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Time-dependent gravimetric measurements can detect subsur-

other eruption precursors. The ability of gravity measurements to

Sbfer a closed-form description of the volcanic source. In principle,this allows one to readily infer the relative importance of thesource parameters. In active volcanic sites such as Long Valleyc

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lenge is to interpret these signals and infer the cause of unrest before

GEOPHYSICS, VOL. 73, NO. 6 NOVEMBER-DECEMBER 2008; P. WA3WA18, 4 FIGS.10.1190/1.2977792re the culmination of multiple intrusions that supply a reservoir,ultiparameter monitoring techniques and robust mathematicalodels are essential for providing effective warnings to civil author-

ties and the public. Gravity measurements are an indispensableomponent for any volcano monitoring strategy and are the focus inhis paper. A key assumption behind gravity monitoring is thathanges in earths gravity reflect mass-transport processes at depthDzurisin, 2003. However, because of the complexity of subsurface

impending eruptions Johnsen et al., 1980; Dvorak and Dzurisin,1997.

The intrinsic ambiguity in interpretation of gravity and/or geodet-ic data alone can be partially removed if they are analyzed jointly.Various authors have shown that combined time-dependent geodeticand gravimetric measurements are a key tool for mid- to long-termhazard assessment because they enable detection of subsurface massredistribution long before other eruption precursors appear. See ex-detect subsurface mass flow is greatly enhanced if gravity mea-surements are analyzed and modeled with ground-deformationdata. Obtaining the maximum information from microgravitystudies requires careful evaluation of the layout of networkbenchmarks, the gravity environmental signal, and the couplingbetween gravity changes and crustal deformation. When changesin the system under study are fast hours to weeks, as in hydro-thermal systems and restless volcanoes, continuous gravity ob-servations at selected sites can help to capture many details of thedynamics of the intrusive sources. Despite the instrumental ef-fects, mainly caused by atmospheric temperature, results frommonitoring at Mt. Etna volcano show that continuous measure-ments are a powerful tool for monitoring and studying volcanoes.

INTRODUCTIONtructures beneath active volcanoes, identifying the source of unrests not straightforward. Active volcanoes often host both hydrother-

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Manuscript received by the Editor 28 February 2008; revised manuscript received1U. S. Geological Survey, Volcano Hazards Team, Menlo Park, California, U.S.A2University of Rome La Sapienza, Department of Earth Sciences, Rome, Italy. E3Department of Earth Sciences, University of Bristol, United Kingdom. E-mail: j.g4Istituto Nazionale di Geofisica e Vulcanologia, Sezione di Catania, Catania, Italy.5Instituto deAstronoma y Geodesia CSIC-UCM, Madrid, Spain. E-mail: josefe2008 Society of Exploration Geophysicists.All rights reserved.

WA3aldera California, U.S.A. and Campi Flegrei Italy, carefulse of analytical models and high-quality data sets has producedood results. However, the simplifications that make analyticalodels tractable might result in misleading volcanological inter-

retations, particularly when the real crust surrounding theource is far from the homogeneous/isotropic assumption. Usingumerical models allows consideration of more realistic descrip-ions of the sources and of the crust where they are located e.g.,ertical and lateral mechanical discontinuities, complex sourceeometries, and topography. Applications at Teide volcanoTenerife and Campi Flegrei demonstrate the importance of thisore realistic description in gravity calculations.

al and magmatic reservoirs at depth. Physical and chemical chang-s in either can produce measurable geophysical signals. The chal-face processes long before magma flow leads to earthquakes orD volcano gravimetry

aurizio Battaglia1,2, Joachim Gottsmann3, D

ABSTRACTle Carbone4, and Jos Fernndez5

everal analytical and numerical mathematical models caneused to fit gravity and deformation data. Analytical models of-mples in Dzurisin, 2003; Rymer and Williams-Jones, 2000; Gotts-ann and Rymer, 2002; Sparks, 2003; and Battaglia et al., 2006.

25 June 2008; published online 20 November 2008.

-mail: maurizio.battaglia@uniroma1.it.ottsmann@bristol.ac.uk.E-mail: carbone@ct.ingv.it.rnandez@mat.ucm.es

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WA4 Battaglia et al.The critical questions that emerge when monitoring volcanoes areow to constrain the source of unrest, how to better assess hazardsssociated with the unrest, and how to refine our ability to forecastolcanic activity. Note that ground-deformation data alone cannotiscriminate between magma and aqueous-fluid intrusion. Defor-ation measurements are sensitive to changes in the source pressure

r volume only. They are completely independent from the nature ofhe source. This ambiguity can be resolved if we know the density ofhe source. Gravity measurements, however, can constrain the massf the intrusion. Combined geodesy and gravity measurements cane used to infer the density of the intrusive fluids and can better con-train the source of unrest Battaglia et al., 2006; Gottsmann et al.,006a.

For volcano monitoring and risk mitigation, assessing gravityime changes is especially important when they occur without mea-urable ground deformation Rymer et al., 1993; Carbone et al.,003a; Gottsmann et al., 2006b.

In this paper, we review the state of the art of identifying sourcesf volcano unrest using microgravity studies. In particular, we dis-uss the potential and the challenges of repeated and continuousravity measurements as tools for monitoring and studying activeolcanoes. We also review the analytical and numerical mathemati-al models available in the literature that can be used to fit and inter-ret the observations.

FIELD SETUP AND SURVEY DESIGN

In designing a survey network at a volcano, it is important to bearn mind the signal from individual sources. Mass/pressure variationsn at least three different levels of subsurface reservoirs might pro-uce observable gravimetric signals at the ground surface:

Hydrothermal reservoirs, extending from surface levels to afew kilometers deep

Midcrustal reservoirs, which can host varying fractions of meltand aqueous fluids

Deep reservoirs, e.g., as formed by underplating at the interfaceof the crust and upper mantle funneling new melt to midcrustallevels

Distribution of benchmarks of the monitoring network is a com-romise among survey target, costs, accessibility, manageability,nd safety. For example, a high-precision local network might cap-ure the shallow feeder system but is unlikely to provide informationbout deep magma plumbing Jousset and Okada, 1999.

icrogravity surveysGravity time series are obtained by time-lapse surveys whereby

elative microgravity readings are obtained at individual bench-arks. These measurements then are related to a reference outside

he area of interest. With the recent advent of portable absoluteravimeters, time-lapse observations also are possible by using ab-olute readings Ferguson et al., 2008 or, where challenging envi-onmental conditions disallow use of absolute gravimeters at allites of the array, through a combination of absolute and relativeravity measurements hybrid microgravimetry. Hybrid micro-ravimetry might be especially important in areas where there is nouarantee of temporally constant gravity at the reference site Fu-

uya et al., 2003b. tRepeated occupation of the network leads to gravity time serieshat are evaluated with respect to data obtained at the reference. Con-equently, one obtains a series of baseline readings between the ref-rence and each survey benchmark. Obviously, baseline correctionsre redundant if an absolute gravimeter is part of the survey network.omplexities arise, particularly on small volcanic islands, where itight be difficult to install a reference outside the zone of interest

Furuya et al., 2003b. Locating a reference too close to the targetolcano causes serious ambiguities as to subsurface processes be-ause deep-seated mass/density changes affect gravity measure-ents at both the reference and the network baselines.Measurement errors are affected not only by the type of field

ravimeter and operator but also by site effects such as benchmarktability and noise and by environmental effects from local pressurend temperature changes. To minimize environmental effects, gravi-y meters are sealed; thus, barometric-pressure changes should notffect the buoyancy of the mass. In addition, the measurement cham-er is kept at constant temperature thermostated. If a meter variesrom its thermostated temperature, there will be intolerable instru-ental drift. Each instrument is thermostated at a different tempera-

ure. In cold climates, using a meter that is thermostated at loweremperatures will conserve battery power. In hot climates, a meterhat is thermostated at a higher temperature is less likely to go overemperature LaCoste & Romberg, 2004.

The standard pressure correction between pressure and gravitybarometric-pressure admittance usually is small, close to 0.3Gal/mbar. Because this effect varies with both time and frequency,

he contribution is spread over the full spectral domain and might in-ibit the observation of small signals on the order of nGal or a fewGal of geophysical origin. This is especially important for high-recision measurements that can be obtained by superconductingravimeters Boy et al., 1998.

Using a Scintrex CG3-M gravimeter, Budetta and Carbone 1997ound a precision of between 3.5 and 4.4 Gal 1 Gal 108/s2 under various field conditions. Over a series of baseline read-

ngs, error propagation can add up to uncertainties of approximately0 Gal Battaglia et al., 2003b. For example, using a global navi-ation satellite system GNSS/GPS for benchmark elevation con-rol and accounting for uncertainties in positioning of 2 to 3 cm inhe vertical readily yields a precision of approximately 15 Gal forndividual gravity baselines Gottsmann and Battaglia, 2008.

Significant uncertainties in the reduction of gravity data usuallyre associated with tidal correction. Solid-earth tides SET are pre-ictable to within reading precision of modern gravimeters, butcean-loading OL contributions to gravimetric data can affect therecision of 4D gravimetric data dramatically Berrino and Riccardi,001 and generally are large near coastlines with complicatedathymetry Van Dam et al., 2007. Despite the availability of nu-erous OL models, local effects on volcanic islands cannot be pre-

icted accurately enough. Loading depends on the immediate sub-arine topography around an island and the shape of the coastline;

eneric global models fail to account for such local effects Arnosot al., 2006.As a consequence, each benchmark of a network cover-ng a small island might suffer from individual OL effects. Ideally,ne would construct a tidal correction model for each benchmark,ut this is not achievable in volcano-monitoring programs now or for

he foreseeable future. A local model applicable to the entire net-

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4D volcano gravimetry WA5ork to reduce residual OL effects could be constructed from tidalravity data obtained from a permanently recording gravimeter op-rated as a tidal meter.

