GEOPHYSICAL RESEARCH LETTERS, VOL. 28, NO. 6, PAGES 1063-1066, MARCH 15,2001

Joint interpretation of displacement and gravity data involcanic areas. A test example: Long Valley Caldera,California

1. Fernández,' M. Charco,' K. F. Tiampo.' G. Jentzsch,' and J. B. Rundle2

Abstract. Volcanic activity produces deformation andgravity changes that many times can be used as precursors offuture eruptions. Applying geodetic techniques to monitoringactivity involves interpretation using deformation models.Usually gravity change data and displacement data areinterpreted separately. We show, using modeling ofdeformation and gravity change data in Long Valley Caldera,California, USA, that this can lead to incorrect interpretations.The results obtained show that displacements and gravitychanges must be interpreted together whenever possible andthat elastic-gravitational models can be a far more appropriateapproximation to problems of volcanic load in the crust thanthe more commonly used purely elastic models. Therefore itis necessary to change the philosophy normally used tointerpret geodetic observations, improving the possibility ofpredicting future eruptions.

1. IntroductionVolcanic activity almost inevitably produces deformation

and gravity changes before, during, between and after theevents. On the basis of this fact and the high levels ofprecision attainable, different geodetic techniques are provingto be a powerful tool in the monitoring of volcanic activity,making it possible to detect ground motion and gravitychanges that reflect magma rising from depth, sometimesmonths or weeks before the magma flow leads to earthquakesor other eruption precursors [e.g.: Delaney and Me Tigue,1994; Rymer, 1996; Dvorak and Dzurisin. 1997; Massonneland Feigl, 1998; Fernández el al., 1999; Rymer andWilliams-Jones, 2000; Stein el al., 2000]. Geodetic monito-ring thus complements seismic monitoring by extending thestudy of voIcanic phenomena from seconds to years andproviding details on the growth of magma bodies within thevolcano [Slein el al., 2000]. Applying such longer-termmonitoring techniques to voIcanically active zones inevitablyinvolves data processing and the subsequent finalinterpretation of observed deformations and gravity changes.Mathematical deformation models are a basic, essential toolfor the latter task.

Present knowledge on critical stages of volcanoes prior toeruption is mostly based on elastostatic views; by studying

¡Instituto de Astronomía y Geodesia (CSIC-UCM), Madrid, Spain2 CIRES, University of Colorado, Boulder, Colorado31nstitute for Geosciences, FSU Jena, Jena, Germany

Copyright 2001 by the American Geophysical Union.

Paper number 2000GLO 12393.0094-8276/01 /2000GLO 12393$05 .00

volcanic unrest in terms of mechanical models involvingoverpressure in magma chambers and conduits. Reachingeruptive conditions is interpreted, in this framework, asovercoming the mechanical rock strength in large volumes,from the top of a magma chamber to the surface. Mogi [1958]applied a center of dilatation (point pressure source) in anelastic space to interpret the ground deformation produced invoIcanic areas. Mogi's model has been extensively applied inmodeling ground deformations in volcanic areas and has beensuccessful in explaining primarily vertical ground defor-mations. This model often poses difficulties in simultaneouslymodeling observed displacements and gravity changes [e.g.:Rymer el al., 1993; Rymer, 1996, Jentzsch el al., 2000] andthere is a large body of evidence for ground deformations andseismicity at calderas that can not be modelled by thesepurely elastic effects [e.g.: Bonafede, 1990; De Natale el al.,1997; Gaeta el al., 1998]. Rundle [1980, 1982] obtains andsolves the equations that represent the coupled elastic-gravitational problem for a stratified half-space ofhomogeneous layers. The magmatic intrusion is considered apoint intrusion located at depth c. This model [Rundle, 1980,1982; Fernández and Rundle, 1994; Fernández et al., 1997]takes into account the interaction between the mass of theintrusion and the ambient gravity field and the effect causedby the change of pressure in the magmatic chamber (due tooverfilling or temperature changes). It has been showntheoretically [Fernández el al., 1997] that consideration ofgravity effects can be fundamental for adjusting and properlyexplaining gravity changes measured in active zones. Verticaldisplacements and gravity changes produced by pressureincreases and the mass of the intrusion have different signs[Rundle, 1982, Fernández el al., 1997]. This is very importantbecause the right combinations of mass, radius and pressure inthe intrusion can serve to explain observations in active zoneswhere major gravity changes appear without any significantdeformation, or vice versa [see e.g., Rundle, 1982; Rymer,1996; Jentzeh el al., 2000]. Furthermore, while gravity changedata and displacement data generally are interpretedseparately, or vertical displacement data are used only forcorrection of observed gravity values, we will see in themodeling of deformation and gravity change data in the LongValley Caldera, California, USA that this can lead to incorrectinterpretations. The results obtained will show that elastic-gravitational models can be a far more appropriateapproximation to problems of volcanic load in the crust thanthe more commonly used purely elastic models [e.g.: Mogi,1958; Me Tigue, 1987; Davis, 1986; Yang el al., 1988]. Wemust take into account that a correct interpretation of theobserved geodetic signals will have implications for theimprovement and development of monitoring and alertsystems for the mitigation of hazards, as well as direct socio-economic implications as it affects urban and industrialinfrastructure planning.

