Infrasound direction of arrival determination using a balloon-borne aeroseismometer

A wide variety of natural and anthropogenic phenomena generate low frequency sound waves (“infrasound,” if below 20 Hz) that can travel great distances in planetary atmospheres (Campus and Christie, 2010; Petculescu and Lueptow, 2007). These waves are typically captured using surface-based microbarometers, which are often arranged in arrays to determine direction of arrival (Christie and Campus, 2010). However, large regions of the Earth are inaccessible to surface-based sensors (e.g., the oceans) and some solar system bodies either lack solid ground entirely (Jupiter) or have hostile lower atmosphere environments (Venus). Microbarometers on high altitude balloons have obviated the location restrictions on Earth (Poler et al., 2020) and have been suggested as a means for monitoring seismic activity on Venus, whose surface is inimical to seismometer deployments (Brissaud et al., 2021; Lognonné et al., 2016; Stevenson et al., 2015). They also tend to experience much lower background noise levels than surface sensors (Krishnamoorthy et al., 2020), and their unique vantage point interrogates portions of the acoustic wavefield that were previously unreachable (Bowman and Lees, 2018).

Despite these advantages, balloon-borne microbarometers have a major flaw: a single station cannot determine the azimuth of an incoming acoustic wave. The required sensor separation for an array capable of analyzing infrasound waves (10¹–10⁴ m wavelength) simply cannot be realized on balloon payloads. On the other hand, it is extremely challenging to keep multiple free-flying balloons close enough together (e.g., a few tens of km separation, maximum) for array-based direction of arrival methods to be effective, even using advanced station-keeping techniques like those described in Bellemare et al. (2020). A compact direction of arrival sensor is therefore critical for balloon-borne acoustic sensing.

Previous attempts at directional low-frequency acoustic sensors consist of limited work on particle velocimeters at frequencies of 20 Hz and above (de Bree, 2003) and an infrasound-range acoustic metamaterial design (Rouse et al., 2021). Neither of these are well suited for high-altitude ballooning in the infrasound range, the former because of its frequency response and the latter because of its bulk. Another approach is to use the response of the balloon itself to the impact of the acoustic wave, in essence, an “aeroseismometer.” Initial design concepts involved measuring the tilt of the flight line in response to an acoustic wave perturbing the balloon envelope (Boslough, 2016). However, a serendipitous recording of an infrasound wave and associated balloon motion during the 2016 NASA High Altitude Student Platform mission suggested that a simple triaxial accelerometer can capture the impact of even very weak acoustic signals. In 2019, the Detection of Earthquakes through a STratospheric INfrasound StudY (DESTINY) project (part of the Balloon Experiments for University Students, or BEXUS, program) again showed that accelerometers on free floating balloons can record acoustic waves (Al Saati et al., 2022). These two results sparked subsequent studies investigating the ability of inertial measurement units (IMUs) attached to tethered balloons to provide the direction of arrival of incident acoustic waves (Garcia et al., 2020; Krishnamoorthy et al., 2019). However, none of these studies demonstrated whether an aeroseismometer on a free flying balloon could obtain the direction of arrival of an acoustic wave and use this information to geolocate the source.

The present work describes a field experiment that tested the aeroseismometer concept using a controlled infrasound source and a stratospheric balloon. The aeroseismometer correctly captured the direction of arrival of five of the six infrasound events during the experiment. That information was then used to determine the location of the acoustic source. The demonstration did not require knowledge of the balloon's impulse response. Aeroseismometery has the potential to improve the effectiveness of balloon-borne acoustic sensing on Earth and other planets.

The experiment consisted of a Raven Aerostar (Sioux Falls, SD) Cyclone zero pressure balloon carrying a Paroscientific (Bellevue, WA) Digiquartz infrasound microbarometer and an InertialSense (Provo, UT) microINS Rugged IMU launched from Lemitar, New Mexico (⁠$34.1615°$ north latitude, $106.902°$ west longitude) on the morning of July 10, 2020. The balloon was 10 m across and was filled with helium. The microbarometer and IMU were contained within a foam shipping carton suspended 30 m beneath the balloon gondola using 550 lb test paracord. The carton and its contents weighed 1.5 kg and had dimensions of 20 × 25 × 23 cm³. Three pairs of two 1 ton trinitrotoluene (TNT) equivalent (⁠$4.184×109$ J) ground chemical explosions were detonated at the Energetic Materials Research and Testing Center (EMRTC) that day as part of the TurboWave II project; these served as acoustic sources for the aeroseismometer test. Each explosion was within 100 m of $34.0596°$ north latitude and $106.991°$ west longitude, and the two explosions per set were separated by 30 s. The first explosion in each pair was detonated at 15:40:00, 16:40:00, and 19:30:00 UTC, respectively. The location of the balloon when each explosion was detonated is shown in Table 1. The resulting pressure and acceleration signatures recorded by the payload is shown in Fig. 1. The acceleration for each event describes rectilinear motion of the IMU which was used to determine the direction of arrival.

