Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

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Journal of Atmospheric and Solar-Terrestrial Physics

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Infrasound in the ionosphere from earthquakes and typhoons

J. Chum a,*, J.-Y. Liu b, K. Podolsk�a a, T. �Sindel�a�rov�a a

a Institute of Atmospheric Physics CAS, Bocni II/1401, 14131 Prague 4, Czech Republicb Institute of Space Science, National Central University, Chung-Li 320, Taiwan

A R T I C L E I N F O

Keywords:InfrasoundEarthquakeIonosphereNonlinear wave propagationTyphoonRemote sensing

* Corresponding author.E-mail addresses: jachu@ufa.cas.cz (J. Chum), jyliu@j

http://dx.doi.org/10.1016/j.jastp.2017.07.022Received 21 February 2017; Received in revised form 29Available online 3 August 20171364-6826/© 2017 Elsevier Ltd. All rights reserved.

A B S T R A C T

Infrasound waves are observed in the ionosphere relatively rarely, in contrast to atmospheric gravity waves.Infrasound waves excited by two distinguished sources as seismic waves from strong earthquakes (M > 7) andsevere tropospheric weather systems (typhoons) are discussed and analyzed. Examples of observation by an in-ternational network of continuous Doppler sounders are presented. It is documented that the co-seismic infra-sound is generated by vertical movement of the ground surface caused by seismic waves propagating at supersonicspeeds. The coseismic infrasound propagates nearly vertically and has usually periods of several tens of secondsfar away from the epicenter. However, in the vicinity of the epicenter (up to distance about 1000–1500 km), thelarge amplitudes might lead to nonlinear formation of N-shaped pulse in the upper atmosphere with much longerdominant period, e.g. around 2 min. The experimental observation is in good agreement with numerical modeling.The spectral content can also be nonlinearly changed at intermediate distances (around 3000–4000 km), thoughthe N-shaped pulse is not obvious. Infrasound waves associated with seven typhoons that passed over Taiwan in2014–2016 were investigated. The infrasound waves were observed at heights approximately from 200 to300 km. Their spectra differed during the individual events and event from event and covered roughly the spectralrange 3.5–20 mHz. The peak of spectral density was usually around 5 mHz. The observed spectra exhibited finestructures that likely resulted from modal resonances. The infrasound was recorded during several hours forstrong events, especially for two typhoons in September 2016.

1. Introduction

Acoustic-gravity waves represent an important coupling mechanismbetween the lower atmosphere and upper atmosphere as they transfermomentum and energy between different atmospheric layers; theirpresence in the ionosphere might also affect radio communications andsignals from GPS satellites (Fritts and Alexander, 2003; La�stovi�cka, 2006;Nishioka et al., 2013). The acoustic mode propagates at frequencieshigher than the acoustic cut-off frequency ωa; the mode propagating atfrequencies lower than the buoyancy frequency ωB (ωa>ωB) is calledgravity waves (GWs) (e.g., Fritts and Alexander, 2003; Kelley, 2009).Whereas the GWs are frequently observed in the ionosphere/thermo-sphere and have been broadly studied since the pioneering work by Hines(1960) as is documented by numerous reports (Vadas, 2007; Shiokawaet al., 2009; Otsuka et al., 2013 among many others), the observation ofinfrasound in the ionosphere is much rare. Only long-period infrasound,with periods longer than approximately 10 s, can reach the ionosphere;the shorter periods (higher frequencies) are significantly damped belowthe ionosphere (Blanc, 1985). The infrasound observed in the ionosphere

upiter.ss.ncu.edu.tw (J.-Y. Liu), kapo@

May 2017; Accepted 31 July 2017

mostly originated from strong (M> 7) earthquakes (Artru et al., 2004; Liuet al., 2016; Chum et al., 2016b and references therein) or severetropospheric weather systems (Georges, 1973; �Sindel�a�rov�a et al., 2009).It is well documented that the coseismic infrasound is mainly generatedby the vertical movement of the ground surface (e.g., Watada et al., 2006;Chum et al., 2012). As the seismic waves propagate at supersonic speeds,the infrasound generated outside the epicenter propagates nearly verti-cally (Maruyama and Shinagawa, 2014; Liu et al., 2016; Chum et al.,2016b). Contrary, the generation and radiation pattern of long periodinfrasound waves from large convective systems, cyclones and gust frontsand their propagation to the ionosphere is much less understood.

Infrasound in the ionosphere is usually detected as perturbations ofthe total electron content (TEC) measured by dual-frequency GPS re-ceivers (Calais and Minster, 1995; Lay et al., 2015) or as changes ofDoppler shift observed by continuous Doppler sounders (Georges, 1973;Chum et al., 2016a, 2016b and references therein). There is a principledifference between these two remote sounding techniques. The GPS TECrepresents an integrated value measured along the signal path betweenthe GPS receiver and the satellite. The heights of TEC perturbations are

ufa.cas.cz (K. Podolsk�a), tersin@ufa.cas.cz (T. �Sindel�a�rov�a).

