Snow Suppresses Seismic Signals From Steamboat Geyser

Geyser and volcano monitoring suffer from temporal, geographic, and instrumental biases. We present a recording bias identified through multiyear monitoring of Steamboat Geyser in Yellowstone National Park, USA. Eruptions of Steamboat are the tallest of any geyser in the world and they produce broadband signals at two nearby stations in the Yellowstone National Park Seismograph Network. In winter, we observe lower eruption signal amplitudes at these seismometers. Instead of a source effect, we find that environmental conditions affect the recorded signals. Lower amplitudes for 23–45 Hz frequencies are correlated with greater snow depths at the station 340 m away from Steamboat, and we calculate an energy attenuation coefficient of 0.21 ± 0.01 dB per cm of snow. More long‐term monitoring is needed at geysers to track changes over time and identify recording biases that may be missed during short, sporadic studies.


Introduction
Geysers are hydrothermal features that episodically erupt a mixture of water and vapor (White, 1967). Because their physical processes and eruption dynamics bear similarities to volcanoes (Kieffer, 1984), geysers are sometimes treated as volcanic analogs with the advantage of erupting more frequently and at smaller scales (Hurwitz et al., 2021). What we learn about geysers and volcanoes is biased by when, where, and how we can monitor them. The National Academies of Sciences, Engineering, and Medicine (2017) highlighted as one of two scientific grand challenges in volcano science the need to "quantify the life cycles of volcanoes globally and overcome our current biased understanding" through expanded monitoring on the ground and from space. The same challenge exists for geyser study, where few geysers are monitored well enough to produce even basic data such as eruption timing.
Seismometers are the most commonly used instrument for monitoring volcanoes because they can detect signals related to magma interaction with rock and fluid in the subsurface (McNutt & Roman, 2015;Moran et al., 2008). They can also detect ground-coupled airwaves, generated when acoustic waves traveling through the air meet the ground at a shallow angle from horizontal, that are produced by explosive eruptions (e.g., Fee et al., 2016;Ichihara et al., 2021;Mendo-Pérez et al., 2021;Palacios et al., 2022;Smith et al., 2016). In contrast to their widespread use in volcano monitoring, seismometers are rarely used for long-term monitoring of geysers despite their usefulness for creating robust eruption interval catalogs (Eibl et al., 2020). Short-term deployments of seismic arrays, broadband instruments, and tiltmeters are more common and have been used to locate tremor and other deformation sources at multiple geysers including Old Faithful (Cros et al., 2011;Kedar et al., 1996;Vandemeulebrouck et al., 2013;Wu et al., 2017Wu et al., , 2019, Steamboat (Wu et al., 2021), and Lone Star (Nayak et al., 2020;Vandemeulebrouck et al., 2014) in Yellowstone, Strokkur, Iceland , and El Jefe, Abstract Geyser and volcano monitoring suffer from temporal, geographic, and instrumental biases. We present a recording bias identified through multiyear monitoring of Steamboat Geyser in Yellowstone National Park, USA. Eruptions of Steamboat are the tallest of any geyser in the world and they produce broadband signals at two nearby stations in the Yellowstone National Park Seismograph Network. In winter, we observe lower eruption signal amplitudes at these seismometers. Instead of a source effect, we find that environmental conditions affect the recorded signals. Lower amplitudes for 23-45 Hz frequencies are correlated with greater snow depths at the station 340 m away from Steamboat, and we calculate an energy attenuation coefficient of 0.21 ± 0.01 dB per cm of snow. More long-term monitoring is needed at geysers to track changes over time and identify recording biases that may be missed during short, sporadic studies.

Plain Language Summary
What we learn about geysers and volcanoes depends on when, where, and how we are able to monitor them. Here we present a case study of how seasonal changes affect data recorded on a seismometer, which is an instrument that measures ground motion. The world's tallest geyser, Steamboat Geyser in Yellowstone National Park, has intense eruptions that eject a mixture of water and steam. The eruptions are powerful enough to cause tiny ground motions from sound waves that begin in the air and then transfer into the ground. In the winter, we see smaller ground motions at two nearby seismometers. This might imply that Steamboat's eruptions are weaker in the winter; however, winter in Yellowstone comes with snow, and snow is good at absorbing sound wave energy. We find that smaller ground motions occur when snow depths are greater, and that the strength of ground motions should not be used to directly compare eruption intensity. Few geysers around the world are monitored with scientific equipment for long periods of time. Our result highlights the need for more of this type of monitoring so that we can identify biases that may be missed during shorter investigations.
Here we report an unexpected recording bias at two broadband seismometers capturing the powerful eruptions of the world's tallest geyser, Steamboat Geyser in Norris Geyser Basin, Yellowstone, USA. We find that all eruptions are recorded by at least one of the instruments and that the signals likely contain a mixture of direct seismic arrivals and ground-coupled airwaves. However, the magnitude of the seismic signals varies strongly throughout the year, with much weaker signals during winter. There is a negative relationship between signal power and snow depth at frequencies >22 Hz at the closer broadband station, and we compare our observed attenuation with other studies of attenuation in snow. Finally, we discuss the implications of our findings on eruption monitoring at geysers and volcanoes and the need for more long-term monitoring that can help identify what environmental changes significantly impact seismic signal recording.

