Acoustic Waves From a Distant Explosion Recorded on a Continuously Ascending Balloon in the Middle Stratosphere

A helium‐filled mylar balloon carrying a smartphone and infrasound sensors ascended to a stratospheric height of 35 km over the surface detonation of a chemical explosive, with a total acoustic propagation distance of 127 km. The smartphone was configured to collect multi‐modal data at high rates from internal sensors. Analysis of the data shows successful collection of the explosion signal by both the smartphone's microphone and its accelerometers, the first from an ascending balloon. Comparison of the acoustic signal with that collected by other infrasound sensors, both airborne and ground‐based, provides insight into the possibilities and limitations of collecting acoustic data from the stratosphere.

• Explosion signals were captured using acoustic sensors in an ascending balloon at a height of 35 km and a propagation distance of 127 km • The signal was briefly trapped in the troposphere before escaping into the stratosphere • Accelerometers can distinguish acoustic signals from wind noise on ascending balloons

Supporting Information:
Supporting Information may be found in the online version of this article.
the vertical accelerometer on the smartphone is able to distinguish the acoustic signal from wind noise recorded during the ascent.
We first consider atmospheric attenuation.The degree of attenuation of an acoustic wave propagating through the atmosphere increases with the frequency of the wave, resulting in low attenuation for infrasonic signals.
However, it also depends on atmospheric conditions such as temperature and humidity, which can be considered approximately constant when horizontal changes in position are small (<1,000 km) and altitude is held constant.
As attenuation tends to increase with increasing altitude (Sutherland & Bass, 2004), we expect to see a greater loss of energy in airborne acoustic data than in data from surface stations at comparable range.
Second, ambient infrasonic noise varies substantially with altitude.Noise levels are high in the troposphere (<10 km above the geoid), with natural and anthropogenic noise persistently present in near-surface acoustic data (Campus & Christie, 2010).In the stratosphere (≈10-50 km above the geoid), relatively little of this noise remains (Bowman & Lees, 2015).Unlike in the troposphere, where colder, denser air overlying warmer, thinner air leads to turbulent overturning and other meteorological and topographical effects, the stratosphere has a more stable stratification, less ambient noise, and more importantly, a low-velocity zone that efficiently traps sound in an elevated waveguide (Garcés et al., 1998).
Lastly, we consider possible sources of additional noise in the stratosphere.Noise due to cable vibrations (strumming) is expected, and other possible relative movements of the balloon system should also be considered, primarily the ability of the payload box to spin (Garcés et al., 2022).Acoustic signals produced by aircraft may also be present (Westcott, 1964).The primary noise concern for an ascending balloon, however, is additional wind noise due to the payload box traveling in the balloon's wake (Barat et al., 1984).Research has shown that wind noise dominates during a balloon's ascent (Krishnamoorthy et al., 2020), thus previous efforts to collect explosion signals have focused on free-floating balloons during periods of neutral buoyancy (Bowman & Albert, 2018;Bowman & Krishnamoorthy, 2021;Young et al., 2018).Studies of stratospheric noise, however, have shown that wind noise during ascent through the stratosphere is drastically reduced compared to the troposphere (Bowman & Lees, 2015).Thus, we show that high signal-to-noise ratios are achievable in the stratosphere even during ascent.
The ability to record sound waves as an airborne platform ascends or descends has important impacts for terrestrial and planetary acoustics.Balloons can "stationkeep" in the vicinity of a target region by rising and falling to take advantage of different wind speeds (Bellemare et al., 2020), but it is not clear whether such maneuvers would prevent concurrent infrasound monitoring.Airborne sensing has also been proposed as a means of recording acoustic waves from seismic activity on Venus (Brissaud et al., 2021), but the previous balloon missions in that planet's atmosphere encountered substantial vertical motion (Sagdeev et al., 1986).Our results suggest that continuous airborne infrasound monitoring of sources of interest on Earth and geophysical activity on Venus (e.g., Brissaud et al. (2021), Rossi et al. (2023)) will be less challenging than previously thought.

