Assessing Seasonal Changes in Microgravityat Yellowstone CalderaMichael P. Poland1 and Elske de Zeeuw‐van Dalfsen2

1U.S. Geological Survey, Vancouver,WA, USA, 2Royal NetherlandsMeteorological Institute (KNMI), De Bilt, Netherlands

Abstract Microgravity time series at active volcanoes can provide an indication of mass change related tosubsurface magmatic processes, but uncertainty is often introduced by hydrologic variations and other noisesources that cannot easily be isolated. We empirically assessed seasonality and noise by conducting foursurveys over the course of May–October 2017 at Yellowstone caldera, Wyoming. Yellowstone experiencesfrequent changes in the rates and styles of seismicity and surface deformation, but the mechanisms ofthese changes are poorly understood. Past gravity data from the caldera have yielded ambiguous results,possibly due to hydrologic noise. Given the strong visually observable changes in surface water and snowconditions over the course of our surveys, we expected to see significant variations in gravity. The net changein gravity, however, was less than 20 μGal at most sites, and there was no strong correlation with riverand lake levels or snow conditions. Seasonal changes in gravity are therefore small compared to those thatwould be expected from magmatic activity, although they may be on the same order as those associatedwith Yellowstone's hydrothermal system.We did find that noise levels in gravity data were highly dependenton site characteristics, with bedrock sites away from trees yielding the lowest levels of noise, and thinconcrete pads in forested areas the highest. These results can be used to plan future surveys at Yellowstoneand to reinterpret past data, and they provide guidance in terms of best practices for repeat gravity work onvolcanoes worldwide.

1. Introduction

Some of the most dynamic volcanoes on Earth are silicic caldera systems, and unrest, such as swarms ofearthquakes and changes in ground deformation, at these volcanic centers can be extreme. For example,Yellowstone, Wyoming, experiences episodic swarms of earthquakes, which can number in the thousands(e.g., Waite & Smith, 2002). Laguna del Maule, Chile, was characterized by uplift rates of about20 cm/year in the mid‐2010s (Le Mével et al., 2015). In addition to persistent seismic activity and inflation,Long Valley caldera, California, has been a site of elevated CO2 emissions that have killed vegetation andcaused a few human fatalities (Werner et al., 2014). At Campi Flegrei, Italy, bivalve borings in Roman ruinsthat are now elevated above sea level provide evidence for several meters of subsidence and subsequentuplift over the past 2000 years (e.g., Dvorak & Berrino, 1991), and about 3.5 m of cumulative uplift was asso-ciated with seismic crises during 1969–1972 and 1982–1984 (Del Gaudio et al., 2010). The cause of calderaunrest is usually attributed to subsurface accumulation, withdrawal, and transport of fluids, but the natureof these fluids (gas, water, or magma) is debated (e.g., Battaglia et al., 2006, 2008; Gottsmann et al., 2006).Constraining the nature of fluids driving unrest has obvious importance for hazards assessment, as wellas forecasting potential future eruptive activity.

Temporal variation in gravity (also called microgravity) combined with measurements of surface deforma-tion can provide a unique window into the nature of subsurface processes and has been particularly valu-able at elucidating the mechanisms responsible for caldera unrest (Carbone et al., 2017). For example,Battaglia et al. (1999, 2003) and Battaglia and Hill (2009) argued that uplift at Long Valley caldera wasdriven by accumulation of magma, rather than water or gas, based on deformation and gravity changethat suggested a fluid density much greater than 1 g/cm3. Gravity data from Campi Flegrei, on the otherhand, suggest that unrest might be driven by migration of hydrothermal fluids (Battaglia et al., 2006). AtLaguna del Maule, Miller et al. (2017) found that the sources of deformation and microgravity change didnot coincide, leading them to conclude that deep intrusion of magma facilitated shallow accumulation ofhydrothermal fluids. Modeling of gravity and deformation data at Yellowstone suggests both hydrother-mal and magmatic sources, but temporal resolution is limited, and spatial patterns are complex and

Published 2019. This article is a U.S.Government work and is in the publicdomain in the USA.

RESEARCH ARTICLE10.1029/2018JB017061

Key Points:• Microgravity changes due to

seasonal variations at Yellowstoneare much less than those expectedfrom magmatic processes

• Noise levels at gravity stations arehighly dependent on site setting andenvironment

• Design of gravity surveys atYellowstone and elsewhere shouldfocus on site characteristics toreduce noise and increase thechances of detecting changes causedby magmatic activity

Supporting Information:• Supporting Information S1

Correspondence to:M. P. Poland,mpoland@usgs.gov

Citation:Poland, M. P., & de Zeeuw‐van Dalfsen,E. (2019). Assessing seasonal changes inmicrogravity at Yellowstone caldera.Journal of Geophysical Research: SolidEarth, 124. https://doi.org/10.1029/2018JB017061

Received 19 NOV 2018Accepted 24 MAR 2019Accepted article online 28 MAR 2019

POLAND AND DE ZEEUW‐VAN DALFSEN 1

difficult to interpret (Arnet et al., 1997; Tizzani et al., 2015) despite a microgravity record that spansseveral decades (Farrell, 2014).

