space-time structures of earthquakes
TRANSCRIPT
ORIGINAL PAPER
Space-time structures of earthquakes
T. N. Krishnamurti Æ Ruby Krishnamurti Æ Anitha D. Sagadevan ÆArindam Chakraborty Æ William K. Dewar ÆCarol Anne Clayson Æ James F. Tull
Received: 11 November 2008 / Accepted: 28 February 2009 / Published online: 13 August 2009
� Springer-Verlag 2009
Abstract Using the United States Geological Survey
global daily data sets for 31 years, we have tabulated the
earthquake intensities on a global latitude longitude grid
and represented them as a finite sum of spherical har-
monics. An interesting aspect of this global view of
earthquakes is that we see a low frequency modulation in
the amplitudes of the spherical harmonic waves. There are
periods when these waves carry larger amplitudes com-
pared to other periods. A power spectral analysis of these
amplitudes clearly shows the presence of a low frequency
oscillation in time with a largest mode around 40 days.
That period also coincides with a well-know period in the
atmosphere and in the ocean called the Madden Julian
Oscillation. This paper also illustrates the existence of a
spatial oscillation in strong earthquake occurrences on the
western rim of the Pacific plate. These are like pendulum
oscillations in the earthquake frequencies that swing north
or south along the western rim at these periods. The spatial
amplitude of the oscillation is nearly 10,000 km and occurs
on an intraseasonal time scale of 20–60 days. A 34-year
long United States Geological Survey earthquake database
was examined in this context; this roughly exhibited 69
swings of these oscillations. Spectral analysis supports the
intraseasonal timescale, and also reveals higher frequencies
on a 7–10 day time scale. These space-time characteristics
of these pendulum-like earthquake oscillations are similar
to those of the MJO. Fluctuations in the length of day on
this time scale are also connected to the MJO. Inasmuch as
the atmospheric component of the MJO will torque the
solid earth through mountain stresses, we speculate the
MJO and our proposed earthquake cycle may be connected.
The closeness of these periods calls for future study.
1 Introduction
This paper examines global earthquake data sets in a
planetary space-time context, and illustrates some inter-
esting aspects that have been overlooked in the past. Plate
tectonic theory presents only a statistical, special (geo-
graphic) and otherwise static picture of earthquake occur-
rences. The search for precursors of individual events is
usually studied on the local scale within a single fault
system. The interrelationship of global and local scales has
generally received less attention, but is the focus here. It
was noted by Knopoff (1996) that ‘‘an ability to predict
earthquakes either on an individual basis or on a statistical
basis remains remote. It is clear that scientific issues
must be understood before routine prediction can be
announced’’. Today, a decade later, earthquake prediction
T. N. Krishnamurti (&) � A. D. Sagadevan � A. Chakraborty �C. A. Clayson
Department of Meteorology, Florida State University,
Tallahassee, FL, USA
e-mail: [email protected]
R. Krishnamurti � W. K. Dewar
Department of Oceanography, Florida State University,
Tallahassee, FL, USA
R. Krishnamurti � C. A. Clayson
Geophysical Fluid Dynamics Institute, Florida State University,
Tallahassee, FL, USA
J. F. Tull
Department of Geological Sciences, Florida State University,
Tallahassee, FL, USA
Present Address:A. Chakraborty
Centre for Atmospheric and Oceanic Sciences,
Indian Institute of Science, Bangalore, India
123
Meteorol Atmos Phys (2009) 105:69–83
DOI 10.1007/s00703-009-0034-7
is still remote, but great progress appears to have been
made on the scientific issues. Whereas weak earthquakes
(magnitude \3) show self-similarity with no detectable
length scale, strong earthquakes do have a length scale
associated with their seismicity. Strong earthquakes
(magnitude C5) are those that rupture a significant area
along lithosphere-bounding faults (Sykes 1996). They have
seismicity related to inhomogeneities with characteristic
length scales on the order of 100 m, according to Aki
(1996), who utilized coda wave interferometry. Coda
waves are late-arriving seismic waves (like the coda sig-
nifying the end of a musical composition). Whereas, the
early (direct) arrivals may show no detectable effect of
small changes in the medium, coda waves represent those
scattered by inhomogeneities and these would have
repeatedly sampled the medium. Thus, coda wave inter-
ferometry has been used successfully in varied applications
such as to detect changes in volcanic activity on a two-day
time lapse (Gret et al. 2006), and to infer weakening of
faults and asperities by the injection of fluids.
Aki’s (1996) analysis on coda waves (late-arriving
seismic waves) trapped in fault zones, describes the process
as a creep flow in the lower plastic part of the fault which
allows for stress release, while in the brittle upper part
there is no stress release. It is the stress release in the brittle
zone that causes seismicity.
Kanamori (1981) used a space-time display of earth-
quakes surrounding major seismic events, for the purpose
of showing the nature of precursors. Long periods, often of
several years duration having notable quiescence, were
shown to precede many major earthquakes. The time scales
of 30–60 days, which are our focus here, were not resolved
in those presentations. A relationship between atmospheric
pressure field and earthquake occurrences over California
was shown by Namias (1988, 1989).
