Background atmospheric acoustic waves
from 0.01 to 0.1 Hz
K. Nishida(1), Y. Fukao (2), S. Watada (1), N. Kobayashi(3)
(1)Earthquake Research Inst., Univ. of Tokyo, Japapn
(2)IFREE, JAMSTEC, Japan
(3)Earth and Planetary Sciences, Tokyo Inst. of Tech., Japan
Abstract
Recently some groups reported Earth’s background free oscillations even
on seismically quiet days. Statistical features of them and annual variations
of their amplitudes suggest that atmospheric disturbance is the most probable excitation source for this phenomenon. If the atmospheric excitation
mechanism is effective, atmospheric acoustic free oscillations must be also
excited persistently. In fact there is evidence of acoustic resonance between
seismic free oscillations and the atmospheric acoustic free oscillations at
around 3.7 and 4.4 mHz but there is no direct observation of them. In attempt to detect the long period acoustic waves, we installed a cross array
of barometers in a 10 km–wide University Forest in Central Honshu from
2002 to 2004. The array has 28 micro–barometers employing quartz crystal resonator technology with station spacing of about 500 m. We analyzed
1-second continuous sampling records in a time period. Acoustic waves
traveled from around northwest direction from 0.01 to 0.1 Hz with phase
velocity of about 400 m/s at 0.1 Hz and about 800m/s at 0.01. These waves
are often associated with mountain region. Our array size is still not large
enough to detect the expected acoustic free oscillations at around 3.7 and
4.4 mHz. For the detection, we have developed more precision barometers
and network data collection system for expansion of the array. Now we have
started test observation at 8 stations.
1
Introduction
It has long been believed that only large earthquakes excite free oscillations of the
solid Earth. Recently, however, a few groups reported Earth’s background free
oscillations even on seismically quiet days [15] [21] [11]. The excited modes are
1
almost exclusively fundamental spheroidal modes, and they fluctuate persistently
in little correlation with their neighboring modes [17]. These features suggest that
the background free oscillations are excited incessantly by random disturbances
globally distributed near the Earth’ surface [17]. The intensities of these modes
clearly show annual variations with a peak in July [18]. The observed amplitudes of some modes are anomalously large relative to the adjacent modes [18].
These are the modes that are theoretically expected to be coupled with the acoustic modes of the atmospheric free oscillations [23]. All of these features suggest
that atmospheric disturbance is one of the most likely excitation sources of this
phenomenon [17][18].
The aim of our installation is to find barometric evidence of background atmospheric acoustic free oscillations that must be excited persistently if the atmospheric excitation mechanism is effective. However, all of the past studies have
been based on seismic observations and there are no direct comparable barometric
observations. With the above aim we started a cross array observation of barometers.
2
An array observation from 2002 to 2004
2.1 Data and Instruments
The barometer system used in this study is composed of a pressure transducer, a
data logger with a compact flash card, and a Quad-Disc static pressure probe designed to reduce undesired effects of dynamic pressure fluctuations [20]. High resolution observation of absolute atmospheric pressure is required to detect acoustic
waves often hidden in the atmospheric turbulence of higher amplitudes. Low electric power consumption is also an important requirement because no power supply
is available in our observation. These requirements are satisfied by an absolute
pressure sensor employing quartz crystal resonator technology [16].
For a sampling interval of 1 sec, the practical resolution is then limited roughly
to 0.1 Pa. The 1–sec continuous sampling records of pressure-related count numbers and temperature-related count numbers are written in a compact flash card.
Upon recovery of the flash cards from the array, the pressure-related count numbers are converted into the absolute values of pressure compensated by the corresponding temperature-related count numbers.
