the ups and downs of volcanic unrest: insights from ... · uturuncu (bolivia), cotopaxi (ecuador),...

The Ups and Downs of VolcanicUnrest: Insights from IntegratedGeodesy and Numerical Modelling

J. Hickey, J. Gottsmann, P. Mothes, H. Odbert, I. Prutkinand P. Vajda

AbstractVolcanic eruptions are often preceded by small changes in the shape of thevolcano. Such volcanic deformation may be measured using precisesurveying techniques and analysed to better understand volcanic pro-cesses. Complicating the matter is the fact that deformation events (e.g.,inflation or deflation) may result from magmatic, non-magmatic ormixed/hybrid sources. Using spatial and temporal patterns in volcanicdeformation data and mathematical models it is possible to infer thelocation and strength of the subsurface driving mechanism. This canprovide essential information to inform hazard assessment, risk mitigationand eruption forecasting. However, most generic models over-simplifytheir representation of the crustal conditions in which the deformationsource resides. We present work from a selection of studies that employadvanced numerical models to interpret deformation and gravity data.These incorporate crustal heterogeneity, topography, viscoelastic rheologyand the influence of temperature, to constrain unrest source parameters atUturuncu (Bolivia), Cotopaxi (Ecuador), Soufrière Hills (Montserrat), andTeide (Tenerife) volcanoes. Such model complexities are justified by

J. Hickey and H. Odbert, previously at School of EarthSciences, University of Bristol, UK.

J. Hickey (&)Camborne School of Mines, University of Exeter,Exeter, UKe-mail: [email protected]

J. GottsmannSchool of Earth Sciences, University of Bristol,Bristol, UK

J. GottsmannCabot Institute, University of Bristol, Bristol, UK

P. MothesInstituto Geofísico, Escuela Politecnica Nacional,Quito, Ecuador

H. OdbertMet Office, Exeter, UK

I. PrutkinInstitute of Geosciences, Jena University, Jena,Germany

P. VajdaEarth Science Institute, Slovak Academy ofSciences, Bratislava, Slovakia

Advs in Volcanology (2019) 203–219DOI 10.1007/11157_2017_13© The Author(s) 2017Published Online: 15 July 2017

http://crossmark.crossref.org/dialog/?doi=10.1007/11157_2017_13&domain=pdf



geophysical, geological, and petrological constraints. Results highlighthow more realistic crustal mechanical conditions alter the way stress andstrain are partitioned in the subsurface. This impacts inferred sourcelocations and magmatic pressures, and demonstrates how generic modelsmay produce misleading interpretations due to their simplified assump-tions. Further model results are used to infer quantitative and qualitativeestimates of magma supply rate and mechanism, respectively. Thesimultaneous inclusion of gravity data alongside deformation measure-ments may additionally allow the magmatic or non-magmatic nature of thesource to be characterised. Together, these results highlight how modelswith more realistic, and geophysically consistent, components canimprove our understanding of the mechanical processes affecting volcanicunrest and geodetic eruption precursors, to aid eruption forecasting, hazardassessment and risk mitigation.

Extended Spanish AbstractLa deformación volcánica, caracterizada por pequeños cambios mediblesen la morfología del volcán, a menudo, pero no siempre, precede a unaerupción volcánica. Esta cuestión, sin embargo, se complica por el hechode que los eventos de deformación (por ejemplo, inflación o deflacción)pueden ser el resultado de una fuente magmática, no magmática o defuentes mixtas/híbridas. Utilizando tanto la amplitud y patronesespacio-temporales de datos de deformación volcánica registrados, asícomo la utilización de modelos matemáticos, es posible inferir laubicación y la fuerza de la fuente impulsora subyacente. Estos métodospueden proporcionar información esencial para la evaluación y mitigaciónde riesgos, así como para el pronóstico de erupciones volcánicas. Sinembargo, la mayoría de los modelos genéricos son insatisfactorios en surepresentación de las condiciones de la corteza en las que reside la fuente.En este trabajo presentamos una selección de estudios que empleanmodelos numéricos avanzados para la interpretación de datos dedeformación y gravedad. Dichos datos incorporan la heterogeneidad dela corteza, la topografía, la reología inelástica y los efectostermo-mecánicos para constreñir los parámetros asociados a la fuente deperturbación en cuatro sistemas volcánicos. Las complejidades de estosmodelos están justificadas por limitaciones geofísicas, geológicas ypetrológicas. El estudio realizado en el volcán Uturuncu, localizado enBolivia, destaca la importancia de la estructura sub-superficial y de losprocesos dependientes de tiempo en la fuente para explicar los patrones dedeformación espacial-temporal. La combinación de dichos resultadosindica un ascenso del magma de tipo diapírico. En el volcán Cotopaxi,localizado en Ecuador, los nuevos modelos de inversión que emplean elAnálisis por Elementos Finitos esclarecen la ubicación y el volumen deuna intrusión magmática durante un episodio de actividad asísmico y noeruptivo con una baja tasa de suministro de magma. Estos modelostambién proporcionan señales observables que podrían estar asociadas confutura actividad volcánica intrusiva o eruptiva. El análisis de ladeformación intra-eruptiva en el volcán Soufrière Hills, en Montserrat,