J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

not known; it is only assumed that the main contribution to the TECvariations is at the altitudes around the peak of maximum ionization, i.e.,in the F layer, approximately from 200 to 300 km. The GPS TEC per-turbations observed by dense networks of GPS receivers are often used tostudy ionospheric responses to earthquakes (Liu et al., 2011; Astafyevaet al., 2011). Contrary, the continuous Doppler sounding provides in-formation about variations at a specific altitude, at which the soundingradio signal reflects. The height of reflection varies during the day andseason; however, it can be determined from a nearby ionosphericsounder or estimated from a model (e.g., international reference iono-sphere, IRI). The knowledge of ionospheric and atmospheric fluctuationsat specific heights makes the comparison with numerical simulationsmuch easier and straightforward than in the case of integral values ob-tained by GPS-TEC measurements.

The main purpose of this paper is to present and compare the char-acter of infrasound in the ionosphere originating from seismic waves andtyphoons (large convective systems) that represent the main sources ofinfrasound in the ionosphere. It will be also shown that character ofcoseismic infrasound depends on distance from the epicenters of strongearthquakes. Recent results obtained from observation of coseismicperturbations by an international network of continuous Dopplersounders (Chum et al., 2012, 2016a, 2016b) will be reviewed and alsopartly reanalyzed using numerical simulation. Namely, the infrasoundwaves related to three distinct earthquakes are compared and discusseda) M 9.0 that occurred near Japan on 11 March 2011, observed in theCzech Republic at about 9000 km distance from the epicenter. b)M 7.8 inNepal on 25 April 2015 observed in the Czech Republic and Taiwan atabout 6300 and 3700 km distance from the epicenter, respectively. c) M8.3 near Chile on 16 September 2015, observed in Argentina at around800 km distance from the epicenter. In addition, first results of analysis ofinfrasound that was observed in the ionosphere over Taiwan duringpassages of seven typhoons are presented and discussed. The paper isorganized as follows: Section 2.1 provides short introduction to Doppler

Fig. 1. Vertical velocity of ground surface motion (a) and Doppler shift spectrogram (b) recorearthquake at 05:46:24 UT. Colors in the Doppler shift spectrogram indicate common logarithinterpretation of the references to colour in this figure legend, the reader is referred to the we

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sounding with application to infrasound. Section 2.2 briefly describesnumerical simulation used to distinguish between linear and nonlinearpropagation of infrasound and to compare with observation. Section 2.3presents analyses and comparison of different cases of coseismic infra-sound observed by continuous Doppler sounders. Section 2.4 shows firstresults of the analysis of infrasound generated by typhoons that passedTaiwan from 2014 to 2016. Section 3 provides discussion and compari-son with previous reports. Section 4 represents a brief summary.

2. Measurements and data analysis

Examples of co-seismic infrasound observed bymultipoint continuousDoppler sounding systems (CDSSs) installed in the Czech Republic(~50.3� N, 14.5� E), Argentina (~26.8� S, 65.2� W), and Taiwan (~23.9�

N, 121.2� E), and examples of infrasound generated by typhoons passingover Taiwan will be presented. The multipoint CDSS used in this study iscomposed of three transmitters forming approximately equilateral tri-angle with about 100 km side and one receiver (minimum configurationfor each location). The CDSS was originally designed to study GWs; threespatially separated reflection points make it possible to determine hori-zontal propagation velocities and directions of GWs and of other iono-spheric perturbations (Chum et al., 2014). The transmitted power is only1 W. All the CDSSs are located close to an ionospheric sounder todetermine the height of reflection. The sounding frequencies are3.59 MHz in the Czech Republic (also 4.65 and 7.04 MHz since 2014),4.63 MHz in Argentina, and 6.57 MHz in Taiwan. The low frequencyCDSS data (after downward frequency conversion) are stored at 305 Hzsampling rate. Data are first visualized in the form of Doppler shiftspectrograms (e.g. Fig. 1b) that are computed by successive spectral an-alyses using overlapping cosine time windows (usually 75% overlap isused) to get smooth spectrograms. The effective length of the time win-dow can be set according the signal character; it is usually on the order of10 s. For the purpose of the next data analysis, maxima of spectral

ded in the Czech Republic on 11 March 2011. Zero time corresponds to the beginning ofm of received power spectral densities in arbitrary units (antenna is not calibrated). (Forb version of this article.)

J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

intensities (visually checked and corrected if necessary) are found atspecific time steps (6 s in the case of infrasound analysis presented in thispaper) separately for each signal path (transmitter-receiver pair).

2.1. Continuous Doppler sounding

The principle of Doppler sounding is based on measurements of theDoppler shift that experiences the sounding radio signal during itsreflection from the ionosphere if the reflection level moves or if theelectron density changes in the reflection region (Davies et al., 1962).Owing to geomagnetic field, radio waves actually propagate in twomodes in the ionosphere: in the ordinary (L-O) and extraordinary (R-X)modes. The vertically propagating L-O mode reflects at the height wherethe local plasma frequency, given by the electron density, matches thefrequency of the sounding signal. In the case of oblique sounding or in thecase of extraordinary wave mode (R-X), the signal is reflected at loweraltitudes compared to vertically propagating L-O mode; a more detaileddiscussion to reflection heights was recently given by Chumet al. (2016a).