We installed a cross array of these barometers in a 10 km–wide forest of the
University of Tokyo in Chiba, which is expected to reduce dynamic pressure due
to winds especially in a trough. The forest is located in the southern part of the
Boso Peninsula, which is about 100 km southeast of Tokyo (Fig. 1: left). The
Boso Peninsula has mild coastal weather with warm temperatures (the annual
2
mean temperature is around 14◦ C) and plenty of rainfall throughout a whole year
(the annual precipitation is around 2000 mm) although their climate differs with
changes in distance from the coast and in elevation. The forest belongs mostly to
a warm-temperate, broad-leaved evergreen forest zone. The array has 28 micro–
barometers with a station spacing of about 500 m. The left figure shows the locations of barometers used in this study. The cross array is composed of two linear
arrays, the Goudai array and the Ippaimizu array. The Goudai array was installed
in March 2002, which consists of 19 barometers in the NWN-SES direction. The
Ippaimizu array was installed in September 2002, that has 7 barometers in the
ENE-WSW direction. We also installed two barometers at Sengoku station in
March 2002. In the present paper we use the records from the beginning to May
2004.
138û
37û
139û
140û
36û
36û
35û
35û
34û
138û
139û
140û
Figure 1: Left: location map of 28 barometers of the cross array. The array is
composed of two linear arrays: (1) The Goudai array and (2) The Ippaimizu array.
We also installed two barometers at Sengoku. Right: location map of 8 stations
of a new observation. At three stations of broad band seismometers (circles) we
installed new barometers.
2.2 Frequency–slowness spectra of background acoustic waves
from 0.01 to 0.1 Hz
In order to determine temporal variations of their incident azimuths and amplitudes, we calculate two-dimensional frequency–slowness spectra [16], using the
3
141û
37û
34û
141û
Goudai array and Ippaimizu array. Fig. 2 and 3 shows resultant temporal variations of 15 days average from April 2002 to May 2004. The left figure shows
integration of frequency–slowness spectra from 0.02 to 0.03 Hz, and the right one
shows that from 0.04 to 0.05 Hz. Most spectra show background acoustic waves
traveling from northwest or west. The difference in spectral sharpness before
and after 255/2002 can be explained by the difference in array response functions before and after the installation (15/09/2002) of the Ippaimizu array. In a
time period of weak amplitudes of background acoustic waves from 140/2003 to
240/2003, we can also observed background acoustic waves traveling from southeast. The spectral maximum indicated by an open circle in each diagram does
not show a significant temporal variation of incident angle of the acoustic waves
within the error of slowness vector determination which is quite different before
and after 255/2002. We calculate the rms amplitude of the acoustic wave signals
[16]. This rms amplitude shows clearly an annual variation as in lower figures,
with the minima around 3 × 10−3 Pa in summer and the maxima around 7 × 10−3
Pa in winter.
2.3 Dispersion curves of the background atmospheric waves
We have not detected acoustic waves below 0.02 Hz where the array response
function is too broad in the slowness domain to identify their possible existence.
However, with a strong assumption of unidirectional propagation of stochastic
stationary waves [16], we could obtain a dispersion curve even below 0.02 Hz.
Fig. 4 plots the resultant phase velocity of the observed atmospheric waves
with its solution error as a function of frequency. The phase velocity curves of
gravity waves and microbaroms do not show significant dispersions, while the
phase velocity curve of long-period acoustic waves exhibits a clear normal dispersion: the phase velocity is about 400 m/s at about 0.1 Hz and reaches about 800
m/s at 0.01 Hz.
The observed acoustic waves could be either internal waves or boundary waves
trapped near the Earth’s surface known as Lamb waves. Lamb waves are hydrostatically balanced in the vertical direction and propagates in horizontal direction
around the Earth’s surface. The phase speed of Lamb wave is known to be around
300 m/s [13]. The phase velocities of all the observed acoustic waves are faster
than 350 m/s, so they are unlikely to be Lamb waves. Hereafter we regard the
observed acoustic waves as internal waves.