At Yellowstone (Figure 1), a major challenge for the interpretation of microgravity data is the unknown con-tribution of groundwater (including hydrothermal sources; Tikku et al., 2006) and surface water to themicrogravity signal (e.g., Tizzani et al., 2015). When constrained by hydrological observations, this effectcan be modeled (Battaglia et al., 1999, 2008; Gottsmann et al., 2006; Kazama & Okubo, 2009; Kazamaet al., 2015; Hemmings et al., 2016). More often, however, hydrological data at active volcanoes, especiallywith regard to groundwater, are sparse to nonexistent. One approach to addressing this issue involves mod-eling groundwater variations based on hydrological models—for example, calculating the likely variationsin groundwater levels based on recharge, as was done at Campi Flegrei (Battaglia et al., 2006). Another strat-egy to account for unknown hydrological changes is to conduct surveys at a similar time of year, assuminggroundwater levels fluctuate along comparable annual patterns (Battaglia et al., 2018; Rymer et al., 1995;Williams‐Jones et al., 2003). This approach is utilized due to the difficulty in quantifying and removing sea-sonal components in gravity data, which might be on the order of tens of microgals based on limitedamounts of data collected from Mount Etna (Rymer et al., 1995) and Campi Flegrei (Gottsmann et al.,2006), in Italy, or might be negligible, as found by Williams‐Jones et al. (2003) at Masaya, Nicaragua. In

Figure 1. Shaded relief map of Yellowstone National Park (outlined in solid black line) with seismicity in 2017 (opencircles), roads (yellow lines), boundary of caldera that formed 631,000 years ago (dashed line), gravity stations occupiedin 2017 (red circles), resurgent domes (labeled green ellipses), and continuous GNSS stations utilized in this study (labeledwhite triangles). Dashed gray box shows area depicted in Figure 5.

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Yellowstone, past gravity studies adopted this latter method for dealing with unknown seasonal variations(Arnet et al., 1997; Farrell, 2014). There remains the possibility of temporal aliasing, since gravity variationsdue to, say, hydrothermal processes will occur at timescales shorter than the survey repeat interval (e.g.,Tikku et al., 2006), but this can be addressed by ensuring that the network is sufficiently dense and broadto distinguish presumably shallow sources of rapid gravity fluctuation from deeper sources of magmaticchange (Battaglia et al., 2008; Gottsmann et al., 2005).

What is the magnitude of seasonal microgravity variation at Yellowstone (or for that matter, at any vol-cano)? And are there specific microgravity sites that are more (or less) prone to seasonal variations ingroundwater and surface water variations? To assess seasonal variations in microgravity at Yellowstone,we conducted four similar surveys at approximately 6‐week intervals during May–October 2017. This per-iod did not span any magmatic events or changes in the rate and pattern of surface deformation, althoughthe large Maple Creek seismic swarm was ongoing northwest of the caldera during June–September(Shelly & Hardebeck, 2019; Figure 1). It also spans the only time of the year that the area is mostly freeof snow and thus accessible for gravity surveys. Based on these data, we gained an understanding of howgravity varies at Yellowstone due to seasonal changes over the course of about 5 months. This knowledgeforms the basis for the design of a gravity network that, when measured annually, will provide betterinsights into the nature of subsurface mass distribution associated with future volcanic unrest than hasheretofore been possible.

2. Background

The 85 × 45‐km Yellowstone caldera formed 631,000 years ago due to the eruption of 1,000 km3 of rhyo-lite magma (Christiansen, 2001; Matthews et al., 2015) and was subsequently filled by numerous erup-tions of thick rhyolite lava flows, the most recent of which was emplaced approximately 70,000 yearsago (Stelten et al., 2015). Tomographic studies have identified at least two low‐velocity zones beneaththe caldera that suggest the presence of partial melt. The upper body, which extends from 5 to 16 kmbeneath the caldera, is interpreted as a ryholitic magma reservoir with 5–15% melt, while a body span-ning 20‐ to 40‐km depth is thought to be a basaltic reservoir with ~2% melt (Farrell et al., 2014;Huang et al., 2015). This magmatic system provides the heat that powers the vigorous hydrothermal sys-tem at the surface (Morgan et al., 2017). Seismicity and surface deformation are dynamic in nature andvary in both time and space. Frequent swarms of earthquakes are driven by a combination of tectonicand hydrothermal processes (Farrell et al., 2009; Shelly & Hardebeck, 2019; Waite & Smith, 2002), andsurface deformation includes both uplift and subsidence at varying rates (Dzurisin et al., 2012; Wickset al., 2006).

