Journal of Volcanology and Geothermal Research 387 (2019) 106667
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Hydrothermal fluid migration due to interaction with shallow magma:Insights from gravity changes before and after the 2015 eruption ofCotopaxi volcano, Ecuador
Antonina Calahorrano-Di Patrea,*, Glyn Williams-Jonesa, Maurizio Battagliab, c,Patricia Mothesd, Elizabeth Gauntd, Jeffrey Zureka, Mario Ruizd, Jeffrey Wittera
aCentre for Natural Hazards Research, Department of Earth Sciences, Simon Fraser University, BC, CanadabUS Geological Survey, Volcano Disaster Assistance Program, Menlo Park, CA, USAcDepartment of Earth Sciences, Sapienza - University of Rome, Rome, ItalydInstituto Geofísico de la Escuela Politécnica Nacional, Quito, Ecuador
A R T I C L E I N F O
Article history:Received 6 May 2019Received in revised form 28 August 2019Accepted 28 August 2019Available online 3 September 2019
On August 14, 2015 Cotopaxi Volcano (Ecuador) erupted with several phreatomagmatic explosions afternearly 135 years of quiescence. Unrest began in April 2015 with an increase in the number of daily seis-mic events and inflation of the flanks of the volcano. Time-lapse gravity measurements started at Cotopaxivolcano in June 2015. Although minor gravity changes were detected prior to eruptive activity, the largestgravity variations at Cotopaxi were measured between October 2015 and March 2016, when other geophys-ical parameters had reached background levels. Inverse modelling of GPS data suggests a deep intrusionprior to the eruptive activity, while inverse modelling of post-eruptive gravity changes suggests variationsin the volcano hydrothermal system. Deformation, seismicity, and gravity changes are consistent with theintrusion of a deep magmatic source between April and August 2015. Part of the magma rose from depth andinteracted with the hydrothermal system, causing the phreatomagmatic activity and pushing hydrothermalfluids from a deep aquifer into a shallow perched aquifer.
Time-lapse gravity measurements have been employed in numer-ous settings to monitor sub-surface mass changes related to volcanicactivity. Although the aim of these observations is usually to eitherinfer the amount of new magma intruded (or extruded) from thevolcanic reservoir (e.g., Rymer and Williams-Jones, 2000; Greco etal., 2012; Carbone et al., 2017) or changes in the density of an alreadyidentified magmatic intrusion (e.g., Williams-Jones and Rymer, 2002;Gottsmann et al., 2003), time-lapse gravity has also been successfullyemployed to monitor hydrothermal systems (e.g., Tizzani et al., 2015;Battaglia et al., 2018; Miller et al., 2018). Thus, these observationscan not only help discriminate between possible causes of measureddeformation and increased seismicity during unrest episodes, theycan also shed light on interactions between magmatic and hydrother-mal systems in a volcano (e.g., Battaglia et al., 2006; Gottsmann etal., 2006, 2007). When Cotopaxi volcano showed signs of renewed
activity after 135 years of quiescence, gravity measurements were avaluable addition to the already extensive seismic, geochemical, andgeodetic monitoring networks installed by the Instituto Geofísico dela Escuela Politécnica Nacional (IG-EPN).
Cotopaxi,aglacier-cladstratovolcanolocated50 kmsouthofQuito,Ecuador, is part of the Northern Volcanic Zone in the Andean VolcanicArc, and the result of the subduction of the Nazca Plate beneath theSouth American Plate (Stern, 2004) (Fig. 1). Ordoñez et al. (2013) andAndrade et al. (2005) proposed 4 different hazard scenarios basedon the energy released by the eruption: Small (VEI 1–2), Moderate(2–3), Large ( 3–4), and Very Large (VEI >4). Considering Cotopaxi’seruptive history, the main hazards for larger, distal cities are ash falland lahars in a Large Eruption scenario (Mothes and Vallance, 2015).Up to 300,000 people currently live in the path of possible lahars, andagricultural lands that provide a large quantity of vegetables grownin Ecuador could be affected by ash fall from Cotopaxi.
