Anomalous magnetic variations were observed by ground magnetometers in East Asia area after the 2011 Tohoku earthquake. Some earlier reports showed that the seismo-magnetic variations have obvious amplitude around the epicenter, we emphasis here that the variations can still be notable at stations 2000–4000 km away from epicenter, and we define it as teleseismic magnetic disturbances (TMDs). TMDs appear about 8 min later after the arrival of seismic Rayleigh waves at teleseismic distances and propagate at a horizontal velocity of 3.9 ± 0.1 km/s. The wave-like TMDs last for no longer than 10 min and have a main period of 2.1–3.3 min. TMDs are not generated by direct effects of processes in focal area crust or tsunami waves, instead, their properties consist with the Rayleigh wave model of seismo-ionospheric disturbances. Hence, we conclude that the TMDs are the magnetic manifestation of seismotraveling ionospheric disturbances (STIDs) generated by the interaction between the ionosphere and atmosphere through acoustic waves launched by traveling Rayleigh waves. Our findings contribute to the knowledge of seismo-electromagnetic effects in the atmosphere-ionosphere system and further our understanding of couplings between various spheres of the Earth.
 Oscillations of the Earth surface due to a large earthquake will couple with the atmosphere. If the atmospheric disturbances thus generated are strong enough, the coseismic ionospheric disturbances (CIDs) or seismotraveling ionospheric disturbances (STIDs) can be detected in the ionosphere. Since early findings of this phenomenon with the Doppler sounding technique after major earthquakes in 1960s [Davies and Baker, 1965; Yuen et al., 1969], great concerns have been raised about comprehensive atmospheric and ionospheric effects excited by earthquake/tsunami and their propagation influence in the above regions. The great Sumatra earthquake on 26 December 2004 had a magnitude of M 9.1 (according to the U. S. Geological Survey, http://comcat.cr.usgs.gov/earthquakes/eventpage/official20041226005853450_30) and triggered a devastating tsunami, which led to extensive investigations on these effects using various measures such as HF Doppler shift [Hao et al., 2006; Liu et al., 2006a], GPS/TEC (total electron content) [Liu et al., 2006b; Astafyeva et al., 2009; Choosakul et al., 2009], and sensitive microbarographs [Le Pichon et al., 2005; Mikumo et al., 2008]. Those observations reveal a clear coupling process among lithosphere, atmosphere, and ionosphere. Particularly, there indeed exists a cause-effect chain from surface oscillation to atmospheric waves and then ionospheric disturbances. Now, the question is whether the chain ends at the ionosphere? That is to say, is it possible that the ionospheric disturbances are in turn to affect the magnetic field through electro-magneto mechanism that it can be observed on the ground? If so, the magnetic field measurements can also be a feasible indicator for the seismo-ionospheric effects.
 Several works have been done on seeking for magnetic disturbances after major earthquakes and related them to earthquake-excited atmospheric oscillations. Iyemori et al.  reported ground-based fluxgate magnetometer observations after the Sumatra earthquake. They found perturbations characterized by a period of ~30 s which can be associated with Pc3 type pulsations and a Pc5 (~3.6 min) geomagnetic pulsation. Hasbi et al.  observed sudden changes in H, D, and Z components of geomagnetic field shortly after another earthquake on 28 March 2005 in Northern Sumatra, Indonesia, and a Pc5 pulsation of 4.8 min was found coincident. The geomagnetic data used by these works are from stations near the epicenter within a distance less than several hundred kilometers. After the 2011 Tohoku earthquake and tsunami, Utada et al.  reported simultaneous measurements of the geomagnetic field by 14 stations operating on Japan islands, at most of the stations magnetic variations were found after the earthquake. Still, all those stations located in distances within 1000 km from epicenter, and it is beneficial for investigating phenomena nearby the epicenter. Closer to the epicenter, the magnetic variations could be larger and easier to be detected. But, since various physics processes occur in the focal area, there are uncertainties to distinguish different propagation modes and their real origins. Therefore, using only data near the epicenter, the magnetic variations have not been well explained yet. Also, due to the lack of simultaneous ionospheric observations, the detectability of magnetic variations from seismo-ionospheric disturbances has not been confirmed, and the connection between them is still a hypothesis.