Data and Methods
A high-altitude balloon was deployed near a 1,000 kg ± 10 kg TNT-equivalent surface chemical explosives test at Nevada National Security Site on 27 October 2020, at 6:37 a.m.local time during the Large Surface Explosion Coupling Experiment (LSECE) (Silber et al., 2023;Wermer et al., 2021).The balloon's payload consisted of acoustic sensors and a SPOT TRACE asset tracker contained in a foam carton.The sensors consisted of a Samsung S10 smartphone using the RedVox application (Garcés et al., 2022) to collect geophysical data from the phone's internal sensors, including the microphone and three-dimensional accelerometers.In addition, two InfraBSU microbarometers (Marcillo et al., 2012) and a prototype condenser microphone digitized on a DiGOS DATA-CUBE logger at 400 Hz were included.The frequency response of the condenser microphone is unknown.The payload did not have wind noise mitigation screens.The balloon was launched at 5:16 a.m.local time and achieved a stratospheric height of 35.2 km before the signal of interest was detected.The flight system, the various smartphone sensors recording data, and the application's data collection protocols are detailed in Garcés et al. (2022).
A surface network of smartphones running the RedVox app was also collecting data during the experiment.The individual phones were located at various distances from the explosion site, including a station at a horizontal distance of 3.1 km, and a station at a horizontal distance of 46.4 km.Despite several stations deployed at ranges comparable to the total distance (126.8 km) of the balloon from the explosion site at the time of the 10.1029/2023GL104031 3 of 8 signal, the station at 46.4 km was the furthest with a confirmed signal arrival.The locations of the surface and airborne stations relative to the explosion site are shown in Figure 1, along with the balloon's launch site and flight path.In Figure 2, time-frequency representations of the recordings from the smartphones on the surface, two of the airborne acoustic sensors, and the vertical channel of the airborne accelerometer are shown for the high-altitude segment of the flight, along with the balloon's altitude for reference.While the background noise levels of surface stations are mostly constant over the time period, this is not true for the airborne sensors.Around 2,200 s before the airborne acoustic wave peak, we see a clear decrease in the background noise levels, indicating the balloon entered the stratosphere.The acoustic explosion signal is not obvious on this time scale, but we can see the airborne accelerometer signal clearly in Figure 2e.Finally, about 200 s after the acoustic wave peak, the noise levels increase dramatically as the balloon bursts and the payload begins its descent.For a more in-depth view of noise levels in the stratosphere, see Figure S3 in Supporting Information S1.
Ray tracing and waveform evolution modeling were calculated using the open-source infraGA/GeoAc software and the "eigenray" methods described in Blom and Waxler (2017).The signal recorded at 3.1 km was used as the input for the evolution modeling.Temperature and wind data were extracted from Ground-to-Space atmospheric specifications (Drob, 2019;Drob et al., 2003) provided by the National Center for Physical Acoustics of the University of Mississippi.A variety of possible ray paths and the calculated eigenrays between the source and the sensors' locations are shown in Figure 3. Due to an idiosyncrasy in the software, it was necessary to perform the eigenray search for the path to the balloon in reverse, by setting the balloon as the source and the detonation site as the receiver.To correct for this, the winds were reversed in the atmospheric profile when calculating this eigenray.Due to reciprocity, we don't expect this to have any effect on the modeled propagation time.
Time-frequency analysis of the signals was performed by computing the continuous wavelet transform (CWT) of eleven-second-long windows centered on the absolute maximum (in bits) of the acoustic signal.The CWT transforms the one-dimensional waveform into two-dimensional coefficients representing scale and position by maximizing the similarity between the signal and scaled and shifted versions of a specified wavelet function.Like the short-time Fourier transform (STFT), the CWT is a windowed transform.Unlike the STFT, however, the size of the window varies with frequency to maximize the resolution of both time and frequency.This improves frequency resolution at low frequencies and time localization at high frequencies compared to the STFT.Choice of wavelet varies between uses.The CWT used in this work is constructed according to the standardized constant-Q variation of the Gabor atom detailed in Garcés (2020), with band order N = 6.The time-frequency representations in this work are shown in bits, a binary logarithmic unit more natural to digital systems than the traditional decibel (Garcés, 2020(Garcés, , 2023)).