1063

1064 FERNÁNDEZ ET AL.: INTERPRETATION OF DISPLACEMENT AND GRAVITY DATA

2. A Test Example: Long Valley Caldera,California, USA

The elliptical-shaped Long Valley Caldera extends 32 kmin east-west direction and 17 km north to south, with anaverage elevation of 2200 m (Figure 1). Information about itsformation and evolution are easy to find in the literature [seee.g.: Bailey el al., 1976; Hill, 1984; Abers, 1985]. Over thelast 20 years in the Long Valley caldera, located to the east ofthe Sierra Nevadas (California), there have been two episodesof rapid inflation of the central resurgent dome, accompaniedby seismicity inside and around the caldera, without anyeruptions between these two episodes. The first episode [Hill,1984] began in the late 1970s and continued through the mid1980s. The second episode [Langbein el al., 1993; Langbeinel al., 1995; Tiampo el al., 2000] started in October 1989 afterseveral years of relative calm. The models used in previousstudies [e.g.: Rundle and Whitcomb, 1984; Langbein el al.,1995; Battaglia el al., 1999; Tiampo el al., 2000] use pointsources beneath the resurgent dome. These models arenormally purely elastic and do not consider displacements andgravity changes together in the inversion. Normally they alsoconsider a homogeneous half-space. Previous works[Langbein el al., 1995; Tiampo el al., 2000] showed thatadditional sources of deformation are needed to model theavailable geodetic observations properly.

Battaglia el al. [1999] study and model gravity changesobserved at Long Valley for the period from 1982 to 1998.The precise relative gravity measurements reveal a decreasein gravity of as much as -107±6 ¡¡Gal (1 u.Gal = 10-8 m S-2)

centered around the uplifting resurgent dome. They found apositive residual gravity change of up to 64±15 u.Gal aftercorrecting the effects of uplift and water table fluctuations(see their Figure 3). They assume a point source of intrusionand obtain a density value for the intruding material of 3300kg m" (the 95% bootstrap confidence bounds on the densityare 2700 to 4000 kg m"). They note that their gravity resultsrequire intrusion of silicate magma and exclude in situthermal expansion or pressurization of the hydrothermalsystem as the cause of uplift and seismicity. They interpretategravity changes and vertical displacement separately and useonly estimations of vertical displacement simultenously with

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Figure 2. Results obtained for Long Valley Caldera and thesecond inflation period considering a homogeneous elastic crustand two Mogi sources. a. Vertical displacements in cm. b. FreeAir gravity changes in ¡¡Gal (1 ¡¡Gal = 10-8 m/s'). See text forcharacteristic of the sources used in the computation.

gravity measurements for the correction of uplift effects.Their results would corresponds with the first modeldescribed by Rymer and Williams-Jones [2000]. Tiampo el al.[2000] model the second inflation period at Long Valleyusing genetic algorithm techniques and high-quality geodeticmeasurements of elevation and baseline extension changes.They compare two source inversions for both spherical Mogipoint sources and the finite prolate ellipsoid [Davis, 1986;Yang el al., 1988]. The spherical sources are well constrained,the larger located at 9.9 km beneath the resurgent dome, witha volume ofO.036 km", while the second with only 0.008 krrr',is located at a depth of 7.3 km beneath the south moat. Thedepths to the ellipsoidal sources are switched, with the largersource at a depth of 9.6 km and the smaller at 11.8 km, withvolumes of 0.037 and 0.002 km' respectively. Tiampo el al.[2000] found that the spherical source solution has a betterfitness than the ellipsoidal model, yet the ellipsoidal modelsolution is not spherical. This lead them to conclude thatadditional sources, in particular the existing normal faulting inthe northwest ofthe caldera, which they do not model in theirstudy, are needed to provide a better solution. They do not usegravity data in their study.

We apply our elastic-gravitational model to the secondinflation period at Long Valley caldera like Tiampo el al.

[2000] as a test. Therefore we used the same characteristicsfor both the medium and the number and location of sources.We try the two spherical point source model in ahomogeneous crust. The volume increment values obtained,which represent the volumes of expansion for the two sourcesconsidered, can be used to obtain the pressure and massesincrement of the intrusions, by only taking into account theinitial source radii of 4 km for the deep magmatic chamber[Elbring and Rundle, 1986] and 1.5 Km for the shallowest,located beneath the south moat [Sanders, 1984] that aroseduring the first period of inflation in Long Valley caldera.Using the relation between pressure and volume changes forspherical intrusions [see Me Tigue, 1987] and the densityvalue of 3300 kg m" [Battaglia el al., 1999], the pressurechanges and the masses increments obtained are 6.9 MPa and0.1188 MU for the source beneath the Resurgent 'dome, 29.0MPa and 0.0264 MU for the shallowest source.

