Constraining volcanic inflation at Three Sisters Volcanic ...12.pdf · Constraining...

Article

Volume 13, Number 10

19 October 2012

Q10013, doi:10.1029/2012GC004341

ISSN: 1525-2027

Constraining volcanic inflation at Three Sisters Volcanic Fieldin Oregon, USA, through microgravityand deformation modeling

Jeffrey Zurek and Glyn William-JonesDepartment of Earth Sciences, Simon Fraser University, 8888 University Drive, Burnaby, BritishColumbia V5A 1S6, Canada ([email protected])

Dan JohnsonDeceased 4 October 2005

Al EggersDepartment of Geology, University of Puget Sound, 1500 N. Warner Street, Tacoma, Washington98416-5000, USA

[1] Microgravity data were collected between 2002 and 2009 at the Three Sisters Volcanic Complex,Oregon, to investigate the causes of an ongoing deformation event west of South Sister volcano. Threedifferent conceptual models have been proposed as the causal mechanism for the deformation event:(1) hydraulic uplift due to continual injection of magma at depth, (2) pressurization of hydrothermal systemsand (3) viscoelastic response to an initial pressurization at depth. The gravitational effect of continual magmainjection was modeled to be 20 to 33 mGal at the center of the deformation field with volumes based on pre-vious deformation studies. The gravity time series, however, did not detect a mass increase suggesting that aviscoelactic response of the crust is the most likely cause for the deformation from 2002 to 2009. The crust,deeper than 3 km, in the Three Sisters region was modeled as a Maxwell viscoelastic material and the resultssuggest a dynamic viscosity between 1018 to 5 � 1019 Pa s. This low crustal viscosity suggests that magmaemplacement or stall depth is controlled by density and not the brittle ductile transition zone. Furthermore,these crustal properties and the observed geochemical composition gaps at Three Sisters can be bestexplained by different melt sources and limited magma mixing rather than fractional crystallization. Moregenerally, low intrusion rates, low crustal viscosity, and multiple melt sources could also explain the wholerock compositional gaps observed at other arc volcanoes.

Components: 9300 words, 7 figures, 2 tables.

Keywords: Three Sisters Volcanic Field; gravity; viscoelastic; volcanology.

Index Terms: 1217 Geodesy and Gravity: Time variable gravity (7223, 7230); 8419 Volcanology: Volcano monitoring(4302, 7280); 8439 Volcanology: Physics and chemistry of magma bodies.

Received 11 July 2012; Revised 18 September 2012; Accepted 24 September 2012; Published 19 October 2012.

Zurek, J., G. William-Jones, D. Johnson, and A. Eggers (2012), Constraining volcanic inflation at Three Sisters Volcanic Fieldin Oregon, USA, through microgravity and deformation modeling, Geochem. Geophys. Geosyst., 13, Q10013, doi:10.1029/2012GC004341.

©2012. American Geophysical Union. All Rights Reserved. 1 of 15

http://dx.doi.org/10.1029/2012GC004341

1. Introduction

[2] Large-scale deformation events are common atactive volcanoes and are most often detected usingseismic or deformation techniques [e.g., Dzurisinet al., 1990]. While these methods can provideinformation about the volume and shape of thedeformation source, they do not constrain the changeor redistribution of mass at depth. Microgravity sur-veys, when used in conjunction with deformationdata, can provide constraints on the mass flux atdepth and source density [e.g., Berrino et al., 1992;Rymer, 1996; Battaglia et al., 2003].

[3] Microgravity has been utilized on numerous vol-canic systems, including Yellowstone (USA) andCampi Flegei (Italy) calderas to constrain and inves-tigate the properties of deformation sources. At bothcalderas, changes in the associated hydrothermalsystems have been postulated by several authors[e.g., Dzurisin et al., 1990, 1994; Berrino, 1994;Bonafede and Mazzanti, 1998; Orsi et al., 1999;Gottsmann et al., 2006] as a possible source of theobserved deformation and gravity change. Micro-gravity provides the possibility to distinguish betweena magmatic and a hydrothermal source, since it candetermine the density of the intruding fluid. Naturalsystems are usually complex and can have multipledeformation sources [e.g.,Dvorak and Berrino, 1991;Trasatti et al., 2011]. For example, Gottsmann et al.[2006] show that it is more realistic to model thedeformation and gravity data at Campi Flegei as acombination of magmatic and hydrothermal sources.When determining the nature of a deformation event,it is also important to consider the possibility that theEarth’s crust may be deforming viscoelastically; anelastic deformation model can result in unrealisticoverpressures needed to reproduce the observeduplift [e.g., Berrino et al., 1984]. Furthermore, vol-canic areas generally consist, at least in part, ofincoherent material produced from eruptions and ahigh crustal heat flow [e.g., Bonafede et al., 1986],which produces a lower effective viscosity for thecrust and thus requires the consideration of itsinelastic properties.

[4] Integrating deformation and microgravity hasbecome the standard approach to determine sourceparameters [e.g., Battaglia et al., 2008] and it is alsoimportant for process identification and forecastingvolcanic behavior [e.g., Rymer and Williams-Jones,2000]. This study combines time series data frommicrogravity measurements (2002 to 2009) anddeformation data [Dzurisin et al., 2006, 2009] atThree Sisters Volcanic Field (Oregon, USA) in

order to further constrain the nature of the inferredintrusion at depth.