204 J. Hickey et al.

mostró cómo la inflación registrada podría deberse a una serie dereservorios magmáticos apilados o un depósito alargado verticalmente,debido a respuestas termo-mecánicas de la corteza similares. Lascondiciones de falla derivadas para las tasas de suministro de magma yreservorio son consistentes con las restricciones térmicas y mecánicasindependientes. Utilizando datos gravimétricos y la curiosa falta dedeformación asociada, el estudio en el volcán Teide, en Tenerife, seidentifican, de forma separada, las contribuciones de fuentes pocoprofundas como de aquellas con más profundidad. La interpretación deambos elementos sugiere que una intrusión magmática profunda activó unsistema hidrotermal superficial localizado encima de ésta, y por lo tantodemuestra un efecto causal de un origen mixto. Estos casos de estudiorepresentan una contribución significativa para la comprensión de losprocesos volcánicos durante los periodos de actividad intra-eruptiva y noeruptiva. La combinación de estos resultados enfatiza cómo una mejorparametrización de condiciones mecánicas de la corteza puede alterarfundamentalmente la forma en que el estrés y la tensión se reparten en lasub-superficie. Del mismo modo, una topografía compleja, como es elcaso en los estratovolcanes con laderas empinadas, puede afectar lapartición de la deformación superficial. Estos dos efectos impactan lainferencia de la localización de las fuentes y presiones magmáticas previoal fallo y la erupción, e indican cómo los modelos genéricos puedenconducir a interpretaciones engañosas debido a la simplificación deinferencias acerca de la corteza y a espacios planos y a medias. Resultadosadicionales de la modelización son utilizados para inferir estimacionescuantitativas y cualitativas de la tasa de suministro de magma y elmecanismo, respectivamente, contribuyendo así al entendimiento de ladinámica del transporte del magma. Además, la inclusión simultánea dedatos de gravedad junto a mediciones de deformación, permiten lacaracterización de la naturaleza magmática o no magmática de la fuente.Juntos, estos estudios destacan cómo los modelos que cuentan concomponentes más plausibles y geofísicamente consistentes, puedenmejorar nuestro entendimiento de los procesos mecánicos que afectan lareactivación volcánica y de precursores geodésicos de erupciones. Estostambién proporcionan un marco para ayudarnos a avanzar en el pronósticode una erupción, así como en la evaluación y mitigación de los riesgos,proporcionando datos cuantitativos derivados de la modelización demecanismos físicos adecuados y robustos.

KeywordsVolcano deformation � Gravity � Modelling � Crustal mechanics �Geodesy

Palabras clavedeformación volcánica � gravedad �modelización �mecánica de la corteza �geodesia

The Ups and Downs of Volcanic Unrest: Insights … 205

Introduction

Volcano deformation is a key observable duringperiods of volcanic unrest, and one of the maintools used to monitor developing crises (Sparkset al. 2012). Non-magmatic causes of volcanicdeformation during an unrest period do notinvolve movement of new magma and are mostcommonly related to active hydrothermal sys-tems (e.g., Fournier and Chardot 2012; Rouwetet al. 2014, and references therein). Magmaticcauses reflect the active migration and accumu-lation of new magma, with usually deeper originsand wider deformation footprints. Hybrid mech-anisms have also been proposed, where contri-butions from magmatic and hydrothermalsystems combine to produce a single complexdeformation pattern (Gottsmann et al. 2006a).

A variety of both ground and satellite basedgeodetic monitoring techniques are used toassess the spatial and temporal evolution ofvolcanic related surface deformation. The twomost common techniques employed today are theGlobal Positioning System (GPS) and Interfero-metric Synthetic Aperture Radar (InSAR), whichtrack changes in position due to the grounddeforming and complement each other withadvantages in their temporal and spatial cover-age, respectively. Volcano gravimetry studies,the monitoring and interpretation of continuousor time-lapse spatio-temporal gravity variations,can also provide additional information on anydensity changes associated with the drivingmechanism (Battaglia et al. 2008), and thusenable an estimate of its nature (e.g., magmaticor hydrothermal), which is particularly importantin cases where there is no significant (observable)surface deformation.

The magnitude, spatial pattern, and temporalevolution of volcanic deformation can be used toinfer the location and ‘strength’ of a causativesubsurface source. These source parameters haveimportant implications for volcanic hazards andrisk mitigation. Geodetic data are also a keycomponent in eruption forecasting efforts (e.g.,

Sparks et al. 2012), and constraints on sourceparameters (e.g., pressure or volume changes)from previous deformation episodes can help toquantitatively improve these forecasts. However,making the transition from surface deformationobservations to subsurface source processesrequires the use of geodetic models, whichdemand assumptions about crustal mechanics.

Generic analytical models of volcanic defor-mation (e.g., Mogi 1958) are often oversimplifiedand do not capture the intrinsic complexities ofsubsurface systems, which are essential for reli-able assessment of causative processes, and thuseruption forecasting and hazard assessment. Theyusually represent the Earth’s crust as a homoge-neous, isotropic, elastic, half-space with a flat, freesurface. These assumptions can cause misleadinginterpretations when compared to numericalmodels that allow for more realistic crustal con-ditions (Masterlark 2007). Numerical models ofvolcanic deformation are thus becoming increas-ingly popular due to this ability to estimate sourceparameters in crustal conditions that are beyondthe analytical realm. These improvements aresynonymous with the recent advances in geodeticmonitoring, which deserve a more in-depth anal-ysis than generic analytical models can offer.

The extra complexities that numerical modelscan account for relate to both the source itself, aswell as the crustal rocks in which it resides. Thedeformation source does not have to be repre-sented as a point or cavity, but can contain itsown material properties (e.g., Hickey et al. 2013;Gottsmann and Odbert 2014). Moreover,numerical models can incorporate inferencesfrom other geophysical, geological and petro-logical observables and thus maintain a higherlevel of consistency by relaxing some of theassumptions that restrict generic analyticalmodels. For example, this enables the inclusionof subsurface heterogeneity, topography, vis-coelastic rheology, and temperature-dependentmechanics (e.g., Hickey et al. 2016, and refer-ences therein). Consequently, more robust sourceparameters and magma transport processes can


be inferred, thereby improving the understandingof the links between deformation and eruption.