Given the dynamic nature of hydrothermal activity at Yellowstone (Hurwitz & Lowenstern, 2014), thepresence of a large magma reservoir system beneath the caldera (Huang et al., 2015), and the broad areaover which changes occur (Dzurisin et al., 2012), understanding the mechanism of caldera unrest there isa particular challenge. Microgravity surveys have been completed at Yellowstone numerous times since1977 (Farrell, 2014), but there are few published results owing to the complexity of the measured signal.Arnet et al. (1997) found that a period of uplift during 1977–1983 was accompanied by mass addition (pre-sumably due to a magmatic intrusion), while subsidence in 1986–1993 had no measurable mass change,implying a mechanism of depressurization and volatile loss. Using the same data but with a more com-plex inverse model, Tizzani et al. (2015) suggested a combination of magma and hydrothermal fluids driv-ing deformation at Yellowstone. Farrell (2014) performed annual microgravity surveys across the caldera'stwo resurgent domes (Sour Creek and Mallard Lake; Figure 1) during 2007–2012 using a ladder‐style sur-vey strategy and four different instruments over those years; the results were not conducive to any specificinterpretation. Tikku et al. (2006) collected an 8‐day continuous gravity record in the southern part of theUpper Geyser Basin (near Old Faithful) and found maximum peak‐to‐peak oscillations of 10–15 μGal,similar to the accuracy of the instrument. Both Arnet et al. (1997) and Farrell (2014) acknowledged thepossibility of a seasonal effect and mitigated this by always conducting their surveys in late summer orearly fall, when rivers and lakes were at their lowest levels, and by assuming the groundwater tablewas the same during the survey periods. This unknown influence of seasonal variations on microgravityobservations is the subject of this study.

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3. Data Collection and Analysis3.1. Instrumentation and Measurement Strategy

In 2017, we conducted four independent but comparable microgravity surveys at Yellowstone: (1) 16–26May, (2) 9–14 July, (3) 25–30 August, and (4) 11–17 October. In total 51 sites were surveyed (Figure 1), focus-ing on the most active regions of Yellowstone caldera in terms of past deformation—the Sour Creek andMallard Lake resurgent domes and the area around the Norris Geyser Basin (Dzurisin et al., 2012). The siteschosen were a mix of those previously measured by the University of Utah (Arnet et al., 1997; Farrell, 2014)and existing leveling benchmarks complemented by new sites installed next to continuous GNSS stationsand absolute gravity stations. Not all sites were measured during each survey because they were not acces-sible due to snow cover or because new sites were added to the surveys over time.

We established a new base station with two measurement sites (called MAWY_PAD and MAWY_ROCK) inthe Mammoth housing area at the northern edge of the park. The new base station is adjacent to a seism-ometer and the continuous GNSS site MAWY, and its location 25 to 40 km from the primary areas of defor-mation and seismicity ensures its functionality as a reference point to which all other sites can be related.Because MAWY is too far from the other sites to make it logistically feasible to remeasure during the middleof every survey day, we used five additional stations as “local” bases (11MDC, G158, 40MDC, 48MDC, and,in May only, U367), and we tied them to the primary base in Mammoth with double‐loop surveys conductedspecifically for that purpose (see below).

The environmental settings and installation types of the gravity stations are diverse (Table 1). Measurementsites include benchmarks cemented into bedrock or large boulders, small concrete pads adjacent to bench-marks, concrete borders around metal access covers that conceal rod‐type benchmarks used for leveling sur-veys, and benchmarks cemented into concrete posts, bridges, culvert headwalls, or foundations. Sitelocations include forests, rocky clearings, populated areas, meadows with no exposed rock, roadcuts, riverbanks, and thermal areas (only 6 out of 51 stations—7MDC, 48MDC, A158, G158, OF_ABS, and X157—werelocated in or within a few hundred meters of known hydrothermal activity, so as to test whether gravitychange in those areas differed significantly from the surroundings). As a result of the variety of settingsand styles, the instrument‐reported standard deviation of gravity measurements varied considerably fromstation to station.

On each day of every survey, we followed a double‐loop approach, measuring the MAWY sites at the startand end of the day, the local base at the start, middle, and end of the day, and other stations early and latein the day. For example, a typical measurement sequence (where G158 serves as the local base) wasas follows:

MAWY PAD=MAWY ROCK>G158>O9>J339>F365>4MDC>G158>O9>J339>

F365>4MDC>G158>MAWY PAD=MAWY ROCK

The measurements at the local base station serve as a means to check for tares—sudden offsets in thedata—and other inconsistencies (e.g., Carbone et al., 2017). To ensure a strong tie between the base sitesand the local bases, one survey day during each measurement campaign was spent measuring the MAWYsites and the local bases using the double‐loop method starting at the MAWY sites (e.g., MAWY_PAD/MAWY_ROCK > G158 > 40MDC > 11MDC > MAWY_PAD/MAWY_ROCK > G158 > 40MDC >11MDC > MAWY_PAD/MAWY_ROCK).

During all four surveys the same two Scintrex CG‐5 gravimeters were used (serial numbers ending in 578and 579). The standard practice (similar to that of Battaglia et al., 2018) was to record five readings, eachof 60‐s duration. At the end of a 5‐min measurement session, we reviewed the data to be sure that the 60‐s readings varied no more than ~5 μGal about a mean value. If the readings failed to settle on a mean value(i.e., readings trended positive or negative throughout the 5‐min measurement session) or were spread bymore than 5–10 μGal (the difference between the highest and lowest readings), we repeated the measure-ment cycle, continuing to do so until five consecutive 60‐s readings met our criteria. Tominimize errors asso-ciated with gravimeter setup, we took photographs of every site, noted the orientation of the bubble leg of thetripod base, and noted the location of the tripod center with respect to the benchmark center so that the

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gravimeter could be positioned in the same location at a given site each time. We also kept the height of theback‐left leg of the tripod base constant over the course of a survey to ensure that the gravimeter was alwaysat the same height above the benchmark.

