Coseismic ionospheric disturbances (CIDs) associated with the 2011 Tohoku earthquake off the Pacific coast (Mw 9.0, Tohoku EQ) were examined using total electron content and seismic wave data. A faster CID propagated at ~3.0 km/s only in the west-southwest, while a slower CID propagated concentrically at 1.2 km/s or slower from the tsunami source area. Taking the propagation speed and oscillation cycle into account, the faster CID was associated with a Rayleigh wave, but the slower CID was associated with an acoustic or gravity wave. The north-south asymmetry of the CID associated with the Rayleigh wave suggests that the Rayleigh wave did not act as a point source of the acoustic wave because a point source propagating in all directions must produce symmetric CID in all directions. Therefore, a superimposed wave front of acoustic waves was excited by the Rayleigh wave and produced the north-south asymmetry of the faster CID due to the magnetic inclination effect, which is different from a well-known north-south asymmetry of CID excited at the epicenter. On the other hand, above and south of the tsunami source area, the CID with a period of 4 min was excited by a point source located at the tsunami source area because atmospheric waves propagating from a point source produce north-south asymmetry in the resulting CID.
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 The earthquake that occurred at 38.322°N, 142.369°E off the Pacific coast of northeastern Japan (Mw 9.0, Tohoku EQ) at 0546 UT on 11 March 2011 produced a massive tsunami. This earthquake also provided a scientific opportunity to investigate lithosphere-atmosphere-ionosphere coupling because many instruments had been installed and were monitoring the environment in Japan at the time of the earthquake. There were, for example, a dense network of Global Positioning System (GPS) receivers (the GPS Earth Observation Network, GEONET, ftp://terras.gsi.go.jp/) and a network of seismometers (F-net, http://www.fnet.bosai.go.jp/), operated by the Geographical Survey Institute of Japan and the National Research Institute for Earth Science and Disaster Prevention, respectively.
 The massive tsunami excited an acoustic wave that propagated to the thermosphere and then disturbed the ionosphere. After the acoustic wave reached the ionosphere, an ionospheric plasma density depletion induced by the tsunami (a “tsunamigenic ionospheric hole”) was produced over the tsunami source area of the Tohoku EQ and other huge earthquakes [Kakinami et al., 2012]. It is also well known that propagating tsunami excites gravity wave following the tsunami wave front [Occhipinti et al., 2008; Rolland et al., 2010]. Focusing on the Tohoku EQ, coseismic ionospheric disturbances (CIDs) associated with Rayleigh waves as well as 4-min monoperiodic atmospheric resonances and other-period atmospheric oscillations have been reported [Liu et al., 2011a; Tsugawa et al., 2011; Rolland et al., 2011; Kamogawa et al., 2012; Galvan et al., 2012]. Although previous studies have reported CIDs related to the Tohoku EQ, these studies did not investigate the north-south asymmetry in the ionospheric perturbations from this event.
 A CID associated with Rayleigh waves was reported after the 3 November 2002 Denali earthquake (Ms 7.9) [Ducic et al., 2003]. Because a Rayleigh surface wave propagates in all directions from the epicenter, CIDs excited by Rayleigh waves might be detected in any direction. However, as discussed later in this study, CIDs associated with Rayleigh waves propagated in only a specific direction after the Tohoku EQ. Although several simulations for the Tohoku EQ event have been done, the CID related to Rayleigh wave has not been discussed carefully so far [e.g., Matsumura et al., 2011]. Furthermore, a north-south asymmetry of the 4-min atmospheric resonance was found. This asymmetry has not yet been addressed and solved well. In this study, we investigated CIDs after the Tohoku EQ and attempted to discern the cause of the north-south asymmetry of the CIDs excited by the Rayleigh and other atmospheric waves.