In this chapter we summarise the key findingsfrom investigations of a variety of unrest epi-sodes at a selection of the VUELCO target vol-canoes; Cotopaxi (Ecuador), Soufrière Hills(Montserrat, British West indies) and the CentralVolcanic Complex on Tenerife (Spain), as wellas at Uturuncu volcano in Bolivia (Table 1).These examples highlight not only differenttimescales of unrest and spatial patterns of vol-cano deformation, but also the influence ofcrustal mechanical heterogeneity, thermal effects,and topography, on observed signals. The unrestepisodes are investigated using both forward andinverse numerical modelling procedures anddemonstrate the process of interpreting differentgeodetic data sets to constrain realistic sourceparameters. Thus, the purpose of this chapter isnot to provide a detailed treatment of the math-ematical and numerical approaches. Instead, it isintended to provide the reader with a generaloverview of the use of advanced numericalmodels to infer volcanic unrest driving mecha-nisms with realistic source characteristics.

Implementing Complex CrustalMechanics

One of the most important aspects of a defor-mation model is the representation of crustalmechanics. This has a fundamental control on theway in which stress and strain is distributed and

transferred through the Earth’s crust, from thesource to the surface. In this regard, as brieflymentioned above, generic analytical models arelimited by their necessary assumptions ofhomogeneous and elastic conditions throughoutthe entire model domain. In reality, the Earth’scrust is known to be layered, and volcanicregions in particular can have wide-rangingregions of stiff (high Young’s Modulus) andsoft (low Young’s Modulus) rocks relating to thetype of volcanic deposit that formed them, e.g.,lava flows (stiff) compared to tuffs (soft) (Gud-mundsson 2011). This is what we call subsurfaceheterogeneity. Where stiff and soft regions areadjacent in the crust, complex subsurface parti-tioning alters the way stress and strain aretransferred to the surface. The outcome is a dif-ferent surface deformation pattern compared toone that would be seen if the crust was in facthomogeneous. Consequently, generic analyticalmodels restricted to homogeneous crustalmechanics will not adequately represent likelysubsurface conditions, and the inferred sourceparameters from these models can be misleading.

Seismic studies are capable of delineatingareas of relatively high and low seismic veloci-ties. They can be used to estimate the dynamicYoung’s Modulus, ED, Poisson’s Ratio, m, anddensity, q, of the crust (Brocher 2005):

m ¼ 0:5� VP

VS

� �2

�2

" #,VP

VS

� �2

�1

" #ð1Þ

Table 1 Summary of geodetic modelling

Volcano Unrestperiod

FWM IVM Data Topo CMX TMX Model Ref

Uturuncu 1992–2006 ✓ – InSAR – ✓ – 2D Hickey et al. (2013)

Cotopaxi 2001–2002 ✓ ✓ EDM ✓ ✓ ✓ 3D Hickey et al. (2015)

Soufrière hills 2003–2005 ✓ – cGPS ✓ ✓ ✓ 2D Gottsmann andOdbert (2014)

Central volcaniccomplex

2004–2005 – ✓ GPS &gravity

✓ – – 3D Prutkin et al. (2014)

FWM forward modelling, IVM inverse modelling, Topo topography, CMX crustal mechanics, TMX thermomechanics,2D two-dimensional axisymmetric, 3D three-dimensional, Ref reference


q ¼ 1:6612VP � 0:4721V2P þ 0:067V3

P

� 0:0043V4P þ 0:000106V5

P ð2Þ

ED ¼ V2Pqð1þ mÞð1� 2mÞ

ð1� mÞ ð3Þ

where VP and VS are the primary and shearseismic velocities, respectively. The staticYoung’s Modulus, E, is usually a factor of 2–9smaller than ED, and is more appropriate fordeformation studies as the dominant processestaking place are significantly slower than thepropagation of seismic waves (e.g., Gud-mundsson 2011, and references therein).Numerical approaches can incorporate thesespatially-variable calculations of Young’sModulus and Poisson’s Ratio by allowing themechanical parameterisation of the crust to varywithin the model (Hickey and Gottsmann 2014).This can be achieved in one-dimension, wherethe values are only changed with depth, or inthree-dimensions, where the mechanical repre-sentation additionally changes in the two hori-zontal axes. The Finite Element Method is themost common technique used when incorporat-ing subsurface heterogeneity. With this approach,a heterogeneous model domain can be built usingmultiple different sized homogeneous ‘blocks’ ofvarying material properties (Hickey et al. 2013),with continuous interpolations as a function ofdepth or distance (Gottsmann and Odbert 2014),or with a three-dimensional coordinate interpo-lation (Hickey et al. 2016).

