Atmospheric pressure changes caused by the 2011 Off the Pacific Coast of Tohoku, Japan earthquake (Mw = 9.0) are investigated. Sensitive microbarographs in and around Japan recorded unequivocal signals associated with the tsunami. We identify them as atmospheric boundary waves excited by the uplift and subsidence of the ocean surface, on the basis of the waveform characteristics as well as similarity with the data from ocean-bottom pressure gauges. Potential usefulness of an observation network of atmospheric pressure is discussed regarding the improvement of the tsunami warning system.
 It is well known that sudden and strong vertical ground displacements caused by earthquakes produce infrasound waves in the atmosphere [Cook, 1971]. Mikumo  modeled long-period acoustic-gravity waves in the atmosphere caused by the Alaskan earthquake of March 27, 1964 to be observed at distant stations. The same excitation mechanism applies also to submarine earthquakes through uplift and subsidence of ocean surface. Mikumo et al.  reported observations of the acoustic-gravity waves radiated from the tsunami source region during the 2004 Sumatra-Andaman earthquake. Le Pichon et al.  detected infrasound radiation from the epicenter and nearby land mass during the shaking and from shorelines during the tsunami arrival.
 The disastrous earthquake (Mw = 9.0) on March 11, 2011 off the Pacific coast of Japan caused large tsunami, which hit vast Pacific coastal areas of the north–eastern part of Honshu Island (Tohoku region). The tsunami source model [Fujii et al., 2011] indicates that a vast area of the ocean surface uplifted and subsided by more than 10 m during the tsunami generation. This event has provided a rare opportunity for investigating long-period atmospheric signals excited by the tsunami generation.
 In this paper, we explore barograph data obtained at a domestic gravity station in the Tohoku region as well as IMS (International Monitoring System for Comprehensive nuclear Test-Ban Treaty (CTBT) verification regime) stations in Far-East Asia in search for atmospheric signals from the tsunami source region. Owing to the size of the event and the short distances to the source, these stations are expected to yield atmospheric signals with the highest signal-to-noise ratio ever obtained.
 At Mizusawa VLBI Observatory, National Astronomical Observatory of Japan, atmospheric pressure was recorded using a digital barometer F-452 manufactured by Yokogawa-Weathac for correction of the atmospheric loading effect on superconducting gravimetry (Dr. Tamura, personal communication, 2011). The resolution of recordings is 0.1 Pa and the sampling interval is 1 second. The atmospheric pressure data at Mizusawa, shown in Figure 2, indicates short period undulations between 05:46 and 05:52 which was induced by the passing of large amplitude seismic waves [Watada et al., 2006]. Following them, a striking, long period wave-train is readily visible in the atmospheric pressure data. This is characterized by a gradual increase followed by a more rapid decrease with oscillatory changes superposed on it. By applying an autoregressive (AR) model for extraction of signals [Arai et al., 2009] and the Akaike Information Criterion (AIC) for picking the on-set [e.g., Sleeman and van Eck, 1999], the on-set time and the peak-to-peak amplitude of the wave train are estimated to be 05:52 and 64 Pa, respectively.
 Similar changes in the atmospheric pressure were also recorded at the following IMS stations; Isumi (IS30), Petropavlovsk-Kamchatskiy (IS44) and Ussuriysk (IS45) (see Figure 1 for their locations). Each station is composed of an array of microbarographs with an aperture of about 2 km, and an array element is equipped with a sensor having a flat frequency response in the range DC - 40 Hz [Le Pichon et al., 2010]. IMS stations provide two kinds of data, one is the band pass filtered output and the other is the absolute pressure output (raw data). Although band pass filtered data are usually used for CTBT's monitoring purpose, here we used absolute pressure data in this study. The sampling rate of the data is 20 Hz. Figure 3a shows six-channel records at Isumi (IS30). From 05:48 to 05:56 and from 06:16 to 06:22, pressure changes induced by the seismic ground motions of the main shock and an aftershock are visible, respectively. Between these co-seismic waves, a similar shaped long period wave train can be recognized from 06:02 to 06:15 with peak-to-peak amplitude ranging between 21 and 28 Pa. Figures 3b and 3c show the records from Petropavlovsk-Kamchatskiy (IS44) and Ussuriysk (IS45), respectively. Similar wave trains with good coherence are also observed at these stations. Table 1 summarizes the arrival times and amplitudes of the observed signals.
