Exploring Background Noise With a Large‐N Infrasound Array: Waterfalls, Thunderstorms, and Earthquakes

Ambient infrasound noise contains an abundance of information that is typically overlooked due to limitations of typical infrasound arrays. To evaluate the ability of large‐N infrasound arrays to identify weak signals hidden in background noise, we examine data from a 22‐element array in central Idaho, USA, spanning 58 days using a standard beamforming method. Our results include nearly continuous detections of diverse weak signals from infrasonic radiators, sometimes at surprising distances. We observe infrasound from both local (8 km) and distant (195 km) waterfalls. Thunderstorms and earthquakes are also notable sources, with distant thunderstorm infrasound observed from ∼800 to 900 km away. Our findings show that large‐N infrasound arrays can detect very weak signals below instrument and environmental noise floors, including from multiple simultaneous sources, enabling new infrasound monitoring applications and helping map the composition of background noise wavefields.

10.1029/2023GL104635 2 of 10 infrasound at a distance of ∼195 km, and an uncommonly distant detection of thunder infrasound 800-900 km away.

Methods
The PARK station is a 22-element infrasound array (Figure 1a) located in the mountains of central Idaho, USA, which was established following the 2020 M6. 5 Stanley, Idaho Earthquake to monitor aftershock activity.Each sensor in the array was a Gem infrasound logger (Anderson et al., 2018) with a flat response between 0.039 and 27 Hz and a root-mean-square self-noise of 2.75 mPa in the 5-20 Hz band of interest.As a "node"-style instrument (small size, internal batteries, cable-free) the Gem reduced the normal challenges associated with remote  and c) The array response and slowness spectrum of the three-element sub-array.The array response contains a wide main lobe around the origin, as well as significant nearby sidelobes.A period of data beamformed by the sub-array produces the slowness spectrum in panel (c), identified as a single source.(d and e) The array response and slowness spectrum of the six-element sub-array.Although the blurring effect in the slowness spectrum for both the 3 and 6-element arrays is significant, it can be improved by deconvolving their respective array response functions, for example, by Lucy-Richardson (Nishida et al., 2008), or CLEAN (Anderson et al., 2023).(f and g) The array response and slowness spectrum of the full array.The array response of the full array lacks the deficiencies of the previous sub-arrays.In the slowness spectrum, the region in the southwest identified as a single source by the sub-array (c) is revealed by the full array to be in fact three distinct sources.Modified from Anderson et al. (2023).
arrays of this size via its ease of deployment, concealment, and infrequent need for battery replacements.The station began monitoring on 15 April 2020 and continued through 11 June 2020.
Compared to a 3 or 6-element array, arrays with more elements provide superior source discrimination/slowness resolution, and redundancy (Figures 1c,1e,and 1g,Figure S5 in Supporting Information S1).Large spacing between the most distant sensors results in superior array resolution (more compact main lobe in array response), whereas short spacing between the nearest sensors reduces susceptibility to spatial aliasing and helps ensure good signal coherence among sensors.Using more sensors makes it possible to accomplish both objectives at once.In this paper, we define "large-N" as the use of many more sensors than the minimum required for locating a source's position or direction with the objective of improved resolution of source characteristics, and we consider our array of 22 elements to be a large-N array.The array was placed in a wooded area to help reduce wind noise, and individual elements were spread over an area of ∼100 by 150 m (Figure 1a).Topographic obstructions from surrounding mountains are present, but minimal.Obstruction angles range from ∼1 to 4° from horizontal.
Back-azimuths and horizontal slownesses are found via a slowness vector grid search using the array_processing() function in the Python package ObsPy (Krischer et al., 2015).X and Y slowness grid values range from −4 to 4 s/km, with 0.1 s/km spacing.Array processing used 10-s sliding windows with 50% overlap.Low and high frequency parameters (the minimum and maximum frequencies that are used in frequency domain beamforming) were 5 and 20 Hz respectively.We define the beamformed result of a single time window as a "detection."For color-mapped panels in Figure 2, we assigned backazimuth values to 2.5° bins, and horizontal slowness to 0.2 s/ km bins.

Results and Discussion
During the 58-day study period, infrasound data from PARK station was analyzed to identify different processes captured by the array.Although the primary goal of establishing this array was to monitor aftershocks, many additional infrasonic radiators were detected by PARK.Waterfalls, thunderstorms, and earthquakes are all identified as significant sources of infrasound in this region (Figure 2).