 Actually, a variety of effects in the ionosphere, caused by earthquakes and tsunamis, are detected not only near the epicenter but also at teleseismic distance (far away from epicenter). Near the epicenter, CIDs have been found to be a combination of effects from kinds of atmospheric waves generated by crustal deformation and tsunami waves [Astafyeva et al., 2009; Rolland et al., 2011a; Galvan et al., 2012]. While far away from the epicenter, the teleseismic ionospheric responses (in the form of STIDs) are rather clear on the physical processes, which are believed to be induced by atmospheric waves seismically launched mainly by Rayleigh waves propagating at the Earth's surface [Ducic et al., 2003; Artru et al., 2004; Hao et al., 2006; Rolland et al., 2011b]. On the great Tohoku earthquake, quake-caused ionospheric and geomagnetic disturbances have been observed with a multi-instrument network, stations of which nearly all have distance more than 2000 km from the epicenter [Hao et al., 2012]. Chum et al.  even observed intense long-period infrasound waves in the ionosphere over Czech Republic (at 9000 km distance from the epicenter) by continuous HF Doppler sounding system. Statistically, Maruyama et al.  examined 43 earthquakes with magnitude ≥8 and concurrent ionograms, they found unusual signatures in ionograms for 8 of 43 events. In their study, the ionospheric disturbances were sometimes detected at distances up to 6000 km from the epicenter.
 Then one would ask the question, since ionospheric response can be detected in a long distance as far as in between 2000 and 9000 km, are there corresponding geomagnetic field disturbances? Qualitatively, this should be so because ionospheric disturbances could perturb the geomagnetic field beneath, and great earthquakes may provide conditions to prove it is true or not. Therefore, if we rule out complicated condition nearby the epicenter, and focus on the far-field magnetic and ionospheric phenomena, it might be capable to prove the connection between them. This is significant in extending our knowledge about the processes of lithosphere-atmosphere-ionosphere coupling. So in this paper, we use data from a number of geomagnetic stations in the East Asia area to find phenomena of variations of geomagnetic field accompanying and immediately after (coseismic and after effects of) the 2011 Tohoku earthquake. Particularly, we concentrate on teleseismic magnetic disturbances (TMDs) to reveal their causing mechanism and propagation process in the Earth's various spheres. The remaining part of this article is organized in the following manner: in section 2, the data sets used are introduced; and in section 3, we demonstrate the records of seismic waves and TMDs observed by ground-based magnetometer. Section 4 contains a discussion on the characteristics of TMDs observed and the information they can provide. Finally, section 5 is a summary on our findings.
2 Instruments and Database
 The 2011 Tohoku earthquake occurred near the east coast of Honshu, Japan at 0546 UT on 11 March 2011. The earthquake is an extremely strong one (M 9.0) and triggered devastating tsunami waves. Both the ground motion of earthquake and tsunami waves excited atmospheric waves propagating into the ionosphere, and the CIDs and STIDs were observed by various kinds of instruments (see [Astafyeva et al., 2011; Liu et al., 2011; Rolland et al., 2011a; Tsugawa et al., 2011; Galvan et al., 2012] and references given in section 1). To study the variations of geomagnetic field after this event, we collected both records of seismic waves (seismogram) and geomagnetic field data. The seismograms were taken from the Incorporated Research Institutions for Seismology (IRIS) Data Management Center (http://www.iris.edu), including data from nine stations with distances up to 6000 km away from the epicenter. Geomagnetic data of multiple stations were obtained from INTERMAGNET (www.intermagnet.org) and World Data Center (wdc.kugi.kyoto-u.ac.jp), as well as from three stations in China. Both of the seismograph and geomagnetic stations are listed in Table 1, along with their geographic locations and angular distances to the epicenter. The distribution of geomagnetic stations is illustrated in Figure 1.
Table 1. Stations and Data Used in This Paper
Distance From Epicenter
34.54 N, 69.04°E
7.27 N, 80.70°E
1-min Geomagnetic Field
1 s Geomagnetic Field
3 Observations and Data Analysis
3.1 Seismic Waves
 When an earthquake occurs, the body waves (P and S waves) travel through Earth's interior and propagate outward. The interaction of P and S waves generates two types of surface wave, Rayleigh waves and Love waves. The energy of surface wave is confined in the shallow surface of the Earth, therefore, they decay more slowly with distance than the body waves do. However, the particle motion of Love waves is mainly horizontal which is inefficient to disturb the atmosphere, but the vertical ground motion from Rayleigh waves plays an essential role in launching upward propagating atmospheric waves. So in this work, we concentrate on the effects of Rayleigh waves, which can be reflected by the ground vibration records from seismometers. A high-gain seismometer measures 3-component velocity of ground vibrations, here the BHZ (broadband, vertical velocity component) channel is selected for analysis. The BHZ channel data have sampling rate of 20 or 40 Hz depending on different stations, and they are converted from velocity data (m/s) to displacement (cm), resampled at 1 Hz rate and finally plotted in Figure 2.
