Sensitivity of ionosonde detection of atmospheric disturbances induced by seismic Rayleigh waves at different latitudes

Large earthquakes are known to cause appreciable ionospheric disturbances through lithosphere–atmosphere–ionosphere coupling. The vertical ground motion of seismic waves launches infrasonic acoustic waves (infrasound) into the atmosphere, and the excited waves propagate upward. The amplitude of waves increases with height owing to conservation of momentum, because the atmosphere is rarefied exponentially with height. The neutral particle motion of the acoustic waves induces alternating enhancements and depletions of plasma density through the neutral–ion collisions at ionospheric heights (Maruyama and Shinagawa 2014). The resulting ionospheric perturbation is detected by various radio techniques. The trans-ionospheric radio propagation of signals transmitted from Global Positioning Satellite System (GPS) satellites is used to observe the coseismic effect on the total electron content (TEC) along the ray path (Calais and Minster 1995; Tsugawa et al. 2011; Rolland et al. 2011). The Doppler sounding with continuous high-frequency (HF) radio waves detects the periodic fluctuation of phase length associated with the electron density perturbation near the reflection level (Yuen et al. 1969; Wolcott et al. 1984; Tanaka et al. 1984; Artru et al. 2004; Chum et al. 2012, 2016). The pulsed HF radar tracks horizontal propagation of the perturbation (Nishitani et al. 2011; Ogawa et al. 2012). A combination of the TEC measurements, HF Doppler sounding, magnetometer, and ground infrasonic sounder tracks the vertical propagation of the perturbation, since each technique is sensitive to the disturbances at different height (Liu et al. 2016). The vertical incidence radio sounding (ionosonde) observes the distortion of echo traces (Leonard and Barnes 1965; Yuen et al. 1969; Liu and Sun 2011; Maruyama et al. 2011, 2012, 2016a, b; Maruyama and Shinagawa 2014; Berngardt et al. 2015) and is a technique dealt with in this paper, as described further below.

At remote distances from the epicenter, Rayleigh waves are the most important source of coseismic infrasound because they propagate along Earth’s surface without significant attenuation of the amplitude due to geometrical spreading (Lay and Wallace 1995). The ionospheric anomaly exhibits a characteristic of traveling ionospheric disturbances following the Rayleigh wave propagation (Liu and Sun 2011; Maruyama et al. 2012). Short-period Rayleigh waves in the range of 15–50 s, near the Airy phase, yield ionospheric density fluctuations with vertical wavelengths of 7.5–50 km, because the sound speed is 500–1000 m/s at ionospheric heights. The vertical wavelength is less than the bottom-half thickness of the ionosphere, and several cycles of alternating enhancements and depletions of electron density cause distortion of the ionograms characterized as a multiple cusp signature (MCS) (Maruyama et al. 2011, 2016a, b; Maruyama and Shinagawa 2014). Each cusp is related to a density ledge, and the vertical separation of the ledges is the wavelength of the infrasound propagating in the thermosphere (Maruyama et al. 2012, 2016a). Thus, MCS ionograms are considered to be a wave snapshot. Note that this type of ionospheric anomaly is not detected by TEC measurement because the alternating enhancements and depletions of electron density along the ray path offset the contribution to the TEC changes.

Maruyama et al. (2012) examined earthquakes that occurred worldwide with a seismic magnitude of 8.0 or greater and ionograms observed at five ionosonde sites over Japan during the period from 1957 to 2011 and concluded that the detection of MCSs was limited to epicentral distances shorter than \(\sim\)6000 km. Contrary to this, however, MCSs were observed at several sites in Russia (Kaliningrad and Kazan) and Finland (Sodankylä) with long epicentral distances of 9000–15,000 km after several large earthquakes (Yusupov and Akchurin 2015). One of those events observed at Kazan, Russia, after the M8.8 Chile earthquake in 2010 was examined in detail by Maruyama et al. (2016a, b). A notable difference between Kazan and Japanese ionosonde sites is the inclination of Earth’s magnetic field (dip angle) \(I\), i.e., \(I=72^\circ\) at Kazan and \(I=38, 45, 49, 53, \text {and } 59^\circ\) at Japanese sites (Okinawa, Yamagawa, Kokubunji, Akita, and Wakkanai, respectively). Maruyama et al. (2016a) briefly discussed magnetic inclination effects that potentially affect the sensitivity of ionosondes to upper atmospheric disturbances induced by upward propagating infrasound. Other differences are the topology of Earth’s surface and jet streams, which may distort the wave fronts of acoustic waves propagating from the ground to the ionospheric level, but these are outside the scope of the current paper. The magnetic inclination effects are discussed quantitatively in this paper. Here we present numerical simulations of infrasonic acoustic waves and electron density perturbation induced by vertical ground motion of seismic Rayleigh waves. Ionograms were synthesized from the simulated electron density profiles for different dip angles. Examples of MCS ionograms are presented in the next section. Magnetic inclination effects, numerical simulations, and synthetic ionograms follow. The results are summarized in the last section.