It was shown that the contribution of compression or rarefaction ofplasma caused by infrasound waves to the observed Doppler shift cannotbe neglected as this contribution might be larger than that from the upand down motion of the reflection level (Chum et al., 2016a). Consid-ering that the main contribution to the observed Doppler shift is in thereflection region in the F layer where the plasma is magnetized and thatthe photoionization and electron losses can be neglected, then the ver-tical component of air particle oscillation velocities w can be estimatedfrom the observed Doppler shift fD by equation (1)

w¼�fD⋅c

2f0 sin2ðIÞ⋅∂N∂z���∂N∂z þ iN 2πfIS

cS

���¼�fD⋅c

2f0 sin2ðIÞ⋅∂N∂zffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�

∂N∂z

�2þ�N 2πfIS

cS

�2r ;

(1)

where c is the speed of light, f0 is the frequency of sounding radio wave, Iis the inclination of geomagnetic field, N and ∂N/∂z is the electron den-sity and its gradient at the height of reflection, cs is the speed of sound atthe height of reflection, fIS is the dominant frequency of the infrasoundwave and i2¼�1. The termN⋅(2πfIS)/cs originates from the compression.For large plasma density gradients, with respect to the compression term∂N/∂z >>N⋅(2πfIS)/cs, the compression can be neglected and equation (1)reduces to the well-known equation (2) that represents approximation ofmirror-like reflection. This approximation only takes into account theradial advection (usually up and down motion of the reflecting level).

w ¼ �fD⋅c

2f0 sin2ðIÞ ; (2)

2.2. Numerical simulation of coseismic infrasound

The numerical simulation used in this study was described by Chumet al. (2016b). Therefore, only main points are mentioned here for con-venience. The simulation is based on the fact that the infrasound wavestriggered by seismic waves outside the epicenter region propagate nearlyvertically. This is because of the supersonic speed of seismic waves; so thegenerated infrasound waves are roughly plane waves with wave vectorsdeviated from zenith by a small angle α, which is usually less than 7�

(Rolland et al., 2011a; Chum et al., 2016a).

sinðαÞ ¼ cS0cG0

; (3)

where cS0 is the speed of sound in the atmosphere above the groundsurface and cG is the speed of seismic wave on the ground surface. Theapproximately vertical propagation of coseismic infrasound was experi-mentally confirmed by a number of independent studies (Chum et al.,

74

2012, 2016a; Maruyama and Shinagawa, 2014; Liu et al., 2016). Thus, itis possible to perform the simulation in 1D, along the vertical z axis. Theunperturbed ambient temperature T0 and mass density of the air ρ0 areobtained by the NRLMSISE-00 model for the location and time of mea-surement. The perturbations of temperature T1, air density ρ1 and verticalair particle velocity w are obtained as a solution of continuity, mo-mentum and heat equations for a compressible fluid (4)–(6)

∂ρ1∂t

¼ �∂ðρ0 þ ρ1Þ∂z

w� ∂w∂z

ðρ0 þ ρ1Þ; (4)

∂w∂t

¼�∂w∂z

w�RðT0þT1Þðρ0þρ1Þ

∂ðρ0þρ1Þ∂z

�R∂ðT0þT1Þ

∂z�gþ4

3μ

ðρ0þρ1Þ∂2w∂z2

;

(5)

∂T1

∂t¼ �∂ðT0 þ T1Þ

∂zw� ðγ � 1ÞðT0 þ T1Þ ∂w∂z þ γμ

Prðρ0 þ ρ1Þ∂2T1

∂z2; (6)

where R is the specific gas constant (R¼kB/m; kB is the Boltzmann'sconstant andm is the mean mass of the air particles), g is the gravitationalacceleration, μ is the molecular (dynamic) viscosity, γ is the adiabaticexponent and Pr is the Prandtl number that relates the molecular vis-cosity with the thermal conductivity; Pr is approximately 0.7 for the air(Vadas and Fritts, 2005). Details about μ values are given by Chum et al.(2016b). The γ values in the gas containing monoatomic and diatomicspecies are computed from the number density weighted degrees offreedom (Walterscheid and Hickey, 2001). The unperturbed valuessatisfy the steady state solution. Thus, there are no perturbations untilthey are introduced at the lower boundary. The boundary condition forz ¼ 0 (on the ground) were determined by seismic measurements; thevelocity perturbations w at z ¼ 0 were equal to the measured verticalvelocities vz of the ground surface, w ¼ vz (Watada et al., 2006; Chumet al., 2016b). The values of ρ1 and T1 at z ¼ 0 are obtained under linearapproximation. Once the lower boundary conditions are defined, theevolution of ρ1,w, and T1 is calculated considering all the nonlinear termsin the set of inhomogeneous equations (4)–(6) up to the height of400 km. The set of equations is solved by the implicit finite differencemethod with the time and spatial resolution of 0.01 s and 40 m,respectively. The height of 400 km for the upper boundary was chosen toensure sufficient attenuation of waves to minimize reflections from theupper boundary. We verified that practically the same results were ob-tained for the upper boundary at 500 km. In addition, the values at upperboundary (grid point number N) were set to be equal as at the point (N-2)to avoid gradients in the last computed point N-1.