Gravimeter 579 displayed unstable behavior during the May survey, with readings often trending positivelyor negatively by tens to hundreds of microgals over the course of tens of minutes before settling on a meanwith total variability of less than 5–10 μGal. The meter had been serviced to repair this issue earlier in 2017,

Table 1Gravity Stations in Yellowstone National Park That Were Occupied in 2017, Including Location, Occupations, Installation Type, and Environmental Setting

Site Latitude Longitude Elevation (m) Installation Environment May July August October

11MDC 44.73631 −110.49201 2,417 bedrock clearing X X X X11MDC NGS 44.73636 −110.49197 2,417 bedrock clearing X X X24MDC 44.69110 −110.49904 2,350 culvert headwall forest X X X X27MDC 44.61843 −110.42083 2,355 concrete pad forest X X X X30MDC 44.57800 −110.37923 2,360 bedrock forest X X X X40MDC 44.62991 −110.85583 2,152 bedrock forest X X X X41MDC 44.60720 −110.84609 2,176 boulder riverside X X X X42MDC 44.58455 −110.82995 2,185 boulder riverside X X X X43MDC 44.55513 −110.80734 2,216 bedrock road cut X X X X45MDC 44.53283 −110.82759 2,213 concrete pad forest X X X X48MDC 44.46877 −110.85616 2,228 bedrock forest X X X X49MDC 44.43586 −110.79475 2,385 bedrock forest X X X X4MDC 44.70801 −110.61690 2,450 bedrock road cut X X X X6MDC 44.70380 −110.58019 2,511 boulder power line corridor X X X X7MDC 44.71363 −110.55531 2,486 bedrock thermal area X X X X85–222 44.61097 −110.40931 2,355 boulder forest X X X X85–230 44.72714 −110.49394 2,416 boulder meadow X X X XA158 44.72664 −110.70363 2,307 concrete post forest X X X XARBEE 44.63061 −110.43913 2,362 access cover meadow X X X XB11 44.59152 −110.38534 2,367 boulder forest X X X XF365 44.72348 −110.67718 2,302 access cover forest X X X XG158 44.67662 −110.74707 2,233 concrete post forest X X X XG367 44.43755 −110.79852 2,369 bedrock forest X X XHOLLIS 44.72261 −110.49487 2,398 boulder meadow X X X XJ339 44.71469 −110.72873 2,272 bedrock forest X X X XJ367 44.43178 −110.74782 2,440 bedrock forest X X X XKAYGEE 44.66288 −110.46403 2,346 bedrock meadow X X X XL367 44.44223 −110.71802 2,528 bedrock roadcut X X XLC58 44.71668 −110.50524 2,367 bedrock forest X X X XLEHARDY 44.59950 −110.38688 2,369 access cover meadow X X X XLK_ABS 44.56268 −110.39621 2,401 asphalt housing area XLKWY 44.56506 −110.40019 2,431 concrete block clearing X X X XM367 44.44803 −110.70744 2,451 bedrock forest X X X XMAWY_PAD 44.97332 −110.68929 1,836 concrete block clearing X X X XMAWY_ROCK 44.97332 −110.68929 1,834 small boulder clearing X X X XNRWY_ABS 44.72454 −110.69337 2,298 concrete foundation building interior X XNRWY_TELE 44.71352 −110.67835 2,366 bedrock forest X X X XO9 44.65377 −110.77163 2,170 bedrock cliff above river X X X XOF_ABS 44.45639 −110.84216 2,240 concrete foundation building interior XOFW2 44.45114 −110.83115 2,291 bedrock clearing X X X XP711 44.63556 −110.86102 2,127 bedrock clearing X X X XP716 44.71821 −110.51152 2,398 bedrock clearing X X X XSHOSHONE 44.43360 −110.64367 2,554 access cover meadow X X XT9 44.71280 −110.64653 2,377 bedrock road cut X X XU157 44.78783 −110.73906 2,298 concrete post meadow X X X XU367 44.56931 −110.38781 2,404 boulder power line corridor X X X XX157 44.75334 −110.72464 2,296 concrete post thermal area X X X XY367 44.70269 −110.50536 2,343 bedrock riverside X X X XY9 44.61715 −110.85563 2,166 bedrock cliff above river X X X XZ157 44.73804 −110.69893 2,281 bridge bridge X X X XZ9 44.59809 −110.83127 2,183 concrete pad forest X X X X

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and it was returned to the manufacturer for investigation and furtherrepair in June. The meter appeared to behave normally for the July,August, and October surveys.

Both gravimeters have been calibrated repeatedly on the U.S. GeologicalSurvey calibration line at Mount Hamilton, California (Battaglia et al.,2018), to assess the relation between gravity recorded by the instrumentand the actual gravity value. The derived calibration factors for bothmeters during 2010–2017 were constant withinmeasurement uncertainty,with the exception of the calibration that was performed in June 2017 forgravimeter 579, just before it was serviced for the second time. After June,the calibration factor returned to its previous value. This suggests that theservice to gravimeter 579 did not impact the instrument's calibration fac-tor but that the instrument was not operating correctly during theMay survey.