1.1 The USGS earthquake data sets
The United States Geological Survey (USGS) is a leading
geological organization allied with seismograph stations
around the world which receives, analyzes, maintains, and
distributes data on earthquake activity worldwide. This
historical (USGS) earthquake data base provides informa-
tion on the time, location, depth, and magnitude of the
earthquakes from 2100 B.C. to the present. The data base
contains earthquakes with known magnitude values
between 0.1 and 9.9. Here, we consider earthquakes along
the western rim of the Pacific plate during the years 1973–
2006 as recorded in the (USGS) earthquake database. The
convergent plate boundaries of the western Pacific clearly
stand out in this distribution as can be seen in Fig. 1a.
These data were binned into the roughly 1,000-km squares
shown in Fig. 1b, and over temporal intervals of 3 days,
retaining only events of magnitude C5 on the Richter scale.
Such space-time binning was necessary given the spatially
sporadic nature of earthquake epicenters.
1.2 Global time scales
If one takes the global distributions of earthquakes for a
given day, that data set can be expressed in the global
context by expanding their intensities using spherical har-
monics. Most places, devoid of earthquakes, will carry a
number zero for the intensity, whereas along or near the
lithospheric plate boundaries there can be many places that
carry non-zero numbers. This representation calls for an
initial tabulation of these zeros and non-zeros on a global
latitude/longitude grid. The spherical harmonic represen-
tation requires a grid to spectral transformation. That finite
representation of data is highly revealing in showing that
the earthquakes do carry space-time scales similar to many
other geophysical problems. The finite representation is
described by a discrete set of spherical harmonics such that
the input field is completely recovered (except for minor
problems at the edge of zeros and adjacent large non-zero
numbers, called the Gibbs phenomena). Figure 2a shows
the earthquake distributions on a given day. Figure 2c, d
shows the positive and negative spectral amplitudes
Fig. 1 a Earthquake intensities plotted during 30 June to 21 July
2009 as obtained from http://neic.usgs.gov/neis/qed/; b 10o latitude/
longitude bins were used for the data analysis
70 T. N. Krishnamurti et al.
123
(triangular truncation) for this data decomposition into
spherical harmonics. This is called a Fourier Legendre
transform of the input data. An inverse transform is next
performed to see the recovery of the input data for the
spectral coefficients. That recovery shown in Fig. 2d mat-
ches closely with the input data of Fig. 2a. The differences,
if any, arise due to what is called a Gibbs phenomenon,
when we expand spatial data sets with sharp changes such
as a zero and large non-zero values adjacent to each other.
The Gibbs phenomenon is not severe and we are able to
replicate the initial field nearly exactly by this finite rep-
resentation from 2-D waves. This aspect has been tested in
the same way as we do in atmospheric spectral modeling,
(Krishnamurti et al. 2007). We show these to emphasize
that the entire set of spectral coefficients is an useful
mathematical representation for the global earthquake of
that day. We will next look at this global representation of
these data sets.
In order to look at the salient time scales of the global
earthquake data sets, we have performed a spectral analysis
of the daily mean spectral amplitude data sets, covering the
years (1973 to 2004) that includes all spatial scales in two
dimensions. The time series of these global amplitudes are
shown in Fig. 3. They are the vector sums of amplitudes of
the real and imaginary parts for all of the spherical har-
monics. In this analysis, we have only included the aver-
aging for the first 20 spherical harmonic waves. The time
series of what can be called a ‘‘daily earthquake index’’
seems to show interesting features on many time scales.
There are often peaks that are values separated by tens of
days and some that seem to occur at more rapid intervals. A
spectral analysis of this data set is shown in Fig. 4. This
covers the power spectra for the entire period of 32 years
and also some at 3-year intervals. Also included in these
illustrations are the lines defining the confidence limits at
95 and 99% levels and the red noise spectra. Here, we see
some peaks in the spectral variances at high frequencies
(less than 10 days), there are also some marked peaks in
the time scales especially around 40 days and higher.
These can be seen in the spectra for the 32-year long data
sets as well in the three yearly segments illustrated here. A
peak around 40 days in the spectra based on 32-year long
data set carries the largest variance.