 The horizontal velocities of surface waves can be computed under the assumption of plane wave propagation from the known distances between seismograph stations and observed travel time to each station. Though the dispersion of surface waves is different when propagating along oceanic and continental paths in terms of properties of the Earth's crust, we can still compute an average speed from seismograms shown in Figure 2. Carefully identifying the beginning of significant ground displacement at each station, a linear fitting gives an average Rayleigh waves horizontal velocity (vR) of 3.77 ± 0.04 km/s. In Figure 2, the arrival of seismic P and S waves can be clearly seen, but at station MAJO, the arrival times of S wave and surface wave are not well separated due to its short distance. So the station MAJO is excluded from the fitting to avoid possible interference from S waves.
3.2 1 Min Resolution Magnetic Data
 Geomagnetic field data at 1 min time resolution are obtained from INTERMAGNET (aaa, bmt, cnh, gua, gzh, hyb, kny, lzh, mmb, and wmq) and from World Data Center (WDC) (esa and miz). The magnetometer at every station gives three-component measurement of the geomagnetic field. For each component, we calculate the background trend by moving average with a time window of 10 min, then the background trend is subtracted from the component time series to get the relative and short time variations.
 Continuous data of 1.5 h around the earthquake origin time of the 12 stations are shown in Figure 3. In studying quake-related disturbances, the traveling velocity is a key parameter to infer relevant physical mechanisms, so the time series data of each station are arranged according to their distance to the epicenter to give a travel-time diagram. As a reference, an oblique line is superimposed on the plot corresponding to a wave front propagating at a horizontal speed of 3.77 km/s. This is actually identical to the fitted line in Figure 2 denoting the arrival time of Rayleigh waves. A parallel dotted line indicates time shifted to 8 min later, when the magnetic disturbances are about to occur. The 8 min time delay is determined and discussed in the next section.
 In Figure 3, the magnetic X component data show synchronous fluctuations at almost all the stations, reflecting the changes in external field (i.e., due to solar-terrestrial interaction). However, there are exceptions for three stations (esa, miz, and mmb) closer to the epicenter that dramatic changes show up shortly after the earthquake origin time in the X component, and in the Y and Z components as well. As analyzed by [Utada et al., 2011], these unusual magnetic variations are either due to strong seismic motion shaking the magnetometer sensors or caused by physical processes occurring in the focal area.
 Besides the near-field effects, at stations rather far away so-called teleseismic magnetic disturbances (TMDs) can be identified. In the Y components, TMDs appear at middle distance stations (kny, cnh, and bmt) with time delays apparently depending on their distances to the epicenter, rather along the oblique reference dotted line. At stations even farther away, TMDs can be hardly identified due to strong background fluctuations. However, in the Z components, the background is less noisy that TMDs are more obvious comparing to relatively quiet magnetic variations before and after them. So TMDs are detectable at even larger distance, such as at gzh, lzh, wmq, and hyb stations, though the absolute amplitude of TMDs is smaller in the Z component.
 As shown in Figure 3, the anomaly magnetic variations have periods of 3 min approximately, so the amplitudes of TMDs were possibly weaken or smoothed away in the 1 min time resolution records, which make them difficult to be detected somewhere. Therefore, it is necessary to have data of higher time resolution to deduce detailed characteristics for the phenomena of TMDs.
3.3 1 s Resolution Magnetic Data
 Data of 1 s time resolution are available for three stations (kak, kny, and mmb) from WDC for Geomagnetism (wdc.kugi.kyoto-u.ac.jp), and for another three stations (SSL, SYS, and TAY) through Chinese Meridian Project. In the same manner as Figure 3, the 1 s data are demonstrated in Figure 4. The horizontal component (H) data show mainly fluctuations of external field, while anomalous seismo-related magnetic variations are apparent in the total intensity (F), as well as in vertical intensity (Z) and declination (D) components. Furthermore, at stations of larger distance (kny, SSL, TAY, and SYS) the amplitudes of TMDs are much more significant in Z and D components comparing to those shown in Figure 3.