2 Data Analysis
 The dual frequency radio signals (1575.42 and 1222.60 MHz) from the GPS are widely used for estimating the total electron content (TEC) between receivers and satellites [e.g., Liu et al., 1996; Kakinami et al., 2009]. In this study, we used data from GEONET with a 30-s time resolution. Assuming the largest contribution to TEC in the F-region, which peaks near 300 km, the subionospheric point (SIP) where the ray path pierced the ionosphere was calculated. Figures 1a and 1b show that TEC distribution band-pass filtered from 2.2 to 8 mHz at 0601 UT using satellites PRN 15 and 26, respectively. Frequencies of 2.2 and 8 mHz are acoustic cut-off frequency and half the Nyquist frequency given the sampling rate of 30 s, respectively [Dautermann et al., 2009]. Colors indicate TEC values in TEC unit (1 TECu = 1 × 1016 electron/m2). Two types of CIDs can be seen in Figures 1a and 1b: a faster CID propagating southwestward and a slower concentric CID. The wave front of the faster CID arrived at a distance of more than 1000 km from the epicenter at 0601 UT, whereas the slower CID arrived at about 400 km from the tsunami source area at 0601 UT.
 Figure 2a displays the distribution of the CID onset which was measured from the time of mainshock as observed by satellites PRN 15, 18, and 26. The SIPs were plotted at the place where the initial disturbances were observed. As shown in Figure 2a, the CID onsets show asymmetric distribution. The CID onset was about 1000 s at 500 km north of the tsunami source area, but it was about 700 s at 500 km west of the tsunami source area. This result suggests that different types of CID propagated in different directions. Figures 1 and 2a indicate that the faster CID only propagated west-southwestward, whereas the slower CID propagated in all directions from the tsunami source area. The intensity of the initial CID is shown in Figure 2b. In this figure, the detection of a negative initial disturbance is marked by the value set to 0, where TEC continually decreased owing to the tsunamigenic ionospheric hole. Around the tsunami source area, the initial CID was positive to the south but negative to the north [Kakinami et al., 2012]. However, at 300 km north of the center of the tsunami source area, the values were positive. This result suggests that the northern boundary of the tsunamigenic ionospheric hole was located there and that another clear perturbation occurred. South of the tsunami source area, the high-intensity region forms a parabola because of the magnetic field inclination, which was predicted by Otsuka et al. .
 Figure 3a shows a travel-time diagram of the vertical component of seismic waves observed by F-net around the mainshock of the Tohoku EQ. The intensities of the data were normalized by the maximum amplitude in a given time (0530–0610 UT) at each station. The waveforms were arranged according to the distance from the epicenter. Positive and negative values denote north and south of the epicenter, respectively. After the primary and secondary waves arrived, a Rayleigh wave with a large-amplitude vertical component was observed both north and south of the epicenter traveling about 3 km/s. Figure 3b displays travel-time diagrams of 10-min high-pass filtered TEC within ±2° of longitude from the center of the tsunami source area. Positive and negative directions denote north and south of the center of the tsunami source area, respectively. Periodic oscillations with a period of about 4 min can be seen above and south of the tsunami source area. The northern edge of the area with the 4-min oscillation approximately corresponds to the northern edge of the tsunamigenic ionospheric hole. In contrast to the south side of the tsunami source area, other longer-period oscillations were only detected at 200 km or farther on the north side of the center of the tsunami source region, i.e., outside the tsunamigenic ionospheric hole. The propagation velocity of the initial disturbance was about 1.2 km/s, and the subsequent CID showed a slower velocity of ~0.3 km/s. Figures 3c and 3d are travel-time diagrams of 10-min high-pass filtered TEC west-southwest (136°E, 35°N) of the epicenter within ±1° of latitude for satellites PRN 15 and 26, respectively. CID-related tsunami wave front is hardly detected near the tsunami source area probably because of the tsunamigenic ionospheric hole.
