.1
2000
1995
1985
1990
1980
1975
1970
1965
1960
1950
1955
1945
1940
1935
1930
1925
1915
1920
1910
1905
1900
0.0
Figure 6. The pole trajectory radius (R - modulus of radius vector) from 1898 to 2000 years. The variations of
the radius vector are presented as angular value.
49
0.3
0.2
T=6.0 year
a)
0.1
0.0
0.5
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
0.4
0.3
T=6.67 year
b)
0.2
T=412-437 days
0.1
0.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Frequency (cycle/year)
Figure 7. a) - Spectrum of the Pacific tsunami occurrence, and b) - the spectrum of Chandler pole motion R(x,y).
The inner core motion and its regular intersection of the plate of equator can lead to an
alternation of a supplementary stress into different hemispheres of the Earth. The envelope
on the Figure 2 may reflect an accumulation and a switching of a supplementary stress
between the Northern and Southern Hemispheres. These processes are very complicated.
Two spectrums (tsunami occurrence in two Pacific Hemispheres and R- variations of
the pole motion) are presented at the same time on the figures 7a and 7b correspondingly.
By comparing the two spectrums, we deserve some coincidence between main periods of
the Pacific tsunami variation and the Chandler pole motion.
4. Discussion and conclusions
By grouping into certain lineaments have found an unknown effect of alternating
tsunami activity between the Northern and Southern Hemispheres of the Earth. This
alternative process is periodic in time and the typical periods are comparable with the wellknown periods of the Chandler pole motion (6-7 years and 412-437 days).
The coincidence between the typical periods of tsunami activity in the Pacific and the
Chandler pole motion periods obtained in our investigation supports our hypothesis that
certain earthquake and tsunamis can be triggered by perturbation of the Earth’s rotation
axis. We believe that the similar analysis may help to understand the physics of
earthquakes and suggest new methods for improvements of tsunami warning systems.
50
Acknowledgements
We are grateful to Y.N. Avsjuk, V.K. Gusiakov, and V.P. Pavlov for useful discussions and
comments. The work was partially supported by the Russian Foundation for Basic
Research, Grants 99-05-64218 and 00-15-98583.
References
1. Geller, R.J., Jackson, D.D., Kagan, Y.Y. and Mulargia, F. (1997) Earthquakes cannot be predicted. Science 275,
1616-1617.
2. Wyss, M. (1997) Cannot earthquake be predicted?, Science 278, 487-488.
3. Levin, B.W. (2001) Can the Earth’s inner core be a conductor of the seismic activity? Zemlja i Vselennaja 3,
(in print); (in Russian).
4. Levin, B.W. and Chirkov, Ey.B. (2000) The latitude distribution of seismicity and the rotation of the Earth,
Volc. Seis., 21, 731-739.
5. Volodichev, N.N., Podorolskii, A.N., Levin, B.W., and Podorolskii, V.A.. (2001) Correlation of major
earthquake sequences with new moon and full moon phases, Volc. Seis., 1, 60-67.
6. Fedorov, V.M. (2000) Gravitation factors and astronomical chronology of geospherical processes, Moscow
State University Publishers, Moscow (in Russian)
7. Gor`kavyi, N.N., Minin, V.A., Tajdakova, T.A., and Fridman, A.M. (1989) Are there any astronomical reasons
for the strongest earthquake? Astronomical circular, 1540, 35-36.
8. Wahr, J.M. (1985) Deformation induced by polar motion, J. Geophys. Res., 90, B11, 9363-9368.
9. Chao, B.F. and Gross, R.S. (1995) Changes in the Earth`s rotational energy induced by earthquakes, Geophys.
J. Int. 122, 776-783.
10. Chao, B.F., Gross, R.S. and Dong, D.N. (1995) Changes in global gravitational energy induced by
earthquakes, Geophys. J. Int. 122, 784-789. 6.
11. Avsjuk, Y.N. (1973) On the Earth’s inner core motion, Doklady Academii Nauk SSSR 212, 5, 1103-1105. (in
Russian).
12. Avsjuk, Y.N. and Levin, B.W. (1999) To M.V. Lomonosov question on the displacement of the Earth’s mass
center, Herald of RFBR (Russian Foundation for Basic Research) 2(16), 4-11. (in Russian)
13. Levin, B.W., Savelieva, N.I., Semiletov, I.P., and Chirkov, Ey.B. (2000) The Chandler pole wobble and its
role in geophysical and meteorological processes, in V.A. Akulichev and I.P.Semiletov
(eds.),
Hydrometeorological and biogeochemical research in the Arctic, Pacific Oceanological Institute of RAS,
Vladivostok, pp.158-165 (in Russian).
14. Gusiakov, V.K. (2000) Historical Tsunami Data Base (http//tsun.sscc.ru/htdbpac).
15. International Earth Rotation Service (IERS) Annual Report of 1997 (1998), Central Bureau of IERS Observatoire de Paris, France.
16. Avsjuk, Y.N. (1996) Tidal forces and natural processes, Russian Academic Sc. Press., Moscow. (in Russian).