Numerical simulations of atmospheric waves excited by the 2011 off the Pacific coast of Tohoku Earthquake
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Numerical simulations are performed to simulate atmospheric perturbations observed at ionospheric heights just after the 2011 off the Pacific coast of Tohoku Earthquake. A time-dependent, two-dimensional, nonlinear, non-hydrostatic, compressible and neutral, numerical model is developed to reproduce the atmospheric perturbations. An impulsive upward surface motion is assumed as the source of the perturbations. Simulated atmospheric perturbations at 300-km altitude show remarkable agreement with oscillations observed in the ionospheric total electron content (TEC) when the source width is about 250 km. In the vicinity of the source, the acoustic resonance modes between the ground surface and the lower thermosphere are dominant. They have three dominant frequencies for the interval between 20 and 60 min after the impulsive input. The perturbation with the maximum amplitude has a frequency of 4.4 mHz. The other dominant modes have frequencies of 3.6 and 5.1 mHz. The beats between the dominant modes are also seen. In the distance, the gravity modes are dominant. The horizontal phase velocities are about 220 to 300 m/s, and the horizontal wavelengths are about 200 to 400 km. The good agreement between the simulation and the observations indicates that ionospheric oscillations generated by the earthquake are mainly due to the motion of the neutral atmosphere.
Key wordsAcoustic wave acoustic resonance gravity wave TEC earthquake
Acoustic waves with low frequencies close to the cutoff frequency can be trapped between some altitudes due to the thermal structure of the atmosphere. Theoretical and numerical studies have shown that atmospheric waves with frequencies around the acoustic cutoff can be trapped between the ground surface and the lower thermosphere. Modal resonance occurs at frequencies of about 3.7 and 4.5 mHz although some part of the energy leaks upward (Jones and Georges, 1976; Lognonné et al., 1998; Kobayashi, 2007; Shinagawa et al., 2007; Watada and Kanamori, 2010).
The upward leakage of the atmospheric oscillations was observed at the ionospheric height. Dautermann et al. (2009) reported a double train of wave-packets of total electron content (TEC) which resulted from the beats of the dominant atmospheric modes around 4 mHz after the 2003 July 13, Soufriére Hills Volcano explosion (Montserrat, Lesser Antilles). Choosakul et al. (2009) reported a periodic fluctuation of TEC measured by GPS receivers after the Sumatra 2004 earthquake. 4-min (4-mHz) periodic TEC variations continued for more than four hours near the epicenter. They were observed by only three GPS stations whose distance from the epicenter was less than 1200 km. Since this observation was carried out by several stations the two-dimensional structures of the ionospheric variations generated by the acoustic resonance were not detected.
After the M 9.0 Tohoku Earthquake (epicenter: 38.32°N, 142.36°E, origin time: 05:46:23 UT on March 11, 2011 (US Geological Survey)), two-dimensional structures of periodic oscillations of TEC were observed by a dense GPS receiver network (Chen et al., 2011; Saito et al., 2011; Tsugawa et al., 2011). The TEC oscillations had circular or concentric structures. The center of the structures was closer to the Japan trench than the epicenter (Tsugawa et al., 2011). This was consistent with the source of the largest tsunami estimated from tsunami waveform inversion (Fujii et al., 2011). This indicates that the atmospheric waves were generated by a displacement of the sea surface caused by the earthquake, and propagated upward to the thermosphere (Saito et al., 2011; Tsugawa et al., 2011). In the vicinity of the epicenter, two-dimensional structures of the ionospheric variations generated by the acoustic resonance between the ground surface and the lower thermosphere was firstly observed (Saito et al., 2011). The area of the acoustic resonance may correspond to that of the sea-surface displacement. This means that the area and the amplitude of the sea-surface displacement can be estimated from those of the observed TEC oscillations. It is necessary for the estimation to simulate the structures of the oscillations qualitatively and quantitatively. In this study, as a first step for the estimation, we simulate qualitatively the neutral atmospheric perturbations at the ionospheric heights.
The horizontal background wind should affect the propagation of gravity waves by altering the intrinsic wave frequency (Kato, 1980). For the acoustic waves around the cutoff frequency, however, the background wind is not very important since the horizontal phase velocity of the acoustic waves is much larger than the background wind velocity. Here, we focus on the structure of the acoustic waves, so the background wind is neglected.