Steamboat Geyser Eruptions
Steamboat Geyser entered an active phase, a period of frequent major eruptions occurring days to weeks apart, in March 2018 (Reed et al., 2021). Two prior active phases occurred in the 1960s and 1980s. During major eruptions, two adjacent vents participate (see inset photo in Figure 1b; Movie S1). The North Vent jet is tallest and reaches maximum heights of 85-137 m (Vander Ley, 2021) in the first few minutes. The South Vent attains ∼50%-70% of the North Vent maximum. Both jets then gradually decrease in height and eventually reach a steam-dominated phase which dissipates over days. Between major eruptions, Steamboat is typically characterized by minor eruptions involving water jetting from one or both vents to <15 m.
Because its eruptions are so tall and active phases are so rare, Steamboat attracts a great deal of attention from park visitors and geyser enthusiasts. GeyserTimes, a crowdsourced database of geyser eruptions, contains a complete catalog of eruption start times for the current active phase (GeyserTimes, 2022) as reported by in-basin observers or inferred from near-real time, publicly available monitoring data. Steamboat produces signals recorded by two broadband seismometers in the Yellowstone National Park Seismograph Network (University of Utah, 2021), a runoff channel temperature logger maintained by the Yellowstone Volcano Observatory, and a United States Geological Survey streamgage on Tantalus Creek. Here we consider the 147 eruptions that occurred from 15 March 2018 through 30 November 2021.

Snow Depth
Ground within Norris Geyser Basin can be warm enough to prevent snow accumulation; however, snow is present in cooler areas between thermal features and where trees are growing. Because there is no weather station near Steamboat that records daily snowfall, we used snow depth data from the 31.4 km distant weather station USC00486845 near Old Faithful (National Centers for Environmental Information, 2021). Snow depths were available for all but 10 eruptions. We justify use of this station by comparing its data to 16 manually recorded depths at snow course 10E19 (National Water and Climate Center, 2021) just outside of Norris Geyser Basin ( Figure S1 in Supporting Information S1). The snow course depths include one measurement in April 2018 and five measurements at ∼monthly intervals in each of the three following winter seasons. There is reasonable agreement; the absolute difference between stations ranges from 0 to 20.3 cm with an average disagreement of 8.1 cm.