In the absence of precise SET and OL model data, reduction maye performed using data from a continuous gravity station operatedn addition to a campaign meter over the period of the survey Gotts-

ann and Battaglia, 2008. Alternatively, the network could be oc-upied with multiple gravimeters and operators to try to deduce theorrect gravimetric baseline values statistically. However, in manyases, neither is achievable because of lack of infrastructure, equip-ent, and/or personnel. If only one meter is available for a survey, aay to account for uncertainties from OL is to propagate tidal-cor-

ection errors directly e.g., at Montserrat, this uncertainty is up to0 Gal; Figure 1a or to avoid benchmark reoccupation on periodshat match the half-width of OL periods.

Ocean-loading effects are particularly dominant over periods ofpproximately 12 hours peak to peak, semidiurnal effects. Dataontamination cannot be avoided entirely, but its effects can be re-uced significantly by doing a baseline loop as quickly as possible,ncluding initial measurement at the reference and at the benchmarknd reoccupation of the reference within approximately 3 hours. Ifravimetric signals are expected to be significantly more than tidalncertainties, errors can be propagated. However, most gravityhanges at active volcanoes reported in the literature are on the orderf tens of Gal; thus it appears reasonable to minimize errors fromndividual contributions, including tidal effects.

ime-lapse microgravimetryAfter correcting for tidal effects, the observed

ravity change gobs is the difference in gravitylong a baseline between benchmark and refer-nce. Under ideal conditions, resolvable gravityhanges might be detectable up to 10 km from theegion of maximum ground deformation if theass change at depth is at least 1012 kg Will-

ams-Jones and Rymer, 2002. To extract theravity signal produced by a subsurface massnd/or density change, gravity residuals must beuantified Eggers, 1987. The residual gravityhange at each benchmarkgr is given by

gr gobs uz gdef gwt.1

ere, denotes a gravity difference over time athe site e.g., gobs gobst2 gobst1; is theree-air gravity gradient the value of the theoreti-al gradient T is 308.6 Gal m1; uz is theertical displacement positive for relative upliftnd negative for relative subsidence; gdef is theouguer effect of deformation the contributionf the volume change arising from compressibili-y of the medium surrounding the source, whichlso implies displacements of density boundariesn heterogeneous media; andgwt is the effect ofroundwater-table variation Figure 1b. Theources geometry significantly affects the Bou-uer reduction for the effect of deformationgdef.spherical symmetry Rundle, 1978; Walsh and

b)

Figure 1. afrom Soufrirgrowth stagnaat this small vgravimetric timchanges durinin the field.Algradient, isice, 1979 results in the correction being exactly 2003b.ero. Deformation effects from a prolate spheroid are negligible,hereas deformation effects can be up to 80% for a horizontal pen-y-shaped crack source Battaglia et al., 2006.

Critical to interpretation of residual gravity variations is the cor-ection for gwt Battaglia et al., 2003b or gravity changes inducedy an active hydrothermal system Gottsmann et al., 2007. Theormer correction can be approximated by

gwt 2Gw z , 2

here 2Gw 42 Gal m1, G is the universal gravitationalonstant 6.6731011 N m2 kg2, is effective porosity, w is theensity of water, and z is the vertical water-table change for an un-onfined aquifer. Gravity signals from shallow hydrothermal sys-ems require installation of a tidal meter to correct for short-termuctuations in aquifers Gottsmann et al., 2007.Failure to account for shallow sources might result in an inability

o differentiate between gravity signals from changes in the magmat-c plumbing system and those from background noise e.g., water ta-le Jachens and Roberts, 1985.As a result, the entire gravitationalignal is attributed to deeper usually magmatic processes, and con-lusions drawn then might be unrealistic.

ata aliasingAliasing effects in gravimetric data are important error sources.

lthough spatial aliasing plays a more important role during static

of OL. The figure shows the residual-gravity trace recorded 4 kmVolcano, Montserrat, British West Indies, during a period of dome-June 2007 that was related predominantly to semidiurnal OL effectsisland. Such time series are indispensable for precise reduction of

se observations and other geodetic observations to assess subsurfacetion. b Different effects that compose the gravity signal measuredants are in Gal m1; uz is vertical displacement, FAG is the free-airity, and z is water-table change. Modified from Battaglia et al.,z

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WA6 Battaglia et al.time-independent surveys, gravimetric-time-series data fromime-lapse microgravity surveys might suffer distortion when dataetween individual surveys are compared. With benchmark occupa-ion typically ranging from a few months to a few years, gravity vari-tions detected between individual surveys might be caused by fun-amental mass/density variations over much shorter time periods.he frequency that corresponds to the sampling interval of periodicurveys might be far lower than that of dynamic changes at depth,eading to a misrepresentation of timescales of subsurface dynamics.

Consequently, the real period of the signal and thus any hypothe-is about its source might not be resolved unambiguously in theime domain because of the Nyquist limit. However, assuming thatources that evolve more quickly are shallower, this ambiguity coulde tentatively solved in the space domain if the available network oftations is dense enough to allow distinction between effects linkedo sources at different depths. Alternatively and ideally, couplingime-lapse observation on an extended network with continuous

easurements at one or more selected sites can provide essential in-ights into mass/density variations at depth over both time and spaceCarbone et al., 2003b. See the Continuous gravity section be-ow. Interpretation of time-lapse data from a few annual or multian-ual surveys therefore must be based on a cautious evaluation ofimescales, especially in volcanic areas where active hydrothermalystems and magma reservoirs might operate over different periods.

A fundamental assumption for quantifying residual gravityhanges is that ground deformation and gravity changes occur in-tantaneously because of a subsurface disturbance, resulting in a lin-ar gravity-height signature. However, this linearly elastic assump-ion sometimes does not hold true e.g., with time-dependent proper-ies of volcanic reservoirs, such as viscoelastic relaxation of stressuildup Yu et al., 1996. The resultant source parameters inferredrom inverting geodetic and gravimetric data thus depend heavily onhe assumption about mechanical properties of the host rock. See theAnalytical modeling and Numerical modeling sections for moreetail.

CONTINUOUS GRAVITY

As stated in the Field setup and survey design section, the usualepetition rate of discrete gravity observations limits the informationbout the development rate of the underground mass redistributions,ften implying an ambiguity about the nature of the driving process-s. Furthermore, weather during winter prohibits gravity changes atummits of higher volcanoes from being identified by discrete mea-urements Carbone et al., 2003b. Using continuous gravity mea-urements helps to overcome these drawbacks and reduces the expo-ure of personnel in active areas during paroxysmal potentially dan-erous activity. See also Williams-Jones et al., 2008.

For attaining appropriate precision with continuously runningravimeters, an ideal site is easily accessible for checking the in-trumentation frequently and has small microseismic disturbancend very small temperature and pressure variations Torge, 1989.evertheless, on an active volcano, the instruments are placed where

here is the greatest chance of detecting meaningful gravity changes,hich might only be close to an active crater Branca et al., 2003;arbone et al., 2008. Conditions at such a site high altitude, inac-essibility for several months at a time, lack of electric power supply,igh peak-to-peak diurnal and seasonal temperature changes, higheismicity are far from the required standard. These constraints dic-

ate that only spring gravimeters Rymer, 1989; Budetta and Car- one, 1997 be used for the set-up because they are small easier toransport and install and need limited power can operate using en-rgy from solar panels and batteries.

Recent technological improvements allow station designs thatvercome at least some of the difficulties linked to site inadequacyCarbone et al., 2003b. However, the effect of meteorological pa-ameters De Meyer et al., 1995; El Wahaby et al., 2000 at a remotetation is unavoidable because the reduced power supply preventsse of an active system to stabilize temperature, pressure, and hu-idity. The only possibility is to continuously measure the parame-

ers that can perturb the gravimeter and to try to remove their effectrom the gravity signal afterward.

The instrumental drift can be modeled as a first-degree curve,hereas the earth-tide and tilt effects are removed from the gravity

ignal using appropriate theoretical models Carbone et al., 2003b.

he instrumental effect from ambient temperatureAmbient-temperature changes can affect the behavior of spring

ravimeters dramatically. El Wahabi et al. 1997 found that over aear, temperature changes can cause an instrumental effect noisef up to 103 Gal. Using three spring gravimeters that were installedide-by-side at a site where gravity changes of geodynamical originere not expected, And and Carbone 2004 demonstrate that the

dmittance and the phase of the instrumental effect from ambientemperature are instrument-specific. Furthermore, using recordsrom the same instrumental setup, operating in different monitoringites, And and Carbone 2006 found that the installation setup in aroad sense has an important influence on the transfer function be-ween temperature and temperature-driven changes to instruments.ffecting parameters could be the construction material of the host

ite, the type of insulation used, and/or the microclimatic conditionsf the installation site.

To investigate the relationship between the gravimeter output andmbient temperature, And and Carbone 2001, 2006 performedpectral-correlation analyses using a Matlab signal-processing tool-ox, which is based on Welchs averaged-periodogram methodWelch, 1967. They calculate the coherence function, which indi-ates how well the meter output corresponds to the temperature atach frequency, and which is given by

CxyPxy2

PxxPyy, 3

here Pxy represents cross-spectral density and Pxx and Pyy representower-spectral density. Using this approach, And and Carbone2001, 2006 found that a significant correlation coherence valueetween 0.6 and 0.8 appears just over the lowest frequencies peri-ds longer than approximately 10 days, with admittances of up to.2 mGal/C Carbone et al., 2003b.