Cotopaxi began showing signs of unrest at the beginning of 2015,after a minor period of unrest in 2002 which did not result in eruptiveactivity. Hickey et al. (2015) modelled the source of the 2002 defor-mation as a shallow oblate magmatic intrusion beneath the SW flankof the volcano. This was reconciled with seismic signals described by
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Fig. 1. Map of continuous GNSS (Global Navigation Satellite System) and time-lapse campaign gravity sites. Inset map of Ecuador shows Cotopaxi in relation with the capital city,Quito. Gravity sites are represented with circles, while continuous GNSS sites are denoted by orange diamonds and have a g subindex in their name. Magenta squares indicatesites of IG-EPN at which other geophysical parameters (e.g., seismicity, infrasound, SO2 flux, etc.) are monitored. InSAR data (Morales Rivera et al., 2017) were used to monitordeformation at sites without GNSS coverage. For a complete map of the IG-EPN monitoring network, see the official website: https://igepn.edu.ec/cotopaxi-red-de-monitoreo.(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Molina et al. (2008) as a combination of thermomechanical viscoelas-tic models (which explain the aseismic intrusion) and mass transportalong NNE-SSW trending faults (consistent with seismicity under theNEflank).Alowmagmasupplyrate isbelievedtoaccountforthelackoferuptive activity (Molina et al., 2008; Hickey et al., 2015). In April 2015,IG-EPN reported an increase in the number of daily seismic eventsand inflation of the flanks at levels that surpassed the 2002 unrest(Mothes et al., 2017). A progressive increase in the SO2 daily flux wasdetected two months later, coincident with an increase in the num-ber of Long Period Events (LP), followed by the appearance of volcanictremor (Hidalgo et al., 2018). Reports of rotten-egg smell (i.e., hydro-gen sulphide) by summit climbers coincided with increased fumarolicactivity, which was visible from neighbouring cities (Mothes et al.,2017). The continuous escalation of unrest culminated in explosivephreatomagmatic activity on August 14, 2015 (Mothes et al., 2017).This phreatomagmatic eruption was preceded by a swarm of VolcanoTectonic(VT)events,andashplumesfromtheexplosionsreached8 kmabove the summit (Bernard et al., 2016; Mothes et al., 2017). Continu-ous ash emissions lasted until November 2015, with the compositiongradually changing from being dominated by lithics and hydrother-mal material (from the August 14 explosions) to dominantly juvenilematerial (up to 60 %) ten days after the eruption (Gaunt et al., 2016).After ash emissions ceased in November 2015, daily SO2 flux fromCotopaxidecreaseddramatically,whileseismicsignalswerestilldom-inated by VT events but the daily number of events declined (Motheset al., 2017; Hidalgo et al., 2018). All geophysical parameters reached
background levels by March 2016. GPS and InSAR data showed thatthe edifice remained inflated during and after the eruptive activity(Morales Rivera et al., 2017).
Cotopaxi is a remote volcano, where the lack of roads makes itdifficult to design and access a high-precision gravity monitoringnetwork. In this work, we used an approach to field measurementsthat allowed us to minimize the environmental/instrument noiseand improve the precision of gravity measurements. This approachcan be easily implemented on other volcanoes with similar charac-teristics. Deformation and gravity data are consistent with the intru-sion of a deep magmatic source between April and August 2015. Partof the magma rose from depth and interacted with the hydrother-mal system, causing the phreatomagmatic activity. Hydrothermalfluids were pushed from a deep hydrothermal aquifer into a shallowperched hydrothermal aquifer.
2. Methods
2.1. Gravity site set-up and stability of measurements
Time lapse gravity measurements started at Cotopaxi in June 2015with the installation of three stations on the W and NE flanks of thevolcano (CAME, NASA, VC1) (Fig. 1). Relative gravity measurementswere made bi-monthly with a Scintrex CG-5 gravity meter. StationCAME was initially used as reference station, however, because of
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the proximity of CAME to the summit, a new reference station (OVC)was installed in October 2015. Other stations around the volcanicedifice (REF, MSUC, TAM, REB, RES) were set up in later surveys.Each station was installed with the aim of ensuring the temporalstability of the site: locations on bedrock were preferred, concretebases were built on each site (if a pre-existing structure was notavailable), and elevation changes were monitored regularly at eachgravity station through a combination of GNSS and InSAR data (Fig. 1).Temporal gravity change at the reference station was ensured tobe non-significant (below measurement error) by comparing OVCmeasurements with two control sites ∼ 55 km and ∼ 26 km fromCotopaxi (ELE - located on IG grounds - and LATA, respectively):the repeatability of the measured difference between OVC, ELE, andLATA was found to be higher than 15 lGal over consequent months.The stability of the instrument was also tracked by repeating a con-trol cycle (a loop of three stations, close to each other, in whichgravity is stable in time) at IG-EPN in Quito before and after the sur-veys. Finally, the long term drift constant of the CG-5 relative gravitymeter was periodically updated using data collected in an IG-EPNtunnel-housed seismic station (OTAV), in which temperature, pres-sure, and gravity vary minimally through time. The long term driftcorrection, as well as other calibration constants of the instrument,were determined following the procedures specified by the ScintrexCG-5 Manual (Scintrex Limited, 2012).
2.2. Data acquisition and processing
Inordertorealisticallymonitorsub-surfacetemporalmasschangesin a volcanic setting using gravity techniques, field procedures mustbe adopted to control data uncertainty and to reduce errors below10–15 lGal (e.g., Rymer and Brown, 1989; Rymer, 1994; Bagnardi etal., 2014; Carbone et al., 2017). This goal can be reached by repeatedoccupation of stations throughout the day, minimizing temperatureand pressure effects on the instrument, and avoiding shocks dur-ing transport. At Cotopaxi, an additional effect must be considered:long-travel time between stations (on the order of 2–3 h, both bydriving and hiking) causes a hysteresis effect on the sensor spring,and therefore drifting and taring of the instrument. Only one gravitymeter was available for the campaigns, so cross-checking measure-ments with another instrument was not possible. The drift and taringeffects were mitigated by increasing stabilization and measurementtimes at each station, which consequently reduced site reoccupationsper day. Drastic temperature changes at Cotopaxi (∼ 10 ◦ C–30 ◦C in6 h) were mitigated by using a foam-insulating cover on top of theinstrumentduringmeasurements.Temperatureandpressurechangeswere monitored with an auto-recording thermometer and a hand-held barometer, respectively. Pressure changes for each station onconsecutive surveys did not surpass 4 mbar, and therefore effects fromatmospheric loading are lower than 2 lGal, well below data error.Although temperature changes during the day at Cotopaxi are large,the measured temperature variation inside the protective foam-boxwas within 1 ◦C per station measurement, and thus no discernibleeffect was found in the gravity data. Additionally, a custom wind pro-tection tarp with built-in poles and ropes was carried from station tostation to protect the instrument from toppling in strong wind gusts,and to reduce wind-induced noise.