 Among the six stations, the station kak is closest to the epicenter and has larger amplitude of magnetic variations. The dramatic changes may be caused by not only the magnetic effects of earthquake but also the sensor tremor by the surface shaking. Actually, two sudden changes occurring at around 0549 UT and 0616 UT are found in the original kak D time series. In Figure 4, segments of D time series are simply shifted at these time points to minimize the discontinuities. Similarly, when using geomagnetic field data from 14 stations operating on Japan islands, Utada et al.  also found that the strong seismic motion caused rotation and/or displacement of the three-component sensors at two stations (including kak), resulting in a discontinuity in the time series of D. To avoid the influence from unreliable data, station kak is excluded in the following analysis.
 It is quite certain from Figures 3 and 4 that after the earthquake, magnetic variations are observable at sites both nearby and far away from the epicenter. Referring to the propagation of Rayleigh waves, TMDs emerge later at larger distance following the arrival of Rayleigh waves but with a time delay of several minutes. This seems to be compatible with previous studies on Rayleigh waves exciting teleseismic ionospheric disturbances (i.e., STIDs) [Ducic et al., 2003; Artru et al., 2004; Hao et al., 2006; Rolland et al., 2011b]. So we could make a primary suggestion that the TMDs phenomena are related to seismo-ionospheric effects at teleseismic sites, hence related to the traveling Rayleigh waves.
 The observational facts given in the preceding section show that the magnetic disturbances are found both near and far from the epicenter. However, near the focal area of earthquake and tsunami, there are several possible sources and mechanisms responsible for magnetic anomalies. The seismo-ionospheric disturbance is only one of them. Based on 14 geomagnetic observatories in Japan, especially those very close to the epicenter of 2011 Tohoku earthquake, Utada et al.  found anomalous geomagnetic field variations and separated them into two categories: the immediate ones after the earthquake origin time 0546 UT were generated by electric current from motional induction of tsunami flow, and the latter ones after 0555 UT were from tsunami-related ionospheric disturbance. This means that around the epicenter, various mechanisms may work together, and it is not easy to discriminate one from the other. To avoid influences from near-field sources, in the following text, we will focus on TMDs occurring far away from the epicenter. Their propagating speed and period of wave-like disturbances will be derived and compared with previous studies, and the mechanism for TMDs will be discussed as well.
4.1 Horizontal Velocity
 Depending on dense and wide coverage of GPS receivers in Japan, three modes of ionospheric disturbances were observed simultaneously in the TEC map after earthquakes [Astafyeva et al., 2009; Rolland et al., 2011a]. Each mode is characterized by its propagating velocity, thus if the velocity of observed magnetic disturbances agrees to one of the modes, then a connection can be established. Based on the travel-time relationship of TMDs given in Figures 3 and 4, we have suggested that they are related to propagation of Rayleigh waves. Among different modes of seismo-ionospheric disturbances, there is one related to traveling Rayleigh waves, which is the fastest one with a velocity of 3–4 km/s. Therefore, we need to estimate the exact speed of TMDs, then the suggestion of TMDs being magnetic effect of seismo-ionospheric disturbances can be checked.
 In order to further remove background long-period (longer than 5 min) variations to isolate the TMD signature, a Butterworth high-pass filter is applied to the geomagnetic Z and D component data. The results of four stations are presented in Figure 5, and the station kak and mmb are not included for their short distance to the focal area. Furthermore, in Figure 5, the kny station is taken as a reference, and traces of the other stations are offsetted to align at the beginning time of TMDs. Since TMDs amplitude are more apparent in D component than in Z component, the leading edges of TMDs are defined as sudden decreases in D traces of SSL, TAY, and SYS, as well as in D trace of kny despite a following steep rise which is a data discontinuity to be ignored. One may notice that there is another valley in kny D trace before the leading edge defined, but it is more possibly due to the ionospheric/magnetic effect of S waves arriving earlier (see Figure 2 for the seismogram of MDJ). This will be discussed later. As a result, for the other three stations, the time offsets of TMDs arrivals relative to kny station are denoted in Figure 5.
 Considering the model of Rayleigh waves exciting ionospheric variations, the appearance time of concurrent magnetic disturbances at station i can be given by
where tE is the earthquake origin time, τRi is the time required for Rayleigh wave from epicenter to station i, and τAi is the time for atmospheric waves to propagate from the surface to ionospheric height. Assuming τAi is constant for every station, then
indicating that the arrival time offset of TMDs should equal to that of Rayleigh waves, i.e., their propagating velocities should agree to each other. Given the distances of a pair stations from the epicenter (si and sj), the horizontal velocity of TMDs can be calculated by vM = (si − sj)/(tMi − tMj).