Figure 2 shows the results obtained without considering thegravity field, purely elastic model, thus considering the twoMogi sources located in a homogeneous elastic half-spacewith Poisson's ratio 0-=0.25 [Tiampo el al., 2000]. Thereforewe only consider the effect of the pressure in the magmaticchamber. In this case it is quite clear that the verticaldisplacements, Figure 2a, are fairly similar to those observed

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during the second period of inflation [Langbein el al., 1993;Langbein el al., 1995; Tiampo el al., 2000], but the free airgravity changes, Figure 2b, are null, and therefore do notresemble those observed [Battaglia el al., 1999]. The reasonfor this can be that in this purely elastic model, the gravitychanges caused by density changes inside the medium arecompensated by the Bouguer effect of the produceddeformation. Now, for comparison, in Figure 3 we show theresults obtained considering an elastic-gravitational model,which takes into account the mass increments of the twointrusions (magma refilling) computed previously and theirinteraction with the gravity field, in addition to the pressures.Vertical displacement, Figure 3a, still being as in Figure 2a,therefore adjusts the observed uplift. The gravity change,Figure 3b, has a similar pattem to the obtained by Battaglia ela/. (1999], see their Figure 3C, with the maximum change ofpositive sign and located also at the resurgent dome.Nevertheless, the magnitude of this maximum effect is aboutl/5 of the observed one (about 13 ¡lGal in place of 64 u.Gal).This can be due to two reasons. One is the probably nottotally correct determination of magma intrusioncharacteristics used, coming from works that use onlydisplacement or only gravity data. The second reason is thatwe are modeling the second inflation period but Battaglia ela/. [1999] consider a longer period of time including part ofthe first inflation periodo If we compare Figures 2 and 3 wecan conclude that during the second inflation period theremay have been some magma recharge together with a certainincrease in pressure inside the chambers, not just a rechargewithout pressure increase, or pressure effects alone.

From our study, it is clear that the results obtained usingonly displacement or gravity data can work incorrectly byadjusting at the same time displacement and gravity changes.Note that the characteristics of the intrusion used in ourcomputations were computed using only displacement data oronly gravity data, not both kinds of data at the same time. Inconsequence, errors result for two primary reasons. Either theeffect of new masses entering the intrusion is not considered,or the masses calculated for the refilling are underestimated,due to errors in the volumes computed using onlydisplacement data, or to the value ofthe considered density ofmagma, estimated using only gravity data, or to a mixture ofboth things.

3. ConclusionsFrom the resu!ts obtained in previous theoretical works and

from applying the model to Long Valley Caldera the firstconclusion we obtain is that interpreting deformations andgravity changes by using purely elastic models often can leadto results that are clearly incorrect in terms of the locationand/or characteristics ofthe intrusion. This easily occurs iftheeffects on the intrusion are not due primarily to pressurechanges in the intrusion, but instead there is a considerableamount of magma recharge in the intrusion. Elastic-gravitational models, which accounts for the interaction of themass of the intrusion with the ambient gravity field andredistribution of densities inside the crust, can be usedreasonably to interpret cases where gravity changes existwithout deformation, and vice versa, considering adequatemass and pressure combinations for the intrusion, taking intoaccount that the effects for both types of source are ofopposite signs. Furthermore, displacements and gravitychanges must be interpreted together whenever possible,because this will allow us to distinguish between the possiblecases and to discriminate between the role played by pressure

1066 FERNÁNDEZ ET AL.: INTERPRET ATION OF DISPLACEMENT AND GRA VITY DATA

changes and that played by mass displacements. lt can bedone using elastic-gravitational models, but is otherwise veryhard to be done correctly with purely elastic models that donot consider the mass of the intrusion and its interaction withthe surrounding medium and the gravity field. Therefore theresults cJearly show the need to change the philosophynormally used to interpret geodetic observations in voJcanism,in which displacement data and gravity change data are notinterpreted together, and very often are interpreted usingpurely elastic models that are both simplistic andinappropriate, giving rise to false alarrns based in incorrectinterpretations. In order to properly compare our model withthe elastic model, we have not considered layering orviscoelastic properties of the media in this work, althoughboth of them can be important in modelling geodeticobservations [see e.g., Bonafede et al., 1990; Fernández et al.,1997]

Acknowledgments. Research by JF and MCh has been mainlysupported by CICYT project AMB99-1 O 15-C02. Research by KFTand JBR was conducted under NASA grants NAG5-3054 and NGT5-30025 respectively. Research by GJ has been supported by contractENV4-CT96-0259 of the European Commission. This reseach hasbeen also partially supported with founds from a New Del AmoProgram project. We thank to A. Donnellan and H. Rymer for theiruse fuI comments and suggestions.

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K. F. Tiampo and J. B. Rundle, Cooperative Institute for Researchin Enviromental Sciences, University of Colorado, Boulder, CO80309.

(Received September 25, 2000; revised December 15, 2000;accepted December 27, 2000.)