A further advantage of a numerical approachusing the Finite Element Method is the ability toinclude a spatially variable inelastic rheology thatis dependent on an estimated temperature distri-bution. Rocks do not always behave in an elasticmanner (Ranalli 1995). Instead, where crustalconditions are hotter than the brittle-ductiletransition, or subject to long-term loading,rocks can deform like very high viscosity fluids,and so viscoelastic effects are more likely(Ranalli 1995). This is especially important whena hot magmatic component is assumed to bepresent, or where elevated geothermal gradientsare observed. Also, when models are restricted to

elastic mechanical behaviour it can be difficult toconstrain realistic source processes, particularlyif there is a complex temporal deformation pat-tern that can not be reproduced with the instan-taneous elastic stress-strain relationship, and maybe better represented by a non-instantaneousviscous stress response. A model that incorpo-rates temperature-dependent mechanics canovercome these difficulties. This is achievedusing the Finite Element Method with a two-stepprocedure (Hickey and Gottsmann 2014). First, aspatially-variable, stationary, temperature distri-bution is derived, primarily dependent on thelocal geothermal gradient(s) and an assumed(magmatic) source temperature. This temperaturedistribution, T , is then used to define a crustalviscosity, g, for example through an Arrheniusrelationship, where:

g ¼ Ad expH

RT

� �ð4Þ

and Ad is the Dorn Parameter, H is the activa-tion energy, and R is the universal gas constant.The viscosity is used in a viscoelastic materialrepresentation (Hickey and Gottsmann 2014), sowhere the viscosity is high the material responseis dominated by elastic behaviour, and when theviscosity is lower the rocks show an increas-ingly higher tendency for viscous behaviour. Todemonstrate the effect of temperature-dependentmechanics, and subsurface heterogeneity, thefollowing case studies include examples ofboth.

Case Studies

Uturuncu

Uturuncu volcano is located in southern Bolivia,within the Altiplano-Puna Volcanic Complex. Ithas been steadily inflating since at least 1992(Pritchard and Simons 2002), and combined withshallow seismicity and near-summit activefumaroles represents a volcanic system showingsignificant signs of unrest (Sparks et al. 2008).


Hickey et al. (2013) focused on the mechanismdriving the 70 km wide region of ground upliftbetween 1992 and 2006. The aim was to con-strain first-order source parameters that explainboth the observed uplift rate of 1–2 cm/year andthe large spatial deformation footprint (Pritchardand Simons 2002). Stress and strain from pres-surised finite sources were solved numericallyusing Finite Element Analysis, accounting forboth homogeneous and heterogeneous subsur-face structure in elastic and viscoelastic rheolo-gies. Crustal heterogeneity was constrained fromseismic velocity data, which indicates a perva-sive large low-velocity zone *17 km below thesurface. This is deduced to represent one of theworld’s largest known regions of partial-melt: theAltiplano-Puna Magma Body (APMB) (Sparkset al. 2008).

The comparison between crustal heterogene-ity and homogeneity highlights the significanteffect of a mechanically weak source-depth layer(Fig. 1). The weak layer, with a lower Young’sModulus, alters surface deformation patterns byaccommodating more of the subsurface strainthan its surrounding layers, thereby acting as amechanical buffer. Continuous and regulartime-dependent deformation, the long-lived nat-ure of the source, and an anomalously highregional crustal heat-flux break the assumption ofelastic conditions (e.g., Ranalli 1995), so a vis-coelastic crustal rheology was tested, using thestandard linear solid representation (e.g. Hickeyand Gottsmann 2014). The elastic models couldalso only account for the spatial component ofthe observed uplift so their results were usedsolely to guide the parameters tested in the vis-coelastic models. A range of possible sourcegeometries were assessed, but spherical andoblate shapes were rejected on the grounds oftheir depth below the APMB and likely unsus-tainable pressurisation given the expected crustalmechanics. This left a prolate shaped source,whose minimum size was determined usingmaximum laboratory values for host-rock tensilestrength. The final preferred model suggests thattemporally-continuous pressurisation of a magmasource protruding from the top of the APMB is

causing the observed spatial and temporal surfaceuplift, whereas the previous models could onlyinfer that a simple-geometry source was beingpressurised somewhere within the APMB(Pritchard and Simons 2002). Hence, this alsodemonstrates how a pressure-time function playsa first-order role in explaining time-dependentdeformation.

Simultaneous work on an extended InSARdata set shows how the central uplift region atUturuncu is surrounded by a ‘moat’ of subsi-dence (Fialko and Pearse 2012). To explain thisobservation they also constrained a model wheremagma rises out and up from the APMB with adiapiric-type ascent mechanism. Further evi-dence for this magmatic process is availablethrough a complementary gravimetric study (delPotro et al. 2013). Therefore, this highlights howcombinations of geodetic data and numericalmodels can not only constrain more plausibledeformation source parameters, but can also infermagma transport dynamics.

Cotopaxi

Cotopaxi is a large, glacier-clad stratovolcanosituated in the Eastern Cordillera of theEcuadorian Andes. The 1 km3 glacier presents asubstantial lahar risk to people in the surroundingareas, and particularly to the 100,000 inhabitantsthat reside in the path of the 1877 lahar whichdescended the Inter-Andean Valley (Pistolesiet al. 2013).

Unrest was detected at Cotopaxi in 2001 and2002. There was a significant increase in theamount of volcanic seismicity in the NE quadrantof the volcano, and this was originally interpretedto represent a dyke intrusion with subsequentgas-release and resonance of the crack (Molinaet al. 2008). Hickey et al. (2015) revisited thisunrest period, but approached it from a volcanodeformation viewpoint. Analysis of an electronicdistance meter (EDM) network over the 2001–2002 period also indicated an asymmetric infla-tion of the edifice that accompanied the recordedseismicity (Fig. 2). However, the irregular


acquisition in time of the EDM data preventedany systematic comparison between the two datasets. To solve for the optimum deformationsource parameters, Hickey et al. (2015) imple-mented a novel numerical inversion procedureusing Finite Element models. This is the first

volcanic deformation inversion study to explic-itly account for both subsurface heterogeneityand surface topography while searching for abest-fit solution with a range of source shapes.The method works by solving for the predictedEDM deformation with an initial model and