Seismic Data Processing
We focused on vertical motions at station YNM (2,311 m elevation) which is located in a shed ∼340 m away from Steamboat Geyser. An additional station, YNR (2,349 m elevation), detects most but not all eruptions and is located ∼2.19 km away ( Figure 1). The stations each use a Nanometrics Trillium instrument with a sampling frequency of 100 Hz and a long period corner of 240 s (YNM) or 120 s (YNR). We downloaded data from the Incorporated Research Institutions for Seismology Data Management Center (IRISDMC) for both stations. YNM and YNR were operating during 91.2% and 99.3% of the eruptions, respectively. Due to its location near a busy trail, YNM is often noisy during summer days when park visitation is high. We limited our analysis to the 93 eruptions for which both YNM and YNR were operating, noise levels were low at YNM (most daytime eruptions in May-September were excluded), and a snow depth value was available.
Eruption signal start times were picked for YNM using a simple algorithm with the GeyserTimes catalog as a reference. First, we demeaned the raw data, removed the instrument response, and converted to units of velocity. We used an initial Butterworth highpass filter above 0.1 Hz to survey the data. Because there was no detectable long period signal, we then filtered the data between 5 and 45 Hz for further processing. The root mean square (RMS) vertical velocity for 10 min of noise prior to the catalog eruption start time was checked against sliding 0.5 s windows. If the RMS amplitude for the window was 20%-60% greater than the noise RMS amplitude and remained above 20% for 5 s, then the beginning of that window was selected as the start time. To obtain signal lag times for the two seismometers, we determined cross-correlation functions ( Figure S2 in Supporting Information S1) using 60 s of seismic data beginning at the seismically derived eruption start times and picked the time corresponding with the maximum value in the first 30 s of the cross-correlation function. We dropped times for 32 eruptions where the maximum cross-correlation coefficient was less than an empirically derived value of 0.04.
Finally, we calculated median power spectral density (PSD) curves for one group of eruptions that occurred during periods with no snow cover (N = 39) and three eruption groups with different snow conditions ( Figure S3 in Supporting Information S1): shallow snow cover (2.5-27.9 cm; N = 22), moderate snow cover (38.1-88.9 cm; N = 25), and deep snow cover (104.1-134.6 cm; N = 7). PSD curves were computed using Welch's method with a Hanning window. The locations of peak frequencies do not shift significantly over the course of individual eruptions ( Figure S4 in Supporting Information S1), so we calculated the PSDs for 3-min data segments centered on the maximum vertical velocity. We obtained the median power for each frequency in the four groups and then converted to decibels referenced to 1 (m/s) 2 /Hz. We followed the same procedure to create ambient noise PSDs for each group using 3-min windows beginning at 8 min prior to the eruption start times picked from YNM data.  Figure 2b). We conclude that activity of the North Vent is responsible for eruptions with varying seismic amplitudes based on visual observations reported in GeyserTimes. When erupted water is blown to the east, it collects on the hillside and runs back into the North Vent which can temporarily lessen or even stop jetting (see http://geysers.org/wordpress/2018/10/20/new-crater-eruption-for-2018-october-15/ for video of this behavior). Abrupt pauses in the signal, such as those seen from 75 to 85 min into the eruption in Figure 2a, correspond to pauses in jetting from both vents. Based on our cross-correlation analysis, there is a median lag time of 5.57 s in a range of 5.39-5.81 s for eruption signals arriving at YNR. The PSD calculations show that eruption signals recorded at both stations are broadband when there is no snow, peaking at 30-35 Hz for YNM and 15 Hz, the same frequency as a local peak in the noise, for YNR ( Figure 3). Ambient noise levels decrease with increasing snow cover. At YNM, the power of eruption signal frequencies >22 Hz decreases dramatically in the moderate and deep snow bins while frequencies of 12-22 Hz remain constant across all bins. The frequency and power of the minor low frequency peak shifts slightly between groups. At YNR, all frequencies decrease in power successively for all snow groups.

Results
Focusing just on frequencies of 23-45 Hz, we compute the signal to noise ratio (SNR) to further quantify the change in amplitude while accounting for variable noise levels. We define SNR as the RMS eruption velocity divided by the RMS noise velocity for the same 3-min windows described for the PSD calculations. The average SNR is 9.5 with a standard deviation of 3.9 for the 39 eruptions that occurred in the absence of a snow cover (Figure 4a). Despite decreasing noise, SNR still decreases with greater snow depths.

Source of Seismic Waves
We hypothesize that both seismometers are recording signals dominated by ground-coupled airwaves at frequencies where power decreases with increasing snow depth. Time lags for signals arriving at YNR yield wave speeds of 318-343 m/s which correspond to the speed of sound in dry air at temperatures of −21 to 20°C. These speeds are slower than the lowest shear wave speeds of 1.19 km/s reported for sinter samples from El Tatio, Chile (Munoz-Saez et al., 2016) and 770 m/s for depths shallower than 6 m near active geysers in El Tatio (Ardid et al., 2019). The frequency distribution for signals at YNR is different than at YNM, which is likely due