Thus, apparent gravity changes caused by ambient-temperatureuctuations have varying character and magnitude, depending on

he temporal development and magnitude of the meteorologicalhange itself and on the characteristics of each gravimeter and instal-ation site. Accordingly, the correction formulas are frequency-de-endent and instrument/setup-specific and thus must be establishedase by case using nonlinear techniques. And and Carbone 2004emonstrate the potential for a neurofuzzy algorithm to reduce con-inuous gravity sequences for the effect of ambient temperature.owever, any fuzzy-model structure must be optimized so-calledtraining process using time series that are much longer than the

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4D volcano gravimetry WA7eriod of the influencing temperature fluctuations. In most cases, thenavailability of time sequences longer than one year implies thatnly the effect of temperature fluctuation with a period of up to a fewonths can be compensated for. Because in such cases it is not possi-

le to resolve the ambiguity affecting the longest-period componentf the gravity signals, it must be removed by using low-order poly-omial fits Bonvalot et al., 1998. This implies the risk of removinghe useful signal along with the undesired one.Agood way to min-mize the amount of useful signal that is removed is to calibrate therder of the polynomial fit by comparing the results of the filteringrocess with gravity data acquired discrete gravity measurement at aite very close to the continuously running station And and Car-one, 2001; Carbone et al., 2003b.

he instrumental effect from atmospheric pressureBesides the real gravity effect caused by the gravitational attrac-

ion of the air column and the distortion of the earths surface fromarometric changes, which is easily removable using the standarddmittance coefficient 0.365 Gal/mbar Merriam, 1992, at-ospheric-pressure changes also have been shown to induce instru-ental effects on continuously recording Scintrex CG-3M gravime-

ers. Bonvelot et al. 1998 demonstrate that the internal temperatureinside the thermostated, air-tight chamber hosting the gravity sen-or of older-aged CG-3M meters which have a less-robust acqui-ition system than later models can be affected by atmospheric-ressure changes, probably because some electronic components ofhe acquisition system are sensitive to pressure variation. Apparenthanges in internal temperature turn into apparent gravity changesecause through their own software, these instruments reduce theravity signal in real time on the basis of the recorded internal tem-erature. This shortcoming can be overcome by performing a corre-ation analysis between instrument internal temperature and atmo-pheric pressure and, if a significant correlation is found, reducinghe thermal signal for the pressure effect and recomputing the cor-ection to be applied to the gravity signal.

Bonvelot et al. 1998 also prove that atmospheric pressure can in-uce an effect on the tilt meters of Scintrex CG-3M instruments be-ause of distortion of the external enclosure of the gravimeter. Thesepparent tilt changes induced apparent gravity changes that wereower than 1 Gal Bonvelot et al., 1998 and thus are negligiblehen volcano-related gravity changes are the target.To our knowledge, gravimeters other than the Scintrex CG-3M

older models are not subject to instrumental effects from atmo-pheric pressure.

he potential of continuous gravity studiesThe difficulty of compensating the gravity signal for the effect of

mbient temperature does not unduly compromise the potential ofontinuous gravity measurement using spring gravimeters.

At Merapi volcano Java, Indonesia, Jousset et al. 2000 in-talled a gravity station 4 km from the summit, inside a temperature-ontrolled room at the Babadan observatory. When using a thermo-nsulating box to improve the gravimeter thermal isolation, tempera-ure fluctuations can be restricted to within 0.3C to 1.0C. Duringhe two-year acquisition 19931995, they show that volcano-relat-d gravity changes exceeded the instrumental noise because of tem-erature changes. Both for long terms few months and short termsfew days, they found clear correlations between residual gravity,

eismicity, and volcanic activity Jousset et al., 2000. In particular, ehey show that residual-gravity decreases corresponded to intensiveeismic activity low-frequency events and the occurrence of pyro-lastic flows. The authors concluded that internal-pressure variationaused by crystallization and gas release to the surface could explainhe gravity variations observed at Babadan, and they suggest that py-oclastic flows and dome collapse could be forecast by using contin-ous gravity monitoring.

When ambient-temperature changes cannot be restricted to an ac-eptable range e.g., because of lack of adequate facilities to host theensors, continuous gravity measurements still hold considerableotential. In fact, some authors demonstrate that the dynamics ofolcanic and hydrothermal systems can cause measurable gravityhanges over periods of between minutes and days Branca et al.,003; Carbone et al., 2006, 2008; Gottsmann et al., 2007.

Study of gravity changes that develop over short periods has twoain advantages: 1 these changes should not be affected by tem-

erature fluctuations, and 2 over short periods, the instrumentalrift of spring gravimeters exhibits an overall linear behavior Torge,989 and thus can be easily removed from the gravity time series.hort-period gravity changes are valuable both for studying the dy-amics of the systems that cause them and for forecasting paroxys-al events.At Mt. Etna Italy, a gravity sequence that encompassed the

reakout of the 2002 NE-Rift eruption was acquired at a summit sta-ion only 1 km away from the upper part of the newly forming frac-ure field Branca et al., 2003.Amarked gravity decrease of approx-mately 400 Gal in less than one hour was observed. This anomalyeversed at an even higher rate just before lava was first emitted fromhe eruptive fissures downslope William-Jones et al., 2008. Brancat al. 2003 conclude that at least a part of the gravity decrease re-ects a local mass decrease caused by the opening of the shallowracture system very close to the gravity station. This conclusionules out magma overpressure as a cause of the upper-fracture open-ng and indicates instead that magma from the central conduit en-ered the new fracture system passively, using it as a path to the erup-ive vents downslope. Thus, the gravity sequence is the only evi-ence that can inform us about the intrusive mechanism that trig-ered Mt. Etnas 2002 NE-Rift eruption.

In the framework of multiparameter geophysical experiments atisyros caldera Greece, residual gravity changes of up to 35 Gal

rom peak to peak were observed over periods of 40 to 60 minutesGottsmann et al., 2005, 2007. When cross analyzed with othervailable data ground-deformation and seismic and electromagnet-c data, these gravity fluctuations were found likely to be caused byegassing-process instabilities inducing thermohydromechanicalisturbances of the hydrothermal system. The potential for continu-us gravity studies to detect these instabilities means that throughonger experiments, the geophysical signature of such processes,hich can tip the system from background to paroxysmal activity,

an be assessed.During the 20022003 eruptions and the December 2005Janu-

ry 2006 noneruptive period, gravity changes that negatively corre-ated with the tremor amplitude were observed in the summit zone of

t. Etna Carbone et al., 2006, 2008. These changes had amplitudesf 10 to 30 Gal and occurred over periods of a few hours.

In particular, during temporary switches of the 20022003 erup-ive activity from vigorous lava fountains to mild Strombolian ex-losions, marked gravity decreases were observed at the only avail-ble summit station simultaneously with tremor-amplitude increas-

s Carbone et al., 2006 Figure 2. These changes in activity were

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WA8 Battaglia et al.ssumed to reflect collapses of the magma/gas mixture within thepper level of the system feeding the active vent. The collapsed col-mn diminished gas flow to the shallowest levels of the discharge

igure 2. During the 20022003 Mount Etna eruption, gravity decrealitude of the volcanic tremor. The joint tremor/gravity anomalies otrombolian activity. Carbone et al. 2006 interpret these anomalies

ux along the upper part of the discharge system was inhibited. See text forystem to the atmosphere, creating conditions under which a foamayer forms Jaupart and Vergniolle, 1988. By substituting denser

aterial magma, a foam layer can induce a local mass gravity de-

ting a few hours were observed simultaneously with increases in am-d during temporary switches from vigorous lava fountains to mildg caused by accumulations of foam layers during periods when gass

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4D volcano gravimetry WA9rease. It also can radiate seismic energy by coupled oscillations ofhe bubbles inside it. Growth of a foam layer thus could explain thebserved joint gravity/tremor anomalies Figure 2.

During the December 2005January 2006 noneruptive period,remor amplitude at Mt. Etna increased and negatively correlatedith the gravity signal from one of the two summit stations thatorked during that period, over 2- to 3-hour fluctuations Carbone

t al., 2008. No correlation was found with the signal from the otherravity station. In this case, by relying on the relative position of thewo stations, it was possible to define the volume that contained theravity source. During the period of marked anticorrelation, theremor source located by inverting the spatial distribution of seis-

ic amplitudes intersected this volume, lending support to the hy-othesis that the anticorrelation marked the activation of a joint-ource process. Relying on independent information, Carbone et al.2008 suggest that this process was related to the arrival of freshagma and the consequent gas separation, implying that the anticor-

elated tremor/gravity anomalies were indicative of a system thatas becoming progressively enriched in volatiles.

ANALYTICAL MODELING

Analytical models offer a closed-form description of the source ofolcano unrest. This means that in principle, we readily may inferhe relative importance of any of the source parameters. In activeolcanic sites such as Long Valley caldera California, U.S.A. andampi Flegrei Italy, careful use of analytical models and high-uality data sets has produced good results. However, simplifica-ions e.g., the assumption that the crust is a homogenous, isotropic,lastic medium that make analytical models tractable can lead toisleading volcanological interpretations, particularly in the case of

tructural discontinuities Fernndez and Rundle, 1994; Gudmunds-on, 2006; Folch and Gottsmann, 2006. Constructing more-realisticcomplex models using numerical techniques requires introducingore model parameters. See the Numerical modeling section.he limited geodetic and gravity measurements available for mostolcanoes might not provide the resolution needed to discriminatelearly between simple analytical models and more-complex nu-erical models for sources of volcano unrest. See also De Natale

nd Pingue, 1996; Dvorak and Dzurisin, 1997; Dzurisin, 2003; Gud-undsson, 2006; and Lisowsky, 2006.Further complication arises if mass movement at depth does not

ause ground deformation, such as with saturation of a permeableedium. There are cases of significant residual gravity changesithout significant ground deformation and vice versa Rymer et al.,993; Carbone et al., 2003a, as well as of nonlinear relationships be-ween gravity and deformation over a survey area Gottsmann et al.,006a, 2006b. These relationships sometimes are difficult to inter-ret Battaglia and Segall, 2004, but several studies Fernndez andundle, 1994; Tiampo et al., 2004 suggest that gravitational cou-ling effects might be fundamental to explaining gravity changes atctive volcanoes.