A windowed region of the triaxial accelerometer data were selected starting at the onset of each acoustic arrival as measured on the microbarometer. The accelerometer data were not filtered. Principal component analysis was used to compute a best-fit unit vector to the acceleration data indicating the dominant vibration direction of the IMU. The unit vector was rotated into Earth-relative coordinates using the IMU orientation quaternion at the onset of each infrasound signal. From the horizontal components of the unit vector, the azimuthal direction to the source was calculated, though with a $180°$ ambiguity. This ambiguity is due to the back-and-forth motion of the fluid parallel to the acoustic propagation path, and removing it requires taking the balloon's impulse response into account.

The accuracy of this method is dependent upon the window length of the accelerometer data. As this is a proof-of-concept investigation, the azimuthal directions computed for a range of window lengths were compared to the actual direction to the acoustic source. Azimuth convergence was achieved for windows greater than 2.5 s with a local minima of error for a 3.5 s window, which was then used for the results presented in this paper.

The error bounds on the estimated vectors presented in Table 1 were calculated using the method for a single source single vector sensor as described in Nehorai and Paldi (1994). They derive an expression for the Cramer–Rao lower bound of the mean square angular error in terms of the signal-to-noise ratio. From this result, the standard deviation of azimuthal error is obtained:

where N is the number of data points in the windowed acceleration, $ρ=σs2/σn2$ is the signal-to-noise ratio, $σs2$ is the sum of the variance of the two horizontal components of the acceleration, and $σn2$ is the sum of the variance of the two horizontal components of the noise. The variance of the noise was computed from a windowed region of the acceleration data from 60 s before the first arrival to the start of the signal.

Because all the explosions were performed in nearly the same place, the source localization problem can be cast as a set of six independent stations (e.g., the position of the balloon acoustic arrival was received) recording the signal from a single location. The result is a virtual network consisting of six deployment locations (Table 1). It is important to note that the explosions happened in pairs, with each event in a pair separated by 30 s, and each pair separated by 1 to several hours. The balloon did not drift very far over those 30 s, resulting in signals being received in essentially the same location for each pair.

Source localization was carried out using the method outlined in Hawkes and Nehorai (2003). A point along the output vector of the ith sensor is given by $ri+μiûiT$ for a set of coordinates $ri$⁠, a direction $ûT$⁠, and range μ_i. The closest approach to some point $θ$ is the μ_i where

or the projection of the vector from $ri$ to $θ$ onto $ûi$⁠. To find a location, a point $θ̂$ must be found where

given weight w_i based on the mean squared angular error of the ith sensor. This expression can be manipulated as shown in Hawkes and Nehorai (2003) to yield a formula for the source location:

where w is a vector of weights $[wi,…,wm]$⁠, I is the identity matrix, W is the diagonal matrix of w, $Û$ is a matrix of aeroseismometer location $ûi$⁠, and

The effects of angular error increase with greater distance between the sensor and the event location. To reduce the impact of distant sensors, Hawkes and Nehorai (2003) suggest performing the above calculation a second time, with the weighting values adjusted based on the range to the first location estimate. They suggest using weighting values of

where l_i is the range to the first location estimate and $δi2$ is the mean squared angular error of the ith sensor.

The balloon-borne microbarometer recorded acoustic arrivals for all six explosions. The IMU observed acoustically induced vertical acceleration of the flight system for each of them as well. Horizontal motions of the flight system are also evident, but the signal is nearly obscured by background noise for the last set of events (Fig. 1). The fact that Event Set 1 recorded the largest pressure and acceleration signals and Event Set 3 recorded the weakest is consistent with the increasing distance between the balloon and the sources as the experiment progressed (Fig. 2).

The actual direction of arrival calculated from aeroseismometry was within at most 45° of the correct value for five of the six events, and within at most 15° of the correct value for four of the six events (Table 1). The event with the largest direction of arrival discrepancy is also the one where the sensor/source separation was the largest, and the signal-to-noise ratio was the poorest (Fig. 1).