When we look at a sequence of global spectral amplitudes
for each of the spherical harmonics, we see an interesting
alternation in the magnitudes with time. There are periods
when these amplitudes in general are all small and there are
periods when they are all quite large in comparison. In
Fig. 5a, b and c, we show a 116-day sequence of these at
intervals of 5 days. Here, the red and purple colorings
denote larger amplitudes, and yellow and green denote
smaller amplitudes on the color scale (also indicated). The
amplitudes of the real and imaginary parts of global repre-
sentation of the earthquakes are shown here. This display
Fig. 2 a The distribution of
earthquake intensities on a
random date. b Backward
transform results from spectral
to grid, showing the rerecorded
earthquake distribution. c Real,
d Imaginary parts of the 2-D
harmonic coefficients conducted
for digitizing a. Here, ordinate:
degree of associate Legendre
polynomials; abscissa: order of
trigonometric waves in the
zonal direction
Space-time structures of earthquakes 71
123
suggests a low frequency oscillation in the global amplitudes
for most of the waves in this spherical harmonic represen-
tation. What this implies is that there are days with large
amplitudes for a large number of global spherical harmonic
components that describe the earthquakes, and then there are
days when the global earthquakes are described by waves of
smaller amplitudes. The same data set confirmed, as shown
in Fig. 4, that there exists a dominant 40-day oscillation in
the global earthquake activity. These amplitude displays of
Fig. 4 merely confirms that finding.
Fig. 3 Daily vector summed amplitude of global earthquake for 4-year segment covering 32 year. Here, ordinate: vector summed amplitude;
abscissa: time in days
72 T. N. Krishnamurti et al.
123
1.3 The Madden Julian Oscillation
There has been a considerable amount of research on a slow
eastward moving wave called the Madden Julian Oscillation
(MJO) in the earth’s atmosphere. This wave has a scale of
nearly 10,000 km and traverses around the earth in roughly
20–60 days (Madden and Julian 1971, 1972). This wave has
its largest amplification in the equatorial latitudes. This
wave carries a disturbed and an undisturbed part as it
propagates, such that roughly one half of this wave includes
cloudy and disturbed weather. Within this disturbed part one
sees a plethora of cumulonimbus rain producing clouds.
Nakazawa (1988) emphasized an envelope of this disturbed
part of the MJO wave that moves west to east whereas the
individual cloud elements within it often move in a different
direction compared to that of the envelope. In the course of
looking at space-time data sets of strong earthquakes with
intensity C5 on the Richter scale, related to the convergent
plate boundaries along the western rim of the Pacific plate,
we noted the possibility of illustrating a large-scale enve-
lope of earthquake occurrences. That envelope carries a
number of individual earthquakes whose position of precise
a b
c d
e f
Fig. 4 Power spectra as a function of period. Here, ordinate: power times the frequency; abscissa: periods in days
Space-time structures of earthquakes 73
123
occurrence would be difficult to predict. The clouds within
the Nakazawa envelope, illustrated in Fig. 6, are difficult to
predict but the envelope’s motion has been predicted by
many authors, e.g., Krishnamurti et al. (2007). The main
objective of this paper is to illustrate an earthquake occur-
rence envelope using some 32 years of data and to draw
some parallels with the MJO, both of which seem to carry
similar time scales.
Figure 6 is based on the findings of Nakazawa (1988).
This is a longitude/time diagram called the Hovmoller
diagram. This shows envelopes of cloud elements that
propagate from west to east in periods roughly of the order
of 20–60 days. This is called the Madden Julian wave.
There is a disturbed (cloudy) part of this wave and a rel-
atively quiescent part of this wave, these are identified in
this illustration. The cloud elements inside the envelope
Fig. 5 This illustration shows the 2-D amplitude (real and imaginary
parts) of global earthquake expressed by spherical harmonic waves.
Here, ordinate: degree of associate Legendre polynomials; abscissa:
order of trigonometric waves in the zonal direction. Different panels
show a sequence of 116 plots at interval of 5 days
74 T. N. Krishnamurti et al.
123
generally propagate westwards at a speed of around 500–
700 km/day. An important point that meteorologists rec-
ognize is that it is very difficult to predict where and when
a single cloud might next form within the cloudy part of the
envelope, although the envelope has its own identity. We
shall illustrate that somewhat similar space-time diagrams
can be constructed to illustrate active and relatively inac-
tive earthquake occurrences along the western Pacific rim.
Here, again the goal is not to predict where and when of a
single event.
2 The space-time organization of earthquakes
on the western Pacific rim
Figure 7a illustrates the space-time evolution of earthquake
occurrence along the western Pacific rim during a 100-day
period beginning in July, 1983. The abscissa represents the
boxes numbered in Fig. 1b with box number 24 denoting
roughly the center of the western rim and also the location
of the greatest activity over the last 32 years. In this
illustration (Fig. 7a), the dark stipplings are regions where
Fig. 5 continued
Space-time structures of earthquakes 75
123
more than one earthquake occurrence was noted within
each of the space-time bins. The stippling utilizes a cubic
rule, i.e., 2 earthquakes are represented by 8 dots, 3 by 27
dots and so on. This was done to see a space-time pattern of
major earthquakes. What one notices in Fig. 7a is the
tendency for earthquake occurrences to swing first toward
the southern tip of the rim (boxes less than 24) and then
back to the northern tip (boxes greater than 24, Fig. 1b).
This repeats for roughly two and one half cycles over the
100-day interval, yielding a roughly 40-day time scale. An
ovular envelope is plotted on the figure to track the oscil-
lation. This envelope’s shape was arrived at after analyzing
nearly 100 such illustrations from the last 34 years of data
sets. The lateral extent of this feature is nearly 10,000 km.