Local Infrasound From a Small Waterfall
Waterfalls and other whitewater features are significant sources of infrasound.We identify two radiators of waterfall infrasound captured by the PARK array: Lady Face Falls (LFF), and a combination of Twin and Shoshone Falls.
LFF is located 7.88 km from PARK on Stanley Lake Creek, a perennial mountain stream whose spring and summer flow is primarily reliant on melting snowpack (Figure 3a).LFF is a small waterfall, with an approximate total height of several meters.
The infrasound signal attributed to LFF is quiet and continuous, although sometimes undetected when wind noise is significant.Both slowness and backazimuth are more constrained during the pure waterfall signal and later spread out-a relationship seen on all days-most likely due to wind noise (Figures 2c and 2d).The signal is not present until the last day of April, and then becomes the dominant source of sound received by PARK (Figure 2a).While this waterfall signal is present in the 5-20 Hz band of interest, it is completely absent below 2 Hz, and intermittent in the 2-5 Hz band (Figures S1-S3 in Supporting Information S1); this corresponds well to the spectrum of infrasound recorded near the waterfall having little energy below 2 Hz (Figure S4 in Supporting Information S1) and to the fact that ambient infrasound noise increases in power spectral density at lower frequencies.Although the Boise metropolitan area lies along a similar backazimuth as LFF at a range of ∼125 km, we find an anthropogenic source unlikely given its distance and dependence on upper atmospheric conditions for refraction, and the lack of human temporal patterns.On the other hand, infrasound originating from 232° backazimuth has characteristics that are well-defined by a waterfall source.The detectability of the falls is affected by wind noise and streamflow, which both vary daily and on longer timescales.
We attribute the beginning of the waterfall signal to rising temperatures, initiating considerable melt in the snowmelt-dominated Stanley Lake basin (Figure 3) and increasing discharge at LFF. Partial snow cover of the waterfall early in the season (which we did observe in an early-spring site visit) may also muffle infrasound at its source (Capelli et al., 2016), so the loss of the waterfall's snow cover may also explain the signal's onset.Stanley Lake Creek is ungauged, so we are unable to directly correlate discharge with infrasound characteristics in the 2020 data set.However, in follow-up visits in 2023, we estimated its discharge on the order of ∼0.25 m 3 /s (22 April 2023, early in the melt-off) to ∼4 m 3 /s (20 May 2023, in the middle of the spring melt-off).During this follow-up study period, infrasound power measured ∼35 m from the waterfall during periods of low background noise show amplitude lowest at the beginning and highest at the end of the recording period, corroborating the seasonal rise in waterfall infrasound detected remotely in our 2020 large-N data set (Figure S4 in Supporting Information S1).Given the small size of LFF and its distance from PARK, the amount of detectable infrasound highlights the utility of large-N arrays with weak sources.

Distant Infrasound From Large Waterfalls
Located on the Snake River ∼195 km from PARK at a backazimuth of ∼164.5°,Twin Falls and Shoshone Falls are among the largest waterfalls in the region (dropping 60 and 65 m respectively).During the study period, Snake River discharge varied from ∼14 to ∼220 m 3 /s (USGS, 2023b).5).(i and j) On 22 May 2020 the cluster of detections with near-zero slowness is identified as primary earthquake infrasound.(k-r) A recreation of panels c-j with a subarray of N = 6 elements.
Infrasound detections ranging from 161.125 to 168.625° backazimuth encompass Shoshone and Twin Falls (Figure 4a).Similar to LFF and other waterfall sources, infrasound from this range is quiet and continuous, although the long-term intermittency of detections is greater than that from LFF.The Twin Falls metropolitan area is also located within this range; however we find an anthropogenic source unlikely, as human temporal patterns are not observed.
The falls are detected at PARK some of the time when discharge exceeds ∼75 m 3 /s, but are not detected when discharge drops below this threshold (Figures 4b and 4c).Follow-up recordings made approximately 200 m from Shoshone Falls indeed show that infrasound power is much higher at high flow (92 m 3 /s) than low flow (10 m 3 /s) (Figure S4 in Supporting Information S1), in accordance with our lack of detections in low-flow periods.
The intermittency of detections during high flow is unsurprising because infrasound arrivals at such a distance (i.e., just beyond the nearest shadow zone) depend on favorable stratospheric weather.Generally, infrasound either arrives directly, or requires atmospheric ducting (refractions dependent on stratospheric or thermospheric wind and temperature) to reach long distances.Acoustic shadow zones, where neither direct arrivals nor refractions of infrasound can reach, have long been recognized (Gutenberg, 1939).The nearest shadow zone often ranges from