A typical single loop at Cotopaxi included at least two occupa-tions of the reference station, two occupations of a mid-point station,and one of a long-travel station. At least fifteen 60 s gravity-averagedvalues were recorded at each station. If the difference betweenseveral sequential measurements was larger than 7 l Gal, or mea-surements exhibited an obvious trend, more data were collecteduntil 15 sequential readings met the above criteria. Each loop wastypically completed twice per campaign in order to constrain dataoutliers. Rough roads, challenging terrain, and drastically changing
environmental conditions limited the number and spacing of gravitystations, in order to not sacrifice the accuracy of data.
Campaign data were reduced using the software GTOOLS(Battaglia et al., 2012). The software corrects the ocean loading andEarth tide effect on gravity data, finds and removes data outliers,calculates the daily drift of the instrument, and finally estimates theerror for each day of measurements. Outputs are then presented bycampaign station as relative gravity differences between benchmarksand the reference station, OVC. The error is then estimated with acustom algorithm as the difference between repeat loops in eachcampaign. Errors on data collected before station OVC was installedhave been matched to the largest error ever recorded on repeatingloops at Cotopaxi.
3. Results
Results from temporal gravity measurements at Cotopaxi beforeand after the August 2015 eruption are presented in Fig. 2. Datafrom before the eruption are referenced to the first base station,CAME, and therefore are not suitable for inverse modelling. Forwardmodelling of these data can be performed using results from GPSdeformation between April and August 2015. Relative gravity changesfrom October 2015 onward are referenced to the second base stationOVC, but no deformation was recorded during that period. Hence,while inverse modelling of gravity change after the eruption can beperformed, no joint inversion with other geophysical data is possible.
Since gravity readings at CAME are influenced by volcanic activityat Cotopaxi, gravity data collected using CAME as reference stationwill be treated only as a gravity difference between stations. There aretwogravitydifferencechangesmeasuredbeforethephreatomagmaticeruption: NASA-CAME, which decreased by 22 lGal between June andAugust 2015, and VC1-CAME, which increased 15 lGal between Juneand August 2015 (Fig. 2). Fig. 2 also shows a steady relative gravitydecrease in almost all measured campaign stations at Cotopaxi (exceptfor the highest elevation station REF) after October 2015. The largestgravity change was measured at station VC1: −72lGal between Octo-ber 2015 and March 2016. In a comparison between volcanic activityand gravity changes measured at Cotopaxi, it is noteworthy that thelargest gravity change was measured after most geophysical signalsreached (or were headed towards) background levels (Fig. 2).
3.1. Modelling of pre-eruptive gravity and GPS data
Deformation at Cotopaxi, albeit small, was detected by GPS,InSAR, and tiltmeters (Morales Rivera et al., 2017; Mothes et al.,2017). Although detected displacements are not large enough tocause free-air gravity changes above instrumental error, elevationdata from the GNSS network of IG-EPN allows for inverse modelling.A juxtaposition of measured gravity changes with relevant measureddisplacement is shown in Fig. 3.
Non-linear inverse modelling of the April–October 2015 displace-ments was performed using the software package dMODELS (Battagliaet al., 2013). Sources are modelled as fluid filled cavities acting ina homogeneous elastic half-space: a common - and often neces-sary - approximation of magmatic reservoirs (Lisowski, 2007). Errorsfor the modelled parameters were determined using a Monte Carloapproach, in which several inversions were performed using “noisydata” generated by a normal distribution with zero mean (e.g.,Wrightet al., 1999; Battaglia et al., 2018). Several possible sources of deforma-tion were tested, including spheres, spheroids, sills and dykes, withthe statistics of the various inverse models listed in Appendix B. Thebest fitting source is a dipping prolate spheroid, located directly belowCotopaxi’s crater (Fig. 4). Table 1 shows a summary of the modelledparameters and errors. Not surprisingly, since deformation is presentat stations far from the main vent, a deep magmatic source is consis-tent with analogous sources proposed for the present and previous
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Fig. 2. Relative gravity change measured at benchmarks on Cotopaxi, alongside a time line of volcanic activity. Gravity measurements made before the reference site OVC wasinstalled (October 2015) are shown only as gravity differences between stations NASA-CAME and VC1-CAME.
periods of unrest at Cotopaxi (see Hickey et al., 2015; Morales Riveraet al., 2017). We calculated the gravity change at stations CAME, NASA,and VC1 using the parameters of the best-fitting deformation source,active at Cotopaxi during April–October 2015 (Table 1). Forward mod-elling was done using the triaxial ellipsoid model for gravity anomalies(Clark et al., 1986). Forward gravity modelling of the dipping spheroid
using a density change of 2450–2500 kg/m3 (andesitic magma) showsthat changes in gravity difference between stations would have beenequivalent to 1 lGal, which is evidently below instrumental error.Therefore, the proposed deformation source can not explain mea-sured gravity data before the eruptive period. Further modelling ofthese gravity difference changes is not possible.