2. Geologic Setting

[5] The Three Sisters Volcanic Field is located incentral Oregon and is part of the Cascade Volcanicarc, which stretches from northern California tosouthwestern British Columbia (Figure 1). TheJuan de Fuca plate, at the Oregon coast, is sub-ducting beneath North America obliquely at a rateof �3 cm yr�1 [Riddihough, 1980; Bates et al.,1981]. The central Oregon section of the volcanicarc has produced more Cenozoic vents and lavathan any other part of the arc, while historicallyproducing very few seismic events [Guffanti andWeaver, 1988; Priest, 1990; Sherrod and Smith,1990; Nichols et al., 2011]. The region’s aseismicbehavior is likely due to a change in tectonicstresses from compression to extension, as well asincreased heat flow. Blackwell et al. [1982, 1990]show that the regional heat flow in the centralOregon arc averages over 100 mW m�2, in com-parison to 60 mW m�2 in the Washington sectionof the arc.

[6] The region’s extensional stresses are a by-product of rotation, as southern Washington andOregon rotate away from the rest of North America[e.g., Magill et al., 1981]. A possible cause for theapparent rotation is the collapse of the Basin andRange [McCaffrey et al., 2000]. It is possible thatthe rotation driven extension is responsible for thehigh regional heat flow, gravity anomaly andincrease in eruptive products in the central OregonCascades [Blackwell et al., 1982, 1990].

[7] Based on tephrachronology, dating and fieldrelationships, the Three Sisters Volcanic Field haslikely been a center of volcanic activity for longerthan 700,000 years [Scott et al., 2001]. There are fivelarge Quaternary age cones that dominate the areaincluding: North Sister (400–55 ka [Schmidt andGrunder, 2009]), Middle Sister (37–14 ka [Calvertet al., 2005]), South Sister (178–2 ka [Hildreth,2007]), Broken Top (150–300 ka [Hildreth, 2007]),and Mount Bachelor (18–8 ka [Scott et al., 1989;Scott and Gardner, 1990, 1992]) (Figure 2). Theyoungest, South Sister, erupted rhyolite tephra andlava flows approximately 2000 years ago [Taylor,1978; Wozniak, 1982; Clark, 1983; Scott, 1987;Fierstein et al., 2011]. This long-lived volcaniccenter has also had considerable eruptive activityaway from the main cones with 10s of vents erupting

GeochemistryGeophysicsGeosystems G3G3 ZUREK ET AL.: INFLATION AT THREE SISTERS USING GRAVITY 10.1029/2012GC004341

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Figure 1. Subduction of the Juan de Fuca, Gorda and Explorer plates off the west coast of North America. Red tri-angles represent major volcanic centers in the Cascade Volcanic arc. Inset: North America with the highlighted area inred representing the Cascade Volcanic arc.

Figure 2. Topographic map of the Three Sisters Volcanic Field. Grey circle represents the approximate area affectedby the current deformation event. Five large Quaternary cones are indicated with red triangles. The gravity networkstations are displayed as black squares and numbered: (1) BASE, (2) BUGS, (3) BRUCE, (4) CUT and (5) CENTER.


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over the last 4000 years [Scott et al., 2001]. The mostrecent eruptive event away from the main conestook place approximately 1500 years ago at BelknapCrater, �20 km north of South Sister, with an erup-tion of basaltic and andesitic lavas [Fierstein et al.,2011].

[8] Eruptive products, from basaltic to rhyolitic, anddifferent vent locations have led to a variety oferuption styles at the Three Sisters Volcanic Field inthe past [Scott et al., 2001]. Large explosive erup-tions are rare but have occurred at least 4 times in thelast 700,000 years [Scott et al., 2001], however, atthis time, there is no evidence of a magma chamberof sufficient size to drive a large Plinian eruption.The vent locations in the area and their link to tec-tonic stresses and general eruptive behavior havebeen discussed by Bacon [1985], who suggests thatthe last silicic eruptive episode was fed from a smalldeep reservoir on the south side of South Sister. Thecurrent unrest and deformation takes place west ofSouth Sister and appears to have no relation to themost recent volcanic eruption.

3. Previous Work

[9] Wicks et al. [2002] discovered that an area westof South Sister was deforming and that it likelystarted as early as 1996. The results of this studyshow that from 1998 to October 2000, the defor-mation was steady with 3 to 5 cm yr�1 of uplift.Modeling of the early results indicated a sourcedepth for the inferred intrusion at 6.5 km, based on a

Mogi point source model [Mogi, 1958;Wicks et al.,2002]. Since the discovery of uplift in the ThreeSisters region, further deformation [Dzurisin et al.,2006, 2009; Riddick and Schmidt, 2011] and watergeochemistry surveys [Evans et al., 2004] havebeen completed in order to better characterize thedeep seated processes responsible for this activity.