The magnitude 8.8 earthquake occurred offshore of Maule \((35.91^\circ \hbox {S}, 72.73^\circ \hbox {W})\), Chile, at 0634:14 UTC on February 27, 2010, and seismic signals were recorded at Obninsk (\(55.11^\circ \hbox {N}\), \(36.57^\circ \hbox {E}\); epicentral distance 14,375 km), Russia, approximately 1 h after the earthquake, as shown in Fig. 1b. During this period, ionograms with 1-min intervals were obtained at Kazan (\(56.43^\circ \hbox {N}\), \(58.56^\circ \hbox {E}\); epicentral distance 15,148 km), Russia. The difference between the epicentral distances for Obninsk and Kazan was approximately 773 km. The most significant MCS was observed at 0800 UTC, as shown in Fig. 1a. The mean propagation velocity of the Rayleigh waves along Earth’s surface was estimated at 3.8 km/s (Maruyama et al. 2016a). Thus, it is estimated that the ground motion of the Rayleigh waves started at around 0740 UTC at Kazan with a delay of \(\sim\)3 min after the occurrence at Obninsk. The ionospheric disturbances shown in Fig. 1a might be caused by the ground motion indicated by the horizontal bar in Fig. 1b, considering the Rayleigh wave propagation time from Obninsk to Kazan and the acoustic wave propagation time from the ground to the ionosphere at Kazan. The maximum amplitude of Rayleigh waves was observed at 0746 UTC at Obninsk. However, a deep amplitude modulation of the seismic signals was observed, as shown in Fig.1b. The modulation was most probably caused by multipathing and interference (Capon 1970), and the modulation pattern may not be the same at Kazan. It is natural to consider that the most significant MCS ionogram at Kazan, as shown in Fig. 1a, was caused by the largest amplitude of Rayleigh waves at a level similar to that at Obninsk (0.9 mm/s).

A similarly significant MCS was observed at Yamagawa (\(31.2^\circ \hbox {N}\), \(130.62^\circ \hbox {E}\); epicentral distance 1124 km), Japan, after the M7.7 aftershock (\(36.12^\circ \hbox {N}\), \(141.25^\circ \hbox {E}\); 0615:34 UTC) of the massive M9.0 Tohoku-Oki earthquake in 2011, as shown in Fig. 2a. The maximum amplitude of the Rayleigh wave responsible for this MCS was 5.0 mm/s at Tashiro \((31.19^\circ \hbox {N}, 130.91^\circ \hbox {E})\), near Yamagawa (difference in epicentral distances of 23 km), as shown by the horizontal bar at \(\sim\) 0621:30 UTC in Fig. 2b. Figure 3a shows another example of an MCS ionogram observed at Yamagawa during the same earthquake. In this ionogram, the amplitude of the deformation was small, showing wiggles at frequencies of 3.5–6 MHz, which is almost the detection limit of coseismic ionogram deformation. Figure 3b shows the ground motion at Tashiro. The large-amplitude signals before \(\sim\)0556 UTC (goes off-scale in the plot) were the Rayleigh waves excited by the M9.0 main shock. The ground motion responsible for the MCS ionogram in Fig. 3a is shown by the horizontal bar in Fig. 3b and was most probably excited by the M6.6 aftershock at 0558 UTC; the amplitude was 0.5–1 mm/s. (Note that the ionosonde was operated at each quarter-hour and no ionogram corresponding to the main shock was obtained.)

When the three ionograms in Figs. 1a, 2a, and 3a after the two earthquakes are compared, it is found that ionograms at Kazan are likely to be roughly five times more susceptible to the seismic ground motion than those at Yamagawa. The two ionosonde sites are characterized by different dip angles: \(I=72^\circ\) at Kazan and \(I= 45^\circ\) at Yamagawa.

The numerical study on the sensitivity of ionograms to atmosphere–ionosphere perturbation induced by ground motion followed two steps. The simulation of acoustic wave propagation and associated electron density perturbation was first conducted. Then ionograms were synthesized from the perturbed electron density distribution. The calculations were conducted for \(I=45\) and \(72^\circ\) corresponding to Yamagawa and Kazan, respectively.