We present some of the analytical models that can be used to studynrest at central volcanoes and calderas that is caused by pressuriza-ion of magma or hydrothermal reservoirs at depth. The most com-

on source geometries used to study this kind of deformation ap-roximate the pressurized reservoir as a spherical, cigarlike, sill-

ike, or dike-like body. ahe spherical magma chamber

The deformation caused by an expanding or contracting magmahamber has been modeled often using a dilatation source in an elas-ic half-space. Mogis point source McTigue, 1987 most common-y is used. The model simulates a small spherical expansion sourcembedded in a homogeneous, isotropic, Poisson-solid half-spaceFigure 3a. The appeal of Mogis model is its combination of com-utational simplicity and remarkable ability to fit real data quite welln many cases. However, the accuracy of an interpretation based on

ogis model is subject to the validity of the assumptions e.g., theource depth is significantly larger than its radius, the land surface isat, Poissons ratio 0.25, the crust is linearly elastic, and theole of pore fluids is negligible, an often-overlooked considerationMasterlark, 2007. For example, Mogis point-source model canxplain stresses and displacements that are far from the chamber, butt the source, the stresses diverge to infinity. McTigues 1987 for-ulation provides an analytical solution that includes higher-order

erms taking into account the finite shape of a spherical body. Thus,he local stresses at and away from the chamber boundary can be cal-ulated. McTigues 1987 results for vertical deformation uz and ra-ial deformation ur from a pressurized P spherical magma cham-er of radius b and depth d Figure 3a can be written in the form

igure 3. Geometry and parameters for source models. aA spheri-al source is described by four parameters: two for location x0,y0,epth d, and volume change V. b Prolate spheroids need sevenarameters: two for location x0,y0, depth d, volume changeV, as-ect ratio A, dip angle , and strike angle . cA horizontal sill-likeource is determined by five parameters: two for location x0,y0,epth d, volume change V, and radius b. d A dike is representedy six parameters: two for location x0,y0, depth d, rectangular faultength L and width W, and dip angle . We can represent the strike-lip along the fault by the dislocation vector U1, the dip-slip by U2

nd the tensile opening component by U3 after Okubo, 1992.

aw

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WA10 Battaglia et al.uz 1 Pb3

dr2 d23/2

1 bd3 1 27 5 152 47 5 d2r2 d24

nd

ur uzr

d, 5

here is Poissons ratio, is the shear modulus, and r is the hori-ontal distance between the vertical projection of the source centernd the observation point. The change in volume of the body V isb3P/. McTigues 1987 equations 4 and 5 reduce to Mogis

oint-source formulation when b/d1.Adirect consequence of thessumption of point of dilatation is that the magma chamber radius bnd pressure change P are inseparable in both the Mogi and thecTigue model becausePb3 is the strength of the point singularity

McTigue, 1987.The gravitational attraction of a spherical magma chamber of fi-

ite size and mass m V, where is magma density, is identicalo that of a point magma chamber with the same mass m:

gz GVd

r2 d23/2, 6

here G is the universal gravitational constant. If the point-sourcepproximation holds and the water table and deformation effects areeglected, then equations 4 and 6 can be combined to get a linear re-ationship for the density of the intrusion Eggers, 1987:

1

G guz , 7here 308.6 Gal/m is the free-air gradient.

ipelike sourcesA simple model of a volcanic system includes two principal ele-ents: a magma reservoir and a conduit through which the magma

an reach the surface. When the volcano is quiescent, the conduitloses, allowing pressure buildup in the reservoir. The surface-de-ormation pattern caused by a cigar-shaped magma chamber is quiteifferent from that from a spherical reservoir. Yang et al. 1988 for-ulated a model for a pressurized cigar-shaped magma body Figure

b. They found an approximate but very accurate solution for a dip-ing prolate ellipsoid in an elastic half-space using a half-space dou-le force and center-of-dilatation solutions. Newman et al. 2006eported minor corrections to the Yang et al. 1988 analytical mod-l. Whereas the expressions in the near field are quite complex, thequations for the surface deformation for a vertical prolate ellipsoidecome relatively simple in the far field when the radial distance r isuch larger than semiminor axis of the ellipsoid:

uzab2

d21 2P* 2P3 3d2P5 83 R RUnd

urab2

3r21 2P* 2PR3 3d2PR5 , 9

here a and b are the semimajor and semiminor axes of the ellipsoid,espectively; P* and P are proportional to the pressure change PYang et al., 1988, p. 4250; and R2 r2 d2. The expression forhe volume change of a pressurized spheroid is V ab2P/Tiampo et al., 2000. The general solution for a prolate spheroid de-ends on seven parameters Figure 3b:P; the geometric aspect ra-io A b/a between the semimajor axis a and the semiminor axis b;hree parameters for the source location x0,y0,d; the dip angle ;nd the azimuth angle , measured clockwise from the positiveorth direction.

The observed residual-gravity component for a prolate spheroidf density is

gz GV3z f1 sin 1.5y f2 cos 10Clark et al., 1986, where the subscript indicates the coordinatesith respect to the principal axes of the spheroid Figure 3b. Note

hat for a vertical prolate spheroid 90, equation 10 reduces to

gz 3GVdf1. 11xpressions for functions f1 and f2 are inAppendix A.

illsSill-like magma intrusions or chambers can be represented by fi-

ite, pressurized, horizontal, circular cracks Fialko et al., 2001Figure 3c. The exact expressions of Fialko et al. 2001 are appro-riate for a sill-like source whose radius is up to five times greaterhan its depth. The expression for surface displacements has the form

uj

0

1

Kr,tt Kr,t tdt j r,z ,

12

here K, K , and are given in equation 27 and Appendix B ofialko et al. 2001.We can approximate the gravity changes caused by a sill-likeass by using a degenerate oblate spheroid seeAppendix A:

g

z

3GMdb3 tan1 b

b

. 13

ikesArectangular, tensile dislocation source that is based on an analyt-

cal expression developed by Okada 1985 for ground displace-ents and one by Okubo 1992 for gravity changes can be used to

epresent the crustal deformation and gravity changes associatedith dike intrusion Okubo et al., 1991; Furuya et al., 2003a.The dike can be approximated by using a rectangular fault of

ength L and width W with dip angle at a depth d in a homoge-eous, isotropic, elastic half-space Figure 3d. We can represent thetrike slip along the fault by the dislocation vector U1, the dip slip by2, and the tensile opening component by U3 Figure 3d. Okada

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4D volcano gravimetry WA111985 gave formulas for the displacement for this fault model sohat the vertical fault displacement hfault can be easily estimated.ollowing the approach of Okubo et al. 1991, the gravity changesaused by faulting on a rectangular plane are

gfaultx,y cGU1 Sg , U2 Dg ,

U3 Tg , GU3 Cg ,

hfaultx,y , 14

here c is the density of the crust, c is the differenceetween the intrusion density and the crust density, and hfault ishe free-air effect. Appendix A contains complete mathematical ex-ressions for the functions in equation 14.

ravity/height gradientsGravity-height analysis also is a straightforward way to assess

ubsurface dynamics. Several applications and theoretical consider-tions of gravity-height signatures at active volcanoes were reportedn Rymer and Williams-Jones 2000, Gottsmann and Rymer 2002,ottsmann et al. 2003, and Gottsmann et al. 2006a.Gravity and height changes are theoretically inversely correlated.positive change in surface elevation inflation causes a net grav-

ty decrease, expressed by the free-air gravity gradient . Ideally, ill be measured directly because conclusions drawn from gravity

hanges caused by subsurface processes might be less meaningful ifhe value of the real free-air gradient deviates substantially from theheoretical gradient T. Alternatively, if the local density anomaly isssumed to be caused by a point source, the local free-air gradient aan be estimated from static gravity data Rymer, 1994:

a Tgb2z 1

z 1215

heregb is the maximum amplitude of the Bouguer anomaly and zs the depth of the point source. At the Campi Flegrei caldera, for ex-mple, the calculated local gradient a matched the measured gradi-nt within error Berrino et al., 1984; Berrino, 1994.

Gravity-height data that deviate from the theoretical gradient Tust be interpreted in terms of subsurface mass changes. No mass

hange is required for data that fall on this gradient, but a subsurfaceensity change is necessary. If there is a mass change but no densityhange, the gravity-height data will follow the Bouguer-correctedradient BC. The value of the corrected gradient BC depends onhe density , the geometry of the source, and the value of the mea-ured gradient Rymer, 1994.