[10] Spring geochemistry of the Three Sisters areawas first investigated by Ingebritsen et al. [1994]who showed that there was a mantle-derived com-ponent of CO2 prior to the start of the current defor-mation event in the Separation creek drainage system(Figure 2). The study also showed an anomalouschloride load of 10 g s�1, suggesting that hydro-thermal fluids were being incorporated into thesprings that drain into Separation creek. More recentdata from 2001 and 2002 [Evans et al., 2004], showsthat there was no change in the chloride load or in thetemperature of the water flowing in Separation creek,suggesting that previous intrusive heat sources werecontrolling the hydrothermal system near the centerof uplift.

[11] Dzurisin et al. [2006, 2009] refined the originaldeformation models of Wicks et al. [2002] with alonger time series and more data from continuousand campaign GPS, as well as leveling surveys.Using 95% confidence levels, these deformationmodels describe the source as a prolate spheroid witha depth of �5 km. Dzurisin et al. [2009] suggestedthat the uplift rate was decaying (Figure 3) and usedit to calculate bounds on the volume change forthe whole event by extrapolation; suggesting the

Figure 3. Modeled decaying deformation curves for each gravity station [Dzurisin et al., 2009]. Shaded areas indi-cate individual gravity surveys.


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total volume may reach 45 to 52 � 106 m3. Theyput forward three conceptual models that couldexplain the current deformation event: (1) hydraulicor instantaneous response of the crust to continuedintrusion at depth; (2) pressurization of the hydro-thermal system in the area of Three Sisters and(3) continued viscoelastic response of the crust dueto an intrusion emplaced at depth. A more recentstudy using InSAR data [Riddick and Schmidt,2011] argues that a sill model is more appropriateresulting in a deeper (�7 km) and a larger source(5–7 � 107 m3). This study better defines the ini-tiation and rates of deformation up to 2001 andsuggests the presence of an inflection in the defor-mation rate in 2004; however, continuous GPSdata since 2004 is best fit by an exponential curve(M. Lisowski, personal communication, 2012). Ourstudy uses the deformation results of Dzurisin et al.[2006, 2009] (Figure 3).

4. Methodology and Results

4.1. Microgravity

[12] Mass flux and redistribution at depth can beconstrained using a combination of microgravity andhigh resolution deformation surveys. The micro-gravity surveys implemented at Three Sisters mea-sure small changes in the gravitational field over timeand space across a network of stations. The applica-tion and theory of this technique is discussed thor-oughly in the literature [e.g., Eggers, 1987; Rymerand Brown, 1986; Rymer, 1996; Battaglia et al.,2008] and hence, will only be summarized here.

[13] Due to the remoteness and rugged nature of thearea, monitoring of only a very limited gravity net-work at Three Sisters was feasible. The networkconsists of 5 stations making a single transect partlyspanning the deforming area, which is approxi-mately 10 � 20 km (Figure 2). Measuring only asingle profile reduces our ability to describe thesource of the event, however, it does cover from theedge to the center of the deformation zone. Repeatmeasurements in part compensate for the poor spa-tial coverage. The station locations were chosensuch that there was less than 1 mGal difference fromthe reference station outside the deforming areawith respect to the rest of the network to reducepossible tares from having to re-level the beamwithin LaCoste & Romberg gravimiters. This wasaccomplished by utilizing both a topographic mapto identify areas of equal elevation along the trailand field testing of these sites with a LaCoste &Romberg spring gravity meter. Each station consists

of three metal rods drilled into bedrock and madeflush with the ground. The rods are arranged suchthat the 3 levelling screws on LaCoste & RombergG- and D- meters rest on them to eliminate the needfor a base plate while ensuring precise positioning.The stations from the edge of the deforming areato the center are: BASE, BUGS, BRUCE, CUT,and CENTER (Figure 2). CENTER is approxi-mately located at the center of the deforming area,near Separation creek; BASE is on the edge of thedeformation zone and is used as the reference stationsince it is not expected to vary appreciably over theperiod of study.

[14] To maximize accuracy, gravity measurementswere collected in station loops where each looprepeats every station at least twice, except CENTER,in order to pinpoint and correct for tares. Taresrepresent high frequency noise in gravity data dueto changes in a gravimeter’s spring length, whichare typically caused by the instrument receiving aphysical shock. Tares in gravity data are either nonrecoverable, represented by a simple offset betweentwo measurements, or recoverable where the springrecovers over time to its original length. To furtherallow for tare correction and the removal of noisydata, surveys (station loops) were completed threetimes over a period of 3 to 6 days; the exception is2008 and 2009 where only one loop was completedover a single day (Table 1). After corrections oneach survey were performed, surveys which werecompleted over a single week were grouped andaveraged to represent one data point. Two gravitymeters were also used on each survey to eliminateany bias due to anomalous results from instrumen-tal malfunction or noise. In some survey sets, sta-tion loops were shortened such that stations couldbe repeated more frequently to increase accuracy(Table 1).

[15] The raw gravity data was first corrected forthe effects of Earth tides. The calculation of Earthtides, based on the recorded time and position ofa gravity measurement, has accuracy better than2 mGal (Quick Tide Pro [Micro-g LaCoste]).Changes in a station’s vertical position were cor-rected by multiplying the height change with thetheoretical free air gradient (�306.8 mGal m�1)and subtracted. The vertical position of each sta-tion was obtained from deformation models andnearby levelling lines [Dzurisin et al., 2009]; themodels have been shown to fit the deformation datawithin 95% confidence levels (Figure 3). Instru-mental factors such as drift can be ignored as themeters used in this study were stable and the


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instrumental drifts were negligible over the courseof a single survey.