The unperturbed electron density profile prior to the application of acoustic waves was obtained by integrating the plasma equation set (1) and (2) with a fixed local time, 1500 LT, until the equilibrium state was attained. This process ensures that the background electron density distribution does not change during the simulation of acoustic wave propagation. Because our major purpose is to examine the effect of magnetic inclination at two locations with different dip angles, background atmospheric parameters and solar zenith angles for both calculations were chosen to be the same as those at Yamagawa when coseismic disturbances were observed after the M9.0 Tohoku-Oki earthquake in 2011, and only \(I\) was changed with the locations. In actual situations, the ionosphere and thermosphere vary widely depending on the local time, latitude, season, solar activity, etc. A key parameter for the detection of MCS in ionograms is the \(f_oF_1\) (Maruyama et al. 2012), which is a measure of the vertical electron density gradient in the lower F region. The \(f_oF_1\) in the two cases (Kazan and Yamagawa) were very similar (4–5 MHz). It is possible to include the above factors in the numerical calculations, but an essential physical mechanism will be obscure. Figure 6 shows the resultant unperturbed density profiles for \(I= 45\) and \(72^\circ\) by the green and orange lines, respectively. In the plots, the electron densities at the peak and in the topside for \(I=72^\circ\) were lower than those for \(I=45^\circ\), which is ascribed to the difference in the vertical component of the field-aligned diffusion that depends on the dip angle.

Figure 7 shows the vertical velocity of the neutral particle associated with the propagation of the acoustic waves. Because the atmospheric parameters were the same for the two calculations and the ion-drag effect on the neutral particle dynamics was neglected, velocities were identical for \(I=45\) and \(72^\circ\). The amplitude increased with height and became visible above \(\sim\)50 km in the diagram. However, it reached the maximum value of approximately 6 m/s at a height of 170 km, i.e., \(1.2\times 10^4\) times the initial value on the ground. At higher altitudes, the wave amplitude decayed with height mostly as a result of viscous damping and almost vanished above the \(F_2\) peak height. Figure 8 shows the percent electron density perturbation for \(I=45\) and \(72^\circ\) by the green and orange lines, respectively. The amplitude of positive perturbation (enhancement) reached a maximum of \(\sim\)0.40 and \(\sim\)0.74% for \(I=45\) and \(72^\circ\), respectively, near 172 km. Similarly, the amplitude of negative perturbation (depletion) reached a maximum of \(\sim\)0.46 and \(\sim\)0.84% for \(I=45\) and \(72^\circ\), respectively, near 165 km. It is noted that the negative half cycle is slightly shorter than the positive half cycle and the net gain or loss of plasma through one cycle of perturbation is nil. The inclination effect on the neutral–ion coupling became visible, and the overall maximum amplitude of the density perturbation for \(I=72^\circ\) (Kazan) was \(\sim\)1.8 times that for \(I=45^\circ\) (Yamagawa), as expected from (1) and (2).

Finally, ionograms were synthesized from the perturbed electron density profiles by calculating virtual heights at frequencies in 0.02-MHz increments, as described by (3)–(11). In this calculation, only O-mode propagation in the vertical direction was considered, and the frequency increments were in accord with the ionosonde operation. Figure 9 shows the ionograms for \(I=45\) and \(72^\circ\) in green and orange, respectively, and the plot for \(I=72^\circ\) is shifted by 30 km. The two ionograms show different responses to the atmosphere–ionosphere perturbations induced by the same amplitude of seismic ground motion. The disturbance in the trace for \(I=72^\circ\) exhibits a well-developed cusp signature, while that for \(I=45^\circ\) merely shows wiggles. The ratio of cusp heights was \(\sim\)3, which was slightly smaller than the combination of two geometrical effects \((1.81\times 2.29)\).

Seismic waves cause ionospheric disturbances at remote distances. Rayleigh waves with a period of 15–50 s induce multiple cusp signatures (MCSs) or wiggles in ionogram traces. In the previous observations, this type of irregularity was found to be significant at higher latitudes, such as Kazan, Russia, than Japan’s latitudes. By numerical simulations, it was shown that the sensitivity of ionograms to seismic ground motion varies depending on the magnetic inclination. At higher latitudes with a large dip angle, coupling between the acoustic waves launched by seismic ground motion and the ionospheric plasma is strong, inducing a large amplitude of perturbation in the electron density than that at lower latitudes with a small dip angle. Radio pulses transmitted by ionosondes are sensitive to the electron density perturbation at a small angle between the ray direction and the magnetic fields at higher latitudes. Thus, the combined effect of atmosphere–ionosphere coupling and radio wave propagation at high latitudes yields a high sensitivity of the ionosonde detection of seismic ground motion, which explains the observations of coseismic ionospheric irregularities at a large epicentral distance of 15,000 km such as at Kazan, after the 2010 Chile earthquake.