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to the attenuating effects of topography, vegetation, and wind on sound waves traveling through the air (e.g., Attenborough, 2002;Piercy et al., 1977). Volcanoes and fumaroles are known to produce low frequency jet noise that arises from large-and fine-scale turbulence Gestrich et al., 2021;Lamb et al., 2022;Matoza et al., 2009;McKee et al., 2017;Taddeucci et al., 2014;Woulff & McGetchin, 1976). Steamboat eruptions produce a low roar that is comparable to that of a jet engine (Movie S1), and given that the much smaller eruptions of Lone Star Geyser are thought to generate jet noise (Quezada-Reyes, 2012), it is possible that jet noise is the origin of acoustic waves at Steamboat.
It is unclear why the 12-22 Hz band on the vertical component of YNM remains at the same power regardless of snow level. Since the emergent signal at these frequencies (especially below ∼20 Hz) is delayed by tens of seconds when compared to higher frequencies ( Figure S6 in Supporting Information S1), we hypothesize that a different process might transmit energy directly through the ground but attenuate before reaching YNR. We rule out erupted water droplet impacts as a source because both water drip experiments (Dean, 2017) and observations from co-located seismometers and drisdrometers (Bakker et al., 2022) show that noise from water droplets is We also plot the interquartile range at each frequency for the eruption bins to illustrate the spread. Note the difference in vertical scales. Similar plots for horizontal motions are shown in Figure S5 in Supporting Information S1. 10.1029/2023GL103904 6 of 10 concentrated at frequencies >50 Hz. Furthermore, Bakker et al. (2022) estimate that 90% of rainfall signal comes from droplets impacting within 5-25 m of the seismometer, well below the 340 m distance between YNM and Steamboat. Hydrothermal tremor, or subsurface bubble collapse and nucleation, is concentrated in the 1-5 Hz band at Steamboat and decreases in amplitude at eruption initiation (Wu et al., 2021), so this would also not be the source of direct seismic arrivals.
The 12-22 Hz band may instead be analogous to the "high frequency wave trains" identified by Kieffer (1984) at Old Faithful and other jetting geysers in Yellowstone. Kieffer (1984) hypothesized that these signals occur due to pressure perturbations through liquid water in the conduit; once an eruption becomes steam-dominated, this signal disappears. This is a plausible source at Steamboat because frequencies below ∼23 Hz decay more quickly than higher frequencies in our data ( Figure S4 in Supporting Information S1) and the steam fraction in the water column generally increases over the course of Steamboat's eruptions. To confirm this, future work might compare 12-22 Hz signal power with steam fraction in the jet, which can be estimated from video (Karlstrom et al., 2013).

Attenuation in Snow
We attribute the dampened wintertime signals to snow accumulation rather than a seasonal change in eruption intensity or weather effect. Though the presence of wind can create a negative sound speed gradient, causing upward refraction and reduced sound levels upwind from the source (Attenborough, 2002), we do not find that wind is a major factor in this case. Data from an eddy covariance tower installed at the northern end of Norris Geyser Basin between 2018 and 2020 (Lewicki & Dobeck, 2020) show that winds at Norris come primarily from the southwest and north, the latter of which blows against sound radiating from Steamboat toward YNM. However, there is little correlation between wind speeds and SNR for the 58 eruptions with available data (r = −0.12; Figure S7 in Supporting Information S1). Biot's (1956aBiot's ( , 1956b) model for propagation of elastic waves in a porous, fluid-saturated medium predicts that attenuation increases as snow depth and signal frequency increase and snow density decreases (Johnson, 1982). We follow the fitting method of Capelli et al. (2016) to model the snow's effect on ground motion, assuming that 20 log 10 ( rms) ∼ −αd , where v rms is the RMS eruption velocity, is the energy attenuation coefficient, and d is the snow depth. We use a least squares method to obtain a linear fit for the snow depth and decibel-converted RMS velocity data and obtain α = 0.21 ± 0.01 dB/cm (Figure 4b). Though we have no data on the physical properties of the snow, we generally see a larger decrease in power for high frequencies at YNM and YNR which is consistent with this model (Figure 3). One caveat is that the PSD for the shallow snow group is nearly identical to bare conditions at YNM. The shallow group distribution is skewed toward depths of just a few cm ( Figure S3 in Supporting Information S1), but this explanation for the lack of attenuation at YNM is inconsistent with observed attenuation at YNR. A more likely explanation is that when temperatures are warmer in late fall and early spring, snow at Norris melts faster than outside the geyser basin due to higher heat flux from the ground. Colder winter air and the presence of a deeper snowpack would suppress this effect.
Sound absorption due to snow has long been documented (e.g., Kaye & Evans, 1939), but few studies investigate signal attenuation at low frequencies. Our value of 0.21 dB/cm is similar to a theoretical attenuation coefficient (∼0.1 dB/cm at 40 Hz) for Biot slow waves, dilatational waves that transmit through pore fluids, in snow and an extrapolated coefficient (∼0.2 dB/cm at frequencies on the order of 10 Hz) based on laboratory measurements performed with signals >8 kHz (Capelli et al., 2016). Other field experiments, however, found somewhat higher values for energy attenuation: 3.6 dB/cm for 5-500 Hz with seismometers buried 25 cm in soil recording coupled airwaves from a pistol shot (Albert & Orcutt, 1989) and 2-3 dB/cm for 150-200 Hz with accelerometers embedded 6-54 cm deep in snowpack responding to directed gas explosions (Simioni et al., 2017). These differences are expected because the frequencies recorded in these experiments extended to a few hundred Hz.
We emphasize that there are limitations in our ability to quantify energy attenuation. Steamboat is a continuous source of variable intensity which makes eruptions difficult to compare. Our snow depth measurements come from a weather station >30 km away, so the exact depth at the seismometers is unknown, and we have no information about snowpack porosity, density, or other parameters that affect attenuation (Johnson, 1982). However, the depth measurements from Old Faithful correlate reasonably well with the monthly measurements from the snow course near Norris ( Figure S1 in Supporting Information S1). Finally, we do not explore the potential effect of changing soil properties due to a lack of data. Freeze-thaw cycles cause seasonal changes in seismic velocity (James et al., 2019;Lindner et al., 2021;Steinmann et al., 2021) and increased soil moisture content can amplify seismic waves (Jefferson et al., 1998;Taylor et al., 2014). More work is needed to quantify any effect of these properties on air-ground coupling.