[16] After corrections, the data were normalizedto the base station; BASE’s closure was averagedand then subtracted from each other measurementin the survey. In surveys that did not close withBASE, the data were normalized to BASE, using anormalized value of BRUCE. This was obtainedfrom other survey days in the same grouping whereboth BRUCE and BASE were collected. With eachstation normalized and repeated in a survey, it iseasy to identify when a data tare occurred. However,correcting and removing the effects of tares is usu-ally non trivial and increases the uncertainty of thedata. It is thus preferable to not use tare-corrupteddata, especially when attempting to obtain precisevalues. The redundancy in the data, by having threesurveys with two meters for each data point in time,allows for strict quality control and as such, the datawere not corrected for tares. If an unrecoverable tareoccurred, either the data from the whole survey withthat meter was discarded or only the data before thetare were used. If there was a recoverable tare suchthat the meter did not display an offset followingit, measurements were thrown out until a reasonableclosure between stations was obtained (less than25 mGal). The upper limit for closures from the firstto last measurement of the survey is 60 mGal if nospecific tare can be identified. Averaging the resultsfrom both meters and the whole survey group sig-nificantly reduces the effect of any larger closures.

[17] With each station within 1 mGal of the next,calibration between meters is less of a concern, afternormalizing each survey to the reference station.The two meters that were used most frequently wereG-209 and G-127. G-209, G-248 and D-52 wereanalogue (with optics and calibration dial) and to

be consistent, each analogue meter had the sameoperator making the measurements at each station.Meters G-127 and D-17 utilize a digital Aliodfeedback system to record and collect field mea-surements. This system allows a 100 mGal dynamicrange and removes the necessity for a surveyorto manually null the meter. It also streams the datato a serial device at 2 Hz; each reading in the surveywas averaged over one minute, with at least5 readings per station to further reduce noise. Thechange in the calibration factor for each G meter ison the order of 0.01 for each 100 mGal of gravitychange; therefore, a change of less than 1 mGalis of the order of 1 � 10�4. The calibration factorbetween G-127 and G-209 has been determinedto be 0.09899 or approximately 10 mGal for every1 mGal of change. This allows for the data ofmultiple meters to be used and merged withouthaving to carefully inter-calibrate each meter.

[18] It is possible to obtain measurement accuraciesof �10 mGal in volcanic areas if strict survey pro-cedures are used [e.g., Rymer and Brown, 1986;Rymer, 1994]. However, as mentioned above, theThree Sisters station network is not in an idealenvironment for measuring gravity. The major dif-ficulty with processing this data set is the presenceof tares, particularly in 2005 (Table 1). In 2004and 2005, D-meters were used and frequently hadlarge tares. In addition to sensitive meters, the trailused to access the gravity network is approximately20 km in length and takes 10 to 12 h to completeon foot over rugged ground. The constant jostlingof walking, even with the spring clamped, cancreate tares [e.g., Crider et al., 2008]. The datacollected in 2002 is some of the cleanest in thisstudy, with very few obvious tares corruptingthe surveys. High frequency noise throughout the

Table 1. Microgravity Data From 2002 to 2009 Normalized to the First Survey in August 2002

Survey Group

Normalized Gravity (mGal)

InstrumentsBASE BUGS BRUCE CUT CENTER

2–8 Aug., 2002 0.0 0.0 0.0 0.0 0.0 G-209, G-2482–4 Sept., 2002 0.0 �17 2 �25 �4 G-209, G-24817–19 Sept., 2002 0.0 �35 �8 �19 �15 G-209, G-24815–18 Jul., 2004 0.0 �24 TAREa TAREa TAREa G-209, D-1730 Jul.–1 Aug., 2004 0.0 �25 TAREa �13 TAREa G-209, D-1723–26 Aug., 2004 0.0 �67 TAREa �6 �5 G-209, D-1724 Sept.–1 Oct., 2004 0.0 �22 �41 �4 16 G-209, G-12728 Jun.–1 Jul., 2005 0.0 �12 5 11 �12 D-52, G-12722–24 Aug., 2005 TAREa TAREa TAREa TAREa TAREa G-209, D-5226–28 Sept., 2005 0.0 �74 TAREa TAREa 32 G-209, D-5212 Oct., 2008 TAREa TAREa TAREa TAREa TAREa G-209, G-1271 Sept., 2009 0.0 17 �48 �148 �52 G-209, G-127

aTARE: data were not used due to excessive high frequency noise.


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survey is, however, still prevalent, as the closuresreached up to 56 mGal. By using repeats andredundant data, much of the noise is averaged outthrough multiple surveys; as a result, no data wereexcluded in 2002. The data collected in 2004, 2005and 2008, however, had many large tares and insome cases, the data was completely unusable. In2004 and 2005, 50% and 40% of the data, respec-tively, were unusable due to tares. There were24 survey loops (12 surveys) completed in each ofthese years, so although large amounts of the datawere unusable, there is no loss of information aboutthe gravitational field. The data collected in 2008had to be thrown out completely, while a tare-freesurvey was collected in 2009. The standard deviationis taken as the estimated error for each data pointaveraged from a survey group. Where there are

insufficient measurements to effectively calculate thestandard deviation, an error of 25 mGal is assumed.The normalized residual gravity through time does notchange appreciably as the majority of the measure-ments are within one standard deviation (Figure 4).The station BUGS has one point which is lower thanthe error bounds in 2005, while all other stations havea lower outlier in 2009.