In Fig. 7a, we also display a line (red color) that con-
nects the 3-day maxima of earthquake activity. This is
an alternate representation for the oscillation presented
in this study. This diagram describes traveling waves of
Fig. 5 continued
76 T. N. Krishnamurti et al.
123
earthquake occurrences that spans the entire western
Pacific rim. It is the recognition of this apparently orga-
nized earthquake behavior that is the major contribution of
this paper.
A connection of events by the straight-line segments in
Fig. 7a is not meant to be deterministic. Our emphasis here
will be on the oscillation of an envelope that carries several
events in space-time.
Figure 7b, c and d includes several more examples of
this pendulum-like swing. Here, the frequency of occur-
rences of major earthquakes is represented by the corre-
sponding numbers in color. A total of 69 such oscillations
were found during the 32 years period between 1973 and
2006. The envelope is again provided to facilitate the
viewing of the phenomenon. It is important to note that the
envelope represents special propagation of regions of
enhanced earthquake probability, not earthquakes per se.
Within the envelope, there are many locations along the
plate boundary where no major earthquake activity occurs.
A time series analysis of the earthquake occurrences sees
periods of the order of 20–60 days for the farthest dis-
placement points of the pendulum-like swings of earth-
quake occurrences (Fig. 8).
3 Possible relationship of atmospheric to solid earth
phenomena
The Earth’s rigid lithospheric plates move across a
deformable zone (asthenosphere) in the underlying upper
mantle driven principally by complex convective motions,
and interact along plate boundaries via faulting and other
modes of deformation. Wind-forced mountain torques
which cyclically alter earth’s angular momentum add an
additional oscillating force component across mountainous
continental plates, and thus a small oscillating compres-
sional/extensional stress component to plate-bounding
fault systems. The amplitude of the oscillation of moun-
tain torques derived from surface pressure data produces
an oscillating horizontal force of *1.6 9 1012 N across
Asia.
A composite structure of the atmospheric low frequency
winds (on the time scale of 20–60 days) at 850-hPa level
for the respective clockwise (ascending) and the counter-
clockwise (descending) swings of the earthquake pendulum
are shown in Fig. 9. These are composites of 54 cases each,
where the amplitude of the wind anomalies was larger than
1 m s-1. The composites show an organized structure in a
pattern not unlike that of the MJO. These lower tropo-
spheric winds on the time scale of 20–60 days rotate in a
clockwise sense when the earthquake occurrences swing to
the north and vice versa. The largest amplitude of these low
frequency winds was around 3 m s-1, and the means
appearing in Fig. 9 are arguably recognizable above the
uncertainty of the estimate. The accuracy of the winds is of
the order of 1 m s-1 and the accuracy of the estimates of
low frequency winds are much less than 1 m s-1.
A possible relationship between the length of day data
sets and the earthquake frequencies is shown in Fig. 10.
Here, we have averaged the filtered length of day mea-
surements to retain the intraseasonal time scales, separately
for the ascending and descending phase of our suggested
western Pacific earthquake occurrence cycle. The ascend-
ing phase is where the earthquake occurrence proceeds
clockwise around the western rim of the Pacific plate and
the descending phase is its inverse. This separate averaging
shows an increased length of day during the ascending
node of earthquake frequencies and vice versa with a peak
to trough amplitude on the order of 0.06 ms. Fluctuations
in the length of day from the unfiltered record are of the
order of a few milliseconds and the accuracy of the length
of day data sets is 0.015 ms (24).