3. Results and Discussion
Further out than 800 km, waves in the simulation have horizontal phase velocities of about 220 m/s on the line “a”, 250 m/s on “b” and 300 m/s on “c”, and horizontal wavelengths of about 200 km on “a” and 400 km on “c” as shown in Fig. 2. These are in good agreement with the observational results (A to C) shown in Fig. 1. Both figures show that waves in the distance with longer horizontal wavelengths have a larger horizontal phase velocity at a certain time. Figure 4 shows that the frequency of the waves becomes lower according to the distance from the epicenter. They are the features of the gravity modes (e.g., Kato, 1980). The amplitudes of lower frequencies below 2 mHz increases as the distance from the source increases as shown in Fig. 4. This indicates that gravity waves with higher frequencies are close to evanescent below 300 km altitude.
The noticeable discrepancy between the simulation and the observational results is the existence of the fast propagating waves with velocities of 3,500 and 780 m/s at early periods, from 05:55 to 06:15 UT in the observation. This could be caused by the assumption of the initial change in the atmospheric motion on the ground-surface as the source. In the simulation, the source is only applied from −125 km to 125 km at time 0. In the actual situation, seismic waves such as Rayleigh waves can also be the source of the atmospheric waves.
A wave with a phase velocity of 490 m/s on “d” in Fig. 2 is a longitudinal wave propagating purely horizontally with a vertical wavefront above 100-km altitude (not shown here). The sound speed at 300-km altitude in the atmosphere used in the simulation is about 640 m/s. Therefore, this wave is neither a gravity wave nor an acoustic wave. A wave with a phase velocity of 420 m/s on “D” in Fig. 1 might be the different mode from “A” to “C” because it decreases more rapidly than the three modes. Further analyses are necessary to determine what mode “d” and “D” belong to.
Another simulation is performed with a source amplitude (win) of 5.0 × 10−3 cm/s (but not shown). The fraction of the atmospheric perturbations to the background at 300-km altitude is about ~0.001% in this case. Both the source amplitude and the amplitudes of upper atmospheric perturbations are smaller by a factor of 100 than for the source amplitude of 0.50 cm/s. The features of the upper atmospheric perturbations are not so different qualitatively from those with the larger source amplitude. This shows that the response of the amplitudes of upper atmospheric perturbations is linear to the source amplitude. Therefore, the source amplitude can be estimated if the amplitudes of upper atmospheric perturbations are obtained by observation.
Most of the features of periodic TEC oscillations can be explained qualitatively with only neutral atmospheric perturbations although the source is assumed to be a fairly simple surface displacement. In several previous studies, it was reported that gravity waves generated by tsunamis were detected in the ionospheric TEC (e.g., Rolland et al., 2010). Our simulation, however, indicates that the dominant atmospheric oscillations observed in the ionospheric TEC near the epicenter were generated by a sea-surface displacement, not by a propagating tsunami.
It is necessary for the estimation of a more realistic source to consider ionospheric plasma motions and reproduce observational results quantitatively. If the surface displacement which generates a tsunami is estimated, the height of a tsunami can be estimated with a general tsunami simulation.
Numerical simulations are performed to simulate the atmospheric perturbations observed at ionospheric heights just after the 2011 off the Pacific coast of Tohoku Earthquake. The oscillations of TEC observed with a GPS receiver array had high frequencies near the epicenter and low frequencies in the distance. The dominant frequencies near the epicenter indicated that the acoustic resonance between the ground-surface and the lower-thermosphere was excited by the earthquake. Simulated atmospheric perturbations at 300-km altitude show remarkable agreement with the observed TEC oscillations qualitatively, although the background wind is neglected. The good agreement indicates that ionospheric oscillations generated by the earthquake are mainly due to the motion of the neutral atmosphere. The area and the amplitude of the initial sea surface displacement which generate a tsunami might be estimated by considering ionospheric plasma motions and simulating observational results quantitatively.
This work was supported by Grant-in-Aid for JSPS Fellows. In this research work we used the supercomputer of ACCMS, Kyoto University. The GPS data of GEONET was provided by Geophysical Information Authority, Japan.
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