4.2. Viscoelastic and Gravity Modeling

[19] In order to test the validity of the hypothesesproposed by Dzurisin et al. [2006, 2009], modelingof both gravity and viscoelastic response of the crustwas performed. A gravity forward modeling program[GRAV3D, 2007] (Figure 5) was used in conjunctionwith volumetric results from 2002 to 2009 [Dzurisin

Figure 4. Residual gravity data for BUGS (red), BRUCE (purple), CUT (green), and CENTER (brown) from2002 to 2009. Error bars are the standard deviation of repeat measurements at each point and the highlighted regionis +/�25 mGal from 0. Dashed lines refer to expected changes due to a viscoelastic response causing a decrease inthe gravitational field.


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et al., 2006, 2009; Riddick and Schmidt, 2011] topredict the gravitational field caused by continualintrusion at depth. Dzurisin et al. [2006] calculatedthe yearly volumetric change using their deforma-tion model to be 3.5 to 6.5 � 106 m3 yr�1. Extrap-olating the yearly volumetric increase from 2002to 2009 gives a total expected volume change of24.5 to 45.5 � 106 m3. In a later study, deformationmodels were updated with more data [Dzurisin et al.,2009]; however, the modeled source volumes arewithin the original volumetric bounds put forthby Dzurisin et al. [2006]. To eliminate any bias oruncertainty in the possible model geometries, theintrusion was modeled from 5 to 6 km depth witha volume of 2.4 to 6.5 � 107 m3. The intrusion isassumed to have approximately the same densityas the crust, which would be the case if the intrusionstalled due to buoyancy forces. The addition ofmaterial to the system is modeled as an increasein mass as a Mogi [1958] point source. Directcomparisons to the gravity data must be made onlyon data that has been corrected for vertical change.

[20] The gravity point source models show a 20 to33 mGal increase in the gravitational field nearthe station CENTER from 2002 to 2009. They pre-dict that the maximum magnitude of the gravityincrease will fall away from CENTER, withCUT having a maximum increase of 25 mGal andBRUCE of 16 mGal (Figure 5). A sensitivity anal-ysis of the intrusion shape and density was per-formed to test what effect initial assumptions haveusing forward gravity modeling software GRAV3D

[GRAV3D, 2007]. Modeling the intrusive source asrectangular or spherical shapes made no appreciabledifference in the resulting gravitational field.

[21] Deformation modeling with a geomechanicssoftware package, FLAC 6.0 (Fast Lagrangian Anal-ysis of Continua [Itasca Consulting Group, 2007]),was used to test the possibility that viscoelasticresponse of the crust is the controlling factor inthe observed deformation. FLAC 6.0 allows forthe analysis of stress fields through elastic, visco-elastic and viscoplastic modeling in two dimensions.It has been used previously in volcanic studies,however, mostly in the application to slope stabilityand flank collapse [e.g.,Apuani and Corazzato, 2005,2009; Casagli et al., 2009]. In this study, only elasticand Maxwell viscoelastic materials were consideredwhen attempting to model the deformation event atThree Sisters Volcanic Field. There are very fewconstraints available to obtain realistic properties forcrustal material thus assumptions about viscosity,density, bulk and shear modulus have to be made.Due to the wide range of eruption types, geologicprocesses and heterogeneity, it is impossible toaccurately represent the crust in the Three Sistersarea. Therefore, a simple model with the elasticproperties of basalt was used (Table 2), as basalt tobasaltic andesite volcanics are the most commoneruptive products near the center of uplift [e.g.,Wozniak 1982; Taylor, 1987] and old intrusions atdepth would presumably also be basaltic in com-position. High heat flow in the Three Sisters region[e.g., Blackwell et al., 1982, 1990; Bonafede et al.,

Figure 5. A forward gravity model using 2900 kg m�3 as the melt density, overlain by 100 m topography contours.Numbered black squares represent gravity stations: (1) BASE; (2) BUGS; (3) BRUCE; (4) CUT; (5) CENTER.


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1986] suggests that viscous deformation cannot beignored; however, there is no rigorous method toaccurately constrain the crustal viscosity at depth.The only values of crustal viscosities that have beeninferred are derived from post-seismic deformationand isostatic rebound for the upper mantle and thelower crust [e.g., Wdowinski and Axen, 1992; Uedaet al., 2003]. Values from these studies range from3 � 1017 to 1 � 1018 Pa s for the upper mantle and1 � 1018 to 1 � 1023 Pa s for the lower crust.