Fernndez et al. 2005 described a method for computing and in-erpreting gravity and height changes and vertical gravity gradientsroduced by magmatic intrusions in a layered elastic-gravitationaledium Rundle, 1982; Fernndez and Rundle, 1994. The theoreti-

al elastic-gravitational model allows computation of geometric andrthometric vertical displacements and different types of gravityhanges, as well as of the corresponding vertical gravity gradients.heir results showed that these gradients are useful for obtaining in-

ormation about the dynamics of the injection processes, includingetection of new magmatic intrusions and source-depth changes. Bysing the elastic-gravitational deformation model, they could ex-lain nonlinear gravity-height relationships that appear in volcanicreas. Fernndez et al. 2005 successfully used this method to inferhe intrusion of new magma beneath Mayon volcano Philippines.

heir inference was confirmed when Mayon volcano erupted in July c006. Gottsmann et al. 2006a applied this methodology to obser-ations at Campi Flegrei caldera to test source multiplicity.

ong Valley calderaCareful use of analytical models and high-quality data sets can

roduce reasonable results. For example, through the combined usef geodetic and gravity data, Battaglia et al. 2003a, 2003b wereble to constrain the density of the intrusion beneath the Long Valleyaldera resurgent dome. Their work provided guidelines for severalroblems that are common to volcano geodesy: 1 measuring theplift by differencing GPS-based and leveled orthometric heights;2 determining a unique geometry for the source e.g., Dietrich andecker, 1975; and 3 obtaining realistic estimates of the source pa-

ameters uncertainties. For example, the standard approach of fit-ing the data to a point source will produce biased results if the trueource does not possess spherical symmetry. Therefore, Battaglia etl. 2003a used a combination of vertical and horizontal geodeticeasurements GPS, leveling, and line-length data to find the best-tting source geometry, in their case, a vertical prolate ellipsoid.hen that source geometry had been uniquely determined, they per-

ormed a joint inversion of the uplift and gravity data to infer the vol-me and mass of the source, and completed a statistical analysiso assess the impact of data uncertainties on the density Battagliat al., 2003b. The sources estimated density range was 1180g/m3 to 2330 kg/m3. Because this density range is too high for hy-rothermal fluids to be the sole source of uplift at Long Valley, theuthors concluded that a silicic magma body or a combination ofagma and hydrothermal fluids must have produced the observed

eformation.

NUMERICAL MODELING

In volcanology, numerical models have been developed mostly toompute displacements produced by magmatic intrusions into elas-ic Dietrich and Decker, 1975; Cayol and Cornet, 1998; Williamsnd Wadge, 2000; Bonaccorso et al., 2005; Lungarini et al., 2005 oriscoelastic media Folch et al., 2000; Trasatti et al., 2003. Most ofhese studies account for the effect of topography and rheologicaleterogeneities on deformation. However, a few studies apply nu-erical methods to model deformation and gravity changes pro-

uced by magma intrusions, using 3D indirect boundary elementethod IBEM Charco et al., 2007c or finite-element method

FEM Currenti et al., 2007.

he effect of topographySeveral studies on the topographic effect McTigue and Stein,

984; McTigue and Segall, 1988; Cayol and Cornet, 1998; Williamsnd Wadge, 1998; 2000; Folch et al., 2000; Charco et al., 2002; Tra-atti et al., 2003; Lungarini et al., 2005 support the conclusions thatopography has a significant effect on the deformation field and thatn many cases the flat half-space approximation could lead to errone-us interpretation of observed ground deformation.

When computing volcanic loading effects, coupling betweenravity and elasticity is negligible for displacements in the spatialcale associated with volcano monitoring, but the absolute effects ofhe existing gravity field become important when rigidity decreasesi.e., viscoelastic media Fernndez et al., 1997; Battaglia and Seg-ll, 2004; Charco et al., 2006. Coupling is a second-order effect that

annot be ignored in flat half-space models when a mass source term

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WA12 Battaglia et al.see, e.g., Rundle, 1980, 1982; Fernndez and Rundle, 1994;ernndez et al., 2001a, 2001b; Fernndez et al., 2006 represents

he emplacement of magma at some depth. The mass and its interac-ion with the surrounding medium can vary the pattern of gravityhange and produce measurable gravity anomalies. Thus, elastic-ravitational half-space models can provide a suitable approxima-ion to problems of volcanic loading in areas where topographic re-ief is negligible. For prominent volcanoes, the rough topographyas greater effect than does self-gravitation Charco et al., 2007a,007c. In these cases, self-gravity can be ignored, whereas the topo-raphic effect on displacements and gravity changes must be com-uted.

Starting from these theoretical results, Charco et al. 2007b com-uted displacement and gravity changes produced by volcanic load-ng internal loading produced by pressure and mass changes. Toepresent the displacement field that was perturbed by 3D topo-raphic features, they used a single-layer boundary integral derivedrom Bettis reciprocal theorem and the solution to Kelvins problemf a point load in an infinite body Snchez-Sesma and Luzn,995. Accounting for topographic effects, they computed the sur-ace gravity change gs as

gs uzp uzmGMc

R3, 16

here is the free-air gradient; uzp is the vertical displacementaused by a massless cavity pressure source; uzm is the vertical dis-lacement produced by a constant-volume pressureless massource see Figure 1b; R x s12 y s22z c21/2,ith x, y, z being the coordinates of the calculation point and

s1,s2,c being the coordinates of the source point magma intrusion; and c c zx,y, where c is the source depth below mean

ea level and zx,y is a function of the computation-point horizontalocation that represents the elevation above mean sea level. In thispproach, topographic contributions to the gravity changes are im-lemented numerically through the change in vertical displacementnd by considering the variation of the gravitational attraction of theass.

Charco et al. 2007b carried out several theoretical tests and ap-lied the numerical model to Teide volcano Tenerife, Canary Is-ands, taking into account the real topography represented by a dig-tal elevation model. They showed that the magnitude and the pat-ern of the gravity signals are significantly different from those ofalf-space solutions, as is the case for displacement. Figure 4 showsome of the results obtained by Charco et al. 2007b for Teide volca-o.

he effects of heterogeneitiesCurrenti et al. 2007 used FEM to model ground deformation and

ravity changes produced by volcanic-pressure sources and to in-estigate the effects of topography and medium heterogeneities. Bypplying finite-element analysis, they were able to account for theeal topography and elastic heterogeneities and thus to appraise theirffects on the computed fields. Currenti et al. 2007 defined theravity changes caused by pressure changes as

g g0 g1 g2 g3, 17

here g0 represents the free-air gravity change, g1 arises fromisplacements of density boundaries in heterogeneous media, g2

enotes the contribution of the inflation source, andg3 is the contri- gution to the gravity change from density variations in the surround-ng medium. The authors stress that gravity changes cannot be inter-reted in terms of additional mass input only, disregarding the defor-ations of the surrounding rocks Bonafede and Mazzanti, 1998;harco et al., 2007b.Currenti et al. 2007 solved the model equations in two steps.

irst they solved the deformation field in terms of elastostatic-equi-ibrium equations, computing displacement and stress fields. Thenhey computed the solution for the coupled problem for the gravityeld, in which the solutions of the deformation field are used to com-ute g1, g2, and g3 contributions. They ran theoretical tests tond ground-deformation and gravity-field discrepancies betweenesults from analytical expressions Hagiwara, 1977, which disre-ard topography, elastic heterogeneities, and density subsurfacetructures, and results from numerical modeling, which takes thesearameters into account.

Currenti et al. 2007 also review the gravity changes and groundeformation at Mt. Etna during the 19931997 period, assuming anllipsoidal pressure source expanding in a heterogeneous mediumith real topography. They show that heterogeneity and topography

ngender deviations from analytical results for a homogeneouslane medium. They also found that perturbations are more evidentn the presence of severe heterogeneities and steeper topography, ass the case for the volcanos summit. Charco et al. 2007b obtained aimilar result for topographic effects and previous models for defor-ation Williams and Wadge, 1998. Currenti et al. 2007 found

hat elastic heterogeneity affects only the magnitude of the anoma-ies, whereas topography greatly changes anomaliesmagnitude andhape, especially in theg1 contribution. They show that neglectingayering and topography leads to underestimation of elevation andravity changes. One limitation of their work is that they only con-ider pressure changes as the source of unrest; they ignore the effectf the mass of the magmatic intrusion on the geodetic signature.ernndez and Rundle 1994 and Fernndez et al. 1997 obtainedimilar results on medium heterogeneity for point sources and lay-red media.

Elisa Trasatti and Maurizio Bonafede personal communication,008 used FEM to investigate gravity changes and uplift at Campilegrei. First they computed displacement and strain fields. Then

hey used the results to integrate the gravity variations numerically.hey separate the observed gravity change into parts that correspond

o the elevation change free-air gravity change gFA and that wereroduced by mass redistribution residual gravity changegR:

g gFA gR. 18

With similar considerations to Currenti et al. 2007, they ex-ressed residual gravity change as

gR gs gM gs gV gL, 19

heregs depends on the density change related to the introductionf new mass,gM is the contribution from deformation of the medi-m that surrounds the source, gV depends on the finite compress-bility of rocks and vanishes if the medium is incompressible, andgL is produced by density changes within the medium and accounts

or the nonhomogeneities of the medium. The expression forgL de-ends on whether the material density varies continuously or discon-inuously in the reference configuration.

E. Trasatti and M. Bonafede personal communication, 2008 be-

an by considering a homogeneous, elastic, isotropic medium, and

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4D volcano gravimetry WA13ater introduced density or rigidity variations and inelastic models.hey also considered different source geometries Mogi sources,pheroid, and sill. Their results confirm previous results regardinghe control that the source geometry has on the deformation Dieter-ch and Decker, 1975. Nonspherical sources yield positive and neg-

a)

b)

c)

f)

d)

)tive gravity changes corresponding to sill and spheroid, respec-ively without input of new mass. E. Trasatti and M. Bonafede per-onal communication, 2008 pointed out the importance that sourcehape and the mediums characteristic has for gravity calculationnd source-density estimation.