0 5 10 15 20 25 30 350

1

2

3

4

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8

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LOS

Dis

plac

emen

t (cm

)

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Radial Displacement [m]0.0 0.4 0.8 1.2 1.6 2.0

suoenegoreteHsuoenegomoH 5 km5 km

A

F

ED

C

B(a) (b)

(c)

Fig. 1 A comparison of the effect crustal heterogeneityfor the same prolate source geometry and depth. a, b Theeffect of a source depth soft layer on the subsurfacedeformation of a source. Both panels show the samesource, embedded in a homogeneous (a) or heterogeneousdomain (b). Colours relate to the radial displacement, andthe white shape shows the exaggerated outline of thedeformed source after the pressure is applied. In theheterogeneous model the source preferentially deforms

into the softer layer (D), compared to the homogeneousmedium, which exhibits a concentric deformation pattern.c Modelled surface displacement profiles from thehomogeneous (a) and heterogeneous (b) models. Thesubsurface layering in b alters the displacement patternproduced at the surface as the soft layer modifies thesubsurface strain partitioning. The blue shaded arearepresents the observed InSAR data and its estimatederror bounds


source configuration. It then continually changesthe source location and/or overpressure, withinsome predefined parameter limits, to minimisethe misfit to the recorded EDM data (Fig. 2).After each inversion, the parameter limits (e.g., Xand Y coordinates) are reduced around the pre-vious solution to produce a set of decreasing size‘Russian-doll-like’ parameter constraint gridsthat ensure a robust solution. Within this work-flow, the Finite Element model geometry andmesh are automatically rebuilt, removing theneed for repeated manual editing.

The inversion models converge on a shal-low source beneath the SW flank. The indi-vidual best-fit model is inferred to represent asmall oblate-shaped magmatic reservoir,approximately 4–5 km beneath the summit,with a volume increase of roughly20 � 106 m3. A deformation source location inthe SW is substantially different to the NElocation proposed by Molina et al. (2008)when explaining the recorded seismicity.Despite this, when the deformation source wasrestricted to the NE quadrant the predicted

−78.50° −78.40°

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(a) (b)

(c) (d)

Fig. 2 Deformation and modelling results from Coto-paxi volcano. a Map of the EDM network operationalbetween 2001 and 2002 around the summit of thevolcano, with the best-fit source from the Finite Elementinversions indicated by a red star. The yellow squaresrepresent the EDM base-stations and the orange trianglesare the reflecting prisms. The inset map and arrow showsthe location of Cotopaxi within Ecuador, South America.

b The variation, and eventual reduction, of the misfitobjective function with each iteration from the final,best-fit Finite Element inversion model. c The modelledvalues from the final inversion for the EDM baselinechanges converge to their near-absolute values afterapproximately 25 iterations. d The best-fitting model(red circles) fits six out of seven of the EDM observations(black circles with error bounds)


EDM measurements had a very poor fit to theobserved data.

To clarify the difference in source locationbetween the seismic and geodetic studies, Hickeyet al. (2015) applied the best-fit source parame-ters from the elastic inversion models in a suiteof temperature-dependent viscoelastic forwardmodels to assess the rheology of the host-rock fora range of thermal parameters. The results indi-cated the most likely subsurface conditionswould have promoted a large component ofviscous deformation and that the deformationsource in the SW would have consequently beenpressurised aseismically. Fluid migration fromthe SW along existing NNE-SSW trending faultscould have then caused the observed seismicityin the NE due to mass transport and excess porepressures. The lack of eruption following this2001–2002 unrest period and the aseismic natureof the event suggests that the magma supply ratefor this period was low. A higher magma supplyrate during a future unrest period would be morelikely to produce seismicity around the reservoir,and could possibly indicate a level of unrest thatsignifies an increased likelihood of a forthcomingeruption.

Soufrière Hills

Starting its latest eruptive episode in 1995 anddisplaying a remarkable diversity of eruptiveactivity, Soufrière Hills volcano (SHV) onMontserrat (British West Indies) is one volcanowhere a correlation between observed deforma-tion and subsequent eruption can be directlyestablished. Ground deformation data at SHVindicate cyclic behaviour of the andesitic mag-matic system from periods of several hours to afew years (Odbert et al. 2014). This sectionfocuses on the analysis of intra-eruptive unrestassociated with island-wide ground upliftobserved via a network of continuous GPSreceivers between 28/07/2003 and 01/08/2005(Odbert et al. 2014). After a major lava domecollapse in 2003, which marked the end of thesecond phase of dome extrusion at SHV, this

period preceded a restart of eruptive activity andrenewed dome extrusion in August 2005.

Gottsmann and Odbert (2014) developednumerical models to test for the influence of tem-perature- and time-dependent stress evolution in amechanically heterogeneous crust to explain thedeformation data. Full details on the model setupand parameter derivation are given in Gottsmannand Odbert (2014) and not repeated here. Theyimplemented two types ofmagma reservoir model.The first explored a series of pressurising,vertically-stacked reservoirs as proposed byHautmann et al. (2010), while the second exploredthe time-dependent pressurisation of a single,vertically-elongated reservoir. Due to a similartemperature distribution from both the stacked andsingle reservoirs, and similar resultant rheologicalcrustal properties, both suites of models providedequally good fits to the observed ground defor-mation. The study could hence not discriminatebetween pressurisation in a magmatic plumbingsystem consisting of either a single verticallyelongated reservoir or a series of stacked reser-voirs. Reservoir pressure changes between 4 and7 MPa, for volumes between 60 and 100 km3 andmagma compressibility between 4 � 10−11 and1 � 10−9 Pa−1, provided plausible thermome-chanical model parameters to explain the defor-mation data. The associated magma volume fluxesare between 0.015 and 0.021 km3/year and matchthose derived from thermal modelling of activesub-volcanic systems (Annen 2009). Introducing adeep-crustal hot zone in the model, which modu-lates the partitioning of strain into the hotterunderlying crust beneath the reservoir(s), promotesa further reduction in reservoir overpressures tovalues of around 1–2 MPa upon reservoir failure(Fig. 3). These pressure changes are significantlylower than those derived from models assuming amechanically homogeneous and elastic crust. Thededuced overpressures match those for sudden andrapid transcrustal reservoir activation prior toexplosions at SHV from the analysis of volumetricstrain data (Hautmann et al. 2014). The emergingeruptionmodel at SHVhence involves the periodicfailure of a compressible magma mush columnbeneath the volcano.