We have noted a lag of roughly 5–10 days between two
low frequency zonal wind atmospheric anomalies (on the
time scale of 20–60 days) and the low frequency repre-
sentation of the earthquake peaks (Fig. 11). The low fre-
quency zonal winds were extracted near the western rim of
the Pacific plate over a box located between 140–150o E
Fig. 6 An x-t (longitude/time) diagram of the clouds over (as seen
from infrared brightness) for a polar orbiting satellite. Data,
meridionally averaged between the equator and 5oN are shown. This
covers the period May and June of 1980. Longitudes are shown along
abscissa. The envelopes (a, b, and c) show ellipse enclose active
cloudy periods while they are separated by quiescent periods
Space-time structures of earthquakes 77
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a
b
Fig. 7 a This is an S–T diagram along the western Pacific plate of
earthquake activity. S follows the western rim and S = 24 denote a
reference point in Indonesia with the largest activity in the last
30 years. The symbols within this S–T plane denote earthquake
intensities. The ordinate shows 100 days of activity and the abscissa
are the bins. The ellipses are schematic enclosing regions of
earthquake activity. The red line is also schematic; it connects some
of the salient earthquakes during the period June through September
1983. b, c, and d show further examples of the pendulum-like
oscillation of earthquake activity along the western rim of the Pacific
plate. The rest are same as in Fig. 7a. The red line, similar to that of
Fig. 7a, is not illustrated here. These cover examples covering several
100-day periods between 1973 and 1997
78 T. N. Krishnamurti et al.
123
12 16 20 24 28 32 36
10
30
50
70
90
Jan−Mar 2000
333
111
111
111
111
1111111221
111
111
1111221
111
111111
222
22333211111211111222111111
11111122422
111
111
222
111
4441221
1221111
1113441
122211
111
11211
111
1111111221
111111
222112132311
22311112111221111
111
111111
111
111
1111112442
222
111
111
111
111
111
111
222111
111
11322
1221
111
111
11111111211
11211
111
111
111
333
1221
111
111
111
111
111
222
111
111
111
111
111
111
111
12 16 20 24 28 32 36
10
30
50
70
90
Jul−Sep 2000
111111
111
111
111
111
111222
111
111111111
222
1221
1221111111
111
11211
233322111111
111222
1221
111
111
111111
11222122222311
111
111
111111
111122211111
111
2442
111111
111
111
111
111111
111
111
111
1132311111
111111111
111
111
111
111
11211
1221
1221
12321
111
111
111
111
111
222
111111111
111111111
111
1221
111
111
1221
111
111
222
111
111111111
111
111
222
111
111
12 16 20 24 28 32 36
10
30
50
70
90
Jan−Mar 1976
111
111111
111
111
3441
4773111112113323830148411122455323312331111111111
11211
1221
111122322
11211
111111222
1111233211221111111
111111111
1221 111
111
111
111
111
111
111111222
11211
111
111
111111222
111233211111111
1221111
111
111
111222
1221
111
222
111
111
111
111
111
111
111133211111111211
111
111
111
111
111
333
111
132830231110423454432211222
12321
111
1332
1221
111
111
111
1111221
111
111
12 16 20 24 28 32 36
10
30
50
70
90
Apr−Jun 1978111
222
111111
111
222
111
111
111
11211
111
111
111111112111221111111
122322
11212112331
11211111
222111112221
111111333222222
11211
111
1221
111
222
111111
111
222111
222222
111
111
11111322
111
11211
111
3331221111
111
111
22422112111221
111
111
111
111111
111
3552
111
111145521
111
11211111
111
334254411222
111
1122432111
1221
2222221221
1132211211
111
1121211111
222
111
111
111
111
111
111
333
111
111
111 444
12 16 20 24 28 32 36
10
30
50
70
90
Oct−Dec 1984
1
2
3
4
>= 5
11322
111
111
111
111
111
22311
134333421
22211122311
111
1221111111
111
111
111
111233112211232122312111111121112455312331111111
111
1221
111111
2331
33522
111
3441
111
111111
111
12321
111
111
111
11111111322
111
11211111
111111222222111
111222
111
111111111
11211
23421
111
222111
222
111
111
111
111
111
111
111
111
1221333
222
111111111
111
1221
111
111
1221
111
111
111
111
111
1221111
111
111
111
312141121221
111
111
222111
111
111
333
11211
111
111
111
111
111
111
11211111
111
12 16 20 24 28 32 36
10
30
50
70
90
Jan−Mar 1987
Boxes along the Pacific Rim
111
111
222
444
111
333
111
11211
1221
111
155733
111
111111111111
111111
1112453111211111111
222111
1221222
11211111
56611221
2342211
1132312221111111
111111111222
111222
111
222111
111111
1221
11122311
111
111111
111
23421
11211
11248141292111211111222
122211
44511111
11222211
111
222
111
111
111
111
111111
122211
111
1332
222
111
222
111111
111
222111111
11211
333
111
11211
111111
111111
222
111
111
111
111
2331111
111
222
111