Fig. 3. Gravity change differences compared to relevant GPS displacement time series at Cotopaxi volcano (left). On the upper right, the horizontal deformation velocities arepictured, while the vertical deformation velocities are shown on the lower right. The green dotted line denotes the chosen profile of the volcano shown on the lower right.Deformation velocities are shown for the period from April to October 2015. Although station PSTO is not directly on the volcanic edifice, it was included since it shows identicaldeformation to stations on the W flank of the volcano. The coordinates of the elevation contour map on the upper-right side of the figure are in UTM WGS84 (Zone 17M).(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 4. GPS data and best fit model of deformation rates from April to October 2015.The best-fit source is a dipping spheroid, ∼12 km below the crater, and due to scaleconstraints is not shown in the bottom figure. The plotted profile (and all subsequentprofiles) follows the green dotted line shown on the upper right of Fig. 3. (For inter-pretation of the references to color in this figure legend, the reader is referred to theweb version of this article.)
3.2. Modelling of post-eruptive gravity data
Measured relative gravity changes at Cotopaxi after October 2015show a steady decrease at most stations, evidence of mass loss belowstation level or addition of mass above the stations, which could indi-cate: 1) Mass loss from a previous magmatic intrusion, or a magmaticintrusion rising above station level; 2) Hydrothermal fluid loss belowor gain above station level; 3) Precipitation or glacier changes; 4) Acombination of some or all of these sources.
Mass loss from the proposed deep magmatic intrusion for theApril–October 2015 deformation is unlikely, since the gravity valuesderived from forward modelling of magmatic inflow (Table 1) holdvalid for fluid outflow if the sign of the gravity change is inverted: grav-ity change caused by mass outflow from the proposed deformationsource would not surpass data uncertainties. Indeed, inverse mod-elling yielded poor fits for gravity changes between October 2015 toMarch 2016, using a spherical, spheroidal, and dyke-shaped intrusion.Mass loss gravity change from sources proposed by Morales Rivera etal. (2017) for deformation detected by InSAR was explored previouslyin Calahorrano-Di Patre et al. (2017) and yielded equally poor results.Forward modelling of fluid outflow from the dipping sheet-like dykeproposed by InSAR inverse modelling did not match the measuredgravity changes, even when the source thickness was increased from0.2 m to 2 m and 20 m. Forward modelling of magma rising above sta-tion level (a shallow magmatic plug) was also explored, and resultsfrom such modelling did not surpass data uncertainty (Calahorrano-DiPatre et al., 2017).
Gravity change induced by glacier variations was considered bycalculating volume change in two DEMs (Digital Elevation Models)from September 2015 and May 2016, and precipitation influenceon Cotopaxi’s water table was investigated using data from thelocal meteorological agency, INHAMI. However, neither effects couldproduce gravity changes detectable above measurement errors(Appendix C). A combination of all the previously mentioned sourcesmay contribute to the signal; however, as its effect is not detectedor directly quantified by this methodology, it is not within our capa-bilities to confirm or deny the existence of such sources. Therefore,hydrothermal fluid migration was considered the most likely scenariofor modelling the measured gravity changes.
3.2.1. Mass loss below stations: outflow from a deep aquiferFluid outflow from a deep aquifer was modelled using a vertical
finite cylinder (Singh, 1977). The aquifer was assumed to be shapedas an annulus-like cylinder, in order to accommodate the magmaticconduit, centred within a 100 m radius circle around Cotopaxi’s vent,in a similar manner to modelling of the hydrothermal system byBattaglia et al. (2018) at Mt. St. Helens. Fixed boundaries for themodel include a minimum depth for the aquifer (3700 m.a.s.l), a min-imum and maximum length for the inner cylinder radius (20 m and100 m, respectively), and the source density (1000 kg/m3). The mini-mum depth for the aquifer was constrained considering the proposedmagmatic-hydrothermal system interaction by Gaunt et al. (2016),previous seismic studies by Molina et al. (2008), and recent numeri-cal heat and fluid flow simulations of volcanic activity loosely basedon the Cotopaxi case (Hemmings et al., 2016). The outer radius of thecylinder was only constrained by topography, which limits the maxi-mum depth of the cylinder to be the base level elevation of Cotopaxi:any deeper would cause the bounds of the lower aquifer outer radiusto be undefined. Finally, the height of the modelled annulus was leftunconstrained for the first minimization, and a more refined search
Table 1Table of deformation source parameters, and forward modelling results of gravity difference change at Cotopaxi volcano. The calculated gravity variation at Cotopaxi’s benchmarkswas computed using the source’s change in volume, and assuming an andesitic magma density of 2450–2500 kg/m3 (Martel et al., 2018). wm
2 refers to the penalty function(a statistical estimate of fit goodness) of the inverse model: the chi-squared per degrees of freedom.
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Fig. 5. Gravity changes at Cotopaxi volcano and modelled gravity data for one of the possible cases of sub-surface mass-change at Cotopaxi. Due to its distance from thesummit, OVC is omitted from the upper plot in order to more clearly show the source and volcano topography. Residual gravity data in the lower plot are presented asa function of distance from the source’s centre. Fluid outflow from a deep aquifer is modelled as mass loss from an annulus cylinder below the gravity sites, and fits themajority of measured gravity data.
was then performed in a constrained space (−100 m to 0 m) in orderto increase the precision when looking for the optimum value.
Modelling results against gravity data are shown in Fig. 5, andTable 2. Best fit source parameters are shown in Table 3. It is worthnotingthateventhoughthemajorityofthestationdataarefittedinthismodel, the largest gravity change measured at VC1 is not explained.