 A velocity value is calculated for every pair of stations, and finally we get an average TMDs velocity (vM) of 3.9 ± 0.1 km/s. This value is not exactly the same as the Rayleigh wave velocity of 3.77 ± 0.04 km/s according to the seismograms, but it is close. Actually, ambiguities exist in the calculation of vM, because disturbances from other sources may interfere the identification of the arrival time of TMDs. This may happen to station kny, because it is less than 1500 km away from the epicenter. According to TEC measurements [Rolland et al., 2011a; Galvan et al., 2012], at this distance, the ionospheric disturbances by direct acoustic and gravity waves from focal area are still significant, including acoustic waves traveling at ~1000 m/s in horizontal direction. Nevertheless, even the fastest acoustic waves arrive at kny much later than STIDs induced by Rayleigh waves. Since we use the leading edges, the late arriving acoustic waves will not affect the result. Instead, the S waves arriving prior to Rayleigh waves may induce ambiguity. Having enough amplitude, seismic P and S waves can also excite atmospheric and ionospheric disturbances, just like what Rayleigh waves do [Chum et al., 2012]. At the distance of kny station, the body and seismic waves have not dispersed enough; their effects cannot be clearly separated either. In Figure 5, the first decrease of kny D component is attributed to S waves, and the second one is considered to be the leading edge of TMDs by Rayleigh waves.
 A recent work on magnetic effects of earthquake is given by Utada et al. , which showed near-field magnetic variations after 2011 Tohoku earthquake. Due to the short distance to the epicenter, they had to carefully separate the magnetic effects from tsunami water flows and those from seismo-ionospheric variations. Also, because the stations are too close to the epicenter and are not dense enough, the estimation of the horizontal velocity of the magnetic variations is not valid. With TEC image of CIDs velocities, several authors have obtained the speed of Rayleigh waves signature in the ionosphere. Liu et al.  observed STIDs with TEC wavefronts propagating at 2.3–3.3 km/s, and larger velocities were also reported to be beyond 3 km/s [Rolland et al., 2011a] or 3.4–3.5 km/s [Galvan et al., 2012; Tsugawa et al., 2011]. These velocities were calculated mainly based on the dense GPS receiver network in Japan, which extends no farther than 2000 km away from the event epicenter. Meanwhile, the velocities were also obtained at larger distance by means of other instruments instead of GPS/TEC. Chum et al.  used seismogram and HF Doppler sounding data recorded at the distance of ~9000 km and found STIDs following Rayleigh waves with horizontal velocity of 3.9 km/s. From ionograms records after eight earthquakes (including the 2011 Tohoku one), Maruyama et al.  found seismo-ionospheric disturbances up to 6000 km away from the events. Although time resolution of ionosonde observations is low, they estimate the average traveling velocity to be 4.0 ± 1.1 km/s. In general, our result of 3.9 km/s for TMDs propagation tends to be consistent with the speed of ionospheric Rayleigh waves signature at large distances.
4.2 Atmospheric Delay of Acoustic Waves
 From the travel-time diagrams in Figures 3 and 4, TMDs began approximately along the dotted line which is 8 min later than the arrival of Rayleigh waves. This time delay corresponds to τAi in equation (1) and is the time needed for atmospheric disturbances to propagate upward to the ionosphere. In the previous subsection, the atmospheric delay τAi is assumed to be constant then vM and vR should be equal, and the consistency between them is checked. On the other hand, having tMi and τRi derived from geomagnetic and seismograph data, τAi can be given based on equation (1) by
 For kny, SSL, TAY, and SYS stations, τAi is calculated to be 466 s, 476 s, 463 s, and 441 s, respectively, with an average value s (~7.7 min).