Phase velocities of the observed acoustic waves at frequencies from 0.01 to
0.1 Hz are faster than 400 m/s so that they are most likely to be refracted in the
stratopause (the boundary between the stratosphere and the mesosphere) or the
thermosphere [5]. The dispersion characteristics of long-period acoustic waves
may be explained by the frequency dependence of incident angle. Higher-frequency
4
From 0.02 to 0.03 Hz
× 10 [Pa ]
-4
4
2
97.5
-4
4
112.5
-2
-4
4
127.5
× 10-3 Slowness [s/m]
1.2
1.8
1.5
1
1.7
1
3.2
2.5
3
3.5
2
232.5
2.3
2.6
2.2
2.4
2.1
0
457.5
2.5
2
352.5
2.5
472.5
× 10-4 [Pa2]
1.6
577.5
1.5
697.5
6
2
2
2
1.1
1
1.5
1.7
3.5
1.6
712.5
3
1.3
1.8
2
1.6
1.4
1.2
1.2
1
1.5
1.1
1
2.4
4.5
2
2.4
3.5
1.8
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
2
1.8
262.5
1.6
1.7
1.5
1.6
1.4
607.5
1.8
2.2
727.5
3
2
1.6
4
847.5
3
382.5
2.5
3
1.4
2.5
1.2
1.4
1.5
1.5
2
1
1.2
1
1
3.5
1.4
2.6
4
3
502.5
622.5
1.3
2.5
1.2
2
1.1
2
1.6
2.4
742.5
3.5
2.2
2
3
2.5
1.8
1.5
1.3
1.6
2
1.4
1.2
1.5
1
1.4
1.5
4
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.3
3.5
1.8
1.8
-4
157.5
2
1.9
0
1.8
1.7
-2
1.6
-4
1.5
4
1.9
2
277.5
172.5
1.8
292.5
1.6
-2
1.5
-4
1.4
4
-4
1.9
1.8
1.7
1.6
1.5
1.4
1.3
1.2
4
2.2
2
187.5
0
-2
2
202.5
2
3
412.5
427.5
1.5
1
1.3
1.5
1
0.8
1.2
1
3
2.3
2.6
532.5
-2
0
2
4
3.5
1.9
1.8
2
1.8
1.8
1.6
1.5
3.5
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
3
1.5
1.5
1
3
2.4
442.5
2.2
3
547.5
562.5
1.4
-4
-2
0
2
4
-4
-2
667.5
0
2
4
2.5
2.5
3.5
787.5
3
2.5
2
2
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.6
1
4
4
2
2
1.5
2
4.5
772.5
2
2
2.5
0
2.4
2.2
1.8
-2
652.5
2
2
-4
2
2.1
2.5
2.5
1.2
-4
2
2.5
1.4
2.2
2
-4
1.6
1.2
3
3
1.4
0
3
1.4
2.2
1.6
-2
-2
3.5
757.5
2.4
1.8
0
1.7
2
2.6
3.5
322.5
637.5
1.6
2.5
2.8
4
307.5
517.5
1.5
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
1.7
0
397.5
2.1
2
1.9
1.8
1.7
1.6
1.5
1.4
862.5
2
-4
2
3.5
2.5
1.8
1.7
1.8
487.5
3.5
2
2.5
1.9
4
2.2
832.5
1.4
2
367.5
2.5
1.2
2
247.5
3
3
1.5
1.5
3.5
4
1.3
592.5
2.5
4
817.5
5
1.4
3
2
× 10-4 [Pa2]
7
2.2
1.9
-2
3
× 10-4 [Pa2]
1.5
1.9
142.5
337.5
2.4
2.8
2
4
2
1.9
1.6
2.1
-4
3.5
2.2
2.2
-2
× 10-4 [Pa2]
2
1.4
217.5
2.1
2.3
0
-4
2.3
1.8
3
0
× 10 [Pa ]
2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
2
-2
2
-4
2.2
0
2
× 10 [Pa ]
2
-2
1.5
1
1
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
682.5
-4
1.5
0
2
4
3
802.5
2.5
2
1.5
1
-4
-2
0
2
4
× 10-3 Slowness [s/m]
× 10-3 [Pa]
20
10
Days from 1/1 2003
0
120
180
240
300
360
420
480
540
600
660
720
780
840
Figure 2: Temporal variation of 15 days average from April 2002 to May 2004.
The left figure shows integration of frequency–slowness spectra from 0.02 to 0.03
Hz. White open circles indicate a phase velocity
of about 500 m/s for these waves.
5
Temporal variation of the amplitude of acoustic waves with the slowness vector
given by small open circles in upper figure.
