First GPS TEC maps of ionospheric disturbances induced 1 by reflected tsunami waves : The Tohoku case study 2 3

12 The straight tsunami waves from epicenter can be reflected when they reach to coasts or 13 underwater obstacles. In this study, we present the first ionospheric maps of reflected tsunami 14 signature caused by the great 11 March 2011 Tohoku earthquake using the dense GPS 15 network GEONET in Japan. We observed tsunami-like travelling ionospheric disturbances 16 (TIDs) with similar propagation characteristics in terms of waveform, horizontal velocity, 17 direction, period and arrival time compared to the reflected tsunami at the sea-level, indicating 18 the TIDs are induced by the reflected tsunami. The results confirm the atmospheric internal 19 gravity waves (IGWs) produced by reflected tsunami can also propagate upward to the 20 atmosphere and interact with the plasma at the ionospheric height. 21


Introduction
A tsunami propagating in an open ocean can produce atmospheric internal gravity waves (IGWs) and they are significantly amplified when propagate upward to the ionosphere (Hines, 1972;Peltier and Hines, 1976).The IGWs interact with the ionospheric plasma and might generate the signatures that can be detectable by ionospheric sounding.of-sight (LOS) between receiver and satellite.The sTEC can be calculated from the geometryfree combination of GPS dual-frequency carrier phases for each satellite-receiver pair, namely where T s is the sTEC with unit of TECU (1 TECU=10 16  Although Eq. ( 1) cannot acquire the absolute value of TEC at a particular time due to the unknown bias, it can capture the TEC variation over time with high precision, which is important for TIDs detection.In this paper, we employ a numerical difference method to eliminate the diurnal variation and the bias in TEC and extract the vTEC variation series where () dt is the vTEC variation; t is the observation epoch;  is the time step for difference.
The time step is set to 300 s, which is suitable for the TIDs detection induced by the IGWs.
The numerical difference method is very simple and beneficial to process large number of data.
The number of the ground-based stations in GEONET is about 1200 and data sampling rate is 30 s.The average distance between GEONET stations is about 25 km, providing us a good opportunity to monitor the ionosphere with high resolution.After processing the data from all GPS stations, we can plot the vTEC variation values with different IPPs at specific epoch in a two-dimensional map.The two-dimensional maps of vTEC variation will be used to detect the tsunami signature in ionosphere.
Nat As showing in Figure 1, when straight tsunami waves from epicenter propagate to the Emperor seamounts (average depth ~2000 km), the reflected waves might be generated due to the powerful energy.
To confirm the existence of reflected tsunami waves, Figure 2  In short, the observation results by DARTs and the MOST model results demonstrate that there were reflected tsunami waves at the sea-level with frequency about 0.40 mHz.