 In association with the Tohoku earthquake, most atmospheric delay results are given based on TEC measurement around the focal area. The time delay has been reported to be approximately 7 min [Liu et al., 2011; Tsugawa et al., 2011] or 10 min [Galvan et al., 2012; Rolland et al., 2011a] for the earliest visible TEC perturbations above the epicenter. Astafyeva et al.  compared TEC perturbations with time delay ranging from 7 to 10 min after the crustal uplift and suppose that the shorter delay may be related to some processes in the ionosphere which have not been well understood, since simple calculation shows that 7 min is far less than enough for normal acoustic waves to reach the ionospheric peak altitude. On the other hand, at teleseismic sites, the time delay of following ionospheric disturbances can be directly measured taking into account in situ seismograph records, according to equation (3). By cross-correlation of vertical component of colocated seismogram and HF Doppler sounding, Chum et al.  obtained time delays of 550–560 s for seismic P and S waves to excite STIDs at the ionospheric altitude where HF radio waves were reflected. Comparing to above mentioned results, our value of 462 s (7.7 min) is apparently shorter. In the paper of Chum et al. , the propagation time of acoustic waves was calculated based on atmospheric parameters from NRLMSISE-00 model. According to their results, regular acoustic waves would reach 150 km altitude after 450 s propagation in the atmosphere. This altitude is significantly lower than normal height of the ionospheric electron density peak. But, supposing that TMDs are induced by perturbations of ionospheric current, the shorter delay might be reasonable for TMDs to be excited. Actually, the ionospheric Hall conductivity peaks around 95–125 km while Pedersen conductivity peaks at 120–145 km; above this altitude, they decrease with height but are still quite large in the F region [Campbell, 1997]. Rishbeth  discussed F region dynamo driven by thermospheric winds, and the dynamo driven currents have been observed by satellite magnetometer [Lühr and Maus, 2006]. Also, due to the fact that the amplitude of atmospheric wave increases with height to keep the conservation of energy in per unit volume, the acoustic waves should modulate the current more efficiently at higher altitude. For this great Tohoku earthquake, it can be concluded that the current below the conductivity peak was possibly not well disturb. But with growing amplitude and still significant conductivity above the peak height, the effects of acoustic waves began to be notable, and the TMDs can be attributed to the current changes by seismic-exciting atmospheric waves at and above 150 km. In this altitude region, similar processes of magnetic field induced by current variation have been revealed recently by CHAMP observations [Tomás et al., 2009]. The satellite magnetometer data showed modulation of the midlatitude ionospheric current system by disturbances from solar eclipse.
 With Rayleigh waves velocity and average atmospheric delay () determined, ground vertical displacement records and geomagnetic field data can be shifted in time to align at t = 0, as illustrated in Figure 6. The time series of ground motion is shifted by t = τRi, and the magnetic Z and D components are shifted by . Then the time t = 0 corresponds to the beginning of both ground motions and TMDs. The purpose of Figure 6 is to display colocated seismic and magnetic records together and makes a straightforward comparison of their respective patterns of variation. In Figure 6, both of vibrations in ground motion and magnetic field last for two or three wave cycles, which is 5–10 min long. This is close to time duration of usually observed STIDs [Artru et al., 2004; Liu et al., 2006a; Chum et al., 2012; Hao et al., 2012]. In general, the amplitude of TMDs shown is proportional to that of local ground displacement, except for Z component of SYS which is much larger than expected. The existence of intense electrojet above low latitude region possibly amplifies the magnetic disturbances at SYS. A major difference between TMDs and seismic motions lies in the variation period that TMDs have longer periods. This is to be presented in the next subsection.
4.3 Wave Periods
 The TMDs discussed above exhibit a traveling velocity of 3.9 km/s and a time delay of 8 min after Rayleigh waves. In general, this is consistent with the previous studies on seismo-ionospheric effects of the Tohoku earthquake that similar properties are present in STIDs observations [Chum et al., 2012; Hao et al., 2012; Maruyama et al., 2012]. However, more proof is needed to clarify the connection between teleseismic ionospheric and magnetic variations and to understand how the magnetic signals originate from seismic energy release. We extracted 1000 s long time serials data of geomagnetic Z and D components, which are between −300 s and 700 s shown in Figure 5. The frequency spectra are calculated with Maximum Entropy Method and presented in Figure 7. For both Z and D data, there are two main frequency components shared by the four stations. The one at low frequency end is around 2 mHz (8.3 min period), and the high frequency one is at 5–8 mHz (2.1–3.3 min) and 5–6 mHz (2.8–3.3 min) for Z and D components, respectively. For each geomagnetic station, Rayleigh waves records of colocated or nearby seismograph stations are selected for comparison. Seismograph data in Figure 2 from 300 s before to 700 s after Rayleigh waves arrival are taken out for spectra analysis, and the results are presented in Figure 7c showing two peaks at 8 mHz (2.1 min) and 11 mHz (1.5 min).