2.3. Coseismic infrasound

Three different events representing observation of the coseismicinfrasound by CDSS far from the earthquake epicenter (around 9000 km),relatively close to the epicenter (around 800 km) and at intermediatedistance at about 3700 km will be compared. The first two events will bedescribed briefly as their analyses were already published. Only the mainpoints will be mentioned for the reader's convenience and for ease ofcomparison. A new analysis for the observation at intermediate distancewill be shown.

Chum et al. (2012) reported observation of coseismic infrasound bythe CDSS located in the Czech Republic, at the about 9000 km distancefrom the epicenter of the disastrous M 9.0 earthquake that started nearthe east coast of Honshu, Japan, on 11 March 2011 at 05:46:24 UT. Fig. 1summarizes this observation showing the vertical velocity vZ of theground surface movement (a) and the Doppler shift spectrogram recor-ded by the multipoint CDSS (b). Wave packets that correspond to P, S, SS,and Rayleigh waves can be distinguished in the seismic record. Impor-tantly, corresponding wave packets can also be found in the ionosphere(at the heights of about 210 km) with about 9 min delays, which are

J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

consistent with (quasi)vertical propagation of infrasound. The absolutevalues of cross-correlation coefficients between the vZ and fD fluctuationswere higher than 0.9 for the wave packets corresponding to P, S, and SSwaves. Actually, the vZ and fD signals are anticorrelated because of minussign in equations (1) and (2).

A completely different picture was observed at about 800 km hori-zontal distance from the epicenter of the M 8.3 earthquake that startednear the Chilean coast on 16 September 2015 at 22:54:32 UT (Chumet al., 2016b). The coseismic fluctuations observed in the ionosphere atheight of about 200 km by CDSS (Fig. 2c and Fig. 2d) had significantlydifferent shape and frequency content than vertical motion vZ of theground surface below (Fig. 2a). Chum et al. (2016b) performed 1D nu-merical simulation described in Section 2.2 for boundary condition basedon the real measurement, namely w ¼ vz at the ground surface, and ob-tained at the height of observation the N-shaped pulse that was verysimilar to that derived from the observed Doppler fD. Importantly, it wasshown that the N-shaped pulse results from nonlinear phenomena. Thesimulated pulse is presented in Fig. 2b.

Chum et al. (2016a) presented observations and analysis of iono-spheric infrasound that was generated by seismic Rayleigh waves prop-agating from the M 7.8 earthquake with the epicenter in Nepal andbeginning time at 06:11:26 UT on 25 April 2015. The reported obser-vations were performed in Taiwan about 3700 km distance from theepicenter, and in the Czech Republic, about 6300 km distance from theepicenter. The observations are summarized by Fig. 3. Chum et al.(2016a) mainly discussed the role of observation height, magnetic fieldinclination and compression mechanism on the observed amplitude of fDfluctuations. However, they also mentioned the difference between thespectral content of vZ and fD fluctuations in Taiwan that was not observedin the Czech Republic. This difference was not analyzed in detail by

Fig. 2. Measured and simulated quantities in Tucum�an on 16 September 2015. Time ¼ 0 corresof ground surface motion b) Simulated air particle velocity w at the altitude of 200 km obtainedobserved in Tucum�an. d) Air particle velocity obtained from the observed Doppler shift fD.

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Chum et al. (2016a). Having now the tool for nonlinear numericalsimulation (Section 2.2) and the experience with it from the analysis ofcoseismic perturbation at small distances (~800 km) from the epicenter,we will investigate a possible role of nonlinear phenomena at interme-diate distances. Fig. 4a and b presents fluctuations of w obtained from fDby equation (1) and corresponding spectrogram, respectively. Equation(1) was used to obtain w from fD (Fig. 3a) as Eq. (2) neglects the effect ofcompression and might significantly overestimate the air particle veloc-ities w (Chum et al., 2016a). Fig. 4c, e, and d, f display the simulated wfluctuations and their spectra, respectively, at the estimated height ofobservation (around 220 km). The numerical simulation was run withtwo different boundary conditions: w ¼ vz on the ground (plots c and d)and w ¼ vz/100 on the ground (plots e and f). Consequently, both sim-ulations provide different amplitudes at the same height as is obviousfrom Fig. 4c and e. Moreover, the simulated waveforms differ also in theirspectral content. The nonlinear phenomena can be neglected for thelatter case because of small amplitudes of perturbations. It is seen that thedynamic spectra of the observed fluctuations (Fig. 4b) and simulation forw¼ vz on the ground (Fig. 4d) are similar, whereas the dynamic spectrumofw obtained forw¼ vz/100 on the ground (Fig. 4f) differs and resemblesmore the dynamic spectrum of vz (Fig. 3a in Chum et al. (2016a)).Therefore, it is concluded that nonlinear phenomena might play a partialrole also at the intermediate distances (3700 km in this case), though theN-shaped pulse is not well developed.