Figure 4. a Mesh of the Tenerife ground surface,formed by 2902 circular and flat elements that cov-er the whole island, and surface gravity change gscaused by a center of dilatation of 50-MPa km3strength. Subplots b through f are gravity calcu-lations, computed as follows: b using IBEM forthe source located at 4 km below the Teide volcanosummit, approximately 300 m below sea level; cusing the analytical Mogi model, in which the topof the half-space is at sea level and the topographyof Tenerife Island is neglected completely; d us-ing the analytical Mogi model and assuming a ref-erence elevation of 2700 m above sea level; e us-ing the analytical Mogi model with the top of thehalf-space at 3718-m height, which is the Teidevolcano height; and f approximating the island asan axisymmetrical cone with a height equal to thatof the Teide volcano and with average slope of theflanks of 16.5. In the last case, IBEM was used andthe mesh was made up of 2561 circular elements. Itcan be seen that characteristics pattern and magni-tude of the gravity variation field are very differentwhen considering flat surface and topography. Themain difference between real and approximate to-pography consideration is the pattern of the gravityvariation. Horizontal coordinates for panels bthrough f are UTM coordinates in meters modi-fied from Charco et al., 2007a.a

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WA14 Battaglia et al.DISCUSSION

Microgravity observations furnish valuable information aboutolcanic processes that precede large eruptions and/or potentiallyangerous paroxysms. Because it is linked intimately to the redistri-ution of underground masses, this information often is difficult toetrieve with other geophysical and geochemical techniques.

Microgravity observations at active volcanoes usually are con-ucted through repeated discrete measurements along an array oftations in the zone of interest and one or a few reference stationsutside the active area. To be most suitable, a station network muste designed to satisfy the needs of monitoring programs. It also ismportant to rigorously apply the best strategies for reducing the ef-ects in the gravity data that are related to instrumental drift, earthide, ocean load, and water table.

Over the past few decades, analytical solutions have been derivednd widely used to model the source mechanisms of volcano-relatedravity changes. The potential for applying these formulations isreatly enhanced if gravity data are analyzed and interpreted jointlyith simultaneous ground-deformation data. Phenomena-inducingnrest can be constrained regarding both the mass that is added to orithdrawn from the system and the stress that is induced in the medi-m that surrounds the source and that eventually is transmitted to theround surface.

Because no one solution addresses how best to track mass varia-ions beneath volcanoes, each case needs dedicated analysis. Ob-erved gravity changes must be considered within the general con-ext of available volcanological and geological observations. Thisacilitates choosing the most appropriate analytical formulation toescribe the driving mechanism and thus helps in making assump-ions about the shape of the source and the nature of the driving

echanism, based on other scientific evidence. The source parame-ers size, position, amount and density of the redistributed mass,tc. are then retrieved by fitting observed and calculated datahrough an appropriate inversion scheme. Many studies have provedhat this approach can supply unique insights into the processes thatead to unrest e.g., Battaglia et al., 2003b; Berrino, 1994; Bonafedend Mazzanti, 1998; Branca et al., 2003; Charco et al., 2007c; Cur-enti et al., 2007; Eggers, 1987; Fernndez et al., 2001b; Furuya etl., 2003b; Gottsmann et al., 2005; Jachens and Roberts, 1985; Jous-et and Okada, 1999; Okubo et al., 1991; and Rymer, 1994.

Major shortcomings of this approach are that the wrong modelight be used to fit the observed data because different elastic mod-

ls can produce similar effects, and that the simplifications e.g., thessumption that the crust is a homogenous, isotropic, elastic medi-m that make analytical models tractable can yield misleading vol-anological interpretations.

More realistic complex models can be obtained by using numer-cal techniques, which allow the effects of topography and of medi-m heterogeneities to be accounted for at the cost of introducingore model parameters. It is worth stressing that the limited extent

nd density of the measurements usually available at most volcanoesoes not provide adequate resolution to clearly discriminate be-ween results from simple analytical models and more-complex nu-

erical models. Thus, numerical models can be very useful for re-earch but might be limited in their operative use during volcano-onitoring programs because of inherent complexities that prevent

heir straightforward and generic incorporation for inversion inter-

retation of observed deformation and gravity changes. aCampaign microgravity measurements also have intrinsic limita-ions related to data aliasing. Because temporal resolution of caus-tive processes are two times the occupation interval Nyquist fre-uency, which usually ranges from months to years, temporal char-cterization of causative source processes might be ambiguous.ince the 1990s, to overcome this restriction, continuous gravityeasurements have been performed at active volcanoes. However,

he cost of gravimeters tens of thousands of dollars has preventedeployment of extended arrays of continuous gravimeters.

Furthermore, the strong instrumental effect that is driven by atmo-pheric effects often prevents resolution of the ambiguity that affectshe longest-period component of the gravity signal acquired bypring gravimeters. Thus, continuous gravity measurements aresed either to integrate campaign data or to evidence quick changesperiods of minutes to days linked to gas/fluid/magma dynamicsver the shallowest part of the plumbing system. This implies that asf now, rather than quantifying the spatial evolution of gravity varia-ions, the useful information that continuous gravity measurementsan assess is the temporal evolution of fast-developing anomalies atne or a few sites close to the active structures. This information isncreasingly acquired at some volcanoes; its rigorous interpretationequires new analytical and numerical models that account for thepatiotemporal evolution of volcanic systems.

CONCLUSIONS

Microgravity studies at active volcanoes can detect states of un-est with a degree of detail that other techniques cannot achieve. Re-rievable information includes not only the source position and themount of mass redistributed, but also the density of the materialriggering the unrest and thus the nature of the causative source. Asuch, processes triggered by magma movements can be distin-uished from mechanisms that are linked to the dynamics of gas orydrothermal fluids. Enhancing the capabilities of this techniqueill require efforts on both the instrumental and the modeling as-ects.

Once they become available, fully portable, low-energy-con-umption and low-cost absolute gravimeters will make time-lapseicrogravity surveys much more effective and easier to accomplish.n large volcanoes such as Mt. Etna, operators using absolute in-

truments will not be forced to reach stable reference stations thatre far from the active areas, at the cost of propagating-measurementrrors and greatly increasing measurement time. On small islandsuch as Montserrat and Stromboli, using an absolute gravimeterould overcome the potential reference instability when situated too

lose to the active zone. Even with absolute meters, it is ideal to haveeference stations because there could be a larger background signalhat could be aliased into a survey, such as postglacial rebound, thatould be critical to quantify with a reference network.Development of low-cost gravimeters possibly not based on the

pring-mass system that are easily installable under harsh volcaniconditions and unaffected by ambient-temperature changes wouldromote wider use of continuous gravity measurements, which de-pite their promising potential still are not widely used as a volcano-onitoring tool.Regarding data modeling, efforts are needed toward finding com-

romises between computational speed and precision in quantifyingass redistributions within volcanic systems to integrate numericalodeling into volcano-monitoring programs. Simulation schemeslso are needed to evaluate the gravity effect in terms of maximum

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4D volcano gravimetry WA15mplitude, duration, and time evolution associated with fast-evolv-ng volcanic processes such as convection, bubble growth, degas-ing, and aqueous-fluid migration.

ACKNOWLEDGMENTS

Maurizio Battaglia was supported by project Rientro dei Cerv-lli funded by the Italian Ministry of Higher Education and Re-earch and the U.S. Geological Survey, Volcano Hazards Team.oachim Gottsmann was supported by a University Research Fel-owship and an International Joint project, both from the Royal Soci-ty, and by National Environmental Research Council NERC grantE/E007961/1. Research by Jos Fernndez has been supported by

esearch project GEOMOD CGL2005-05500-C02, funded by thepanish Ministry of Education and Science MEC. Comments by

he editor, P. Gettings,A. Tikku, and an anonymous reviewer greatlymproved the manuscript.

APPENDIX A

MODELING GRAVITY RESIDUALS

rolate spheroid

The observed residual-gravity component for a prolate spheroidf density is Clark et al., 1986

g

z 3GMz f1, gy 1.5GMy f2,

g

x 1.5GMx f2,

f11

a2 b21.5a2 b2a2 0.5 log a2 b20.5 a2 0.5b2 0.5

f21

a2 b21.5log a2 b20.5 a2 0.5b2 0.5

a2 b20.5a2 0.5

b2 , A-1here is the largest real root of cubic equation

z

2

a2 s

r

2

b2 s 1, r

2 x

2 y

2 A-2

r

s3 p2s2 p1s p0 0, A-3

here

p2 a2 2b2 z

2 r

2,

p1 2a2b2 b4 2b2z

2 a2 b2r

2,

p0 a2b4 b4z

2 a2b2r

2. A-4

The observed vertical component of the gravity acceleration re-

idual gravity isgz g

z sin g

y cos

GV3z f1 sin 1.5y f2 cos . A-5ote that for a vertical prolate spheroid 90, equation A-5 re-uces to

gz 3GVd f1, A-6hereas the observed gravity for a horizontal prolate spheroid

0 is

gz 1.5GVd f2. A-7

blate spheroidWe can use a degenerate oblate spheroid to approximate gravity

hanges caused by a sill-like mass Clark et al., 1986:

g

z

3GMzdb2 a21.5tan1b2 a2a2 0.5 b2 a2a2 0.5

A-8

n the limit of a/b0, equation A-8 reduces to

g

z

3GMdb3 tan1 b

b

. A-9

gain, is the largest real root of the cubic equation A-3.