3.2. Data Reduction

All data were automatically corrected for solid earth tides, instrument tilt,linear drift, and sensor temperature. Options for seismic noise filteringand noisy reading rejection were active, as recommended by the manufac-turer. We also carefully examined the data set for tares and for measure-ments that were clearly inconsistent with the rest of the data (often

caused by high noise due to wind or traffic). We found only one tare, which was an offset of 45 μGal for datacollected by gravimeter 579 on the afternoon of 12 July.

Ambient changes in atmospheric pressure and temperature should not affect the sensor itself because thesensor is housed in a sealed temperature‐controlled chamber. Changes in atmospheric pressure can, how-ever, impact gravity readings due to the gravitational attraction of the air column above the measurementpoint, with an expected effect of −0.365 μGal/mbar (Battaglia et al., 2008; Merriam, 1992; Tikku et al.,2006). The greatest difference in barometric pressure over the course of any survey measured at a weatherstation near the outlet of Yellowstone Lake occurred in May and was +20 mbar (an effect of about−7 μGal). The maximum barometric pressure difference on any single day occurred on May 24 and was−12 mbar (about +4 μGal). Because repeat measurements at a given station occur only a few hours apart,the variations in pressure during a survey are even less than those that occur over an entire day; therefore,we did not apply any corrections for atmospheric pressure variations.

The automatic linear drift correction is based on an empirically determined factor that is resolved by fitting aline to data recorded for 24–48 hr in the lab. The overall drift rate changes over time, however, so the longerit has been since the automatic drift factor was determined, the more residual drift is present in the correcteddata. We considered multiple approaches to account for this residual drift. The residual drift can be modeledvia a linear fit to all data from a given survey, or to some subset of the data from that survey (for example, allmeasurements collected at MAWY and the local base stations). While this procedure can provide a goodoverall fit, the whole‐survey drift is not always a good approximation for the drift on a given day. For exam-ple, the whole‐survey linear drift for gravimeter 579 during the August campaign is approximately46 μGal/day (this value is consistent whether the linear fit is calculated using only data from the MAWYsites, using data from the MAWY sites and the local base stations, or using all data). Individual days, how-ever, had drift rates that varied between 8 and 99 μGal/day (Figure 2). This is likely caused by a nonlinearcomponent in the residual drift, subtle changes in behavior of the instrument due to transport and use,imperfect temperature regulation of the sensor, and/or variations in environmental conditions. We thereforechose to calculate the best linear fit to the residual drift for each day independently using all measurementscollected on that day, and we used the gTOOLS software package (Battaglia et al., 2012) to performthese corrections.

3.3. Free‐Air Correction

Once gravity values relative to the base station are obtained for each survey, it is possible to create gravitytime series for each site. The observed variations in gravity contain contributions from (1) any mass

Figure 2. Drift of gravimeter 579 during August survey (time in UTC). Reddots are measurements at individual stations (composed of a minimum offive 60‐s readings), with values normalized so that they define an overalldrift trend for the entire survey (gray line, with a rate of 46 ± 0.5 μGal/day).Drift rates of individual days (black lines) vary from 8 ± 5 to 99 ± 11 μGal/day. Outliers on 30 August are from station Z157, which is located on abridge and characterized by extremely high noise. Error bars, which aregenerally about 5–10 μGal per measurement, are omitted for clarity.

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change, (2) noise introduced by environmental conditions and instrumentsetup, and (3) changes in vertical elevation. The latter factor is the so‐called “free‐air” effect, which is due to the changing distance betweenthe measurement site and the center of Earth and has a theoretical valueof −3.086 μGal/cm. Any assessment of gravity change over time musttherefore account for vertical deformation at the measurement locations.

Vertical deformation at Yellowstone is monitored by InSAR and a net-work of continuous GNSS stations (Dzurisin et al., 2012). As six of ourgravity sites are collocated with a continuous GNSS site (Figure 1), weuse GNSS data to account for the vertical deformation. Over the courseof 2017, GNSS data indicate that overall the caldera experienced somesubsidence, while uplift occurred in the area around Norris GeyserBasin, both at rates of a few centimeters per year (Figure 3). Data fromGNSS station MAWY show no vertical deformation, confirming the stabi-lity of our gravity reference site. During May–October, the maximumamount of vertical change in Yellowstone was 2 cm (at GNSS stationNRWY near Norris Geyser Basin), which corresponds to a free‐air effect

of 6 μGal. Given this low value and the fact that we do not have vertical deformation measurements at everygravity site, we did not correct the gravity time series for changes due to the free‐air effect.

3.4. Problem With Gravimeter 579

Examination of the relative gravity values for each site throughout all surveys revealed significant outliers inMay and July for gravimeter 579, with values differing from gravimeter 578 by dozens of microgals. For theMay survey this is not a surprise, as we experienced difficulty operating the instrument in the field. The Julysurvey was conducted within days of the gravimeter being serviced by the manufacturer, and the results sug-gest the instrument was still settling after its repair, thereby compromising the data. Consultation with themanufacturer supports this interpretation, since resetting the spring results in a period of adjustment that isnot linear. Results from August and October, however, are very consistent with those from gravimeter 578,with relative gravity values from the two instruments within 10–20 μGal of each other. Although the Augustand October data appear robust, those provide only one epoch for comparison, which is not enough to assessseasonal changes. We therefore decided to omit all data collected by gravimeter 579 from further analysis.Gravimeter 578, in contrast, functioned well throughout all four surveys and provides three epochs ofchange—critical to our goal of assessing seasonal variations in gravity.