111
222
222
111
111111
144311211
11211
111
111
111
111
12 16 20 24 28 32 36
10
30
50
70
90
Oct−Dec 1989
222
111
222222
11113321111332111
111
1221
111
111
111
222111
1221
11111211
1332111
112232111112211332111
111
222
122111433111111
111
222
222
1111332111111
111
122211
11112211111111121211
111
3331111121211
111
111
11211
111111
222
111
111
111
111
2331
111
111
111
111
111111111
1221111111222
222111
111111
111
111
111
111
111111111111
111
2559666896652111
111
22222422
222
111
12211221
111111
111
11211
111
1443
111
111
111
111
101010
111
111
111
111
111
12 16 20 24 28 32 36
10
30
50
70
90
Jan−Mar 1991
111
111
222111
13542
111
111
222
111
111
111111
111222111
111
111111
111
223222121235643111221
111
133311
111111111
111224442
12221211
1111111221
222
111
1332
111111
111111
1111332
111
111
11211222
24531122211111
222
2222442
111111
999111
1221111
111
1111221
111
222
111
1221
2222331
5661111
111
111111
111
111
111
111
111111
111111111
111
111
111
111
111
111
111
111
111
111111111
111
111111
111
111111
111
111
111
111
12 16 20 24 28 32 36
10
30
50
70
90
Jan−Mar 1992
111
111
111
111
111
111111
11223321111
1121211
11211
11211
1111143311111211111
112221111111111
111
13331112321555
112221
2331111
111
1221
111
1221
11111211
1221
11211
111
111
111
112111114551
111
111
1111221
333
222111223111221111111
11211
11111322
122111112321
11211
111
111
111
111111
111
111
111
111
111
111
111
111
111
111
222
111
111
111
333
111
111111
111
111
1111111221
11211
111
1221
111
111
111
111
111
11111322
111
1221
111
12 16 20 24 28 32 36
10
30
50
70
90
Oct−Dec 1992
111
111
111
111
111
111
111
1221
7101611822331111
111
11211
111
333444
111
222111
22311
111111
1111111332
223121113321111221111
111
111
111
111
111
12212297811
112111221
1221
122211333
111111111
111111
111
111
577212221134411221
111
111
111111111
222
1111111226661
11211111
11211
111
111
222
111111111
222
11322
2224474521
1332
111
111
111
111
111
111
111111111
1111332222
222
111
111111
111
333
111
111
11211
111
111
111
111
111223221
111
1221
111
111
222
12 16 20 24 28 32 36
10
30
50
70
90
Jul−Sep 1993
1
2
3
4
>= 5
111
111
111
111
111
111
1332111
222111
111
1111281114951
111
111111
111111222
1111122321
1221
111
111
1221
2243421111
111
111
444
1222221
1221
111111
111
11211111111
7881
111
111
111
111
1221
222
11211
111
11211
111
111
111
1221111111
111111
222
111111
111
2331
111
111111
111
111
111
111
11149119531111111
111111111
1221
111
1221
1221
111
111
11211
111
111
222
111
111
111
11211
111111
111111
111
111
111
111
111
111
111
111
111
111
111
12 16 20 24 28 32 36
10
30
50
70
90
Oct−Dec 1997
Boxes along the Pacific Rim
111
333111
111111
111111111
111
111
111
11211
111
111
111
2221134421111112331
222
111111
1221
1221
111
112221111
1221
111
111
111
111111
1221111
333111
1221
11211
11211111
1221111
111
12322111221
111
111111
111
111
111
111
11322
111
111
111
111
111
1332
111
111144411
111
111
1121211111
111
1332
111
111
111
130465227137532111
333
222
111
111
111
1111443
111
1221
111
c
d
Fig. 7 continued
Space-time structures of earthquakes 79
123
and 10oS-EQ. The low frequency earthquake frequencies
were extracted from box 24 of the western rim of the
Pacific plate. The ordinate of Fig. 11 shows days after the
start (day 0) of any of the seasons when a strong
([0.5 m s-1) peak in the zonal wind anomaly was noted.
The abscissa shows the low frequency peaks of the earth-
quakes with respect to the same start data of a season. After
examining 36 such major peaks of earthquakes, this scatter
diagram was plotted which shows an interesting phase lag,
i.e., the zonal wind anomalies seem to peak roughly
10 days prior to a peak of the low frequency earthquake
activity. This can be coincidental since both peaks carry
low frequency representation for the same time scales.
Further study is clearly warranted.
Finally, we consider simple models for communication
between atmosphere and solid earth. Note that the angular
momentum of the earth can be altered by frictional and
mountain torques. However, the surface frictional torqueses
are smaller in magnitude compared to the mountain torques
(Krishnamurti et al. 1992). The change in length of day by
the wind-forced mountain torques on intraseasonal time
scales has been well established in the references cited
below. Here, we consider the consequences on tectonic plate
boundaries as the earth is spun up or spun down with each
0.01 0.03 0.1 0.50
0.02
0.04
0.062102040
First half of 1973
↓
a
0.01 0.03 0.1 0.50
0.02
0.042102040
Second half of 1973
↓
b Power Spectrum of Earth Quake Frequency
Time Period (Days)