 In order to emphasize CID related to acoustic wave, 2.2- to 8-mHz band-pass filter was applied to the data shown in Figures 3b and 3c (Figure 4). Slowly propagating (~0.3 km/s) and longer-period CIDs seen in Figures 3b and 3d were eliminated. CIDs with a period of about 7–8 min are detected at 200 km or farther on the north side of the epicenter (Figure 4a). Velocities of the CIDs are about 0.6 km/s. Intensity of the CIDs are so much weaker than CIDs with 0.3 m/s that they are not clearly seen in Figure 3b. Figures 4b and 4c show that the 4-min oscillation exists in the west-southwest direction from the epicenter. Their results indicate that longer-period oscillations are superimposed on the 4-min oscillation.
 The 4-min oscillations are clearly visible in Figures 3 and 4. A slow CID traveling at 1.2 km/s was observed near the epicenter, but a fast CID appeared at a distance of 500 km at 0600 UT ahead of the slow CID. The fast CID is not clear near the epicenter. Another fast CID with a velocity similar to that of the initial CID followed. A similar phenomenon is apparent in Figure 3d. We emphasize that the fast CID is not observed northward from the tsunami source area even over land, which is also confirmed in Figure 1. Furthermore, another slow CID with a velocity of ~0.3 km/s was superimposed on the 4-min oscillation. Note that weak depressions in Figure 3b which seem to propagate northward at 3.0 km/s is an artificial depression coming from a high-pass filter. They were not seen when 2.2- to 8-mHz band-pass filter was applied (Figure 4a).
 As shown in Figures 1-4, the initial CIDs propagated asymmetrically to the north and west-southwest from the tsunami source area. To investigate the difference in the TEC oscillation, the Hilbert-Huang transform (HHT) [Huang and Wu, 2008; Wu et al., 2011; Liu et al., 2011b] was applied to the TEC variation, and spectra were calculated. Chen et al.  showed that the performance of the HHT was better than that of Fourier spectrum analysis when applied to the spatial structure of equatorial spread F. Liu et al. [2011b] also applied HHT to TEC variation and revealed bow and stern waves trigged by the Moon's shadow boat during a solar eclipse in the ionosphere. Figures 5a and 5b show the spectrum of TEC variation obtained by satellite PRN 26 for the west-southwest region of the epicenter (136°E–140°E, 32°N–38°N) and north region of the epicenter (140°E–150°E, 42°N–50°N), respectively. Both regions are located outside of the tsunamigenic ionospheric hole. The spectrum diagram was calculated at each receiver after applying a 1-h high-pass filter. Then, the spectrum diagrams of all the receivers were averaged in a 30-s and 0.1-mHz grid. In both areas, no significant oscillation was observed except for a long period variation with a frequency lower than 0.2 mHz before the mainshock. The TEC then suddenly increased south of the tsunami source area and decreased north of it at 9 min after the mainshock (0555 UT) [Kakinami et al., 2012]. After the initial TEC variation, very strong wide-range oscillations were detected west-southwest of the epicenter (Figure 5a) because the sharp TEC variations caused by the initial acoustic wave excited oscillations having a wide frequency range. After the strong wide-range oscillations were observed, oscillations with a peak frequency range of 4–7 mHz were clearly detected in the west-southwest (Figure 5a; 4 mHz corresponds to 4-min oscillations). After the initial shock from the tsunami reached the ionosphere, an oscillation of ~1 mHz was also excited as a background variation. This is consistent with the result in Figure 3d. In contrast to the case west-southwest of the epicenter, the wide-range oscillation was not detected north of the epicenter (Figure 5b). This indicates that there was no initial sharp TEC variation north of the epicenter. Indeed, the sharp TEC variation was not found north of the epicenter when slant TEC variations were investigated. Oscillations of 1–2 mHz were observed after about 0602 UT when the initial disturbance arrived at the north side of the epicenter (Figure 5b). However, the 4-min oscillation was not detected on the north side of the epicenter, whereas it was detected in the west-southwest. The results indicate that the 4-min oscillation has a north-south asymmetry, which is also shown in Figures 3 and 4.