4
From 0.04 to 0.05 Hz
× 10
-4
4
× 10
2
-4
[Pa ]
× 10
-4
[Pa ]
× 10- 4 [Pa2]
-2
0.2
0.3
0.3
0.3
0.19
-4
0.15
0.28
0.25
0.25
0.18
4
0.6
0.42
0.4
0.38
0.36
0.34
0.32
0.3
0.28
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.7
0.23
0.8
217.5
0
2
112.5
0.55
232.5
0.5
0.45
-2
0.4
-4
0.35
4
0.44
-4
0.32
0.38
0.36
0.34
0.32
0.3
0.28
0.26
0.24
4
0.36
0.24
127.5
0.42
0.38
0.36
-2
× 10- 3 Slowness [s/m]
247.5
0.4
0
2
0.5
457.5
577.5
0.45
0.45
0.34
0.23
0.22
0.4
0.21
0.35
0.2
697.5
0.4
0
2
337.5
0.36
0.3
0.5
× 10- 4 [Pa2]
0.32
0.35
0.55
× 10- 4 [Pa2]
0.25
97.5
0.38
[Pa2]
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
2
0.4
2
0.34
142.5
0.34
0
-2
-4
262.5
0.35
352.5
367.5
0.22
0.3
0.21
0.28
0.2
0.26
0.19
0.24
0.18
0.8
592.5
0.6
0.22
0.5
0.9
487.5
712.5
0.7
0.21
1.4
817.5
1
0.8
0.6
0.4
0.2
0.34
832.5
-4
0.24
0.3
0.29
0.28
0.27
0.26
0.25
0.24
0.23
4
0.27
0.34
2
0.36
157.5
0.34
0.3
0.28
-2
2
277.5
0.32
0
0.26
172.5
0.26
292.5
382.5
0.3
0.5
0.28
0.4
0.26
0.4
0.2
0.3
0.19
0.3
0.24
0.2
0.18
0.2
0.22
0.3
0.4
0.7
607.5
0.28
0.35
727.5
0.6
0.7
0.26
0.6
0.24
0.5
0.22
0.4
0.2
0.2
0.2
0.65
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.22
0.4
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
502.5
1
847.5
0.3
0.24
0.28
-2
0.23
0.26
-4
0.22
4
0.25
0.24
0.23
0.22
0.21
0.2
0.19
0.18
2
0.6
0.4
0.25
622.5
0.35
742.5
0.3
0.19
0.18
0.25
0.17
0.2
0.4
0.3
0.2
0
-2
-4
4
2
397.5
0.7
412.5
0.26
517.5
0.32
0.3
0.28
0.26
0.24
0.22
0.2
0.18
202.5
0
-2
-4
-4 -2
0
2
4
307.5
0.2
0.2
0.32
862.5
0.4
0.18
0.3
0.16
0.22
0.2
0.14
0.2
0.5
0.4
532.5
0.28
0.26
0.24
0.22
0.2
0.25
0.7
0.22
0.45
0.3
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.7
0.36
442.5
562.5
0.3
0.4
0.28
0.3
0.26
0.2
4
0.24
-4 -2
0
2
4
-4 -2
0
2
4
0.5
0.4
667.5
0.21
0.32
0.5
0.7
0.6
0.2
0.34
2
0.8
0.3
0.3
0.6
2
772.5
0.35
0.3
547.5
0
0.9
0.4
652.5
0.24
427.5
757.5
0.24
0.35
0.3
0.6
0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.26
0.25
0.4
0
0.28
0.22
0.45
0.5
-4 -2
637.5
0.24
0.5
0.35
0.6
322.5
0.3
0.6
0.4
187.5
0.8
0.5
0.21
0.8
0.32
0.25
0
0.32
0.6
-4 -2
4
1.2
0.3
0.23
0.32
472.5
× 10- 4 [Pa2]
0.4
0.3
0.7
787.5
0.6
0.2
0.35
0.5
0.19
0.3
0.4
0.18
0.25
0.3
0.17
0.2
0.2
0.255
0.25
0.245
0.24
0.235
0.23
0.225
0.22
0.4
682.5
0.35
0.6
802.5
0.5
0.3
0.4
0.25
0.3
0.2
-4 -2
0
2
4
0.2
-4 -2
0
2
4
× 10- 3 Slowness [s/m]
× 10- 3 [Pa]
10
Days from 1/1 2003
0
120
180
240
300
360
420
480
540
600
660
720
780
840
Figure 3: Temporal variation of 15 days average from April 2002 to May 2004.