Thunderstorm Infrasound
Thunderstorm-generated infrasound is a prevalent sound source in the region, and many storms are recorded by the PARK array.We compared infrasound backazimuths during three periods of high storm activity with World Wide Lightning Location Network (WWLLN) data (Figure 5).The World Wide Lightning Location Network uses a network of very low frequency radio sensors to locate lightning strokes all over the globe (Lay et al., 2005).The comparison of infrasound and WWLLN data proved effective in identifying individual storms, where many densely-packed and slowly changing backazimuths match WWLLN location data.Although nearby storms are detected more often than far-away ones, they sometimes remain undetected.Thunderstorm characteristics, shadow zones (as discussed in Section 3.2), and atmospheric conditions may explain inconsistencies in PARK's ability to detect nearby thunder.We observed much variation with time, backazimuth, and distance in PARK's ability to detect thunder infrasound, as is observed by Farges et al. (2021).For example, two storms on 29 April 2020 and 19 May 2020 share very similar characteristics; both storms appear from ∼260° and dissipate at ∼360°, and their distances to PARK are similar (100-300 km).Despite these similarities, one storm is reasonably well-captured by infrasound data (Figure 5a), the other lacks detections altogether (Figure 5c).One well-tracked storm occurring on hour 22 at ∼280° backazimuth that is (indicated by WWLLN) getting closer to PARK appears to lose detections altogether when it reaches a certain distance from the array (Figure 5a).
Thunderstorms moving in and out of shadow zones may contribute to this phenomenon.We also note azimuthal detection biases on all 3 days where thunder infrasound is only detected in certain, time-variable azimuth ranges despite the presence of thunderstorms at other ranges.
The furthest storm detected by infrasound was 800-900 km away from PARK, beginning hour 18 on 19 May 2020 in the 90-120° range (Figure 5b).This particularly powerful storm was associated with 2.5 cm hail and 30 m/s winds and classified as "severe" (NOAA, 2020), and therefore may be more likely to be detected at long distances.Storm-generated infrasound detections at this distance is uncommon, but has been previously observed at distances exceeding 1,000 km (Bowman & Bedard, 1971).

Earthquake Infrasound
On 31 March 2020 a M6.5 earthquake occurred approximately 30 km northwest of Stanley, ID.Following this mainshock, the PARK infrasound array was established to monitor ensuing aftershocks.Here, we focus on primary earthquake infrasound from local earthquakes.Primary earthquake infrasound is the conversion of seismic to infrasonic waves at the array, propagating upwards.Near-zero slowness values are indicative of primary earthquake infrasound, as wave arrivals are nearly synchronous for all array elements due to the high seismic wave speeds (compared to infrasound).In the 5-20 Hz band of interest, near-zero slowness values associated with earthquakes are clearly visible, however below 5 Hz the presence of primary earthquake infrasound is absent (Figures S1-S3 in Supporting Information S1).We consider slowness values other than those associated with typical horizontal infrasound (centered around 3 s/km) and earthquakes to be likely wind noise.
Consecutive days with high concentrations of earthquake detections are observed near the beginning of the study period (Figure 2b).These higher concentrations are consistent with the rapid decay of aftershock occurrence soon after the mainshock (Liberty et al., 2020).After 2 May 2020 (day 17) near-zero slowness detections become more intermittent, and the occurrence of near-zero slowness detections correspond well with the 13 highest magnitude earthquakes (≥M3.2) within 10 km of PARK (Figure 2b).For example, observations of slowness on 22 May 2020 reveal a significant number of near-zero slowness values immediately following a M3.8 earthquake (Figure 2j).Near-zero slowness values exist before the M3.8 because multiple earthquakes occurred in the hours beforehand, generating primary infrasound (USGS, 2023a).When looking at backazimuth values that coincide with the timing of this earthquake, we observe a potential source of secondary infrasound from ∼110° where sporadic clusters of detections overpower the drone of LFF (Figure 2i).We interpret these increases in primary infrasound detections as swarms of small aftershocks (many being too small to be detected by a permanent seismic network) following a significant earthquake.

Conclusions
In order to better understand the capabilities of a large-N infrasound array (22 sensors over a 100 by 150 m area) we studied 58 days of data and identified diverse infrasonic sources.Signals from waterfalls, thunderstorms, and earthquakes were found, many of which are weak and may have been lost to background noise if only a 3-element array was used.
We recorded infrasound from a small waterfall 8 km from the PARK array, and found nearly continuous low-level radiation after mid-spring warming led to increased discharge from snowmelt.Intermittent, ducted infrasound was detected from two distant waterfalls (Twin and Shoshone Falls, at 195 km), during periods of high flow through the falls.Three periods of high thunderstorm activity were recorded and compared to WWLLN data, where thunder infrasound was identified at distances approaching 900 km.Aftershocks following the 2020 M6.5 Stanley, Idaho earthquake were associated with frequent infrasound over the following days with very low horizontal slowness (typical of converted seismic waves), and uncovered low-magnitude earthquakes that may be unnoticeable to a permanent seismic network.
We demonstrate that, using a large-N array and standard beamforming method, infrasound scientists can identify a variety of phenomena that would otherwise be hidden in background noise and that the significant challenges of deploying and maintaining a large-N array can be mitigated by the use of small, low-power, cable-free instruments.We envision widespread application of large-N infrasound for identifying weaker signals than can normally be studied, both for traditional geophysical studies and in other disciplines.For example, we note that this strategy is useful for monitoring waterfalls at much longer ranges than would be possible ordinarily, with hydrological and geomorphological applications for monitoring stream morphology and discharge.Additionally, the improved sensitivity of large-N arrays to weak signals may facilitate monitoring atmospheric conditions using infrasound, either via ambient noise interferometry (Haney, 2009;Ortiz et al., 2021), passive-source (Johnson et al., 2012) or active-source (Averbuch et al., 2021).Finally, the logistical benefits of small, low-power instruments also apply to airborne infrasound (e.g., Garcia et al., 2021); potential applications of flying infrasound arrays include avoiding ground-level acoustic shadow zones and instead recording within acoustic waveguides, and performing aerial seismology on planets lacking a ground surface where seismometers can function.