3.2.2. Mass increase above stations: inflow into a shallow perchedaquifer
In general, shallow hydrothermal sources at Cotopaxi are poorlyconstrained by geophysical and geological data, although thepresence of flank fumaroles and constant recharge from both glaciermelt and precipitation point to their probable existence. Analogous
Table 2Time-lapse gravity change measured at Cotopaxi volcano, gravity results from inverse modelling, and residual data from best fit fluid outflow model. Modelling results are shownin gray (columns B, C, and D). Residual gravity refers to the remanent data resulting from deducting model B from data A. Column D is obtained by inverse modelling of residualgravity A–B. w2 is the statistical estimate of fit goodness for each inverse model. As denoted by the very low wm
2 value obtained for the “Aquifer Fluid Outflow and Inflow” model,this model has a much better fit to the data compared to the other model options shown above.
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Table 3Source parameters for the three best fit models at Cotopaxi: fluid outflow from a deep aquifer, fluid inflow into a perched aquifer, and modelled perched aquifer mass increasefrom residual gravity of the mass outflow from a deep aquifer. The parameters of the “Aquifer Outflow and Inflow” row are obtained by fixing the parameters presented in row 1of this Table (“Deep Aquifer Outflow” model).
Source X (m) Y (m) Z (m.a.s.l) Length (m) Ext. Radius (m) Density (kg/m3) D M (kg)
studies on stratovolcanoes (e.g., Mt. St. Helens, Battaglia et al., 2018;Tongariro, Miller et al., 2018) as well as the constantly changinghydrothermal systems on shield volcanoes and calderas (e.g., Gotts-mann et al., 2007; Mauri et al., 2018) support the possibility of fluidinflow into a shallower Cotopaxi aquifer.
Similar to the previous out-flow model, the gravitational changeis modelled as mass addition to a vertical cylinder above the stations(Singh, 1977; Battaglia et al., 2018). In this case, however, the cen-tre of the aquifer is not fixed around the vent, and the density of thesource is not predetermined. This allows for greater freedom withinthe models, and considers the possibility of less dense fluids (e.g., vol-canic gases) constituting part of the mass change. Modelling resultscompared to gravity data are shown in Fig. 6, and Table 2, whilebest fit source parameters are shown in Table 3. Although the grav-ity changes at stations VC1 and REF are now properly modelled, the
majority of measured gravity change at Cotopaxi is not, and thereforea better fitting model must be considered.
3.2.3. Modelling of residual gravity from the deep aquifer mass outflowcase
Considering results from the hydrothermal fluid inflow and out-flow cases, a combination of both models can explain the majority ofmeasured gravity change from October 2015–March 2016. The resid-ual gravity is calculated by subtracting results of the fluid outflowmodel from the original gravity data. This was inversely modelled inthe same fashion as the perched fluid inflow case. The source param-eters are shown in Table 3, while the model fit is shown in Fig. 7. Themodel fit to the residual gravity is within error.
A 3D representation of the combined models of fluid outflow froma deep aquifer and fluid inflow into a shallower aquifer is shown in
Fig. 6. Gravity changes at Cotopaxi volcano and modelled gravity data for another possible case of sub-surface mass change at Cotopaxi. Fluid inflow into a shallower level ismodelled as mass increase in a cylindrical perched aquifer, and fits the largest gravity variations detected at Cotopaxi.
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Fig. 7. Residuals from the deep aquifer fluid outflow model and the resulting inverse model. Best fit model of the residual gravity indicates fluid inflow into a cylindrical perchedaquifer above station level.
Fig. 8. Errors for the positions, radii, and length of the simple aquifercylinders are also shown graphically in Fig. 8, and are listed in Table 3.It is worth noting, however, that the modelling algorithm assumesmass inflow into a void space. Therefore, in order to consider a morerealistic ground water level change in the aquifer, ground poros-ity must be taken into account. Due to the lack of porosity dataat Cotopaxi, it is reasonable to estimate minimum and maximumbounds for ground water level change (Table 4).
4. Discussion
While inversion models that can fit geophysical data are valuableas working tools, it is important to compare their results with geo-logical data in order to assess their plausibility. As such, the modelspresented are simple approximations of complex physical processeswithin Cotopaxi. Moreover, the challenges of performing time-lapsegravity campaigns at Cotopaxi limited the data coverage and, as aconsequence, the complexity of the models (with respect to geome-try and density contrast): the shapes of the sources were simple andfixed for each inversion, a uniform density was assumed, and porositywas not considered during the modelling.
At present, the best fit model for the gravity change measuredat Cotopaxi during October 2015 to March 2016 is a combination of
fluid outflow from a deep aquifer, and fluid inflow into a shalloweraquifer. The mass loss and gain from the aquifers is substantial, and itis important to consider why such fluid movement would occur, espe-cially given that it was detected while most geophysical data wereapproaching background levels. Insights can be gained by consideringthe petrological data analyzed by Gaunt et al. (2016). Samples of ashfrom the August 2015 explosive activity at Cotopaxi show evidenceof a direct interaction between a magmatic source and a hydrother-mal system. Moreover, geochemical and seismic data confirm thisinteraction: Hidalgo et al. (2018) found a correlation between chang-ing styles of seismicity through time (specifically the variation in thenumber of LP events, followed by the appearance of volcanic tremor,and later the predominance of VT seismicity) and SO2 (and its ratioin comparison with other volcanic gases) degassing which, overall,points to a complex interplay between the hydrothermal system anda shallow ( 2–5 km b.s.l.) magmatic source. Moreover, interaction ofglacier melt water and hot material at shallow depths has been pro-posed in the past by Ruiz et al. (1998) as the source of LP signals atCotopaxi. As such, the physical process detected by gravity changesduring Cotopaxi’s unrest could be explained by fluid flow from adeep level of Cotopaxi’s hydrothermal system into a shallower level,caused by heat flow from the shallow magmatic source that wasdirectly responsible for the explosive activity in August 2015 (Fig. 9).