[22] The two dimensional viscoelastic model usedhere is 6 km deep and 6 km wide consisting of a flatelastic top layer 4.5 km thick and a bottom visco-elastic layer 1 km thick. The intrusion is representedby an applied constant upward vertical force at 5 kmdepth across a small 100 m long surface. The sideand bottom boundaries of the model are fixed to

stop the edges from deforming outward, whilethe top is allowed to deform freely. The models havea dynamic viscosity range of 1018 to 1020 Pa sand show two end-members of the deformationresponse (Figure 6). For each viscosity, the modelrun time was 30 years using a time step of 1 day.Models with viscosities 1020 Pa s or higher aredominated by a nearly instantaneous elastic defor-mation with a small viscoelastic component, whilemodels with viscosities on the order of 1018 Pa sare dominated by a linear viscoelastic response.Results show that a viscosity of 1018 Pa s can pro-duce the observed uplift after the elastic responsehas ceased. However, for a viscosity of 1020 Pa s,there is essentially no viscoelastic response, thus itcannot produce the continual deformation at ratesobserved, unless there is a continuous injection ofmaterial at depth.

5. Discussion

5.1. Crustal and Magmatic Properties

[23] The deformation episode at the Three Sistersbegan in 1997 [Dzurisin et al. 2009] and continues

Table 2. Average Elastic Properties for Basalt Usedin Viscoelastic Modeling of the Crust

Property Value

Density 2700 kg m�3

Bulk modulus 3.32 � 1010 PaShear modulus 1.32 � 1010 Pa

Figure 6. Modeled viscoelastic responses of the crust for different viscosities with their corresponding applied force.In each case, the elastic properties were that of basalt (see Table 1).


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at a declining rate to the present. Previous workhas outlined three possible end-member modelsthat can explain the deformation event (Figure 7).(1) Continuous injection of material at depth wherethe magma flow rate from the lower crust is pro-portional to the pressure causing uplift. (2) Instan-taneous pressurization of the crust and the timedependent response of a Maxwell fluid causingcontinued uplift at the surface. (3) Pressurizationof hydrothermal fluids due to the injection ofmagmatic volatiles from a previous crustal magmabody. Each of these possibilities is discussed belowwith reference to the expected gravitational fieldand models.

[24] In order to interpret the microgravity data span-ning the deforming area at Three Sisters, the effect ofwater table fluctuations must first be addressed. Thesurveys performed in 2004 and 2005 occurred fromearly summer into fall, in an effort to characterizethe seasonal effects in groundwater levels. However,the large number of tares and loss of data limit theeffectiveness of this approach. Instead, it is better toanalyze the data as a whole in conjunction withmonthly precipitation as it is more robust and lesssensitive to a single anomalous survey. The precip-itation data shows that 2004 had more rain than anyother year during the survey months (Figure S1 in

the auxiliary material).1 If water tables are a con-trolling factor, a positive gravity anomaly would beexpected in 2004. The corrected data shows nochange throughout the data set greater then esti-mated error for the surveys (Figure 4). There is,however, an exception where small gravity decrea-ses were measured at stations CUT and CENTER in2009. The precipitation in 2009 is comparable tothat in 2002 and thus a gravity decrease from 2002to 2009 based on water table changes is not expec-ted. Since the gravity signal has no measurablechange outside the estimated error in both 2004 and2005, we assume that changes in groundwater tableshave no obvious influence on the gravity data set.

[25] Within the microgravity data set, there are 4points that fall outside the estimated error, 3 ofthem in 2009. Each shows a smaller gravitationalfield than what was originally measured in 2002.The 2009 decrease at CUT could be wholly orpartially attributed to unobserved mass wasting asthe station is located near a small �5 to 10 m highcliff; a failure of only 125 m3 could explain theobserved gravity decrease (�150 mGal). This can-not, however, explain a smaller decrease at both

Figure 7. Schematic model to explain the activity to the west of South Sister. (a) Viscoelastic model with a continualresponse of the crust to past overpressure. (b) Hydraulic model with a continual response of the crust to pressure fromintrusive injection of material. (c) Hydrothermal pressurization causing continual uplift.

1Auxiliary materials are available in the HTML. doi:10.1029/2012GC004341.


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BRUCE and CENTER stations in 2009. If thegravitational field is solely created through visco-elastic deformation, then the crustal density iseffectively decreasing due to expansion. The totaldeformation from 2002 to 2009 would result in a�16 to �24 mGal drop in the gravitational fieldat CENTER, �14 to �19 mGal at CUT, �13to �10 mGal BRUCE, �3 mGal at BUGS and�1 mGal at BASE. If this correction due to visco-elastic expansion is applied to the residual gravitydata for CENTER and BRUCE, the values wouldfall within error around zero (Figure 3 and Text S1).Regardless, it is clear that there is no observedincrease in the gravitational field which would beexpected from a positive mass flux.

[26] The data collected by Evans et al. [2004] showthat the geochemical anomalies in the Separationcreek drainage are most likely caused by previousintrusions and not directly connected with the cur-rent event. If hydrothermal pressurization is themain cause of deformation then it would also beexpected to increase the amount of hydrothermalfluids at depth. Residual gravity would then increaseas hydrothermal fluids add mass to the system.However, depending on the volume and depth, thismass increase may be too small to detect above thenoise in the gravity data. The steady state nature ofthe geochemical results suggests that any hydro-thermal pressurization would have to be deepenough not to interact with groundwater. The depthof the deformation source at 4.9 km inferred byDzurisin et al. [2009] is sufficiently deep that thereis essentially 0% porosity, suggesting that at thisdepth, hydrothermal fluids cannot be the cause ofuplift. While the models and data presented do notsufficiently constrain the deformation and massflux to completely rule out hydrothermal pressuri-zation as a possible cause, they do suggest that thisis the least likely conceptual model to explain thecurrent deformation event at the Three Sisters Vol-canic field.