3 Discussion and Conclusions
 The slower CID that propagated at 1.2 km/s was observed from 0 to 200 km from the epicenter, while the faster CID that propagated at 3.0 km/s was observed at 200 km or more in a west-southwest direction from the epicenter (Figures 3c and 3d). They are also confirmed in Figures 3a and 3b of Kakinami et al. . This asymmetry was also clear in the distribution of CID onsets (Figure 2a). Taking the propagation speed and frequency range shown in Figure 5 into account [Heki and Ping, 2005; Liu et al., 2011a], the slow CID was induced by acoustic waves from the tsunami source area. Because the velocity of the Rayleigh wave was very close to that of the faster CID, the faster CID seems to have been induced by the Rayleigh wave. The epicenter of the earthquake was located about 140 km off Japan's coast at 35°N, 136°E. The Rayleigh wave propagated away from the epicenter along the bottom of the sea and then along the ground in a west-southwest direction. Thus, it is reasonable that the CID associated with the Rayleigh wave was not detected near the epicenter. A CID associated with the Rayleigh wave was also not detected above the sea after the 1999 Chi-Chi earthquake [Liu et al., 2010].
 The fast CID was not observed above the ground north of the epicenter, but the slow CID at 1.2 km/s was observed in all directions (Figures 1, 3, and 4). The faster CID associated with the Rayleigh wave was observed in only a west-southwest direction from the epicenter, although the Rayleigh wave itself propagated in all the directions from the epicenter (Figure 3a). This is a large unresolved problem. Furthermore, although the slow CID propagated concentrically [Tsugawa et al., 2011], the 4-min oscillation was detected only in the west-southwest. What caused these asymmetries?
 According to Heki and Ping , a CID associated with a Rayleigh wave was not observed after the 2003 Tokachi-Oki earthquake or the 2004 offshore earthquake southeast of the Kii Peninsula. Those authors inferred that the Rayleigh wave and S wave signatures were not well distinguishable because the waves arrived almost simultaneously. As a result of the mixture of seismic waves, the acoustic wave was insufficiently excited. In Figure 3a, P and S waves are well distinguished from the Rayleigh wave even north of the epicenter where the CID associated with the Rayleigh wave was not observed. Therefore, a mixture of seismic waves is a difficult explanation for the asymmetry of the CID associated with the Rayleigh wave in the Tohoku EQ case.
 When a CID is excited by a point source, it is only detected in a magnetic equatorward direction due to magnetic field inclination [Heki and Ping, 2005; Otsuka et al., 2006]. Following these conclusions, such a CID should be detected only south of the source in the Northern Hemisphere. If a Rayleigh wave acts as a point source of an acoustic wave, the CID excited by the Rayleigh wave must be observable in any direction because the Rayleigh wave propagates in all directions. However, the Tohoku EQ observations show clear north-south asymmetry of the CID excited by the Rayleigh wave. The results, therefore, suggest that the Rayleigh wave did not act as a point source of the acoustic waves. The problem of why the fast CID associated with the Rayleigh wave was only detected west-southwest of the epicenter will be solved next.