Las Cañadas

The Las Cañadas caldera (LCC) hosts the centralvolcanic complex (CVC) on Tenerife (CanaryIslands), which includes the twin-volcanoes ofPico Viejo (PV) and Pico Teide (PT). Volcanicunrest on Tenerife started in April 2004 andended a period of quiescence after the mostrecent magmatic eruption on the island in 1909.The unrest was geophysically characterised byanomalous seismic activity including a numberof felt earthquakes and significant changes in theacceleration of gravity, yet, an absence of sig-nificant ground deformation (Gottsmann et al.2006b). The initial interpretation of the gravitychanges by Gottsmann et al. (2006b) pointedtowards shallow (*2 km depth) fluid migrationas the main source of the unrest, possibly relatedto a magma intrusion at greater depth. As part ofthe VUELCO project, Prutkin et al. (2014)revisited the microgravity data recorded betweenMay 2004 and July 2005 and inverted thespatio-temporal residual gravity changes for thegravitational attraction of three-dimensional linesegments.

The line segments are defined by 7 parame-ters: two end point coordinates (X, Y, Z) and aline strength (see Table 2). The latter is a proxyfor the amplitude of sub-surface mass change,whereby a “weak” line segment represents asmall amount of added mass compared to a“strong” line segment of greater added mass. Aninitial non-linear inversion yielded three linesegments of different strengths at depths between1 km a.s.l. and 2 km b.s.l. (i.e. between 1 and4 km beneath the surface). Two of the segmentswere located to the NW of the PV-PT complex,while a third segment was located below the SWrim of the LCC (sources marked Sh 1–3 inFig. 4). The locations of the segments corre-spond broadly to zones of heightened seismicactivity and the unrest source location identifiedearlier by Gottsmann et al. (2006b).

Fig. 3 a The temperature distribution (in K) of the 2-Daxisymmetric model domains, caused by a combination ofa basal heat flux, the heat from the plumbing system(magma reservoir plus feeder pipe), and a deep-crustal hotzone. Background thermal distribution in the far field iscaused exclusively by a basal heat flux of 0.09 W/m2.Arrows indicate deformation of the medium by reservoirpressurisation. Substantial deformation is accommodatedby hot and ductile parts of the mid and lower crust. b Themodel parameter space for reservoir volume, volumechange, and magma compressibility (shown in log unitson the colour bar) from the best fit model solutions to the2003–2005 intra-eruptive deformation time series atSoufrière Hills Volcano. The overall fit quality decreasessubstantially toward higher compressibility (order10−9 Pa−1) and toward smaller reservoir volumes(<50 km3). The preferred parameter space is encompassedbetween the mapped upper limit of compressibility (ULC)and the lower limit of the magma reservoir volume(LLRV)


However, closer inspection of the initialinversion results revealed that the line segmentsrepresent the superposition of deep and shallowseated sources. The decomposition of the gravitychange data into shallow and deep fields (seePrutkin et al. 2014 for details) provided the basis

for the separate inversions of the two fields usingthe three-dimensional line segment approxima-tion. The deep field inversion constrained twoconnected and strong line segments at a depth ofabout 5.8 km b.s.l. (marked Dp1 and Dp2 inFig. 4), while the inversion of the shallow field

Table 2 UTM coordinates X (Easting in m), Y (Northing in m), and Z (elevation in m with respect to sea level) of theend points of the modelled shallow (Sh) and deep (Dp) sources represented by line segments (see Fig. 4)

Line segment X1 Y1 Z1 X2 Y2 Z2 ΔM

Sh1 327,500 3,137,930 1280 330,330 3,137,260 600 0.31

Sh2 336,560 3,132,050 590 334,210 3,134,040 420 0.83

Sh3 335,460 3,120,730 1380 332,100 3,121,210 380 0.53

Dp1 334,890 3,133,910 −5440 334,630 3,134,200 −5680 7.25

Dp2 334,310 3,134,590 −5840 334,630 3,134,200 −5680 8.24

Mass additions (ΔM) are given in 1010 kg. Data Prutkin et al. (2014)

Fig. 4 Location of line segments from gravity datainversion. The figure shows the surface projections ofthree shallow sources (line segments Sh1–3 in turquoise)and the two deep sources (line segments Dp1 and 2 inred) superimposed over a Google Earth image of theCentral Volcanic complex of Tenerife island (Spain). Thesource locations are derived by a nonlinear inversion ofspatiotemporal residual gravity changes shown bycoloured contours (in lGal) observed between 2004 and2005 (see Prutkin et al. (2014) for details on inversionroutine). The thickness of a line segment is indicative ofthe “strength” of the deduced mass change; i.e., the

amount of added mass. The mass added to the deepsources is more than 10 times higher than to the shallowsources. Line segments Sh1–3 are interpreted to representnear-surface sources in the NW and SW part of the PicoTeide (PT; 3718 m a.s.l.) and Pico Viejo (PV; 3135 m a.s.l.) volcanic complex, associated with fluid migration as aresult of an intrusion of magma at around 5.8 km b.s.l.(Dp sources). See Table 2 for details on segments andassociated mass changes. The southern caldera rim (CR)is shown for reference and the inset shows a digitalelevation model of Tenerife, with the study area identifiedby a white rectangle


identified three similarly weak line segmentssituated at near-surface depths (<2 km fromground surface; see Fig. 4 and Table 2).