Figure 1 .
Figure 1.(a) Map of the full PARK array and, for comparison, a three-element and six-element sub-array representative of common infrasound arrays.(b and c) The array response and slowness spectrum of the three-element sub-array.The array response contains a wide main lobe around the origin, as well as significant nearby sidelobes.A period of data beamformed by the sub-array produces the slowness spectrum in panel (c), identified as a single source.(dand e) The array response and slowness spectrum of the six-element sub-array.Although the blurring effect in the slowness spectrum for both the 3 and 6-element arrays is significant, it can be improved by deconvolving their respective array response functions, for example, by Lucy-Richardson(Nishida et al., 2008), or CLEAN(Anderson et al., 2023).(f and g) The array response and slowness spectrum of the full array.The array response of the full array lacks the deficiencies of the previous sub-arrays.In the slowness spectrum, the region in the southwest identified as a single source by the sub-array (c) is revealed by the full array to be in fact three distinct sources.Modified fromAnderson et al. (2023).

Figure 2 .
Figure 2. Overview of infrasound detection characteristics at PARK station from 15 April 2020 to 11 June 2020.(a) Backazimuth versus time, colors indicate the number of detections each day in 2.5° bins.Two backazimuths with especially high detections correspond to waterfalls: Lady Face Falls (LFF) (∼232°, 7.9 km distance) and Twin/Shoshone Falls (∼165°, which, at ∼195 km, cannot be distinguished).(b) Horizontal slowness versus time.Days with a higher density of detections with nearzero slowness are indicative of seismic activity (Day 37, panels (i and j)).(c and d) On 11 May 2020 the first 8 hrs show nearly every detection centered about ∼232°, the direction of LFF.(e and f) On 24 May 2020, the band of detections at ∼165° backazimuth are inferred to be radiated from Shoshone and Twin Falls, almost 200 km away.(g and h) On 19 May 2020 repeated, slowly-changing backazimuth detections are identified as thunderstorms (see Figure5).(i and j) On 22 May 2020 the cluster of detections with near-zero slowness is identified as primary earthquake infrasound.(k-r) A recreation of panels c-j with a subarray of N = 6 elements.

Figure 3 .
Figure 3. (a) Map of PARK infrasound array in relation to Lady Face Falls (LFF) and the azimuthal range of detections from Twin and Shoshone Falls.(b and c) Comparison of detections per day from LFF (227-237°) with temperature at Stanley Ranger Station (∼15 km from LFF, and 100-950 m lower than the basin).Stanley Lake basin is primarily east, west, and north-aspect.The general trend shows infrasound detections increasing with warming temperatures.

Figure 4 .
Figure 4. (a) Location Map of Shoshone and Twin Falls, with the bounds of infrasound detections represented with pink lines.(b) Number of infrasound detections per 4-hrs, from 162.125 to 168.625° backazimuth.Detections are intermittent, where we observe multi-day periods of both high and low detection values.(c) Snake River Discharge from USGS13090500, downstream of Shoshone and Twin Falls.The approximate threshold of 75 m 3 /s represents the minimum discharge where infrasound detections occur.Note that discharge measurements are unavailable from approximately day 48-52.

Figure 5 .
Figure 5.Comparison of infrasound detection backazimuth from PARK (black) and lightning detections from the World Wide Lightning Location Network (WWLLN) (colors).WWLLN colors represent the distance from a detection to the PARK array.Intermittent infrasound detections around ∼232° radiate from Lady Face Falls.(a) Thunder from multiple lightning storms is detected throughout the day, although some storms lack infrasound detections.(b) Infrasound captured the repeated storms in the 20-80° range, as well as a storm ∼850 km away from hour 18 to 21. (c) Notice the lack of infrasound detections from fairly proximal storms in the 260-360° range, where similarly located storms were detected in panel (a).