The left figure shows integration of frequency–slowness spectra from 0.04 to 0.05
Hz. White open circles indicate a phase velocity
of about 500 m/s for these waves.
6
Temporal variation of the amplitude of acoustic waves with the slowness vector
given by small open circles in upper figure.
4
Phase velocity [m/s]
104
Long period
acoustic waves
103
Internal gravity waves
Microbaroms
102
101
10-4
10-3
10-2
10-1
100
Frequency [Hz]
Figure 4: Measured phase velocity with its solution error as a function of frequency from September 2003 to May 2003.
acoustic waves are radiated with lower angles from the ground and bounce in the
stratopause to reach stations with lower angles and hence with lower horizontal
phase velocities. On the other hand, lower-frequency acoustic waves are radiated
with higher angles from the ground and undergone steep reflection in the thermosphere to reach stations with higher angles and hence with higher phase velocities.
When a source near the Earth’s surface radiates internal acoustic waves refracted in the stratopause or the thermosphere, they cannot reach the Earth’s surface over a certain distance range corresponding to the shadow zone. The zone
typically starts about 50 ∼ 100 km from the source and extends out to about 175
∼ 200 km [5] [6]. In regions at middle and high latitudes, especially in winter,
acoustic waves can travel eastward even in the shadow zone because tropospheric
jet streams refract the acoustic waves in the troposphere [4]. However their horizontal apparent phase velocity of about 330 m/s [5] would be too slow to explain
the phase velocities of the observed acoustic waves from 0.01 to 0.1 Hz in terms
of the tropospheric refraction. We suggest that the excitation sources are either
more than about 200 km far away from the array or within about 50 km if they are
located near the Earth’s surface.
2.4 Possible excitation mechanisms of the background atmospheric acoustic waves from 0.01 to 0.1 Hz
We discuss two possible excitation mechanisms of the observed acoustic waves
from 0.01 to 0.1 Hz. The first mechanism is the excitation by severe weather
[8], which has been proposed through the two kinds of observations. One is the
7
observation of infrasonic waves in a frequency range from 0.03 to 0.07 Hz with
amplitudes of about 0.05 Pa recorded on ground barometers in a stormy period
[7]. Another one is the observation of acoustic waves around 3.7 and 4.4 mHz
detected as ionospheric waves by ground-based sounders associated with severe
convective storms [9]. Georges (1973) suggested that both waves are different
manifestations in different parts of the acoustic spectrum of the same emission
mechanism. With this mechanism significant temporal changes of incident azimuths of acoustic waves in accordance with the motion of storm systems could
be anticipated, yet our observation does not show such changes. We also find little correlation between the observed acoustic amplitudes and the storm activities.
Severe weather is unlikely to be a dominant source for the long-period acoustic
waves we observed.
The second mechanism is the aerodynamic excitation by atmospheric turbulence in mountain regions [1]. Turbulence on a curved boundary (mountain regions) excites a dipole field of acoustic waves [3], a mechanism more effective
than a quadrapole field exited by turbulence on a plane boundary [12]. The observed mountain-associated infrasonic waves have several common features [1]:
(1) wave periods from 30 to 70 s, (2) duration longer than 3 hours with amplitudes
of about 0.05 Pa at a distance of 400 km [2], (3) fixed azimuths of arrivals from
definite directions, (4) a strong tendency to be observed during winter months,
and (5) group velocity of 325 ∼ 425 m/s. These features are consistent with our
observations, suggesting that atmospheric disturbance in the mountain regions is
the most likely source of the observed acoustic waves. If this mechanism is dominant, excitation sources in the mountain regions are about 200 km apart from our
array in the west or northwest directions.