The most plausible interpretation of theinversion results is that the weak line segmentsrepresent sources dominated by hydrothermalfluids. In contrast, the deeper-seated sources canbe interpreted as parts of an intrusion of newmagma. This intrusion may have released fluidswhich consequently migrated towards shallowerdepths where they excited a shallow hydrother-mal system. The geophysical signals resultingfrom these coupled magmatic-hydrothermalprocesses point towards a hybrid source naturefor the unrest on Tenerife in 2004–2005. Theidentified link between deep and shallow unrestsources suggests the presence of permeablepathways for shallow fluid migration at the CVC.

Discussion

The Effect of Crustal Mechanicson Stress, Strain and Pressure

The presented investigations at Uturuncu, Coto-paxi and SHV all incorporate subsurfaceheterogeneity, however the effects are somewhatdifferent. At Cotopaxi the final inferred defor-mation source is shallow, at a level where themodel does not incorporate substantial hetero-geneity due to the limited amount of availableseismic data. Hence, with this model configura-tion, the heterogeneity has not played a signifi-cant role in altering the location of the source. Itis likely, however, that in reality the volcanicedifice and shallow subsurface does have a cer-tain level of heterogeneity. It is therefore possiblethat had this been taken into account the inferreddeformation source might be located more cen-trally beneath the edifice. Conversely, at Utu-runcu and SHV subsurface heterogeneity playeda crucial role in determining the deformationsource locations. In both cases, the inclusion ofvertical layering in the Young’s Modulus distri-bution altered the inferred depth of the source;the heterogeneous models predict deeper sourcesthan the generic homogeneous analytical models.

From this, it also follows that a horizontal vari-ation in mechanical properties would influencethe horizontal location of a deformation source(e.g., Hickey et al. 2016).

A second effect of subsurface heterogeneityrelates to source pressure requirements. It iscommon with homogeneous crustal mechanics torequire unrealistically high source pressurisation(>100’s MPa) when attempting to fit an observeddeformation signal, yet there is no petrological ormechanical evidence for such conditions. Theo-retical work from a mechanical viewpoint sug-gests that the maximum overpressure a sourcecan sustain without failing is equal to the tensilestrength of the host rock (e.g., Gudmundsson2011). Above this limit, a magmatic reservoirwould trigger a dyke intrusion. Work at Utu-runcu and SHV shows that elastic heterogeneousdeformation models bring source over-pressurerequirements more in line with both in situ andlaboratory values of tensile strength. This is dueto a relative reduction in the average Young’sModulus above the source, compared to a higherhomogeneous Young’s Modulus through theentirety of the crust, and thus a greater amount ofdeformation for a given pressure increment.Furthermore, with a maximum value for thesource over-pressure, constraints can be placedon the minimum size of a deformation source,given the two are directly linked. This allows, forexample, an estimate to be placed on the volumeof a magma reservoir. When multiple magmaticsources might be present numerical models canadditionally account for stress interactionsbetween the two, something not considered bygeneric analytical models (Pascal et al. 2013).

As a next step to subsurface heterogeneity, thecase studies at Cotopaxi and SHV incorporatedtemperature-dependent mechanics to evaluate theeffect of a viscoelastic rheology. At Uturuncu,investigations were also carried out using a vis-coelastic rheology without temperature-dependence. In all three cases, a viscoelasticmedium reduced the over-pressure requirementsfurther when compared to the purely elasticmodels. This is due to the viscous expansion thatfollows an initial elastic inflation. The effect ofthermomechanics is greater than just modifying


source over-pressure requirements, however.Prolonged magma emplacement over thousandsto millions of years in active volcanic areasbuilds up a significant thermal legacy within thecrust. This results in elevated geothermal gradi-ents, and in the case of continued active mag-matism, deep crustal hot-zones (Annen 2009).These thermal perturbations are significant forthe transfer of stress and strain. For example, atSHV, the combined thermomechanical effects ofa deep-crustal hot zone and hot encasing rocksaround a mid-crustal andesitic reservoir funda-mentally alter the time-dependent subsurfacestress and strain partitioning upon priming of themagma reservoir. These effects substantiallyinfluence surface strains recorded by volcanogeodetic monitoring.

Hybrid Unrest and SourceCharacterisation

An intrusion of magma commonly leads to theexsolution of fluids upon decompression, andfluid migration (and accumulation) in itself canproduce measurable geodetic surface signals(e.g., Fournier and Chardot 2012; Rouwet et al.2014, and references therein). A deep intrusionof magma, such as the 2004–2005 unrest onTenerife, may not necessarily lead to observablesurface deformation, meaning deformation dataon its own can not provide any meaningfulinsights on the source process(es). In this case,the combination of deformation and gravity sur-veys allowed the characterisation of the unrestsources in much greater detail owing to theirdensity contrasts, relative depths and massadditions. This highlights that, especially for thecase of hybrid mechanisms where both magmaticand hydrothermal components are present,multi-disciplinary geodetic surveys can providevaluable information on source characterisationto help distinguish the processes driving unrest.This identification and discrimination of sourcesdriving volcanic unrest via mathematical mod-elling of surface data is of vital importance forhazard and risk characterisation, given the dif-ferent connotations associated with magmatic

and non-magmatic unrest, and plays a major rolein probabilistic eruption forecasting (Rouwetet al. 2014).