It should also be noted that we did not get (contrary to the 16September event presented in Fig. 2) a good agreement for the ampli-tudes of w fluctuations; the modeled velocities w obtained for w ¼ vz onthe ground are about 7 times larger than the velocities w obtained fromthe observed fD. A likely reason for it is a large uncertainty in determiningof ∂N/∂z that is used in Eq. (1). This uncertainty arises from the character

ponds to the beginning of earthquake at 22:54:32 UT in all the plots. a) Vertical velocity vzfor vertical propagation and boundary condition w ¼ vz on the ground. c) Doppler shift fD

Fig. 3. Observed quantities for the Nepal earthquake on 25 April 2015. Time ¼ 0 corresponds to the beginning of earthquake at 06:11:26 UT in all the plots. a), b) Vertical velocity vz ofground surface motion in Taiwan and Czech Republic, respectively. c), d) Observed Doppler shift fD in Taiwan and Czech Republic, respectively. e), f) Air particle velocity w calculated fromthe observed Doppler shift in Taiwan and Czech Republic, respectively.

J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

of the ionogram recorded in Taiwan; it cannot be excluded that the real∂N/∂z is several times larger. We also cannot exclude that nearby ocean,ocean-to land interface, and complicated orography in Taiwan are lesseffective in generating coherent upward propagating waves; the realinfrasound waves could differ from plane waves more than expected inthis case.

2.4. Ionospheric infrasound from typhoons

Altogether seven typhoons passed over Taiwan or in its close vicinityin the time period 2014–2016. The trajectories of these typhoons aredisplayed in Fig. 5 that also shows the locations of the CDSS's transmittersand receivers and the closest distance dMIN of the trajectories of the in-dividual typhoons to the CDSS's reference point, determined as the centerof the anticipated reflection points. The trajectories are displayed in 6-htime step according to http://weather.unisys.com/hurricane/index.php.The date and time that corresponds to the closest distance dMIN is eval-uated for each typhoon and is given as a reference time tR for each event.The list of events, together with typhoon parameters and parametersrelated to infrasound propagation to the upper atmosphere, is presentedin Table 1.

Examples of 30-min time intervals during which infrasound waveswere observed by the CDSS are presented in the Doppler shift spectro-grams in Fig. 6. Fig. 6a shows record from 13:45 to 14:15 UT on 21September 2014 (event 1), when relatively monochromatic infrasound offrequency around 0.0045 Hz was observed. The mean value of Dopplershift changes as the infrasound is superposed on variations of longer timescales, caused by GWs. Only one sounding path, corresponding to Tx3-Rxpair, was operating at that time. Fig. 6b and c shows examples of infra-sound observations from 08:30 to 09:00 UT on 14 September 2016 (event5) and 06:30 to 07:00 UT on 27 September 2016 (event 6), respectively;

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signals from two sounding paths, corresponding to Tx1-Rx and Tx2-Rxpairs are displayed. It is obvious that the signals are not correlated inall the details. However, the main peaks occur at about the same time inboth sounding paths; it means that the observed infrasound wavespropagated quasi-vertically (time delays would be observed if there was asignificant horizontal component of propagation). These intervalsrepresent cases, when the infrasound waves are less monochromatic thanthose displayed in Fig. 6a. Especially Fig. 6c shows the time intervalwhen the infrasound covered relatively broad spectral range, approxi-mately from 0.0035 to 0.022 Hz. Fig. 6a, b, and c represent time intervalsin which the observed infrasound waves could be spectrally analyzed. Toperform the spectral analysis, first the maximum of spectral density wasfound with the time step of 6 s for each available sounding path, thenvisually checked and manually corrected if necessary. In other words, theDoppler shift was approximated by a single valued function of time foreach sounding path. Contrary, Fig. 6d shows an example of the time in-terval in which the Doppler shifted signals could not be reliablyapproximated by single valued functions of time as multiple signals withdifferent Doppler shifts were received on each sounding path at the sametime. Consequently, spectral analysis could not be done for such in-tervals. Typically, spectral analysis of the received signals is impossibleduring spread F occurrences.

Figs. 7 and 8 show evolutions of dynamic spectra in the long periodinfrasound frequency range from 0.003 to 0.08 Hz for the events 1–6during 36-h long time intervals centered along the reference time tR foreach individual event. The lower limit of the displayed frequency range isgiven by the minimum of the acoustic cut-off frequency fAMIN in the at-mosphere, which is around 0.004 Hz (Table 1). The minimum of acousticcut-off frequency is usually in the mesopause region and sets the lowerfrequency limit on infrasound waves propagating to the thermosphere/ionosphere from below, because waves of frequencies lower than fAMIN

Fig. 4. Air particle velocities w and their spectrograms. Time ¼ 0 corresponds to the beginning of earthquake at 06:11:26 UT in all the plots. a) and b) w obtained from the measuredDoppler shift and corresponding spectrogram, respectively. c) and d) w obtained from the numerical simulation simulated for boundary condition w ¼ vz on the ground and correspondingspectrogram, respectively. e) and f) w obtained from the numerical simulation simulated for boundary condition w ¼ vz/100 on the ground and corresponding spectrogram, respectively.