 The low frequency peak (2 mHz) of magnetic components is close to the resolution limit (1 mHz), which is decided by the length of analyzed time series (1000 s). So this period will not be discussed here. Regarding high frequency one of ~3 min for both Z and D components, periods in this range (3–4 min) have been reported in ionospheric variations after major earthquakes (e.g., see [Choosakul et al., 2009; Rolland et al., 2011a] and references therein). This period is mainly found in CIDs from TEC observations around epicentral area shortly after earthquake commencements and is usually interpreted as atmospheric particles oscillate and acoustic waves generated by atmospheric duct resonance. Acoustic waves with periods of about 3–5 min are considered to be trapped between the ground and the lower thermosphere with a standing wave character [Tahira, 1995; Shinagawa et al., 2007]. Due to the fact that coherent wave periods are found in the variations of atmosphere, ionosphere, and geomagnetic field, one may relate these disturbances to each other. Indeed, Iyemori et al.  also found ~3.6 min periods of magnetic pulsations at a station about 1000 km away from the 2004 Sumatra earthquake epicenter. They proposed a dynamo mechanism in the ionospheric E layer, where disturbances in ionospheric electric field and currents are generated by atmospheric duct resonance set up by the earthquake. The common features existing in the observations of both ionospheric plasma and magnetic field include similar periods and long-lasting variations (more than 1 h), indicating that the duct resonance mechanism is appropriate for coupled CIDs and magnetic pulsations in near-field region. However, when far from the epicenter, the ground motion may not be strong enough to set up duct resonance. And no long duration wave-like disturbances have been found in the ionosphere or magnetic field at teleseismic distance so far. The TMDs we observed attenuated soon after the passage of seismic waves and persist no longer than 10 min. This deviates from the features of resonance mechanism, but is identical to that of Rayleigh wave exciting STIDs usually observed after major earthquake events (e.g., [Artru et al., 2004; Hao et al., 2006, 2012; Chum et al., 2012]). That is to say, though the periods agree well, no evidence shows that strong atmospheric duct resonance had been set up in far-field region, then the condition responsible for ~3 min period needs to be interpreted in more detail.
4.4 Mechanisms and Models
 The relationship between earthquake and its magnetic effects is not a new topic to seismologists, and there are indeed several candidate mechanisms for earthquake-induced magnetic anomalous variations. However, our study shows that away from the epicenter (e.g., more than 1500 km), the connections between TMDs and seismo-ionospheric disturbances are convincing. Referring to studies on far-field STIDs (e.g., [Chum et al., 2012; Hao et al., 2012]), the occurrence of TMDs approximately coincides with the ionospheric disturbances observed by HF Doppler sounding. Furthermore, the features of TMDs given above, such as velocity and atmospheric delay, are consistent with the Rayleigh wave model. It can thus be concluded that the phenomena of TMDs are correlated with atmospheric and ionospheric variations excited by teleseismic propagating Rayleigh waves, and the observed TMDs should be independent of non-ionospheric processes in the epicentral region.
 Since studies on magnetic effects of seismo-ionospheric disturbances are still rare, comparison can be made to them which are mainly based on near-field observations (e.g., [Iyemori et al., 2005; Utada et al., 2011]). The TMDs presented here are wave-like fluctuations of two or three cycles, which is different from either long time pulsations from duct resonant atmospheric waves [Iyemori et al., 2005] or sudden changes from ionospheric plasma depletion caused by initial crustal deformation [Utada et al., 2011]. So TMDs cannot share the discussion with these near-field phenomena, but the estimated atmospheric delay and period of 5–8 mHz (~3 min) still imply the important role of atmosphere in energy transfer among Earth's spheres.
 Due to the exponential decrease of the atmospheric density, the amplitudes of acoustic waves are largely amplified when they propagate upward. For low frequency (<20 mHz) waves, the atmospheric viscosity is negligible, so the resulting amplification can reach factors of 104 − 105 at ionospheric altitudes and make the waves easier to be detected. The seismic waves at the surface, despite the small size of displacements, actually present a unique combination of frequency and horizontal wavelength range necessary for an efficient coupling with internal waves in the atmosphere. The frequency of internal waves in the atmosphere is indeed further selected by the conditions of the solid earth-atmosphere system. By computing the normal modes of given configuration of the solid earth and atmosphere, Lognonné et al.  found two frequencies (about 3.7 and 4.4 mHz) at which a much larger fraction of the seismic waves is transferred in the atmosphere. Acoustic waves of the two atmospheric modes are trapped in the low atmosphere and are considered to be the major cause of ionospheric waves detected between 3.5 and 5 mHz. With GPS/TEC measurements, Rolland et al. [2011b] compared the Rayleigh wave exciting TEC perturbations after both near-field and far-field events, showing that they have a common frequency centered at 5 mHz.