ikeFollowing the approach of Okubo et al. 1991, the gravity chang-

s caused by faulting on a rectangular plane are

gfaultx,y cGU1 Sg , U2 Dg ,

U3 Tg ,

GU3 Cg , hfaultx,y ,A-10

here c is density of the crust, c is the difference be-ween the intrusion density and the density of the crust, and hfaults the free-air effect. The symbol in equation A-10 stands for thehimneys notation:

f , fx,p fx,pW fx L,p fx L,pW , A-11

here p is related to x2 by

p y cos d sin . A-12

Sg,Dg,Tg,Cg in equations 14 and A-10 are given by

Sg ,q sin

R

q2 cos RR

, A-13

Dg , 2I2 ,sin

q sin q cos

, A-14

RR

aT

w

q

a

A

A

B

B

B

B

B

B

B

B

B

B

B

B

B

C

C

C

C

C

C

C

C

C

C

C

C

D

D

D

D

D

E

E

F

F

F

F

WA16 Battaglia et al.Tg , 2I2 ,cos

q cos q sin

RR

q

RR , A-15

nd

g , 2I2 ,cos sin logR , A-16here

y sin d cos , R 2 2 q2 A-17nd

I2 , tan1R q . A-18REFERENCES

nd, B., and D. Carbone, 2001, Amethodology for reducing a continuouslyrecording gravity meter for the effect of meteorological parameters: IEEETransactions on Instrumentation and Measurements, 50, 12481254., 2004, A test on a neuro-fuzzy algorithm used to reduce continuousgravity records for the effect of meteorological parameters: Physics of theEarth and Planetary Interiors, 142, 3747., 2006, A new computational approach to reduce the signal from con-tinuously recording gravimeters for the effect of atmospheric temperature:Physics of the Earth and Planetary Interiors, 159, 247256.

rnoso, J., M. Benavent, B. Ducarme, and F. G. Montesinos, 2006, A newocean tide loading model in the Canary Islands region: Journal of Geody-namics, 41, 100111.

attaglia, M., and P. Segall, 2004, The interpretation of gravity changes andcrustal deformation in active volcanic areas: Pure and Applied Geophys-ics, 161, 14531467.

attaglia, M., P. Segall, J. Murray, P. Cervelli, and J. Langbein, 2003a, Themechanics of unrest at Long Valley caldera, California: 1. Modeling thegeometry of the source using GPS, leveling and 2-color EDM data: Journalof Volcanolological and Geothermal Research, 127, 195217.

attaglia, M., P. Segall, and C. Roberts, 2003b, The mechanics of unrest atLong Valley caldera, California: 2. Constraining the nature of the sourceusing geodetic and micro-gravity data: Journal of Volcanology and Geo-thermal Research, 127, 219245.

attaglia, M., C. Troise, F. Obrizzo, F. Pingue, and G. De Natale, 2006, Evi-dence for fluid migration as the source of deformation at Campi Flegreicaldera Italy: Geophysical Research Letters, 33, L01307, doi: 10.1029/2005GL024904.

errino, G., 1994, Gravity changes induced by height-mass variations at theCampi Flegrei caldera: Journal of Volcanology and Geothermal Research,61, 293309.

errino, G., G. Corrado, G. Luongo, and B. Toro, 1984, Ground deformationand gravity changes accompanying the 1982 Pozzuoli uplift: Bulletin ofVolcanology, 47, 187200.

errino, G., and U. Riccardi, 2001, Gravity tide at Mt. Vesuvius southern It-aly: Correlations with different geophysical data and volcanological im-plications: Journal of the Geodetic Society of Japan, 47, 121127.

onaccorso, A., S. Cianetti, C. Giunchi, E. Trasatti, M. Bonafede, and E.Boschi, 2005, Analytical and 3-D numerical modelling of Mt. Etna Italyvolcano inflation: Geophysical Journal International, 163, 852862.

onafede, M., and M. Mazzanti, 1998, Modelling gravity variations consis-tent with ground deformation in the Campi Flegrei caldera Italy: Journalof Volcanological and Geothermal Research, 81, 137157.

onvalot, S., M. Diament, and G. Gabalda, 1998, Continuous gravity record-ing with Scintrex CG-3M meters: A promising tool for monitoring activezones: Geophysical Journal International, 135, 470494.

oy, J.-P., J. Hinderer, and P. Gegout, 1998, Global atmospheric loading andgravity: Physics of the Earth and Planetary Interiors, 109, 161177.

ranca, S., D. Carbone, and F. Greco, 2003, Intrusive mechanism of the 2002NE-Rift eruption at Mt. Etna Italy inferred through continuous micro-gravity data and volcanological evidences: Geophysical Research Letters,30, doi: 10.1029/2003GL018250.

udetta, G., and D. Carbone, 1997, Potential application of the Scintrex CG-

3M gravimeter for monitoring volcanic activity: Results of field trials on FMt. Etna, Sicily: Journal of Volcanology and Geothermal Research, 76,199214.

arbone, D., G. Budetta, and F. Greco, 2003a, Bulk processes some monthsbefore the start of the 2001 Mt. Etna eruption, highlighted through micro-gravity studies: Journal of Geophysical Research, 108, doi: 10.1029/2003JB002542.

arbone, D., G. Budetta, F. Greco, and H. Rymer, 2003b, Combined discreteand continuous gravity observations at Mount Etna: Journal of Volcanolo-gy and Geothermal Research, 123, 123135.

arbone, D., L. Zuccarello, and G. Saccorotti, 2008, Geophysical indicationsof magma uprising at Mt. Etna during the December 2005 to January 2006non-eruptive period: Geophysical Research Letters, 35, L06305, doi:10.1029/2008GL033212.

arbone, D., L. Zuccarello, G. Saccorotti, and F. Greco, 2006, Analysis of si-multaneous gravity and tremor anomalies observed during the 2002-2003Etna eruption: Earth and Planetary Science Letters, 245, 616629.

ayol, V., and F. Cornet, 1998, Effects of topography on the interpretation ofthe deformation field of prominent volcanoes: Application to Etna: Geo-physical Research Letters, 25, 19791982.

harco, M., L. Brimich, and J. Fernndez, 2002, Topography effects on thedisplacements and gravity changes due to magma intrusion: GeologicaCarpathica, 53, 215221.

harco, M., J. Fernndez, F. Luzn, and J. B. Rundle, 2006, On the relativeimportance of self-gravitation and elasticity in modelling volcanic grounddeformation and gravity changes: Journal of Geophysical Research, 111,B03404, doi: 10.1029/2005JB003754.

harco, M., J. Fernndez, F. Luzn, K. F. Tiampo, and J. B. Rundle, 2007a,Some insights about topographic, elastic and self-gravitation interaction inmodelling ground deformation and gravity changes in active volcanic ar-eas: Pure andApplied Geophysics, 164, 865878.

harco, M., F. Luzn, J. Fernndez, and K. F. Tiampo, 2007c, Topographyand self-gravitation interaction in elastic-gravitational modeling: Geo-chemistry, Geophysics, Geosystems G3, 8, Q01001, doi: 10.1029/2006GC001412.

harco, M., F. Luzn, J. Fernndez, K. F. Tiampo, and F. J. Snchez-Sesma,2007b, Three-dimensional indirect boundary element method for defor-mation and gravity changes in volcanic areas: Application to Teide volca-no Tenerife, Canary Islands: Journal of Geophysical Research, 112,B08409, doi: 10.1029/2006JB004740.

lark, D. A., S. J. Saul, and D. W. Emerson, 1986, Magnetic and gravityanomalies of a triaxial ellipsoid: Exploration Geophysics, 17, 189200.

urrenti, G., C. Del Negro, and G. Ganci, 2007, Modelling of ground defor-mation and gravity fields using finite element method: An application toEtna volcano: Geophysical Journal International, 169, doi: 10.111/j.1365246X.2007.03380.x.

e Meyer, F., B. Ducarme, A. Elwahabi, G. Berrino, and H. Rymer, 1995,Continuous gravity observations at Mount Etna Sicily: Presented at the21st GeneralAssembly, IUGG.

e Natale, G., and F. Pingue, 1996, Ground deformation modeling in volca-nic areas, in R. Tilling and R. Scarpa, eds., Monitoring and mitigation ofvolcano hazard: Springer, 385389.

ieterich, J. H., and R. W. Decker, 1975, Finite element modeling of surfacedeformation associated with volcanism: Journal of Geophysical Research,80, 40954102.

vorak, J. J., and D. Dzurisin, 1997, Volcano geodesy: The search for magmareservoirs and the formation of eruptive vents: Reviews of Geophysics, 35,343384.

zurisin, D., 2003, A comprehensive approach to monitoring volcano defor-mation as a window on the eruptive cycle: Reviews of Geophysics, 41,1009, doi: 10.1029/2003RG000134.

ggers, A. A., 1987, Residual gravity changes and eruption magnitudes:Journal of Volcanology and Geothermal Research, 33, 201216.

l Wahabi, A., B. Ducarme, M. Van Ruymbeke, N. dOrey, and A. Somer-hausen, 1997, Continuous gravity observations at Mount Etna Sicily andcorrelations between temperature and gravimetric records: Cahiers duCentre Europen de Godynamique et de Sismologie, 14, 105119.

erguson, J. F., F. J. Klopping, T. Chen, J. E. Seibert, J. L. Hare, and J. L.Brady, 2008, The 4D microgravity method for waterflood surveillance:Part III 4D absolute microgravity surveys at Prudhoe Bay,Alaska: Geo-physics 0016-8033, 73, this issue.