 If an acoustic wave was continuously excited by a propagating Rayleigh wave and a superimposed wave front of the acoustic wave formed, this puzzle could be solved as shown in Figure 6. The oscillation of the superimposed wave front would be directed in one direction. Specifically, the direction of oscillation would be nearly perpendicular to magnetic field lines north of the epicenter but nearly parallel to magnetic field lines south of the epicenter in the Northern Hemisphere. The discrepancy in angle between the direction of oscillation and magnetic field lines would produce asymmetry of the CID because plasma is easily driven along the magnetic field lines by collision with the neutral atmosphere. Ducic et al.  showed that a CID associated with a Rayleigh wave propagated in a southward direction from the epicenter after the 2002 Denali earthquake. Interestingly, the CID was not clearly detected at 2000 km or closer but was clearly detected at 3000 km or farther from the epicenter [see Ducic et al., 2003, Figure 2]. The inclination angle calculated with the International Geomagnetic Reference Field ver. 11 was 52.5° at the epicenter of the Tohoku EQ, but angles of 75.2°, 69.0°, and 58.1° were calculated at the epicenter of the Denali earthquake, a distance of 1700 km from the epicenter (52°N, 128°W) where the CID was not clearly detected and a distance of 3000 km from the epicenter (40°N, 123°W) where the CID was clearly detected, respectively. These results indicate that a CID associated with the Rayleigh wave is detected when the angle of oscillation of the superimposed wave front is close to parallel with the magnetic field lines. These results also support our idea that the angle between the superimposed wave front excited by a Rayleigh wave propagating southward and the magnetic field lines is important. Rather than the point source perturbation discussed by Heki and Ping  and Otsuka et al. , the superimposed wave front of the acoustic wave excited the CID associated with the Rayleigh wave. The north-south asymmetry of CID related to the Rayleigh wave is very similar to the well-known north-south asymmetry of CID excited at the epicenter at the first glance. However, we have to note that the source of CID excited at the epicenter is fixed while the source of CID related to the Rayleigh wave is propagating. The CID associated with the Rayleigh wave must be observed even north of the epicenter because the Rayleigh wave propagated northward must excite the CID southward from that point, which is located north of the epicenter if the source acts as a point source. Since the CID associated with the Rayleigh wave clearly shows the north-south asymmetry, our results suggest that the superimposed wave front was excited by the Rayleigh wave and it disturbed the ionosphere.
 We next discuss the reason why the 4-min oscillation was only observed in the region west-southwest of the epicenter. If an acoustic wave excited by a Rayleigh wave shows a 4-min atmospheric resonance, as discussed by Watada , the 4-min oscillation should be detected north of the epicenter, as discussed in the previous paragraph. Since the 4-min oscillation was not detected north of the epicenter, the Rayleigh wave seems to have not excited the 4-min oscillation. The 4-min oscillation was observed over and to the south of the tsunamigenic ionospheric hole region. Hence, the 4-min oscillation clearly showed a north-south asymmetry. Heki and Ping  and Otsuka et al.  discussed that when an atmospheric disturbance is excited by a point source, the CID shows a north-south asymmetry owing to the inclination angle of the magnetic field lines. Therefore, this result implies that the 4-min oscillation was excited by the initial uplift and downwelling of the sea surface at the tsunami source region, which was a point source (Figure 6).
 Finally, we discuss the 1- to 2-mHz oscillation. Considering its propagation speed, this oscillation was likely associated with a gravity wave. However, several questions remain unresolved. For instance, the arrival time of the gravity wave at the ionosphere was too early if the gravity wave was excited at the sea surface at the tsunami source area because the estimated arrival time for a gravity wave at the F region peak is about 1.6 h [Hickey and Cole, 1987]. Why the wave front of the gravity wave propagated concentrically and whether the intensity of the CID was stronger in the north than in the south are additional questions that should be solved in the near future.
 We investigated TEC variation before and after the 2011 Tohoku EQ. The results show the following: (1) The CID showed north-south asymmetry, that is, the CID associated with the Rayleigh wave was observed only west-southwest of the epicenter. (2) The 4-min oscillation was observed in the tsunamigenic ionospheric hole region and the region west-southwest of the tsunami source area. Our results suggest that acoustic waves were continuously excited by Rayleigh waves and that they then formed a superimposed wave front. The superimposed wave front produced the north-south asymmetry of the CID due to magnetic field inclination. The 4-min oscillation was excited by a point source at the tsunami source area.
 The GPS and seismograph data used in this study were provided by the Geographical Survey Institute of Japan and the National Research Institute for Earth Science and Disaster Prevention, respectively. This study was supported by a Grant-in-Aid for Scientific Research (B), number 24310129, 2012 (Y. K. and M. K.), the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, under its Observation and Research Program for Prediction of Earthquakes and Volcanic Eruptions (Y. K., T. M. and T. Y.), the Heiwa Nakajima Foundation, 2011 (Y. K. and M. K.), and the Earth Observation Research Center, Japan Aerospace Exploration Agency (Y. K. and S. W.).