Reflected tsunami signatures in ionosphere
The ionospheric disturbances induced by origins from epicenter such as Rayleigh waves, acoustic-gravity waves and gravity waves (tsunami waves) were observed by several scholars after the 11 March 2011 Tohoku earthquake (Liu et al., 2011;Rolland et al., 2011;Tsugawa et al., 2011;Occhipinti et al., 2013;Occhipinti, 2015).Here, we focus on possible reflected tsunami signature in ionosphere induced by this event.The time-distance map of vTEC variations is usually used to estimate the velocity of disturbances with a point origin, such as the epicenter.However, the origin for the reflected tsunami is not a point but a line (the Emperor seamounts).So, the method obtaining the velocity of disturbances by time-distance map is not suitable.Here, we estimate the horizontal velocities of the TIDs in vTEC variations following the approach of Garrison et al. (2007).
The horizontal velocities of the TIDs vary 240-290 m/s approximately from eastern area to western area, which is consistent to the observed results in the ionospheric maps.According by the two satellites).Compared Figure 4 and Figure 2, it is easy to find the waveform of the TIDs is very similar to that of the reflected tsunami waves at the sea-level.According to the time-frequency diagrams, the center frequency of the TIDs is about 0.55 mHz, which is larger than that of the reflected tsunami waves.This can be attributed to the Doppler Effect caused by the relative motion between the GPS satellite and the TIDs.As seen from Figure 1, the direction of PRN 25 or PRN 29 is almost opposite to the TIDs, leading to the shortened period when observe the disturbances.The center frequency of TIDs is about 0.44 mHz after amending the Doppler Effect, which is basically consistent to that of reflected tsunami waves.
According to the NOAA's MOST model for this event, the direction of the reflected tsunami waves at the sea-level is also southwest and turns around counterclockwise, which is consistent to that of the observed TIDs in Figure 3.As described in the previous section, the reflected tsunami waves reach the epicenter at about 6 h after the earthquake.So, the observed time for the TIDs and reflected tsunami is basically consistent with ~35 min delay.The magnitude of the observed delay is also observed on the case of 2009 Samoa tsunami (Rolland et al., 2010), which might be due to combined influence of thin shell approximation, horizontal wind and horizontal delay when IGWs propagated to the ionosphere.The horizontal group velocity of IGWs at different height is always smaller than the tsunami velocity, leading to the horizontal delay when propagating to the ionosphere (Occhipinti et al., 2013).According to the HWM93 wind model (Hedin et al, 1991), the background horizontal winds propagate along the northwest at the studied times and areas, which are opposite to that of tsunami waves.When IGWs propagate against the winds, the horizontal group velocity will decrease (Ding et al., 2003), further prolonging the horizontal delay.
According to above analysis, the observed TIDs have similar horizontal velocity, direction, period, waveform and observed time compared to the reflected tsunami waves at the sea-level.
Furthermore, to remove possible recurrent TIDs, we also verified that there weren't significant perturbations on the day before and after the event day at the study times.These results can confirm that the observed TIDs in Figure 3 are triggered by the reflected tsunami waves.This is the first time that the reflected tsunami signature in ionosphere is detected by the GPS TEC.
presents the sea-level measurements recorded by the DART 21401 and DART 21419.The DART 21401 that near the epicenter first observes the straight tsunami at 06:46 UT and then the waves propagates to the DART 21419 at 07:09 UT.However, the DART 21419 and DART 21401 observes another augmented signal at 09:28 UT and at 09:52 UT, suggesting there are tsunami waves propagated along the opposite direction of the straight tsunami waves.Furthermore, the amplitude of the waves recorded in DART 21419 (0.139 m) is slightly larger than that in DART 21401 (0.111 m), which can serve as further evidence that the waves propagated from DART 21419 to DART 21401.As shown in Figure 2, the spectral analysis for the time-series of the tsunami signals indicate they have similar center frequency of ~0.40 mHz.Another significant signal (~0.66 mHz) in time-series of DART 21401 is the frequency of straight tsunami (Makela et al., 2011; Occhipinti et al., 2011).In addition, the model of sea-level variation due to tsunami waves can further support the reflected tsunami waves.The NOAA's Method of Splitting Tsunami (MOST) model (see the animation for Tohoku tsunami: ftp://ftp.pmel.noaa.gov/tsunami/honshu/)can offer the propagation characteristics of the reflected tsunami at the sea-level.According to the MOST model, the straight tsunami waves reach the Emperor seamounts at about 3 h after the earthquake.Then, the tsunami waves are divided into two parts: one part continued to propagate ahead, another part along the opposite direction.The opposite tsunami waves pass the DART 21419 and DART 21401 successively, and reach the epicenter at about 6 h after the earthquake.Nat.Hazards Earth Syst.Sci.Discuss., doi:10.5194/nhess-2016-11,2016 Manuscript under review for journal Nat.Hazards Earth Syst.Sci.Published: 26 January 2016 c Author(s) 2016.CC-BY 3.0 License.

Figure 3
Figure 3 presents the two-dimensional maps of vTEC variations derived from GPS observations in GEONET on 11 March 2011 at studied times.As shown in the upper left panel, the ionospheric disturbances induced by origins from epicenter are basically invisible at about 08:30 UT.However, TIDs (indicated by the blue arrow) began to appear again at about 11:50 UT.As shown in Figure 3, the TIDs propagated along the southwest that is accord with the observation results by the DARTs in Figure 2. In addition, the direction slightly turns around counterclockwise, suggesting that the horizontal velocities on the western area close to the Kuril and Japan trenches are larger than that on the eastern area.As shown in the bottom right panel of Figure 3, the TIDs propagate to the epicenter at about 12:20 UT.
to the ocean depths ( h ) from ETOPO1 grid data supplied by U.S. NOAA (about 5900-9000 m at adjacent area), the tsunami velocities are about 242-300 m/s obtained from the shallowwater equation v gh  with gravity ( g ) of 9.8 m/s 2 .This indicates the horizontal velocities of the observed TIDs are similar to the tsunami velocities at the sea-level.To further examine the correlation of TIDs and tsunami waves, we plot vTEC variation timeseries derived from satellite PRN 25 and satellite PRN 29 in Figure 4 (The TIDs are observed Nat.Hazards Earth Syst.Sci.Discuss., doi:10.5194/nhess-2016-11,2016 Manuscript under review for journal Nat.Hazards Earth Syst.Sci.Published: 26 January 2016 c Author(s) 2016.CC-BY 3.0 License.

Figure 1 .Figure 2 .Figure 3 .
Figure 1.The locations of epicenter, DART stations and IPPs.The red pentagram indicate the 2 epicenter of 2011 Tohoku earthquake, the blue squares note the DART stations and the color 3 bar denotes the observation time of IPPs. 4

Figure 4 .
Figure 4.The vTEC variation series and time-frequency diagrams.The left panels are vTEC variation series derived from satellite PRN 25 and satellite PRN 29.The right panels are corresponding time-frequency diagrams for the time-series of the tsunami signals denoted by red rectangles.