Application to Eruption Forecasting

The primary objective of the case studies was todevelop advanced geodetic models to interpretspatial and temporal deformation monitoringsignals, and provide better constraints on thesubsurface processes causing volcanic unrest.This has been achieved by incorporating moreplausible model components, such as subsurfaceheterogeneity, topography and temperature-dependent mechanics, to relax the assumptionsthat hinder analytical models and maintain con-sistency with inferences from geophysics, geol-ogy and petrology. Crucially, this highlighted theimportance of pressure-time functions andinelastic rheology in deciphering temporaldeformation patterns. In turn, a more thoroughunderstanding of how a volcanic system behavesthrough time will benefit eruption forecasting, asquantitative estimates of key parameters such asmagma supply rate and mechanism can bededuced.

When only considering the spatial deforma-tion pattern, this work has further demonstratedsome of the pitfalls associated with modelsassuming homogeneous, elastic, half-spaces(e.g., Mogi 1958). Crustal heterogeneity signifi-cantly effects the horizontal and vertical locationof a deformation source by altering the subsur-face strain distribution. Surface strain partition-ing by complex topography is equally important,such as at steep-sided stratovolcanoes. TheCotopaxi case highlighted complex partitioningbehaviour along deep ravines and adjacent lavaflow ridges. If ground-based geodetic monitoringsites are positioned at localities with steep topo-graphic gradients, surface strain partitioningplays a first-order role and needs to be accountedfor during data modelling. Consequently, esti-mates of source parameters from generic, ana-lytical models which cannot account forheterogeneities or complex topography mayskew eruption forecasting and risk mitigation


efforts. On the other hand, more reliable defor-mation source locations from numerical modelscan be used to better estimate where and when aneruption might occur, and the associated hazard.It should also be pointed out that data limitationsat some volcanoes may prevent complexnumerical models being used, in which casesimpler models may be the only option and theirresults should be carefully scrutinised and onlyapplied cautiously to further analyses.

Conclusions

The case studies provide new interpretations ofvolcanic processes during intra-eruptive andnon-eruptive unrest. They also provide observa-tions for distinct magmatic settings, thus con-tributing to the ongoing global comparisons ofdeformation and unrest, and the process of pat-tern recognition for identification of eruptionprecursors. The incorporation ofmulti-disciplinary data into integrated geodeticmodels has closed the gap between observationsand interpretations of volcanic deformation andgravimetric changes. This will help to improveeruption forecasting as it moves away from aqualitative approach towards incorporation ofmore quantitative data derived fromwell-constrained physical mechanisms.

Acknowledgements Work presented herein has receivedfunding by the European Commission (FP7; Theme:ENV.2011.1.3.3-1; Grant 282759: VUELCO). We arevery grateful to Alvaro Guevara and Irving MunguíaGonzalez for their help translating Spanish, and to twoanonymous reviewers for their constructive comments.

Glossary Terms

Deformation the action of changing the shapeof a physical object (e.g., a volcano) under theinfluence of some stress.

Elastic rheological behaviour in which anapplied stress causes an immediate strain thatis 100% recoverable when the stress isremoved. See also rheology and viscoelastic.

Finite Element Method/Analysis a numericalmodelling technique that subdivides anentire problem into a set of smaller ‘ele-ments’. Mathematical problems are thensolved in each of the elements and com-bined together to calculate the response ofthe whole object.

Geodesy applied mathematics with the aim ofmeasuring the geometric spatial representationof the Earth and its gravitational field intime-varying three-dimensions, as well astheir orientation in space. Volcano geodesyspecifically deals with recording the spatialand temporal patterns of crustal deformationand gravimetric changes in volcanic settings.

Gravimetry field of geophysics devoted toobserving, processing and interpreting minutechanges in the Earth’s gravitational field.

Hydrothermal system an area in which heatand fluids from a partially molten magmaticbody interact with a multi-phase groundwatersystem, causing chemical and thermal (heat-ing) perturbations to the water.

Mechanics (crustal, thermal) the branch ofphysics that studies how stress can effect aphysical object. Crustal mechanics relates tothe values of the material parameters thatdescribe the mechanical behaviour of theEarth’s crust. Thermal mechanics relates tothe variation in mechanical material propertiesdue to changes in temperature.

Model (inverse, forward) a simulation of aprocess. Inverse models solve ‘backwards’ todetermine optimal model parameters that fit aset of data. Forward models use predefinedconstant input parameters to calculate theexpected model response.

Rheology (crustal) the behavioural response ofthe Earth’s crust to forces that act upon orwithin it. See also elastic and viscoelastic.

Strain the change in dimension of an object(e.g., DX) relative to the original dimension ofthe object (e.g., X). It has no units, as the unitscancel: DX=X.

Stress a measure of force per unit area, with theunit of pascals, Pa. 1 Pa = 1 N/m2.


Viscoelastic rheological behaviour in which anapplied stress causes an elastic response, fol-lowed by a delayed (viscous) response. Seealso rheology and elastic.

Index Terms

Magma reservoir, deformation, gravity, GPS,InSAR, Cotopaxi, Soufrière Hills, Las Cañadas,Uturuncu, unrest, thermomechanics, modelling,finite element, inversion/inverse model, crustalmechanics, hybrid unrest, Young’s Modulus,Poisson’s Ratio, viscosity.

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