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Fig. 8. Map and 3D view of the best fit models for gravity changes at Cotopaxi from October 2015 to March 2016, and their uncertainties. Errors in the source location are indicatedby red lines in the map view (two upper panels), while modelling errors in the size of the aquifers are shown by red cylinders in the 3D view (bottom panel). Errors were foundusing a classical Monte Carlo approach. Errors in the location of the centre of the lower aquifer are too small to be visualized in the figure. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)
Numerical models of hydrothermal changes for a case analogous toCotopaxi (Hemmings et al., 2016) result in the formation of a shallowperched aquifer in their initial (stable) model and, in the case of ther-modynamic variations, an increase over 300 m of the elevation of theaquifer. A complex dynamic water-table behaviour was observed inmost perturbation simulations during numerical modelling, with thesaturated zone persisting in some cases ∼30 years after the onset ofperturbation (Hemmings et al., 2016).
Table 4Change of aquifer length dependent on porosity (modelled changes assume vol-ume change inside a perfect cavity). Due to the lack of measurements of porosityat Cotopaxi, maximum and minimum bounds of porosity from a study at Colimavolcano (another andesite stratovolcano) were used (Farquharson et al., 2015). Min-imum porosity was assumed to be 2.5 % (maximum length change of aquifer), whilemaximum porosity was assumed as 73 % (minimum length change of aquifer).
Source Model length (m) Min. length (m) Max. length (m)
The influence of precipitation and glacier melt (Arnold et al.,2018) was considered (see Appendix A) and, while it is an impor-tant consideration for more complex models, at this stage it is notdetectable by our gravity network. Moreover, mass loss from thedeep aquifer is too large to be explained solely by evaporation ofwater exiting the volcanic complex through the summit plume. Theorder of magnitude of both fluid inflow and outflow are equiva-lent, further supporting the movement of fluids from a deeper toshallower level.
Finally, shallow hydrothermal changes could have generated addi-tional independent geophysical signals. Between September 2015 andMarch 2016, a new type of infrasound signal was detected by Johnsonet al. (2018) at Cotopaxi volcano. “Tornillo” (or screw-shaped) infra-sound events were recorded during and after eruptive activity, withtheorized source mechanisms ranging from crater-collapse due tohydrothermal or magmatic movement, to a strong modulating influ-ence from the crater shape. There is not enough evidence to concludethat a direct link exists between these signals and post-eruptive masschanges inferred by gravity measurements at Cotopaxi.
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Fig. 9. Conceptual model of physical processes inferred from temporal gravity changes, GPS displacement, petrology, geochemistry, and seismic data at Cotopaxi volcano for its2015–2016 unrest period. A dipping magmatic source, located 12 km below the summit, caused deformation detected by GPS stations. An inferred magmatic source rose fromdepth and interacted with the hydrothermal system at Cotopaxi, causing fluids to migrate to a shallower level.
5. Summary and conclusions
Temporal gravity changes at Cotopaxi volcano were measuredduring volcanic unrest in 2015–2016. Gravity data measured beforeeruptive activity in August 2015 were compared to results frominverse modelling of GPS displacements between April and October2015. The best fit model considering deformation data was a dippingspheroid, located 12 km below the vent with a positive DV equalto 30 × 106 m3. Forward modelling of gravity showed no relationbetween measurements before eruptive activity and the inferredsource of deformation. No further conclusions can be inferred fromthe limited gravity data collected before the eruption.
Gravity changes measured from October 2015 to March 2016 pointto changes in the hydrothermal system of Cotopaxi. Inverse mod-elling of gravity data suggests fluid movement from a deep aquifer(modelled as an annulus cylinder, located at 3.5 km a.s.l and centredbelow the vent) to a shallower perched aquifer (modelled as a simplecylinder at an elevation of 4.4 km a.s.l.). Due to the simplicity of themodel and the limited spatial coverage of the gravity benchmarks, nodefinitive location or source geometry can be determined. However,detected mass movement (∼1 × 1011 kg) from a deeper to a shallowerlevel gives insights into the physical processes occurring at Cotopaxiafter October 2015. Considering results from petrology (Gaunt et al.,2016), geochemistry, and seismicity (Hidalgo et al., 2018), an inter-action between a shallower inferred magmatic source (rising from adeeper magmatic intrusion) and the hydrothermal system caused flu-ids to shift from the vicinity of the contact level (∼ 3.5 km a.s.l.) intoa shallower perched aquifer(s) (∼ 4.4 km a.s.l.).
Time-lapse gravity data at Cotopaxi will be used in the future tocontinue the monitoring of volcanic activity, and especially variationsin its hydrothermal system. Challenges in data collection impede ahigh resolution campaign network, and therefore complex models atthe moment cannot be derived from Cotopaxi gravity data. Never-theless, if the limitations of the data are considered and input fromother geophysical results is taken into account, simple models canbe created that provide insight into physical processes otherwisepoorly constrained in this large volcanic complex and similar systemsprone to poorly-forecasted phreatic and phreatomagmatic eruptions.