Table 1. Parameters of the Atmospheric Signals Observed at the Four Stations
 At each station the back-azimuth of the signals is measured by applying the F-K analysis to the array. Considering the long wave-lengths of the observed atmospheric pressure signals, the aperture of each IMS station is too small to yield accurate results. Nevertheless, the estimates of the back azimuths (Table 1) are roughly consistent with the direction of the tsunami source region as measured from each station.
 Using the origin time (05:46:18) of the earthquake determined by Japan Meteorological Agency (JMA) and assuming that these waves were generated in the tsunami source region at the origin time of the event, the apparent group velocity was calculated for each station. The calculated group velocity falls within the range of 282-327 ms−1.
 The attenuation relation of atmospheric pressure changes is shown in Figure 4. The amplitude is proportional to r−1/2, where r is the distance between the tsunami source region and each station, although the amplitude appears to depend also on the direction.
 These facts strongly suggest that the observed atmospheric wave trains were generated in the tsunami source region and propagated to each station as surface waves with the speed of about 300 ms−1.
3. Interpretation of the Extracted Characteristics of the Observed Atmospheric Waves
 Here we show that the observed atmospheric pressure changes can be consistently interpreted as the propagation of atmospheric boundary waves excited by the co-seismic uplift and subsidence of the ocean surface.
 In a compressible fluid with gravitational stratification, propagating waves are classified into two families; acoustic waves and gravity waves. In addition to these, there is a special branch known as the boundary wave or Lamb wave, which propagates along the bottom boundary of the atmosphere [e.g., Watada, 2009]. This wave shows little dispersion, and the group velocity is about 300 ms−1 [e.g., Watada and Kanamori, 2010]. Phase velocities of three kind of atmospheric waves and the energy density distribution of boundary wave are shown in Figure 5. Because the boundary wave propagates along the surface of the Earth, its amplitude is inversely proportional to the square root of distance.
 Sudden vertical deformation of the sea surface during the tsunami generation produces instant changes of the atmospheric pressure in the source region (Figure 6a). The resultant pressure changes will have a spatial dependence similar to the deformed profile of the sea surface in the tsunami source area (Figure 6b). If this atmospheric disturbance has a period longer than the local acoustic cutoff period (∼300 s), it propagates horizontally as boundary waves with little dispersion. Then, the width of the tsunami source region in the radial direction gives the apparent wavelength of the barometric signal. The great Tohoku-Oki earthquake was a shallow dipping thrust with a strike parallel to the Japan trench and is interpreted as an interplate earthquake associated with the subduction of the Pacific plate. Because the fault was longer along the trench axis, the wavelength is shorter in the dip direction and longer in the strike direction. This is consistent with the observed wavelength (Figures 2 and 3), considering that Mizusawa and IS45 are approximately in the dip direction, whereas IS30 and IS44 are in the strike direction.
 On the other hand, propagating gravity waves or acoustic waves in high altitude more than 90 km associated with the Tohoku-Oki earthquake were reported [e.g., Tsugawa et al., 2011]. Atmospheric wave discussed in this paper is a boundary wave, in other words, an evanescent wave (see Figure 5), and therefore, the atmospheric pressure changes focused on here may not be easily observed in high altitude unless it is excited strongly. So it is not inconsistent that observed waves in high altitude had different characteristics from our observations.