ernndez, J., M. Charco, J. B. Rundle, and K. F. Tiampo, 2006, Arevision ofthe FORTRAN codes GRAVW to compute deformation produced by apoint magma intrusion in elastic-gravitational layered earth models: Com-puters & Geosciences, 32, 275281, doi: 10.1016/j.cageo.2005.06.015.

ernndez, J., M. Charco, K. F. Tiampo, G. Jentzsch, and J. B. Rundle, 2001a,Joint interpretation of displacements and gravity data in volcanic areas: Atest example: Long Valley Caldera, California: Geophysical Research Let-ters, 28, 10631066.

ernndez, J., and J. B. Rundle, 1994, Gravity changes and deformation dueto a magmatic intrusion in a two-layered crustal model: Journal of Geo-physical Research, 99, 27372746.ernndez, J., J. B. Rundle, R. D. R. Granell, and T.-T. Yu, 1997, Programs to

FF

F

F

F

F

F

G

G

G

G

G

G

G

G

H

J

J

J

J

J

L

L

L

M

M

M

M

M

N

O

O

O

R

R

R

R

S

S

T

T

TT

V

W

W

W

4D volcano gravimetry WA17compute deformation due to a magma intrusion in elastic-gravitationallayered earth models: Computers & Geosciences, 23, 231249.

ernndez, J., K. F. Tiampo, G. Jentzsch, M. Charco, and J. B. Rundle,2001b, Inflation or deflation? New results for Mayon volcano applyingelastic-gravitational modeling: Geophysical Research Letters, 28, 23492352.

ernndez, J., K. F. Tiampo, J. B. Rundle, and G. Jentzsch, 2005, On the in-terpretation of vertical gravity gradients produced by magmaticintrusions: Journal of Geodynamics, 39, 475492, doi: 10.1016/j.jog.2005.04.005.

ialko, Y., Y. Khazan, and M. Simons, 2001, Deformation due to a pressur-ized horizontal circular crack in an elastic half-space, with applications tovolcano geodesy: Geophysical Journal International, 146, 181190.

olch, A., J. Fernndez, J. B. Rundle, and J. Mart, 2000, Ground deforma-tion in a viscoelastic medium composed of a layer overlying a half space:Acomparison between point and extended sources: Geophysical Journal In-ternational, 140, 3750.

olch, A., and J. Gottsmann, 2006, Faults and ground uplift at activecalderas: in C. Troise, G. De Natale, and C. Kilburn, eds., Mechanisms ofactivity and unrest at large calderas: Special Publications, Geological So-ciety London, 109120.

uruya, M., S. Okubo, F. Kimata, R. Miyajima, I. Meilano, W. Sun, Y.Tanaka, and T. Miyazaki, 2003a, Mass budget of the magma flow in the2000 volcano-seismic activity at Izu-islands, Japan: Earth Planets Space,55, 375385.

uruya, M., S. Okubo, W. Sun, Y. Tanaka, J. Oikawa, H. Watanabe, and T.Maekawa, 2003b, Spatiotemporal gravity changes at Miyakejima volca-no: Japan: Caldera collapse, explosive eruptions and magma movement:Journal of Geophysical Research, 108, doi: 10.1029/2002JB001989.

ottsmann, J., and M. Battaglia, 2008, Deciphering causes of unrest at col-lapse calderas: Recent advances and future challenges of joint gravimetricand ground deformation studies: in J. Gottsmann and J. Mart, eds.,Caldera volcanoes:Analysis, modeling and response: Elsevier, 417446.

ottsmann, J., G. Berrino, H. Rymer, and G. Williams-Jones, 2003, Hazardassessment during caldera unrest at the Campi Flegrei, Italy: A contribu-tion from gravity-height gradients: Earth and Planetary Science Letters,211, 295309.

ottsmann, J., A. Camacho, K. F. Tiampo, and J. Fernndez, 2006a, Spa-tiotemporal variations in vertical gravity gradients at the Campi Flegreicaldera Italy: A case for source multiplicity during unrest?: GeophysicalJournal International, 167, 10891096.

ottsmann, J., R. Carniel, N. Coppo, L. Wooller, S. Hautmann, and H.Rymer, 2007, Oscillations in hydrothermal systems as a source of peri-odic unrest at caldera volcanoes: Multiparameter insights from NisyrosGreece: Geophysical Research Letters, 34, L07307, doi: 10.1029/2007GL029594.

ottsmann, J., and H. Rymer, 2002, Deflation during caldera unrest: Con-straints on subsurface processes and hazard prediction from gravity-heightdata: Bulletin of Volcanology, 64, 338348.

ottsmann, J., H. Rymer, and L. K. Wooller, 2005, On the interpretation ofgravity variations in the presence of active hydrothermal systems: Insightsfrom the Nisyros caldera, Greece: Geophysical Research Letters, 32,L23310, doi: 10.1029/2005GL024061.

ottsmann, J., L. K. Wooller, J. Marti, J. Fernndez, A. G. Camacho, P.Gonzalez, A. Garca, and H. Rymer, 2006b, New evidence for the reactiva-tion of Teide volcano: Geophysical Research Letters, 33, L20311, doi:10.1029/2006GL027523.

udmundsson, A., 2006, How local stresses control magma-chamber rup-tures, dyke injections, and eruptions in composite volcanoes: Earth-Sci-ence Review, 79, 131.

agiwara, Y., 1978, The Mogi model as a possible cause of the crustal upliftin the eastern part of Izu Peninsula and related gravity change: Bulletin ofthe Earthquake Research Institute, University of Tokyo, 52, 301309.

achens, R. C., and C. W. Roberts, 1985, Temporal and areal gravity investi-gations at Long Valley caldera, California: Journal of Geophysical Re-search, 90, 1121011218.

aupart, C., and S. Vergniolle, 1988, Dynamics of degassing at Kilauea vol-cano, Hawaii: Nature, 311, 5860.

ohnsen, G. V., A. Bjornsson, and S. Sigurdsson, 1980, Gravity and elevationchanges caused by magma movement beneath the Krafla caldera, north-east Iceland: Journal of Geophysics, 47, 132140.

ousset, P., S. Dwipa, F. Beauducel, T. Duquesnoy, and M. Diament, 2000,Temporal gravity at Merapi during the 19931995 crisis: An insight intothe dynamical behavior of volcanoes: Journal of Volcanological and Geo-thermal Research, 100, 289320.

ousset, P., and H. Okada, 1999, Post-eruptive volcanic dome evolution as re-vealed by deformation and microgravity observations at Usu volcanoHokkaido, Japan: Journal of Volcanology and Geothermal Research, 89,255273.

aCoste & Romberg, 2004, Instruction manual. Model G and D gravitymeters: www.gravity-meta-repair.com/images/gdmanual.pdf last access-

edAugust, 5, 2008.isowsky, M., 2006, Analytical volcano deformation source parameters, inD. Dzurisin, Volcano deformation: New geodetic monitoring techniques:Springer-Verlag, 441481.

ungarini, L., C. Troise, M. Meo, and G. De Natale, 2005, Finite elementmodelling of topographic effects on elastic ground deformation at Mt.Etna: Journal of Volcanology and Geothermal Research, 144, 257271.asterlark, T., 2007, Magma intrusion and deformation predictions: Sensi-tivities to the Mogi assumptions: Journal of Geophysical Research, 112,B06419, doi: 10.1029/2006JB004860.cTigue, D. F., 1987, Elastic stress and deformation near a finite sphericalmagma body: Resolution of the point source paradox: Journal of Geophys-ical Research, 92, 1293112940.cTigue, D. F., and P. Segall, 1988, Displacements and tilts from dip-slipfaults and magma chambers beneath irregular surface topography: Geo-physical Research Letters, 15, 601604.cTigue, D. F., and D. Stein, 1984, Topographic amplification of tectonicdisplacements: Implications for geodetic measurements of strain changes:Journal of Geophysical Research, 89, 11231131.erriam, J. B., 1992, Atmospheric pressure and gravity: Geophysical Jour-nal International, 109, 488500.

ewman, A. V., T. H. Dixon, and N. Gourmelen, 2006, A four-dimensionalviscoelastic deformation model for Long Valley caldera, California, be-tween 1995 and 2000: Journal of Volcanology and Geothermal Research,150, 244269.

kada, Y., 1985, Surface deformation due to shear and tensile faults in a half-space: Bulletin of the Seismological Society ofAmerica, 75, 11351154.

kubo, S., 1992, Gravity and potential changes due to shear and tensile faultsin a half-space: Journal Geophysical Research, 97, 71377144.

kubo, S., Y. Hirata, M. Sawada, and K. Nagasawa, 1991, Gravity changecaused by the 1989 earthquake swarm and submarine eruption off Ito, Ja-pan: Test on the magmatic intrusion hypothesis: Journal of Physics of theEarth, 39, 219230.

undle, J. B., 1978, Gravity changes and the Palmdale uplift: GeophysicalResearch Letters, 5, 4144., 1980, Static elastic-gravitational deformation of a layered half spaceby point couple sources: Journal of Geophysical Research, 85, 53555363., 1982, Deformation, gravity, and potential changes due to volcanicloading of the crust: Journal of Geophysical Research, 87, 1072910744.

ymer, H., 1989, A contribution to precision microgravity data analysis us-ing LaCoste and Romberg gravity meters: Geophysical Journal, 97,311322., 1994, Microgravity change as a precursor to volcanic activity: Journalof Volcanology and Geothermal Research, 61, 311328.

ymer, H., J. B. Murray, G. C. Brown, F. Ferrucci, and J. McGuire, 1993,Mechanisms of magma eruption and emplacement at Mt. Etna between1989 and 1992: Nature, 361, 439441.

ymer, H., and G. William