Acknowledgments
Special thankstoallmembersof IG-EPN,andespeciallytoFranciscoMejía and Santiago Aguaiza, for their steadfast help during gravitycampaigns. We also want to acknowledge the assistance of staff andmanagement from ACOSA, who allowed access to and helped navigatetheir private land on Cotopaxi. This study was supported by a NSERCDiscovery grant to G. Williams-Jones, aswell as the EPN SemillaProjectPIS-16-10 to M. Ruiz. We thank Dr. Emily Montgomery-Brown (USGS)and two anonymous reviewers for improving this work with theirconstructive comments. Rain gauge data was generously provided byINAMHI. Our deep gratitude also goes to members of IGM, who builtconcrete bases in several Cotopaxi gravity sites, and contributed tothe October 2015 surveys. Any use of trade, firm, or product namesis for descriptive purposes only and does not imply endorsement bythe U.S. Government.
Appendix A. Glacier and precipitation influence on gravity changes at Cotopaxi
Glacier gravity noise was calculated simply by subtracting two Digital Elevation Models (DEM) for Cotopaxi, prepared in September 2015(shortly after the start of eruptive activity) and May 2016 (after geophysical signals reached background level). The September 2015 DEM wasprepared by the local Geographical Survey (Instituto Geográfico Militar) and has a precision of 3 m (Marrero et al., 2018), while the May 2016
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DEM has a 30 m precision and was created by the Earth Observation Research Center (EORC) and the Japan Aerospace Exploration Agency(JAXA) from a 5 m Digital Surface Model (EORC and JAXA, 2017). In order to be able to compare the two Cotopaxi maps, the 2015 DEM pixelswere averaged to equal the 30 × 30 m precision of the May 2016 DEM.
The change in thickness is shown in Figs. A.1 and A.2. The glacier (approximate) area has been manually contoured in order to reducecomputational time when substracting the DEMs, and the crater region has been excluded from the calculation since it has historically beenfree of any glacier.
After the thickness change was calculated, the gravity noise at each station was calculated by forward modelling the volume change of eachpixel, converting it into mass change by multiplying it by a standard solid-ice density of 917 kg/m3. The total calculated volume change was5.93 × 106 m3, which is bound to be over estimated due to the assumption of each pixel as a block of change (thus, assuming the volume change asthe thickness change multiplied by the area of each pixel). In previous estimates of glacier change assuming only the influence of volcanic activity(e.g., Hemmings et al., 2016) or climate-change induced glacier loss (e.g., Jordan et al., 2005), the observed volume change was either orders ofmagnitude less than the calculated result (∼102 lower) or closer in the case of climate-change induced glacier change, but lower nonetheless.
Fig. A.1. Maps of thickness change at Cotopaxi volcano, obtained by substracting two digital elevation models (May 2016–Sep 2015). The pixel size is 30 by 30 m. The horizontaland vertical lines denote the volcano profiles shown on the right hand side of the image.
Fig. A.2. Glacier thickness change on Cotopaxi volcano between May 2016 and September 2015, as seen in the two cross sections shown in Fig. A.1. The thickness change was notcalculated inside the crater since historically there has not been any glacier inside, and therefore any detected changes would have been due to other mass addition (ash, rocks, orsimilar) inside the crater.
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Fig. A.3. Gravity noise resulting form glacier change between September 2015 and March 2016, calculated for gravity sites at Cotopaxi volcano.
Even with the over-estimated volume change, and the simplicity of the calculation of the gravity noise (using Singh’s analytical gravity expressionfor a cylindrical mass variation for each pixel; Singh, 1977), the largest gravity influence due to glacier change at Cotopaxi volcano is belowdata error (Fig. A.3) and therefore it is not an important contribution to the gravity change detected between October 2015 and March 2016.
A.1. Precipitation influence on gravity change
It is a distinct possibility that precipitation could be an important contribution to shallow water table recharge. However, the lack of properdatasets documenting discharge of streams from the volcano, precipitation during gravity measurement times, permeability of the volcanicedifice, and other crucial information prevents a clear assessment of recharge through precipitation. Thus, numerical modelling in analogoussettings (e.g., Hurwitz et al., 2003; Hemmings et al., 2016) has to be used as a guide to estimate the contribution of rainfall in changes in thehydrothermal system of Cotopaxi.
Data from rain gauge stations (courtesy of the local meteorological institution INAMHI) located approximately 22 km (station M0371)and 30 km (station M1066) from Cotopaxi’s crater are used (Fig. A.4). A summary of gravity change in comparison with average monthlyprecipitation data for the aforementioned stations is shown in Fig. A.5. Although certainly a seasonal effect can be seen in the precipitationmonthly averages, long-term measurements of gravity changes at Cotopaxi (Fig. A.6) seem to oscillate steadily around an average value.Moreover, the rate of change never surpasses that of the period of October 2015–March 2016, supporting the hypothesis that the seasonaleffect of precipitation is not the main source for temporal gravity variations. The monthly rain fall average is possibly underestimated due toits distance from the summit of Cotopaxi, however, a very simplistic calculation of maximum recharge volume at a shallower level can be doneby assuming all precipitation is captured by the upper level of Cotopaxi. By over-estimating water collection by the edifice, a maximum boundfor precipitation influence can be calculated. The total amount of rain fall measured between October 2015 and March 2016 was 428.3 mm,which is consistent with data presented for previous years by Veettil et al. (2014). By multiplying this value by the surface area of the volcanicedifice above 4393 m.a.s.l, the maximum precipitation that would be able to recharge the modelled perched hydrothermal aquifer is found tobe 0.17 × 108 m3. This value is equal to 16% of the total volume change on the upper perched aquifer necessary to fit the residual gravity data.An alternative method of calculating precipitation influence on the measured gravity changes is to assume an infinite Bouguer slab variationin the water table, considering different porosities of surrounding ground. Results of such analysis did not yield gravity changes above 10 l Galfor water table changes below 1.5 m, and considering a generalised porosity of 50 %. It is worth noting from the previous case in this appendixthat the total glacier change is several orders of magnitude less than the maximum volume of precipitation: glacier melt is not relevant foraquifer recharge.