0.01 0.03 0.1 0.50
0.02
0.04
0.06
2102040First half of 1976
↓
c
0.01 0.03 0.1 0.50
0.05
0.1
2102040Second half of 1976
↓
d
0.01 0.03 0.1 0.50
0.02
0.04
0.06
21020401983
↓
e
0.01 0.03 0.1 0.50
0.02
0.04
0.06
0.082102040
1984↓
f
0.01 0.03 0.1 0.50
0.02
0.04
0.06
2102040First half of 1987
↓
g
Pow
er ×
Fre
quen
cy
0.01 0.03 0.1 0.50
0.1
0.22102040
Second half of 1987
↓
h
0.01 0.03 0.1 0.50
0.01
0.02
0.03
21020401989
↓
i
0.01 0.03 0.1 0.50
0.02
0.042102040
1991
↓
j
0.01 0.03 0.1 0.50
0.02
0.04
0.06
2102040First half of 1992
↓
k
0.01 0.03 0.1 0.50
0.02
0.042102040
Second half of 1992↓
l
0.01 0.03 0.1 0.50
0.02
0.042102040
1993
↓
m
0.01 0.03 0.1 0.50
0.02
0.04
0.06
21020401997
↓
n
0.01 0.03 0.1 0.50
0.01
0.02
0.03
21020402000
↓
o
Fig. 8 Power spectra for selected years. These are power spectra for
the bins 18 and 23 where the low frequency oscillations were quite
evident. The ordinate denotes power times the frequency and the
abscissa denotes frequency as period. The spectra of the red noise are
shown by the dashed line. The arrow indicates a peak on frequency
on the MJO time scale
80 T. N. Krishnamurti et al.
123
change in length of day. The model is one in which the
continent carrying plates with mountains that stand tall into
the atmosphere effectively act as sails, giving rise to
mountain torques that apply a net surface force to conti-
nental plates. Wind-induced torques on the continental
Eurasian landmass transmit an oscillating force through the
elastic (or visco-elastic) Eurasian plate in a direction highly
oblique to the general north–south trend of the Pacific plate’s
convergent plate boundaries (Fig. 1b). This action would
have the perturbing effect of alternately slightly increasing/
decreasing the differential compressive stresses along the
western Pacific plate boundaries over a 20–60 day period.
As subduction zone faults are progressively loaded with
increasing stress by convergent lithospheric plate motion,
isolated segments of these faults are continuously brought
toward the critical threshold differential stress required for
brittle failure. Triggering of Coulomb-type failure and
resulting earthquake generation occurs in regions of built-
up elastic stress along fault systems that are locked (stable)
but have stress states close to the failure criteria. Stress
redistribution due to adjacent or distant seismic events can
either induce or suppress seismicity depending upon the
local Coulomb stress changes (Freed 2005). Failure can be
induced by either increasing the shear stress on the fault
plane or by decreasing the effective normal stress on the
plane. During the Pacific rim’s earthquake ascending
mode, the wind-induced torques on Asia could cause a
slight decrease in effective normal stress on west Pacific
subduction zones, thus possibly contributing to a positive
Coulomb stress change resulting in failure. During the
Fig. 10 The length of day anomalies in milliseconds are shown along
the ordinates, and the ascending and descending modes are identified
along the abscissa. These are averages based on 28-years earthquake
data sets
Fig. 11 This shows a scatter plot of the days when the MJO time
scale wind anomalies at the 850 hPa reached a peak (along the
ordinate) and the day when the earthquake occurrences reached a
peak. That scatter suggests a relationship between these two
parameters
Fig. 9 This illustration shows the averaged MJO time scale circu-
lations during two different epochs of the pendulum-like oscillation of
the earthquake activity. The ascending node is when the activity is
moving northwards (of bin 24) and the descending node is its
converse. The topography, especially the mountain chains of East
Asia and neighboring Islands, are also shown here. The circulation
center and its amplitude increase during the descending node when
these circulations are closer to the high mountains
Space-time structures of earthquakes 81
123
opposite mode, the net effective normal stress increase on
subduction zone faults could serve as a more efficient
‘‘clamping’’ stress, inhibiting earthquake activity. The
force F (retrievable from the torque given by Madden and
Speth (1995)) represents a time- and space-varying com-
ponent to the stress field affecting subduction zone faults,
since F itself varies with latitude and with time according
to the MJO. However, a more detailed model is clearly
needed.
4 Conclusions
The USGS data set on earthquake intensity carries global
activity information on a daily basis covering several
decades. A global view of this problem has not appeared
much in the literature. If one tabulates the earthquake data
sets using a global latitude/longitude grid on a daily basis
and casts it using a spherical harmonic representation of a
finite sum of waves, we find that the summed vector
spectral amplitudes show a potentially important low fre-
quency oscillation in time that is clearly evident in 32 years
from the use of daily data sets. A prominent low frequency
time scale of around 40 days is evident in the power
spectral analysis. This is illustrated here from the distri-
bution and time variability of the spectral amplitudes of the
global earthquake data sets.
We have also shown that earthquake activity on the
western rim of the Pacific plate moves alternately clock-
wise then counterclockwise along the rim with a time scale
of 20–60 days. The pendulum-like swing has a spatial
extent of roughly 10,000 km. This is a related major
finding of this paper. This happens to be the same time
scale found in the atmosphere and ocean called the MJO,
where the wind-induced mountain torques reverse direc-
tion, and the length of day decreases and increases. An
analogy to the atmospheric cloud elements of the MJO is
drawn here for the earthquake cycle and its quiescent
phase. This important space-time feature possibly suggests
for the prediction of a space-time earthquake envelope to
infer periods of activity or quiescence. The activity of
individual earthquakes along given fault systems is not the
goal of this study.