Fig. 5. Trajectories of seven typhoons that passed over Taiwan or in its close vicinity during 2014–2016. Red circle marks position of Doppler receiver, blue diamonds depict positions oftransmitters, and blue crosses the anticipated positions of reflection points. The blue circle displays the center of the reflection points (reference point) and the asterisks show the closestlocations of eyes of the individual typhoons to this reference point. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version ofthis article.)

J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

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Table 1List of typhoon events.

Event Date and Time (tR)related to dMIN

dMIN

(km)v(m/s)

vL(m/s)

fAMIN

(Hz)(∂cS/∂z)max

(s�1)

0 22/07/2014 20:05UT

67 34.2 7.0 0.0042 0.0101

1 21/09/2014 10:18UT

91 22.3 9.5 0.0039 0.0088

2 08/08/2015 01:30UT

11 38.5 7.1 0.0040 0.0084

3 28/09/2015 13:38UT

25 43.5 6.6 0.0038 0.0104

4 08/07/2016 03:18UT

166 37.8 5.0 0.0039 0.0101

5 14/09/2016 08:22UT

236 64.0 6.4 0.0040 0.0094

6 27/09/2016 05:54UT

17 51.3 11.3 0.0038 0.0114

dMIN is the closest distance of typhoon trajectory to the CDSS's reference point, tR is thereference time corresponding to the dMIN position on the trajectory, v is the wind speedaccording to http://weather.unisys.com/hurricane/index.php server interpolated to thereference time tR, vL is the speed of motion along the typhoon trajectory, fAMIN is theminimum acoustic cut-off frequency in the vertical profile above the CDSS at tR, and (∂cS/∂z)max is the maximum of ∂cS/∂z gradient in the vertical profile above the CDSS at tR (cS isthe speed of sound).

J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

are evanescent in the region where f < fAMIN (Jones and Georges, 1976).The upper limit is determined by the time resolution of CDSS; also, thewaves of higher frequencies dissipate below the reflection heights. Thepower spectral intensities are averaged over the available sounding

Fig. 6. Examples of infrasound observation in the Doppler shift spectrograms during 30 min losingle valued functions of time and further processed by spectral analysis. d) Doppler shift spectrpair); consequently, the spectral analysis could not be done. Colors indicate common logarithinterpretation of the references to colour in this figure legend, the reader is referred to the we

78

paths. Only the time intervals in which the sounding signals reflectedfrom the ionosphere (critical frequency of the extraordinary mode fxF2>f0), and in which the received Doppler shifts could be approximated bysingle valued functions of time are displayed. The dynamic spectra for theremaining event 0, the reflection heights estimated by IRI2016 model,and the evolutions of distances between the eyes of individual typhoonsand CDSS's reference point during the 36-h time intervals centered atreferenced times tR are shown in the plots in Fig. 9. The reflection heightsand distances for the individual events are color coded. It is obvious thatthe reflection heights were usually between 200 and 300 km. The highestamplitudes of the Doppler shifts caused by infrasound waves wereobserved for the events 2, 5, and 6, usually at time differences from thereference time, jt-tR j, less than about 8 h. The maximum of spectraldensity was often around 0.005 Hz. Fig. 10 shows spectra for selectedtime intervals with continuous record of Doppler. The selected time in-tervals cover the period of quasi-monochromatic waves (Fig. 6a) and theintervals with highest intensities. Namely, the spectra for the followingtime intervals are displayed: Fig. 10a from 11:00 to 17:30 UT on 21September 2014 (event 1), Fig. 10b from 22:30 UT on 7 August to 01:30UT on 8 August 2015 (event 2), Fig. 10c from 23:00 UT on 13 Septemberto 12:00 UT on 14 September 2016 (event 5), and Fig. 10d from 22:30 UTon 26 September to 12:00 UT on 27 September 2016 (event 6). Thedisplayed spectra were averaged over all the available sounding pathsand filtered using running average over cosine frequency window witheffective width of 0.5 mHz with a 0.125 mHz step in all the plots. Thespectra differ event from event. A relatively distinct maxima of spectraldensities are observed for event 1 (Fig. 10a) and 6 (Fig. 10d) at 4.5 and

ng time intervals. a), b), and c) Time intervals in which the signals were approximated byogram in which multiple signals were received for each sounding path (transmitter receiverm of received power spectral densities in arbitrary units (antenna is not calibrated). (Forb version of this article.)

Fig. 7. Spectrograms of the recorded infrasound during events 1–3. Time ¼ 0 corresponds to the time of dMIN for each event.

Fig. 8. Spectrograms of the recorded infrasound during events 4–6. Time ¼ 0 corresponds to the time of dMIN for each event.