Recharge into deeper aquifer levels is much more difficult to model without additional data, and prompts the need for more complex mod-els. Numerical modelling of analogous cases in stratovolcanoes (e.g., Hurwitz et al., 2003; Hemmings et al., 2016) consider a rapid increasingpermeability of the ground with increased depth and therefore precipitation recharge is modelled only in surface cells, limiting the possibilityof recharge at a deeper level due to precipitation. However, more complex models and detailed hydrological data will have to be collected inthe future for further monitoring of the hydrothermal system at Cotopaxi.
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Fig. A.4. Pluviometer stations (white stars) where rain fall data was collected between October 2015 and March 2016. Rain gauge data courtesy of INAMHI.
Fig. A.5. Monthly rain fall data (gray columns) and relative gravity change (green and blue lines) between October 2015 and March 2016. Rain gauge data courtesy of INAMHI.
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Fig. A.6. Long-term gravity change at Cotopaxi volcano. It is noteworthy the lack of large variations in all stations during the period of October 2016 to March 2017, and againduring the period of October 2017 to March 2018, thus voiding the hypothesis of seasonal precipitation effects as the main source for the gravity changes studied in this work.
Appendix B. Ill fitting inverse models
In order to test all possibilities for the models, inverse modelling of mass loss from a magmatic source was attempted with the samealgorithm used for the inverse modelling presented in the main work. The modelling was unsuccessful, both for an (almost) unconstraineddecrease in mass (density varying from −2800 to 0 kg/m3, maximum depth 5500 m.b.s.l., radius of source 10 to 1000 m, and thickness of source10 to 1000 m; Figs. B.1 and B.2) as it was for a more constrained source (density varying from −2800 to 0 kg/m3, maximum depth 2500 m.b.s.l.,radius of source 10 to 700 m, and thickness of source 10 to 700 m; Figs. B.3 and B.4). Different boundaries for the model yielded similar results,with the goodness of fit described by w2 always becoming negative (a mathematical non-sense), and therefore cutting the simulation short.Some of the “best” ill-fit statistics are presented in Figs. B.5 and B.6.
Fig. B.1. Location and modelled gravity from the (almost) unconstrained inverse modelling of mass decrease from a magmatic cylindrical intrusion at Cotopaxi volcano. The fitbetween modelled and residual gravity is extremely poor, as shown from the parameters presented in Fig. B.5.
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Fig. B.2. Map view of the source location from the unconstrained modelled magmatic mass decrease.
Fig. B.3. Location and modelled gravity from the constrained inverse modelling of mass decrease from a magmatic cylindrical intrusion at Cotopaxi volcano. The fit betweenmodelled and residual gravity is extremely poor, as shown from the parameters presented in Fig. B.6.
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Fig. B.4. Map view of the source location from the constrained modelled magmatic mass decrease.
Fig. B.5. Model parameters and fit statistic for the unconstrained mass decrease from a magmatic cylindrical source at Cotopaxi. Descriptions of the parameters can be found onTable 2 of the main text.
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Fig. B.6. Model parameters and fit statistic for the constrained mass decrease from a magmatic cylindrical source at Cotopaxi. Descriptions of the parameters can be found onTable 2 of the main text.
B.1. Ill fitting models of deformation data
In this section, a list of statistics is presented from inverse modelling of deformation data at Cotopaxi volcano before eruptive activity.Sources modelled include spheres, dykes, sills, and spheroids. The best fitting source for the detected deformation was a prolate spheroid, asdiscussed in detail in the main work. As such, statistics from inverse modelling using a spheroidal source are not presented here alongsideresults from other sources. Statistics from preliminary modelling using a spherical source are shown in Fig. B.7, for a sill source are shown inFig. B.8, and statistics for inverse modelling using a dyke source are shown in Fig. B.9. Sources that had a better initial fit, or were geologicallymore likely were modelled again using a higher number of inversion cycles (as was the case with the dyke source), however, none of themproduced better results than the inverse modelling using a prolate spheroid.
Fig. B.7. Model parameters and fit statistic for the inverse modelling of deformation data using a spherical source. Descriptions of most of the parameters can be found on Table 1of the main text. DP/l refers to Pressure change over shear modulus.
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Fig. B.8. Model parameters and fit statistic for the inverse modelling of deformation data using a sill-like source. Descriptions of most of the parameters can be found on Table 1of the main text. DP/l refers to Pressure change over shear modulus.
Fig. B.9. Model parameters and fit statistic for the inverse modelling of deformation data using a dyke-like source. Descriptions of most of the parameters can be found on Table 1of the main text. U refers to dislocation displacement, W to width, and L to length of source.
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