4. Results4.1. Station Noise

CG‐5 gravimeters calculate the standard deviation of the series of measurements that are collected over thecourse of a single 60‐s reading. The value of the standard deviation is therefore a quantification of the noiseat a given site and a given time. We averaged the standard deviations for all measurements at every site todetermine the types of sites that had the lowest levels of noise, and we identified a number of general trends.For example, noise values were usually lower in mornings and evenings and higher in the afternoons, fol-lowing the trend of anthropogenic noise (like traffic), and windy days had higher standard deviations thancalm days. Noise may also be generated by seismic energy (from both large, distal earthquakes and localmicroseismicity; Tikku et al., 2006), but we did not detect such effects during our surveys. We found thatthe most significant trends were associated with benchmark installation type and environmental setting(Figure 4). In general, the installation types with the lowest noise were bedrock, concrete foundations,and buried concrete posts, while those with the highest noise were thin concrete pads, bridges, and boulders.In terms of environment, clearings containing bare rock and thin sedimentary cover had the lowest standarddeviations, while meadows (which are distinguished from clearings by thick sedimentary cover and the lackof exposed rock), forests, and thermal areas were highest (presumably reflecting amplification of groundvibrations, vibrations caused by tree roots, and unsteady subsurface fluid migration, respectively). Thus, ageneral rule of thumb for Yellowstone (and perhaps more broadly) is that a bedrock installation in a rockyclearing will offer lower noise compared to, say, a thin concrete pad in the forest.

Figure 3. Vertical displacements at continuousGNSS stations in YellowstoneNational Park during 2016–2017. Station locations given in Figure 1. Graylines denote times of gravity surveys in 2017. Transient apparent subsidenceat the end of 2016 is an artifact due to snow cover on GNSS antennas.

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4.2. Residual Gravity Change

Figure 5 gives epoch‐by‐epoch maps of residual gravity change measured by gravimeter 578, as well as thetotal change measured from May to October. Relative to the MAWY base stations, most sites experienceda residual gravity decrease from May to July, an increase between July and August, and both increasesand decreases during August–October. Although the August–October pattern of residual gravity decreaseat stations around the Norris Geyser Basin, when nearly all other stations saw increases, may seem like asystematic error, this is unlikely because the stations were surveyed on different days and associated withmultiple local base stations during both August and October. Both epoch‐to‐epoch and cumulative (fromMay to October) residual gravity changes are within ±20 μGal at about 90% of the sites. The formal uncer-tainty in residual gravity values for individual stations is less than 10 μGal in most cases (see supportinginformation Table S1).

5. Interpretation and Implications

We set out to test whether there were seasonal variations in gravity at Yellowstone, given that most gravitysurveys there (and elsewhere) are carried out at similar times of year to minimize any such effects. Visually,we observed major changes in surface hydrologic conditions over the course of the four surveys. Forinstance, at site J367, at least 1 m of densely packed snow and ice (and more in places) was present on theground in May, the ground was snow‐free in July and August, and about 0.5 m of light snow was presentin October (Figure 6). Levels of surface water were also highly variable. At station Y367, the YellowstoneRiver, which is in contact with the rock in which the benchmark is cemented, rose by 0.5 m from May toJuly and dropped by 1.05 m between July and October (Figure 7). Over the course of our four surveys, therewere variations in air temperature, atmospheric pressure, precipitation, and the level of Yellowstone Lake(Figure 8), yet none of these appear to correlate with the residual gravity change over time (Figure 5).

Given these dramatic environmental changes, the lack of significant variations in residual gravity beyond±20 μGal over the course of the entire sequence of surveys is unexpected. As an example, one might haveanticipated that the residual gravity change at Y367 would be positive during May–July and negative duringJuly–October based on the change in river level (Figure 7). In fact, the residual gravity did not changebetween May and July, and the changes in July–August and August–October were −17 and 11 μGal, respec-tively (Figure 5). The rather surprising conclusion is therefore that seasonal changes in residual gravity atYellowstone were small (on the order of the uncertainty in the measurements) during the course of our2017 surveys, despite the large changes in surface water levels and snow conditions.

Figure 4. Standard deviation of gravity measurements recorded by gravimeter 578 during morning, afternoon, and eve-ning occupations of sites for May (M), July (J), August (A), and October (O) surveys. Plots show standard deviationcompared to style of benchmark installation (a) and environmental setting (b). Morning and evening occupations tend tobe quieter than those done in the afternoon, probably due to higher levels of anthropogenic noise (like traffic) in theafternoons. Bedrock installations offer the lowest noise levels, with concrete pads, boulders, and concrete access covers thehighest. Rocky clearings are the quietest environmental settings, while forests and meadows without bedrock are char-acterized by higher standard deviations.