J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

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Fig. 9. a) Height of reflection obtained from IRI2016 at times related to the reference time tR for each event. The individual events (0–6) are color-coded as follows: 0-grey, 1-black, 2- red,3-orange, 4-green, 5-blue, and 6-magenta. The solid lines are for reflection height of ordinary mode, the dotted lines for extraordinary mode. The time intervals at which the signals couldbe spectrally analyzed are marked by asterisks. b) Distance between the typhoon's eye and the reference point (center) of the CDSS. c) Spectrogram of the recorded infrasound during theevent 0. Time ¼ 0 corresponds to the reference time tR. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 10. Examples of spectra for events 1, 2, 5, and 6 calculated over time intervals of continuous record. The time intervals are related to the reference times tR of each event. Red linesmark distinct peaks at 4.5 and 5.25 mHz. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

5.25 mHz, respectively (marked by red lines in corresponding Figures).All the spectra have several local maxima.

3. Discussion, comparison and potential future research

Coseismic responses in the ionosphere at large, close and intermedi-ate distances from the epicenters of strong (M > 7 earthquakes) werecompared in Section 2.3 using observations by CDSS. It was shown thatthe propagation of coseismic infrasound was linear at distances largerthan about 6000 km from the epicenters, whereas the nonlinear phe-nomena resulted in the formation of the N-shaped pulse at distance ofabout 800 km from the epicenter. The observation of N-shaped pulse wasconsistent with the 1D nonlinear simulation of infrasound propagation tothe height of observation; the real measurement of the ground surfacemotion was used as the boundary condition and as the source of theinitial perturbation. It should be noted in this respect that the observa-tions of N-shaped pulses were previously reported from GPS TEC mea-surements in the vicinity (up to about 1500 km) from the epicenters ofstrong,M> 7, earthquakes (Afraimovich et al., 2001; Astafyeva and Heki,2009; Reddy and Seemala, 2015). The previously suggested explanationby Afraimovich et al. (2001) was based on linear interference of infra-sound waves that were generated at different places on the ground.However, they did not use real seismic measurement of the ground sur-face movement and did not consider wave attenuation. Moreover, on thebasis of new analysis presented in section 2.3, it was shown that thenonlinear phenomena can play a role also at intermediate distances,around 3700 km in the investigated case, though the N-shaped pulsemight be not well developed. Coseismic infrasound was observed in allthe cases in the form of short, relatively compact wave packets (severalminutes long) that could be associated with individual seismic waves thatwere observed below, namely with the vertical velocity of ground surfacemotion. The (quasi)vertical propagation is a consequence of supersonicpropagation of seismic waves (Rolland et al., 2011a; Chum et al., 2016a).

On the other hand, the cotyphoon infrasound is continually generatedby slowly moving source (with respect to seismic waves and soundspeed). Likely, only only wave packets with initial quasi-vertical wavevectors reach the ionospheric heights as they avoid the reflection fromtemperature gradients in the stratosphere and lower thermosphere.Contrary to the coseismic infrasound, the cotyphoon infrasound can beobserved for several hours; its intensity and spectral content mightfluctuate. In general, the frequencies of cotyphoon infrasound are lowerthan those of coseismic infrasound; the frequencies of cotyphoon infra-sound often approach the acoustic cut-off frequency in the meso-pause region.

Ionospheric perturbations generated by typhoons and observed bycontinuous Doppler sounder were studied by Huang et al. (1985) inTaiwan, Okuzawa et al. (1986) in Japan and Xiao et al. (2007) in China.Huang et al. (1985) analyzed measurements in Taiwan and focused onGWs, rather than on infrasound. They found that the observed GWs couldbe reliably associated to typhoon only in 2 out of 12 typhoon events.Okuzawa et al. (1986) investigated two typhoons that passed over Japanin September 1982. They found distinct perturbation in the period rangeof infrasound. The spectral content changed with time and was differentfor each event, which is consistent with our results. Okuzawa et al.(1986) reported that the shortest periods of perturbations that theyobserved were around 1.4 min (~0.012 Hz). In our case, we alsoobserved higher frequencies, up to about 0.02 Hz, though for relativelyshort periods of time (Figs. 7b, 8b and c). Numerous studies showedGPS-TEC variations associated with typhoons (e.g., Lin, 2012; Polyakovaand Perevalova, 2013; Song et al., 2016). Recently, Chou et al. (2017)analyzed the concentric GPS-TEC perturbations observed over Taiwan on13 September 2016 when the super typhoon Meranti (event 5 in ourpaper) was approaching Taiwan. These concentric perturbations propa-gated from the eye of typhoon with horizontal velocities of about106–220 m/s. Contrary to our work, focused on infrasound, Chou et al.(2017) analyzed GWs in the period range from 8 to 30 min (frequency

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range from 0.56 to 2.1 mHz). The infrasound waves in the ionospherewere also observed from convective storms (Georges, 1973; Jones andGeorges, 1976; �Sindel�a�rov�a et al., 2009, and references therein). Thespectral characteristics of the ionospheric infrasound from convectivestorms are practically the same as for the cotyphoon infrasound; thehighest spectral densities were observed in the period range of approxi-mately 2–5 min (3.3–8.3 mHz).