3
New observation for detection of background acoustic waves at 3.7 mHz and 4.4 mHz
We cannot detect background acoustic waves below 0.01 Hz using the above data
set. The array size is still not large enough to detect background atmospheric
acoustic waves possibly excited by the same sources as for the Earth’s background
free oscillations. In order to detect the oscillations, we expand the array (∼ 10 km)
to a larger scale (∼ 100 km) this year. Fig. 1 shows location map of stations of an
old array and those of a new array. We have installed barometers at three observatories, three stations of University and two stations of the University forest.For
this observation we made a new data acquisition system via internet by a Linux
box. The system time of the Linux box is synchronized with GPS. We show the
block diagram of data acquisition in Fig. 5. Data acquisition is now underway.
8
APDL
RS232C
GPS
NetCUBE
A pressure sensorN is programable
1/N counter
228 counter
A crystal resonator
pressure
output
RS232C
1boad Linux
fp
CPU
35 kHz
A crystal resonator
temperature
output
fT
147 kHz
228 counter
1/N counter
A reference oscillator
RS232C
Modem
106divider
OCXO
50 MHz + 0.1ppm
6V
LAN
+12V
0V
Phone line
DC/DC 2
12 - 6 V
0.1 sec
Interrupt
A pulse for
time correction
Reset
DC/DC 1
12 - 5 V
Figure 5: Block diagram of the observational system.
We also modify resolution of barometers (APDL in Fig.5 ). The pressure
sensor measures atmospheric pressure using a precision quarts crystal resonator
whose oscillation frequency of about 35 kHz is sensitive to pressure-induced
stress. The guaranteed sensor accuracy and resolution are 0.01 % of reading and
10−8 of the full scale range, respectively. Sensor pulses are sent into the 1/N
counter, where the gate opening and closing are synchronized with the onsets of
the incoming 0-th pulse and N -th pulse, respectively. The integration time T from
the gate opening to closing is measured by a high pression reference oscillator of
10 MHz in the case of past observation. The resonant period of a pressure sensor
is then given by T /N with a measurement error of less than δt. Then frequency
of the reference oscillator constrains resolution of this sensor. Now we can use
oven controlled crystal oscillator of 50 MHz because of availability of power consumption. This clock up make an improvement from resolution of 0.125 Pa to
that of 0.025 Pa. Fig. 6 shows comparison between data of an old barometer and
that of a new one. Left figure shows typical barographs. The upper barograph
of an old sensor shows digits of data, whereas the lower figure of a new sensor
shows clear waveform. Discretization error of an old sensor increases noise level,
which is shown by power spectra in the right figure. Thus, these figures show
improvement of resolution.
9
PSD [Pa2/Hz]
1000
100
10
1
0.1
Microbaroms
0.01
Noise lebel by discretization [0.125Pa]
0.001
0.01
0.1
1
Frequency [Hz]
Figure 6: Comparison between data of new system and data of old system.
4
Conclusions
We installed a cross array of about 30 barometers in the university forest. A special care of system designing was taken for accurate measurement of resonant
frequency of a pressure-sensitive quartz resonator. The one-year records of the
cross array were analyzed to calculate two-dimensional frequency–slowness spectra and to measure dispersion of atmospheric acoustic waves with an assumption
of stochastic stationary plane waves. The analyses showed background acoustic waves traveling from northwest with a frequency-dependent phase velocity of
400 m/s at 0.1 Hz and 800 m/s at 0.01 Hz, which are interpreted as internal acoustic waves refracted in the stratopause and the thermosphere from distant sources
more than 200 km away from the array. The observed features of infrasounds
are consistent with those of mountain-associated waves but we still did not detect background atmospheric acoustic waves at 3.7 mHz and 4.4 mHz. In order
to detect the background acoustic waves, we develop new barometers of higher
resolution. In this year we expand the array (∼ 10 km) to a larger scale (∼ 100
km) this, now we are collecting data.
Acknowledgments
We are grateful to Director Hirokazu Yamamoto and his colleagues of the University Forest in Chiba, University of Tokyo, for generously allowing us to use
many spots of observation in the forest and for kindly helping us to install and
maintain the array. Our thanks also go to a number of people at the ERI who
helped us analyzing seismic records. This work was supported by JSPS grant in
10
aid (Kiban-Kenkyu (B) No. 17340135).
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