The MJO is a much referenced (Madden and Julian
1971, 1972; Krishnamurti et al. 1992; Wang 2006) tropical
wave. It has been cited in reference to the birth and demise
of the El-Nino time scale (4–6 years) phenomena (We-
ickmann 1991). The passage of this MJO wave clearly
modulates the amplitude of the monsoon westerlies and the
trade wind easterlies (Waliser 2006). This passage of MJO
waves over the western Pacific Ocean modulates typhoon
tracks (Chan 2000) and tropical cyclone activity (Hall et al.
2001). More recently, we have mapped the passage of this
wave in the sub-surface oceans (Krishnamurti et al. 2007).
Atmospheric scientists have carried out extensive studies
on estimating mountain torques over the globe (Lott et al.
2001). The 1–2 weeklong persistent MJO winds with
amplitude of the order of 3–5 m s-1 at the earth’s surface
can communicate such torques to the mountain chains of
Asia. Those data sets of the mountain torques do carry
pronounced signals on the MJO time scale (Newton 1971;
Dickey et al. 1991; Iskenderian and Salstein 1998). Future
research on the global scale earthquake amplitude variation
and the relationships among the pendulum-like swings of
the earthquake frequencies on the western rim of the
Pacific plate to the atmosphere-ocean phenomena on those
same scales would be very worthwhile.
Acknowledgments We acknowledge NSF grants ATM-0419618,
OCE-242535 and OCE-0424227.
References
Aki K (1996) Scale dependence in earthquake phenomena and its
relevance to earthquake prediction. Proc Natl Acad Sci 93:3740–
7347
Chan JCL (2000) Tropical cyclone activity over the western North
Pacific associated with El Nino and La Nina events. J Climate
13:997–1004
Dickey J, Ghil M, Marcus S (1991) Extratropical aspects of the 40–
50 day oscillation in length-of-day and atmospheric angular
momentum. J Geophys Res 96:22643–22658
Freed A (2005) Earthquake triggering by static, dynamic, and
postseismic stress transfer. Annu Rev Earth Planet Sci 33:335–
368
Gret A, Snieder R, Scaled J (2006) Time-lapse monitoring of rock
properties with coda wave interferometry. J Geophys Res 111.
doi:10.1029/2004JB003354
Hall JD, Matthewsb AJ, Karoly DJ (2001) The modulation of tropical
cyclone activity in the Australian region by the Madden-Julian
Oscillation. Mon Weather Rev 129:2970–2982
Iskenderian H, Salstein DA (1998) Regional sources of mountain
torque variability and high frequency fluctuations in atmospheric
angular momentum. Mon Weather Rev 126:1681–1694
Kanamori H (1981) In: Simpson DW, Richards P (eds) Earthquake
prediction an international review. American Geophysical Union,
Washington, DC
Knopoff L (1996) Earthquake prediction: the scientific challenge.
Proc Natl Acad Sci 93:3719–3720
Krishnamurti TN, Sinha MC, Krishnamurti R, Oosterhof D, Comeaux
J (1992) Angular momentum, length of day and monsoonal low
frequency mode. J Meteorol Soc Jpn 70:131–166
Krishnamurti TN, Chakraborty A, Krishnamurti R, Dewar WK,
Clayson CA (2007) Passage of intraseasonal waves in the sub-
surface oceans. Geophys Res Lett 34:L14712. doi:10.1029/
2007GL030,496
Lott F, Robertson AW, Ghil M (2001) Mountain torques and
atmospheric oscillations. Geophys Res Lett 28:1207–1210
Madden RA, Julian PR (1971) Detection of a 40–50 day oscillation in
the zonal wind in the tropical pacific. J Atmos Sci 28:702–708
Madden RA, Julian PR (1972) Description of global-scale circulation
cells in the tropics with a 40–50 day period. J Atmos Sci 29:
1109–1123
82 T. N. Krishnamurti et al.
123
Madden RA, Speth P (1995) Estimates of atmospheric angular
momentum, friction, and mountain torques during 1987–1988.
J Atmos Sci 52:3681–3694
Nakazawa T (1988) Tropical super cloud clusters within intraseasonal
variations over the western pacific. J Meteorol Soc Jpn 66:823–
839
Namias J (1988) Similarity of anomalous sea level pressure fields
during the July 1986 and September 1987 southern California
quakes—accidental or indicative & quest. Geophys Res Lett
15(4):350–352
Namias J (1989) Summer earthquakes in southern California related
to pressure patterns at sea level and aloft. J Geophys Res
94(B12):17671–17679
Newton CW (1971) Mountain torques in the global angular momen-
tum balance. J Atmos Sci 28:623–628
Sykes LR (1996) Intermediate- and long-term earthquake prediction.
Proc Natl Acad Sci 93:3732–3739
Waliser DE (2006) Intraseasonal variability. In: Wang B (ed) The
asian monsoon. Springer, Heidelberg, pp 203–257
Wang B (Ed) (2006) The asian monsoon. Springer, Heidelberg
Weickmann KM (1991) El Nino/Southern Oscillation and Madden-
Julian (30–60 day) oscillations during 1981–1982. J Geophy Res
96:3187–3195
Space-time structures of earthquakes 83
123