 Another evidence for the common origin of the atmospheric waves and the tsunami is provided by comparison with the data of ocean-bottom pressure gauges. The two ocean-bottom pressure gauges near the tsunami source area deployed by The University of Tokyo recorded significant tsunami waves [Maeda et al., 2011]. The gauges are located about 45 and 75 km off the Pacific coast of Tohoku and 1013 and 1618 m in depth, respectively. Tsunami records obtained by them indicate a characteristic sea level changes following the earthquake. The sea level rose gradually from 0 to 2 m in the first 700 s and the sea level went suddenly up to 3 m within an approximate duration of 150 s, resulting in a total of 5 m of sea surface elevation. We point out similarity between these waveforms and the atmospheric signals recorded at Mizusawa and IS45 (Figures 2 and 3c). Because the tsunami wave is well described as a non-dispersive long-wave in the deep ocean where the two pressure gauges are located, the sea level changes observed by them reflect the original shape of the tsunami, only distorted by the local propagation speed proportional to (gh)1/2,where g is local gravity and h is sea depth. Similarly, atmospheric disturbances with long wavelength caused by the ocean surface displacements during tsunami generation must have traveled with little distortion to the barometer stations in the dip direction.
 On the other hand, the ocean-bottom pressure gauges deployed by Japan Agency for Marine-Earth Science and Technology (JAMSTEC) are located off the Pacific coast of Hokkaido and therefore in the strike direction. They also recorded tsunami signals [Maeda et al., 2011], but the wavelength is longer than that off the Pacific coast of Tohoku. This is also consistent with what are recorded at IS30 and IS44, the barometer stations in the strike direction.
 The atmospheric pressure change excited by uplift or subsidence of the sea surface (P) can be approximately given by P = ρcw, if the ratio of the time constant of co-seismic vertical deformation to the local buoyancy period (∼340 s) is less than 0.3, and if the phase velocity of the expanding deformation is much faster than the sound velocity [Watada et al., 2006; Watada, 2009]; where ρ is ambient air density near the sea surface, c is air sound velocity near the sea surface and w is the corresponding particle velocity of the vertical deformation of the sea surface. The w is estimated as the observed tsunami wave height (5 m) at ocean-bottom pressure gauges near the tsunami source region divided by the time constant (30 s) of co-seismic vertical deformation [Fujii et al., 2011]. Using ρ = 1.3 kgm−3, c = 330 ms−1, the maximum amplitude at the source region can be roughly calculated as 70 Pa. This estimate is consistent with the amplitude observed at Mizusawa, which is located 260 km from the maximum slip area investigated by Fujii et al. . If the source is rectangular shape, the tsunami energy in the direction of the major axis decreases much faster than the energy in the direction of the minor axis [Kajiura, 1970]. The directivity of the amplitude of atmospheric waves is explained by the same mechanism. The observed amplitude at IS45 is comparable to that at IS30 in spite of the much longer distance because of the directivity of energy radiation. Amplitude at other stations is also explained by taking the geometrical decay into account (Figure 4).
 Given these features of the observed wave trains and their physical interpretations, we conclude that the signals observed at the barograph stations are the atmospheric boundary waves excited by the sea surface deformation in the tsunami source region and traveled with little dispersion.
4. Discussion and Conclusion
 It is noted that the atmospheric boundary waves, once excited, travel in the atmosphere significantly faster than the tsunami waves in the ocean. In addition, they retain the original shape of the tsunami, because they are little dispersive.
 When JMA issues a tsunami early warning to the public, JMA forecasts initially the tsunami height based on the hypocenter location and the magnitude of the earthquake without using the information about the tsunami source area and actual initial height in the source region [Kamigaichi, 2011]. Therefore, tsunami warnings do not reflect the real tsunami height until the actual tsunami height is measured by various types of tsunami gauges along or near the coast. Establishment of a network of infrasound observation along the coast line facing the subduction zone would improve the tsunami warning system, because it would provide information on the tsunami source. Feasibility study on applying our scientific discoveries to the tsunami warning system shall be done in the future.
 We wish to thank Y. Tamura for providing the barograph data observed at Mizusawa VLBI Observatory, National Astronomical Observatory of Japan.
 The Editor wishes to thank two anonymous reviewers for their assistance evaluating this paper.