Acoustic Data
The observed waveforms from the surface and airborne sensors are shown in Figure 4, along with the results of infraGA's weakly non-linear waveform evolution modeling along the calculated eigenray.All the waveforms are unfiltered, and all the acoustic waveforms are normalized.Looking at the results from the two airborne audio sensors, we see that both detected a signal at 13:43:46 UTC, at which time the location data shows a height of 35.2 km and a total distance from the explosion of 126.8 km.This timing is consistent with propagation modeling results within 5 s, corresponding to a true propagation path about 2 km longer than the modeled one, or a true speed of sound slightly slower than that estimated by the modeling software.The two airborne audio signals differ.The first difference is due to the sensitivities of the microphones.The condenser microphone was able to collect the signal in significantly more detail compared to the smartphone microphone, which was approaching its sensitivity limit.This can be seen in the waveform itself, where individual bits of information can be observed visually.There is also a difference in phase between the two signals, likely due to the phase change of the smartphone in the 2-10 Hz passband (Asmar et al., 2019).The smartphone frequency response at the temperatures and pressures in the stratosphere is unknown and beyond the scope of this paper.However, theory suggests that the infraBSU microbarometer (see Figure S1 in Supporting Information S1) frequency response should be stable at high altitudes in the passband of interest (see Equation 4in Marcillo et al. (2012)).The phase of the infraBSU microbarometer signal matches that of the condenser microphone signal, indicating that the phase of the condenser microphone signal is correct.
For this to be true, the classic "blast wave" signal recorded on the ground must have experienced a phase shift during its journey into the middle stratosphere.This is supported by infraGA's weakly linear waveform evolution modeling, as the shape of the resulting waveform (seen in Figures 4c and 4d) closely resembles the condenser microphone signal.As the wave followed a direct path from source to receiver, this distortion was unexpected (Bowman & Krishnamoorthy, 2021), but explainable.We can attribute this phase shift to Hilbert transforms resulting from the acoustic wave being trapped near turning points in the tropopause temporarily before escaping into the stratosphere.The nearly horizontal path in the calculated eigenray between 20 and 50 km (see Figure 3) and the modeled waveform evolutions (see Figure 4) mentioned above both support this conclusion.
For further confirmation of the validity of the airborne detection, time-frequency analysis was performed on all the acoustic signals.The resulting multiresolution spectrograms are shown in Figure 5. From the CWT of the signal collected on the ground at a horizontal distance of 3.1 km from the explosion shows (Figures 5a and 5b), we can identify two high energy regions in the frequency domain.The first, near 5 Hz, is clearly present in all the acoustic signals.The presence of the second, near 10 Hz, is less obvious in the signals collected at greater range, particularly in the signals from the airborne sensors.This is consistent with the expected loss of energy to attenuation during propagation, as lower frequency energy is less effected, and attenuation is greater at higher altitudes.Additionally, we see that despite the phase difference between the two airborne acoustic signals, their energy distributions are nearly identical in the frequency domain (Takazawa et al., 2023).Thus, time-frequency analysis of the acoustic signals provides additional evidence of successful airborne detection.

Acceleration Data
The airborne acceleration data in the z-direction is shown in Figure 4e.A sudden increase in energy at the moment of the signal's arrival is clearly seen in the second half of the shown window.Damped oscillation continues for approximately 5 s post-arrival, after which the amplitude returns to pre-arrival levels.This behavior is most obvious in the z-direction, but an increase in energy was also seen in the x-and y-directions (see Figure S2 in Supporting Information S1).We see in Figure 2e that this sudden increase in energy was not observed at any other point throughout the stratospheric flight, providing further evidence of the acoustic wave arrival.