[27] Gravity forward modeling shows that theexpected gravitational increase, if continual injec-tion of material is the sole process, is between 20 to33 mGal. Field measurements, however, do notshow any increase and may suggest a decreasinggravitational field near CENTER and CUT. Thelack of gravitational increase suggests that a con-tinual flow of material at depth into an intrusion isnot responsible for the deformation. The amplitudeof the modeled gravitational field, however, strad-dles the error levels of the microgravity data set.Hence, it is not possible to completely rule out thepossibility that the crust is behaving hydraulically as

material is injected continuously at depth. It doessuggest, though, that viscoelastic response of thecrust is at least partially responsible for the continualuplift.

[28] The increased heat flow for the central Oregonsection of the Cascade arc could play a dominantrole in determining how the crust is responding tothe inferred deep-seated source. Blackwell et al.[1990] made measurements of heat flow through-out much of Oregon and although the measurementsdo not cover the Three Sisters region, they do pro-vide an estimate of the heat flow and geothermalgradient. An average of 65�C km�1 was obtainedalong arc near volcanic centers but the values couldbe much higher near the main cones, to as much as100�C km�1 [Blackwell et al., 1982, 1990]. Thiswould suggest that the crust around the inferredintrusion at 5 km depth could be between 325 and500�C. The strength of quartz greatly decreases attemperatures greater than 350�C [e.g., Buck, 1991]and incoherent material can reduce the effectiveviscosity [Bonafede et al., 1986]. While theseproperties are known, there have been no rigorousstudies to obtain a crustal viscosity in local areas ofhigh heat flow. Therefore, any viscosity used isconjecture based on studies that infer lower crustalviscosities from post seismic relaxation (e.g., 4 �1018 Pa s, Japan [Ueda et al., 2003]). The tempera-ture may be similar in volcanic areas to that in thelower crust; however, the confining pressure is sig-nificantly less.

[29] Furthermore, there is also a conspicuously lowlevel of seismic activity in the central Oregon partof the Cascade Volcanic Range [Weaver andMichaelson, 1985]. This includes the currentdeformation event at Three Sisters as there havebeen very few seismic events associated with it,apart from a seismic swarm in 2004 that consistedof over 300 seismic events [Dzurisin et al., 2006].High heat flow, low levels of seismic activity, andthe presence of incoherent material suggest it isnot unreasonable that the crust beneath the ThreeSisters could have viscosities lower than 1020 Pa s.

[30] If deformation is solely caused by viscoleasticresponse of the crust, there would be no additionalmass added to the system. Therefore, if the observeddeformation from 2002 to 2009 is primarily causedby a viscoelastic response due to an intrusion, theresults of the microgravity data would show no netincrease after being corrected for changes in eleva-tion. Furthermore, viscoelastic models providelimited bounds on the expected viscosity and sug-gest the possibility that the deformation event is a


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hybrid of viscoelastic response and continualinjection. Modeling shows that it is possible toobtain the observed rate of deformation with anearly instantaneous intrusion of magma if thecrustal viscosity beneath the Three Sisters is on theorder of 1018 to 5� 1019 Pa s. Viscosities that are anorder of magnitude higher have a strong elasticcomponent to the deformation and hence wouldrequire some magmatic injection to continue whilealso deforming viscoelasticly. It should be notedthat the modeled response to the intrusion does notdecay (Figure 6). This is due to the intrusion beingmodeled as a constant force and not a realisticintrusion where the force decays and generates anexponentially decaying deformation field. Thegravity data does not rule out this possibility asmaterial injected in this way would be below thedetection limits of the survey. If viscosities reach1021 Pa s, the modeled deformation is nearly allelastic and would require continual injection ofmaterial. The gravity data does not show an increasehence it does not support continual injection as thesole cause of the continuing deformation event aspreviously discussed. The viscosity, as determinedfrom these simple models for the crust beneaththe Three Sisters, is most likely between 1018 and5 � 1019 Pa s with the deformation from 2002 to2009 being either dominated by a viscoelasticresponse or a combination of elastic and viscoelas-tic. The viscosity range is much lower than expectedfor upper crustal rocks, however, it falls within therange of that expected for the lower crust [e.g.,Wdowinski and Axen, 1992].

5.2. Magma Emplacement ThroughDensity Sieving

[31] If the viscosity beneath the Three Sisters vol-canic field is low (1018 to 5 � 1019 Pa s at 5 km), itmust have a profound impact on magma rise andemplacement. It has been suggested that the loca-tions of magma chambers at other volcanic centersare controlled by the ductile-brittle transition zone[e.g., Burov et al., 2003]. High heat flow and lowcrustal viscosity allows buoyancy forces to be thedefining factor if or where magma will stall atdepth. If buoyancy forces dictate where magma willstall and intrusion rates are relatively low, onewould expect a series of magma bodies with depthsdependant only on the density of the rising fluidlike a density sieve.