 Comparing TMDs and STIDs at teleseismic distances, however, there is one final discrepancy needs to be explained. In HF Doppler sounding observations, STIDs are usually variations with periods of tens of seconds (>10 mHz) which are in the range of infrasonic waves. This has been reported after several major earthquakes including the 2011 Tohoku one [Artru et al., 2004; Liu et al., 2006a; Chum et al., 2012; Hao et al., 2012] and obviously differs from periods found in both GPS/TEC and TMDs observations. Neglecting the electron density changes on the wave path, the Doppler frequency shift of HF radio waves is proportional to the vertical velocity of reflecting layer. So the HF Doppler sounding detects disturbances at fixed heights, which were often about 200 km in those cases. On the other hand, GPS/TEC is the total electron content along a path throughout the whole ionosphere; geomagnetic variations inducing by ionospheric current overhead are also an integration result of a spatial region. Then fast evolving perturbations may be smoothed out in GPS/TEC and magnetic field data, instead, they can be notable in HF Doppler measurements. This will also help to explain the fact that the major wave periods of TMDs and the external forces (ground vertical motions) are not exactly identical (Figures 6 and 7). In addition, the atmosphere-ionosphere interaction may be subject to other processes, such as photochemical reactions, which should be taken into consideration in modeling studies.
 So far, models on coupling energy from Earth's surface vibrations to the ionosphere have been established to confirm the interaction among spheres and simulate both seismo-induced neutral atmospheric waves and therefore ionospheric variations [Artru et al., 2001, 2004; Watada et al., 2006; Rolland et al., 2011b]. Recently, Imtiaz and Marchand  present a model to account for magnetic field perturbation, when given an acoustic impulse in the atmosphere. But no model has been completed so far to simulate the whole coupling system, from seismic waves to the magnetic disturbances. Considering the variations in magnetic field as a ground-based indicator for the atmosphere-ionosphere coupling, and their impact on the plasma environment, it is necessary to extend these models to include the magnetic effects of ionospheric plasma or current variations. Then the seismo-magnetic variations could be detailed investigated, and their detectability can be assessed when a seismic event occurs.
 Anomalous magnetic variations were observed by ground-based magnetometers after the 2011 Tohoku earthquake. We focus on the phenomena of teleseismic magnetic disturbances (TMDs) which appear far away from the epicenter. According to the available 1 s or 1 min geomagnetic field data, TMDs can be detected at distances up to ~4000 km or ~6000 km.
 The TMDs reported here have a horizontal phase velocity of 3.9 ± 0.1 km/s. They occur following the arrival of seismic Rayleigh waves on the Earth's surface and have a time delay of 8 min. Through spectrum analysis, major periods of 2.1–3.3 min (~3 min) are found in the magnetic variations. In general, the velocity and time delay agree well with the Rayleigh wave model of seismo-ionospheric disturbances, and the time delay of 8 min is enough for regular acoustic waves to propagate from ground upward to 150 km altitude, then to modulate the ionospheric current at and above this altitude to induce magnetic variations. So we conclude that TMDs are the magnetic manifestation of seismotraveling ionospheric disturbances (STIDs), resulting from interaction between the ionosphere and atmosphere.
 The detectability of teleseismic magnetic and ionospheric disturbances is extended by our observations. The mechanism for TMDs, in brief, is that Rayleigh waves arrive at teleseismic sites; atmospheric disturbances are caused locally and propagate upwards into the ionosphere overhead, and then variations of ionospheric electron density induce (may though current change) magnetic field disturbances beneath. This cause-effect chain seems reasonable. Surely, modeling studies are necessary for better understanding the detailed mechanism of magnetic effect, and coupling efficiency of seismic energy at far-field sites needs to be further investigated as well.
 The results presented in this paper rely on data collected at magnetic observatories. We thank WDC for Geomagnetism, Kyoto for providing the 1 s magnetic data (kak, mmb, and kny). We acknowledge the use of data (SSL and SYS) from the Chinese Meridian Project. The data of TAY were from Institute of Geophysics, China Earthquake Administration. For the other 1 min magnetic data, we thank the national institutes that support them and INTERMAGNET for promoting high standards of magnetic observatory practice (www.intermagnet.org). The facilities of the IRIS Data Management System, and specifically the IRIS Data Management Center, were used for access to waveform and metadata required in this study. The IRIS DMS is funded through the National Science Foundation and specifically the GEO Directorate through the Instrumentation and Facilities Program of the National Science Foundation under Cooperative Agreement EAR-1063471. This work was jointly supported by NSFC (41274155 and 40904036), China NIBRP (2011CB811405), and Project Supported by the Specialized Research Fund for State Key Laboratories.
 Robert Lysak thanks Jann-Yenq Liu and another reviewer for their assistance in evaluating this paper.