It should be noted that a quantitative analysis and modeling ofinfrasound generated by weather systems and propagating at frequenciesaround 5 mHz is complicated from several reasons. First, the initialwaveforms and their spatial variations in the thunderstorm and typhoonsas well as the radiation pattern are usually not known in necessary detail.Second, investigations based onWKB approximation, like ray tracing thatis often used to study wave propagation, give inaccurate results. This isbecause the substantial changes of temperature and hence also the sub-stantial changes of refractive index (wave vector k) occur at scales thatare comparable with wavelength λ. The condition for the validity of WKBapproximation can be formulated in the simplest 1D case as follows: λ ∂k/∂z << k, which can be for acoustic waves rewritten as

1f∂cS∂z

< <1: (7)

Considering the typically observed frequency f¼ 0.005 Hz and ∂cS/∂z~0.01 (Table 1), the left hand side of inequality (7) is 2. If the waves donot propagate vertically, horizontal winds will also influence the prop-agation. Thus, full wave approach for realistic atmosphere with viscosityand thermal conductivity and proper boundary conditions is needed tohandle the coupling between upgoing and downgoing waves that mightpartially reflect at regions of large temperature gradients. Jones andGeorges (1976) investigated this problem in more detail for 1 D case andfound modal resonances at f~3.7, 4.6, and 5.3 mHz. They also pointedout that peaks of spectral densities at around 3.7 and 4.6 mHz wereexperimentally observed by Davies and Jones (1972), reanalyzed theirdata and showed the averaged observed spectrum. The modal resonancesat f~3.7 and ~4.4 mHz were also reported from GPS-TEC perturbationsafter earthquakes (Rolland et al., 2011b and references therein). We havenot observed significant modal resonances in the case of coseismicinfrasound observed by CDSSs. However, spectral peaks that are likelycaused by modal resonances are seen in the spectra of cotyphoon infra-sound presented in Fig. 10. For example, the main peak of spectraldensity at around 4.5 mHz and the local maximum at around 3.6 mHz inFig. 10a correspond well with the first two modal resonances reported byJones and Georges (1976). Similarly, the modal resonance at about5.3 mHz can be revealed in Fig. 10d as the main peak, and as localmaxima in Fig. 10b and 10c. Obviously, the dominant modes change casefrom case. Understanding the reasons for the variability of dominantmodes is a challenge for possible future research that could provide in-formation about the state and dynamics of the atmosphere above ty-phoons and large convective cells. Also, the analysis of simultaneousmeasurements by CDSS and by network of dual-frequency GPS receiversin both acoustic and GW frequency ranges might help to better under-stand the wave propagation in the upper atmosphere and is a potentialsubject for future work.

4. Conclusions

It was shown that the waveforms and spectra of vertical component ofthe ground surface motion are very similar to waveforms and spectraobserved in the ionosphere at large horizontal distances (approximatelylarger than 6000 km) from the epicenters of strong (M > 7) earthquakes.This similarity is consistent with linear regime of propagation. It isreminded that only strong earthquakes generate infrasound with suffi-ciently long periods (larger than about 10s) that is able to reach iono-spheric heights. Contrary, at intermediate and short distances fromstrong earthquakes, the amplitudes of infrasound waves in the upper

J. Chum et al. Journal of Atmospheric and Solar-Terrestrial Physics 171 (2018) 72–82

atmosphere are so large that the nonlinear phenomena start playing animportant role. It results in significant differences between spectraobserved on the ground and in the upper atmosphere that cannot beexplained by the linear approach, even if the attenuation of higher fre-quencies owing to viscosity and thermal conductivity is considered.Especially, at short distances the nonlinear phenomena lead to formationof the N-shaped pulse that resembles a shock wave. The observation ofinfrasound at heights around 200 km by continuous Doppler soundingare in agreement with numerical simulations.

Infrasound waves generated by seven typhoons that passed overTaiwan or in its close vicinity in 2014–2016 were investigated. It wasshown that the cotyphoon infrasound waves were recorded in the spec-tral range from ~3.5 to 20 mHz with maximum of spectral densityaround 5 mHz (dominant periods between 3 and 4 min). The spectrarevealed fine structures that were likely caused bymodal resonances. Thespectral content of the observed waves differed event from event, andalso during the event. The waves were observed at the height range fromabout 200 to 300 km by continuous Doppler sounder located in Taiwan.For some events (typhoons), the infrasound was observed duringseveral hours.

Acknowledgements

NASA Community Coordinated Modeling Center is acknowledged forNRLMSISE-00 atmospheric model, http://ccmc.gsfc.nasa.gov/modelweb/atmos/nrlmsise00.html.The earthquake data archive http://earthquake.usgs.gov/earthquakes is acknowledged. The IRI2016model, http://irimodel.org/ is acknowledged. The Doppler data in theform of spectrograms are available at http://datacenter.ufa.cas.cz/ underthe link to Spectrogram archive. The support under the grant 15–07281Jby the Czech Science Foundation is acknowledged.

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