Aeroseismometry results for Event Set 1 correctly indicated that the source was to the north or the south of the balloon. The calculated azimuth to Event Set 2 was to the northwest or southeast, which was also correct. The first arrival from Event Set 3 indicated an acoustic wave from the east/southeast or the west/northwest, which was true–but the second arrival was rotated nearly $90°$ from the actual direction (Fig. 2).

Using the arrival directions calculated from all but the last acoustic event, the source is located about 15 km north of the true site. Once the arrival azimuths are reweighted due to distance to the first trial location, the error drops to about 11 km (Fig. 3). Some of the magnitude of this error is likely due to the geometry of the recording locations. Since the aeroseismometer “network” consisted of a line of virtual “stations” oriented northwest/southeast, the least constrained direction is to the northeast/southwest–and indeed, the calculated location is northeast of the true one. Other potential sources of error include azimuth deviations due to crosswinds (Ostashev and Norris, 2022) or acoustic scattering off of topography some distance away from the source (Bird et al., 2022).

The background noise azimuth distribution does not show an obvious trend just before Event Set 1 but shows a curious northeast/southwest orientation for Event Sets 2 and 3 (Fig. 4). The direction of arrival reported for Event 3B is aligned with the background noise, explaining the much larger error for that observation. This directivity is not an artifact of the processing method, since replacing the accelerometer data with random noise does not reproduce it. It is possible that this represents a vibrational mode of the flight system itself that happened to be oriented in the same way for Event Sets 2 and 3. Alternatively, it could arise for external forcing, such as wind shear, gravity waves, or a directional ambient infrasound wavefield.

Acoustic waves can impose measurable acceleration on free floating balloons. Since these waves are longitudinal, the direction of arrival can be determined as long as the orientation of the accelerometer axes is known. The simple experiment presented here shows that even very lightweight and relatively low cost IMUs can record this directional information and use it to calculate the arrival azimuth of the incoming wave. A source location can be formulated given two or more balloons and/or two or more co-located events separated by a sufficient amount of time. This is possible even without taking the impulse response of the balloon or the structure of the background noise into account.

The study presented here is a demonstration under fairly controlled conditions; it is intended to encourage further investigation of the aeroseismometer concept. It also does not consider the impulse response of the balloon–taking this into account would almost certainly improve the quality of the direction finding and geolocation for this and future experiments. It would likely resolve $180°$ azimuth ambiguity as well. This is under investigation right now and will be submitted as a journal length manuscript in the future. Following this, it will be necessary to determine the impulse response of various types of balloons to different infrasound frequencies and incidence angles to produce a general description of aeroseismometer capabilities. Another important avenue of future research is determining what drives the background noise level, and why it appears to have a consistent orientation for the latter part of the flight.

Vast regions of the Earth are inimical to ground infrasound monitoring. A sparse, freely drifting balloon network circulating in the stratospheric polar vortex could observe large areas continuously (e.g., the Southern Ocean), or more targeted, altitude-maneuverable deployments could surveil specific points of interest (e.g., remote volcanic islands). This has implications for nuclear monitoring (Green and Bowers, 2010) and could provide early warning of volcanic ash emissions that may pose a risk to commercial aircraft (Lamb et al., 2015). Balloon-borne infrasound sensing is a promising avenue for quantifying geophysical activity on Venus as well. Free floating aeroseismometers could help localize events, such as volcanic eruptions (Byrne and Krishnamoorthy, 2022) and venusquakes (Brissaud et al., 2021), although the problem of orienting the accelerometer axes in the absence of a global magnetic field will need to be addressed first.

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 No. DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The authors acknowledge support from the DARPA AtmoSense program under Contract No. 067201110A. The balloon flight was performed with support from the NASA Flight Opportunities Program. This research was also funded by the National Nuclear Security Administration, Defense Nuclear Nonproliferation Research and Development (NNSA DNN R&D). The authors acknowledge important interdisciplinary collaboration with scientists and engineers from LANL, LLNL, MSTS, PNNL, and SNL. The research was also funded by Contract No. 80 NM0018D004 with the National Aeronautics and Space Administration. Maps were generated using the ggmap package in R (Kahle and Wickham, 2013). The authors thank Bill McIntosh and Nelia Dunbar for use of their property during the balloon launch.