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How can this be? In fact, simple models suggest the sorts of changes seen in Yellowstone's hydrologic con-ditions over the course of May–October 2017 might not be expected to produce large changes in residualgravity. For example, the gravity change Δg expected from variations in river level can be approximatedby an infinite linear mass source (Yi et al., 2016):

Δg ¼ GρWΔz=d

whereG is the gravitational constant, ρ is the density of water,W is the width of the river, Δz is the change inriver level, and d is the distance between the river and gravity site. Assuming a width of 25 m, a level change

Figure 5. Maps of residual gravity change for May–July (a), July–August (b), August–October (c), and May–October (d).Warm colors indicate increases in residual gravity and cool colors indicate decreases, all relative to the base station atMAWY_PAD/MAWY_ROCK. Station names are given in part (c). Not all stations were measured during every survey; seeTable 1 for a list of station occupations.

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of 0.5 m, and a distance of 15 m between the gravity site and the center of the river, the expected gravitychange is 5.5 μGal. Variations in Yellowstone Lake and associated groundwater conditions could possiblycause a gravity change, which can be modeled as an infinite slab source (Battaglia et al., 2003; de Zeeuw‐van Dalfsen et al., 2005):

Figure 6. Photographs showing the same view of gravity station J367 during each of the four surveys. Location of gravitystation is noted by red circle in May photograph.

Figure 7. Photographs showing the same view of gravity station Y367 during each of the four surveys. Location of gravitystation is noted by red circle in May photograph.

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Δg ¼ 2 πGɸρΔz

where ɸ is the porosity of the host rock. Assuming a porosity of 20% (de Zeeuw‐van Dalfsen et al., 2005) anda Δz of 0.5 m yields a gravity change of 4.2 μGal. Even though these calculations are simplified approxima-tions, they do lend insight into the magnitude of potential changes due to hydrologic variations that are onthe order of those observed in the field.

We note that there is a possibility that the base station experiences gravity changes caused by variations inhydrological conditions, although we have no immediate indication that this is the case. Since all measure-ments are relative to the MAWY base station, any gravity variations at that site will appear in all other mea-surement locations. Without an absolute gravity time series, this ambiguity is impossible to resolve.

Our results, supported by simple models, imply that residual gravity changes at Yellowstone caused by var-iations in atmospheric pressure, surface or groundwater levels, or other seasonal factors are not significantbeyond ±20 μGal (indeed, this envelope may define the repeatability of a microgravity survey when donefollowing our methods, given the changes in residual gravity at station Y367 along the bank of theYellowstone River; Figure 7). This result is similar to those of Battaglia et al. (2018), who found similar levelsof background noise (up to 25 μGal) for gravity changes at Mount St. Helens; Miller et al. (2017), whoachieved an average standard error of 19 μGal for surveys at Laguna del Maule; and Tikku et al. (2006),

Figure 8. Environmental conditions over 2016–2017 measured near GNSS station LKWY, on the northern edge ofYellowstone Lake, including (a) discharge of the Yellowstone river at the outlet of Yellowstone lake (a proxy for lakelevel); (b) cumulative precipitation, (c) air temperature; and (d) atmospheric pressure. Red dashed lines are times ofgravity surveys in 2017. River discharge was measured at U.S. Geological Survey stream gage 06186500, and other para-meters are from National Weather Service station KP60.

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who noted that gravity variations were on the order of 10–15 μGal duringan 8‐day period of continuous measurements near Old Faithful (duringwhich time the gravimeter was not moved). To better visualize this point,we grouped the gravity sites depending on their distance from continuousGNSS sites (OFW2, NRWY, P711, P716, and LKWY; Figure 1) and plottedthe change in residual gravity over time (Figure 9, with station groupingsdefined by color shades). The residual gravity changes are generallywithin ±20 μGal, which we consider to be the overall uncertainty whenconsidering all sources of potential error (from variations in instrumentsetup to environmental factors). Despite the small magnitudes of the resi-dual gravity changes over time, there are some consistent behaviors. Forexample, stations in the area of Norris Geyser Basin (red‐shaded lines inFigure 9) were all characterized by a decrease, then increase, and thendecrease over the three epochs covered by our surveys (the stations inthe area were surveyed on different days, so these trends are not a resultof a systematic error that affects a single day of measurements). Stationsin the vicinity of the LKWY continuous GNSS site (black‐shaded lines inFigure 9), in contrast, showed mostly positive changes over time. It is

impossible to assess howmuch of the observed variability is due to seasonality and howmuch is due to otherfactors. Regardless, these potential seasonal and other signals are minor compared to those that mightaccompany magmatic activity, which (when occurring in the upper few kilometers beneath the surface) isusually on the order of many tens to hundreds of microgals (e.g., Carbone et al., 2017), and so should notimpact the ability of gravity campaigns to detect significant changes in Yellowstone magmatism.

Confirmation of the limited impact of seasonal changes on residual gravity variations is an important out-come, as it argues that the practice of measuring gravity at a given location at the same time of year to avoidseasonality may not reduce the ambiguity in results. Yi et al. (2016) reached the same conclusion based ongravity studies in Tibet, where heavy precipitation resulted in only a fewmicrogals of gravity change over thecourse of a year. A continuous gravimeter, coupled with meteorological measurements, would be better ableto assess seasonal variations due to hydrological changes (the short‐term impacts of rainfall, snowmelt, andother seasonal changes, as well as hydrothermal activity, would be easier to assess with a continuous timeseries; Gottsmann et al., 2005, 2007; Tikku et al., 2006).