Discussion and Conclusions
Using data collected by multiple sensors, we successfully observed the arrival of the acoustic wave generated by an explosion from a stratospheric height of 35.2 km and a total range of 126.8 km from the site of the explosion.
The balloon carrying the sensors was still ascending when the signal was collected, as evidenced by location data from both the smartphone and a Balloon Ascent Technologies HAB Bounder Balloon Cut-Down Device included in the balloon's payload, and supported by the smartphone's barometer and accelerometers.Propagation modeling predicted the arrival at this location within a few seconds of the observation.
Comparison of the airborne audio data and data collected on the ground at 46.4 km and at 3.1 km revealed disproportionate loss of energy above 10 Hz frequency as the acoustic wave propagated through the atmosphere.This confirms the expected increase in attenuation of acoustic waves with frequency.The effect of the attenuation was significantly greater in the airborne data than in the ground-based data, which was also expected, as attenuation generally increases with altitude, and the propagation path to the balloon was significantly longer.It may also suggest other nonlinear effects enhanced by stratospheric conditions.
Nevertheless, the energy of the signal at frequencies below 9 Hz, particularly the peak near 5 Hz seen in the short-range surface data, was clear in the airborne audio data collected by both the smartphone and the condenser microphone, while the surface stations at comparable ranges were unable to detect the signal at all.Given the decrease in signal-to-noise ratio from the surface station at 3.1 km to that at 46.4 km, it is not surprising that the signal was not detected at surface ranges comparable to the propagation distance of the balloon.These results demonstrate that infrasound signals can not only be successfully collected from an ascending balloon at sufficiently high altitudes, but can be successfully collected in the stratosphere at propagation distances much greater than the detectable range of the signal on the ground.The ability to collect from a balloon while it's ascending could potentially lengthen the signal collection window of future balloon deployments by allowing for collection during periods of both neutral buoyancy and ascent.
Additionally, analysis of acceleration data at the time of the arrival suggests that accelerometers included with the other sensors carried by a balloon can provide evidence of an acoustic wave arrival.As wave propagation modeling is only possible if the location of the source is known, using acceleration data to discriminate between noise and true acoustic wave arrivals would be a valuable tool for infrasound monitoring applications both terrestrial and extraterrestrial.The Large Surface Explosion Coupling Experiment (LSECE) would not have been possible without the support of many people from several organizations.The authors wish to express our gratitude to the LSECE working group and multi-institutional and interdisciplinary group of scientists and engineers for the field experiment.This work was supported by the Department of Energy National Nuclear Security Administration under Award Numbers DE-NA0003920 (MTV) and DE-NA0003921 (ETI).Work was also done by Mission Support and Test Services, LLC, under Contract No. DE-NA0003624 with the U.S. Department of Energy and the NNSA Office of Defense Nuclear Nonproliferation (DOE/NV/03624-1538).This report was prepared as an account of work sponsored by agencies of the United States Government.Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights.Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof.The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.The United States Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525.We thank the National Center for Physical Acoustics for providing Ground 2 Space profiles, and the NOAA-SORD team at the Nevada National Security Site for assistance during the balloon launch.We are grateful to Fransiska Dannemann Dugick for reading through the manuscript draft and offering comments.

Figure 1 .
Figure 1.Visualization of sensor locations (black triangles) relative to the blast pad location (red star).The launch site of the balloon is marked by a blue dot, and the balloon's ascending path is shown as a solid blue line.

Figure 2 .
Figure 2. Spectrograms showing the short-time Fourier transforms of the (a) short-range and (b) long-range surface smartphone acoustic data, (c) airborne acoustic data from the condenser microphone, (d) airborne smartphone acoustic and (e) acceleration data, and (f) balloon altitude in kilometers for the high-altitude segment of the flight.Time is relative to the acoustic wave peak at the balloon stations and observed arrival times are indicated.

Figure 3 .
Figure 3. Results of propagation modeling.Solid gray lines show possible ray paths, the dashed black lines show the propagation paths from the source to the balloon and ground stations, and the station locations are marked with black triangles.

Figure 4 .
Figure 4. Waveforms of the signals from surface microphones at (a) 3.1 km and (b) 46.4 km, airborne (c) condenser and (d) smartphone microphones, and (e) the smartphone accelerometer.The modeled waveform evolutions are plotted as orange lines in panels (b)-(d).Time is relative to the acoustic wave peak at each location.

Figure 5 .
Figure 5. Spectrograms showing the continuous wavelet transforms of the acoustic signals.From top to bottom, the rows display: the smartphone microphone data from the surface at 3.1 km (a-b) and 46.4 km (c-d), the airborne condenser microphone data (e-f), and the airborne smartphone microphone data (g-h).