Implications for Geyser and Volcano Monitoring
Though snow loading is known to influence relative seismic velocity at volcanoes (Cannata et al., 2017;Hotovec-Ellis et al., 2014), we found only one report of signal attenuation due to snow in existing volcano literature. At Villarrica, Chile, sound levels declined by ∼5 orders of magnitude over 50 days as snow accumulated on infrasound sensors (Richardson et al., 2014). In this case, the seismometers did not record a decrease in amplitude, but the seismic signals were dominated by direct seismic arrivals. Our findings have implications for studies interpreting seismo-acoustic data at volcanoes where snow is present on the path between source and monitoring equipment, as the attenuating effect might be misinterpreted as a change in source activity. Additionally, varying snow depths at different stations will produce varying attenuation.
This recording bias would not have been identified without long-term monitoring. The existing seismic network in Yellowstone was not built to detect geyser activity and most geysers' eruptions do not produce ground motion above noise levels at large distances. Giantess Geyser in the Upper Geyser Basin is the only other geyser known to produce signals at a Yellowstone network station (YFT at ∼1.5 km distance). Especially in areas with many active geysers, future monitoring deployments must be designed to both detect and correctly attribute signals to different geysers. Infrasound monitoring, which is increasingly used at volcanoes (De Angelis et al., 2019;Johnson & Ripepe, 2011;Watson et al., 2022), may help address this challenge. Analysis of data from a week-long deployment of an infrasound array in the Lower Geyser Basin, Yellowstone readily discriminated bursting activity from nearby fountain-type geysers but did not register jetting from cone-type geysers (Johnson et al., 2013). Jetting can still be detected if it is both tall and energetic: Steamboat's eruptions have been recorded through targeted infrasound monitoring (Holahan et al., 2021) as have Old Faithful's and Lone Star's (Johnson et al., 2013). Pilot studies should be conducted for planned infrasound arrays and/or seismometers in multiple seasons to ensure signals can be recorded year-round.

Conclusions
We analyzed seismic data from Steamboat Geyser eruptions and found that snow depth negatively correlates with signal amplitude. At a station 340 m distant from Steamboat, attenuation occurs at frequencies >22 Hz where ground-coupled airwaves dominate the signal. We calculate an energy attenuation coefficient of 0.21 ± 0.01 dB/ cm. Steamboat has powerful eruptions; for less energetic geysers, deep snow could lead to eruptions being missed in seismic data. Changing snow depth should be considered when modeling eruption parameters using seismic amplitude if the signal contains ground-coupled airwaves. Long-term monitoring is required to track geyser activity over time and identify environmental conditions that introduce recording biases.

Conflict of Interest
M. H. Reed volunteers as a scientific advisor for GeyserTimes.

Data Availability Statement
Data from the Yellowstone National Park Seismograph Network can be downloaded from the IRISDMC (see http://ds.iris.edu/mda/WY/ for availability), and we acknowledge the use of ObsPy v1.2.2 (Krischer et al., 2015; The ObsPy Development Team, 2020) for seismic data retrieval and processing. Daily summaries of weather data at Old Faithful, including snow depth, are available from https://www.ncdc.noaa.gov/cdo-web/datasets/GHCND/ stations/GHCND:USC00486845/detail while data from the snow course at Norris can be accessed at https:// wcc.sc.egov.usda.gov/reportGenerator/. Wind data comes from https://doi.org/10.5066/P9AKQFGV. The catalog of eruptions from GeyserTimes may be generated at https://geysertimes.org/retrieve.php by searching primary entries for Steamboat Geyser for the period 15 March 2018 through 30 November 2021. The GIS data used for Figure 1 can be downloaded from https://www.wsgs.wyo.gov/pubs-maps/gis.aspx and https://irma.nps.gov/ DataStore/Reference/Profile/1038193.