A second important outcome of our work is the recognition that the environmental setting and installationtype of a gravity site exerts a strong control on the magnitude of gravity change that can be resolved. A net-work composed of sites on boulders or thin concrete pads in forested areas will have much higher noiselevels compared to a network of sites on bedrock and away from trees. This information is critical for (1)the design of future surveys at Yellowstone and (2) reinterpreting past data. These insights can be extendedto gravity work in other volcanic regions as well. Our results will help us to choose low‐noise sites that arebest suited to study subsurface mass change due to magmatic activity. Past data, which are highly variableand ambiguous in terms of implications for the magmatic system (Arnet et al., 1997; Farrell, 2014), mightbe reinterpreted focusing on changes at stations that are characterized by the lowest noise.

The outcomes of our work give confidence that microgravity can be used to detect magmatic activity beneathYellowstone (and other active volcanic systems). Previous studies in diverse volcanic settings have generallyfound magmatic activity to be associated with residual gravity variations of many tens to hundreds of micro-gals over years to decades. For example, increases in residual gravity at Kīlauea due to shallow magma accu-mulation were ~450 μGal during 1975–2008 (Johnson et al., 2010) and ~150 μGal during 2011–2012(Bagnardi et al., 2014), andmore than 400 μGal of change was associated with Etna's 1991–1993 eruptive epi-sode (Rymer et al., 1995). A cumulative residual gravity decrease of up to 150 μGal during 1988–2010 wasmodeled as a combination of magma withdrawal and cooling/contraction of the magma reservoir atAskja, Iceland (de Zeeuw‐van Dalfsen et al., 2005, 2013; Rymer et al., 2010), while an increase of~140 μGal in the crater and 50–60 μGal on the flanks of Mount St. Helens between 2010 and 2016 was attrib-uted in part to magma accumulation (Battaglia et al., 2018). Over 60 μGal of residual gravity increase at LongValley was associated with uplift during 1982–1999 (Battaglia et al., 1999, 2003); rapid inflation and deflationduring 1981–1987 and subsequent slow deflation during 1988–2001 at Campi Flegrei were accompanied by

Figure 9. Cumulative residual gravity variations measured during 2017 atstations in Yellowstone National Park. Error bars are omitted for claritybut are less than 10 μGal in all cases. Line colors indicate locations of sta-tions with respect to the closest continuous GNSS sites (Figure 1). Grayshaded area denotes ±20 μGal.

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residual gravity changes of over 100 μGal; and annual maximum residual gravity changes of 60–120 μGalwere measured at Laguna del Maule (Miller et al., 2017). In the cases of restless silicic calderas, sources ofmass change calculated from residual gravity variations have been attributed to magma (Long Valley),hydrothermal fluids (Laguna del Maule), and a combination of the two (Campi Flegrei), although magmaticactivity was probably occurring in all locations. At Laguna del Maule, for example, large changes in the shal-low hydrothermal system were caused by a deeper magmatic intrusion (Miller et al., 2017). Gravity changesassociated with isolated shallow hydrothermal systems, like geyser basins and hot springs, are usually smallin terms of magnitude (on the order of a few tens of microgals), extent (hundreds of meters to a few kilo-meters), and timescales (minutes to days; Gottsmann et al., 2005, 2007; Tikku et al., 2006). AtYellowstone, we demonstrate that seasonal variations plus measurement uncertainty are on the order of±20 μGal. This level may be too high to identify changes due to shallow isolated hydrothermal activity,but it is well below the magnitude of gravity change that results frommagma accumulation and withdrawal,as well as broad‐scale variability in hydrothermal systems that is caused by magmatic intrusions. We aretherefore confident that a carefully planned survey that utilizes only sites that are characterized by low noiseand that is repeated at least every few years will be well positioned to detect future transient magmatic pro-cesses at Yellowstone.

6. Conclusions

Gravity measurements at active volcanoes are subject to a variety of sources of noise and uncertainty, includ-ing seasonal changes that are mostly due to hydrological processes, like variations in groundwater level.When there are no observations to constrain these processes, repeat gravity surveys of a given location atthe same time of year could limit background noise, although the applicability of this practice had not beentested until now. We conducted four gravity surveys at Yellowstone during 2017, in May, July, August, andOctober, and found that gravity changes over time were not strongly correlated with visible hydrologic pro-cesses (like river levels and snow cover). Indeed, the gravity variations over time showed only minor trends,and the magnitudes of the epoch‐to‐epoch and net gravity changes at individual stations over the 4‐monthperiod were generally ±20 μGal. The most likely reason for this observation is that the gravity signature ofseasonality in Yellowstone's hydrologic system is relatively minor. This result suggests that the timing of agravity survey with respect to seasons is not critical at Yellowstone, and potentially elsewhere, and that sea-sonal and other changes are small in scale compared to changes that are expected due to magmatic activity.We also noted that the environmental setting and installation type had a strong influence on the noise levelsat a given station, with gravity data collected at bedrock sites within a clearing having much lower noiselevels than measurements on boulders or thin concrete pads in a forest. These insights can be used to helpguide the establishment of future gravity networks at Yellowstone and other active volcanoes that experi-ence geophysical unrest.

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