[32] A geochemical study on South Sister showsthat there are two compositional gaps between 56–

62% SiO2 and 66–73% SiO2 [Brophy and Dreher,2000]. The study argues that the compositionalgaps are created through magmas stalling at depth,fractionating to higher silica melts and then break-ing through the top of the crystallizing intrusionto rise, stall and fractionate further. A similarmodel has been proposed for Medicine Lake vol-cano in California [Brophy et al., 1996] based on thecompositional gaps found there. Fractional crystal-lization fits the whole rock geochemistry; however,with crustal viscosity so low, magma should con-tinue to rise as it fractionates and becomes lessdense, instead of stalling. More recently, U-seriesdating together with trace element data on plagio-clase and zircon crystals for two different eruptionson South Sister suggest a different explanation.The two eruptions occurred �2000 and �2300years ago and while they both show similar crys-tallization ages, they have distinct trace elementconcentrations [Stelten and Cooper, 2012]. Theauthors suggest that melt for these two eruptionsmust have been derived from different sourceregions and evolved separately. Furthermore, othergeochemical data show compositional gaps between59 to 66% SiO2 in melt inclusions from many vol-canic arcs, even where volcanoes erupt a continuousspectrum of compositions [e.g., Naumov et al.,1997; Reubi and Blundy, 2009]. Due to the lack ofandesitic melt inclusions and laboratory experi-ments, it is suggested that arc compositional gapsform due to differences in melt source. The twogeneral melt source regions that have been used toexplain the bimodal distribution are a mantel sourcethat produces mafic magmas and melting in the deepto mid-crustal levels that produces silicic magmas[e.g., Reubi and Blundy, 2009; Kent et al., 2010].

[33] Intrusion rates at South Sister have been esti-mated at 0.0003 km3 yr�1 [Evans et al., 2004] whichis an order of magnitude lower than other volcanoeslike Mount St. Helens and Mount Fuji [Crisp, 1984;Sherrod and Smith, 1990]. Low intrusion rates willreduce the possibility that magmas will have theopportunity to vigorously mix and produce a con-tinuous eruptive chemical spectrum from basalt torhyolite, leaving compositional gaps recorded in thewhole rock chemistry. While there has not been adetailed melt inclusion study on South Sister, thehigh heat flow, low viscosity, low intrusion rate andgeochemical evidence at other volcanoes, suggestthat different melt sources are responsible for thecomposition gaps. Furthermore, low crustal viscos-ity acts as a density sieve dictating where magmawill stall. This model should also be applicable to


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other arc setting volcanoes with high heat flow andlow intrusion rates.

6. Conclusion

[34] Three general conceptual models have beensuggested by past studies [Dzurisin et al., 2006,2009] to explain the cause of the deformation event atthe Three Sisters Volcanic complex: (1) viscoelasticresponse of the crust due to instantaneous pressuri-zation from an intrusion; (2) continual intrusion ofmaterial at depth causing constant deformation;(3) overpressure caused by many shallow hydro-thermal sources. Spring geochemistry studies indi-cated that there has been nomeasurable change in thehydrothermal system following the start of thedeformation event [Ingebritsen et al., 1994; Evanset al., 2004] suggesting that model 3 is the leastlikely. Models 2 and 3 require a positive mass flux todrive uplift from 2002 to 2009, whereas viscoelasticdeformation (model 1) does not. Furthermore, theuplift event has been generally aseismic suggestingthat viscoelastic deformation probably plays a majorrole. Microgravity surveys were completed to con-strain the deformation process by determiningwhether any mass was added beneath the deformingarea. Gravity results show no significant change,within error, in the mass flux across the deformingarea, suggesting that the crust is deforming viscoe-lastically. While it is impossible to quantify theamount of deformation that could be attributed toviscoelastic response due to noise within the gravitysurveys, it is possible to provide some constraints onthe crustal viscosity in the Three Sisters region.Viscosities greater than 5 � 1019 Pa s have a veryweak viscoelastic component requiring the constantaddition of material to drive deformation, however,if the crustal viscosity is 1018 Pa s, then it is possibleto continue the deformation event from a singleinstantaneous pressurization. The most likely causeof this deformation event is the combination ofhydraulic and viscoelastic responses due to a mag-matic intrusion with average crustal viscositiesbeneath the Three Sisters between 5 � 1019 Pa s and1018 Pa s. This agrees with previous studies that themost likely cause of the deformation event is theintrusion of magma at depth. The suggested lowcrustal viscosity also argues for density and buoyancyforces as the controlling factor for magma emplace-ment beneath South Sister. To further ground truthboth the geothermal gradient and crustal viscosity, aset of drill holes could be made or an active seismicsurvey could be performed. This would provide betterconstraints for building a comprehensive model of

this continual process, however, the area is a pro-tected wilderness and these approaches are invasive.Unless there is reactivation with a larger intrusion toreverse the decaying deformation trend, this event isextremely unlikely to lead to an eruption.

Acknowledgments

[35] Financial support for this study came from a NSF grantEAR-0208490 to D. Johnson and a NSERC Discovery grantto G. Williams-Jones. Special thanks to Dan Dzurisin, MikePoland, Nico Fournier, Hazel Rymer, Doug Stead, and PatriciaMacQueen for their discussions and support. Thanks also to theG-Cubed editor, James Tyburczy, the associate editor, MichaelLisowski, Giovanna Berrino and two anonymous reviewers fortheir thoughtful and constructive suggestions.

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