{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:25:59Z","timestamp":1760235959397,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T00:00:00Z","timestamp":1633910400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Volcano Science Center \u2013 US Geological Survey, and by Sapienza\u2013University of Rome, Piccoli Progetti Universitari 2020","award":["N\/A"],"award-info":[{"award-number":["N\/A"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The Long Valley Caldera, located at the eastern edge of the Sierra Nevada range in California, has been in a state of unrest since the late 1970s. Seismic, gravity and geodetic data strongly suggest that the source of unrest is an intrusion beneath the caldera resurgent dome. However, it is not clear yet if the main contribution to the deformation comes from pulses of ascending high-pressure hydrothermal fluids or low viscosity magmatic melts. To characterize the nature of the intrusion, we developed a 3D finite element model which includes topography and crust heterogeneities. We first performed joint numerical inversions of uplift and Electronic Distance Measurement baseline length change data, collected during the period 1985\u20131999, to infer the deformation-source size, position, and overpressure. Successively, we used this information to refine the source overpressure estimation, compute the gravity potential and infer the intrusion density from the inversion of deformation and gravity data collected in 1982\u20131998. The deformation source is located beneath the resurgent dome, at a depth of 7.5 \u00b1 0.5 km and a volume change of 0.21 \u00b1 0.04 km3. We assumed a rhyolite compressibility of 0.026 \u00b1 0.0011 GPa\u22121 (volume fraction of water between 0% and 30%) and estimated a reservoir compressibility of 0.147 \u00b1 0.037 GPa\u22121. We obtained a density of 1856 \u00b1 72 kg\/m3. This density is consistent with a rhyolite melt, with 20% to 30% of dissolved hydrothermal fluids.<\/jats:p>","DOI":"10.3390\/rs13204054","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T21:45:32Z","timestamp":1633988732000},"page":"4054","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A New Analysis of Caldera Unrest through the Integration of Geophysical Data and FEM Modeling: The Long Valley Caldera Case Study"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7676-4758","authenticated-orcid":false,"given":"Fabio","family":"Pulvirenti","sequence":"first","affiliation":[{"name":"School of Remote Sensing and Geomatics Engineering, Nanjing University of Information Science and Technology, 219 Ningliu Road, Pukou District, Nanjing 210044, China"}]},{"given":"Francesca","family":"Silverii","sequence":"additional","affiliation":[{"name":"Department of Physics of Earthquakes and Volcanoes, German Research Centre for Geosciences (GFZ), Helmholtzstra\u00dfe 6\/7, 14467 Potsdam, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4726-5287","authenticated-orcid":false,"given":"Maurizio","family":"Battaglia","sequence":"additional","affiliation":[{"name":"U.S. Geological Survey, Volcano Disaster Assistance Program, NASA Ames Research Center, Moffett Field, CA 94035, USA"},{"name":"Department of Earth Sciences, Sapienza\u2014University of Rome, 00185 Rome, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hill, D.P., Montgomery-Brown, E.-K., Shelly, D.R., Flinders, A.F., and Prejean, S. (2020). Post-1978 tumescence at Long Valley Caldera, California: A geophysical perspective. J. Volcanol. Geotherm. Res., 400.","DOI":"10.1016\/j.jvolgeores.2020.106900"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/S0377-0273(00)00185-2","article-title":"Spherical and ellipsoidal volcanic sources at Long Valley caldera, California, using a genetic algorithm inversion technique","volume":"102","author":"Tiampo","year":"2000","journal-title":"J. Volcanol. Geotherm. Res."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/S0377-0273(00)00255-9","article-title":"Geodetic and seismic constraints on recent activity at Long Valley Caldera, California: Evidence for viscoelastic rheology","volume":"105","author":"Newman","year":"2001","journal-title":"J. Volcanol. Geotherm. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0377-0273(03)00172-0","article-title":"Deformation of the Long Valley Caldera, California: Inferences from measurements from 1988 to 2001","volume":"127","author":"Langbein","year":"2003","journal-title":"J. Volcanol. Geotherm. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.jvolgeores.2005.07.017","article-title":"A four-dimensional viscoelastic deformation model for Long Valley Caldera, California, between 1995 and 2000","volume":"150","author":"Newman","year":"2006","journal-title":"J. Volcanol. Geotherm. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1283","DOI":"10.1111\/j.1365-246X.2011.05214.x","article-title":"Constraints on time-dependent volcanic source models at Long Valley Caldera from 1996 to 2009 using InSAR and geodetic measurements","volume":"187","author":"Liu","year":"2011","journal-title":"Geophys. J. Int."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"5250","DOI":"10.1002\/2015GL064338","article-title":"Renewed inflation of Long Valley Caldera, California (2011 to 2014)","volume":"42","author":"Wicks","year":"2015","journal-title":"Geophys. Res. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Silverii, F., Pulvirenti, F., Montgomery-Brown, E.K., and Neely, W.R. (2021). The 2011-2019 Long Valley Caldera inflation: New insights from separation of superimposed geodetic signals and 3D modeling. Earth Planet. Sci. Lett., 569.","DOI":"10.1016\/j.epsl.2021.117055"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1126\/science.217.4559.531","article-title":"Magmatic resurgence in Long Valley Caldera, California: Possible Cause of the 1980 Mammoth Lakes Earthquakes","volume":"217","author":"Savage","year":"1982","journal-title":"Science"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2721","DOI":"10.1029\/JB092iB03p02721","article-title":"Deformation near the Long Valley Caldera, eastern California, 1982-1986","volume":"92","author":"Savage","year":"1987","journal-title":"J. Geophys. Res."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"12487","DOI":"10.1029\/95JB01052","article-title":"Shallow and peripheral volcanic sources of inflation revealed by modeling two-color geodimeter and leveling data from Long Valley Caldera, California, 1988-1992","volume":"100","author":"Langbein","year":"1995","journal-title":"J. Geophys. Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2119","DOI":"10.1126\/science.285.5436.2119","article-title":"Magma intrusion beneath Long Valley caldera confirmed by temporal changes in gravity","volume":"285","author":"Battaglia","year":"1999","journal-title":"Science"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Battaglia, M., Segall, P., Murray, J., Cervelli, P., and Langbein, J. (2003). The mechanics of unrest at Long Valley Caldera, California: 1. Modeling the geometry of the source using GPS, leveling and 2-color EDM data. J. Volcanol. Geotherm. Res., 16.","DOI":"10.1016\/S0377-0273(03)00170-7"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1046\/j.1365-246X.2001.00453.x","article-title":"Finite source modelling of magmatic unrest in Socorro, New Mexico, and Long Valley, California","volume":"146","author":"Fialko","year":"2001","journal-title":"Geophys. J. Intern."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Feng, L., and Newman, A.V. (2009). Constraints on continued episodic inflation at Long Valley Caldera, based on seismic and geodetic observations. J. Geophys. Res., 114.","DOI":"10.1029\/2008JB006240"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1002\/grl.50258","article-title":"Near real-time monitoring of volcanic surface deformation from GPS measurements at Long Valley Caldera, California","volume":"40","author":"Ji","year":"2013","journal-title":"Geophys. Res. Let."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"15851","DOI":"10.1029\/93JB00558","article-title":"An episode of reinflation of the Long Valley Caldera, eastern California, 1989\u20131991","volume":"98","author":"Langbein","year":"1993","journal-title":"J. Geophys. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1016\/j.jvolgeores.2017.06.010","article-title":"Fluid-driven uplift at Long Valley Caldera, California: Geologic perspectives","volume":"341","author":"Hildreth","year":"2017","journal-title":"J. Volcanol. Geotherm. Res."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/s00445-006-0090-5","article-title":"Elastic model for the gravity and elevation changes before the 2001 eruption of Etna volcano","volume":"69","author":"Carbone","year":"2007","journal-title":"Bull. Volcanol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1029\/JB084iB01p00165","article-title":"Local changes in gravity resulting from deformation","volume":"84","author":"Walsh","year":"1979","journal-title":"J. Geophys. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/S0377-0273(97)00071-1","article-title":"Modelling gravity variations consistent with ground deformation in the Campi Flegrei caldera (Italy)","volume":"81","author":"Bonafede","year":"1998","journal-title":"J. Volcanol. Geotherm. Res."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1111\/j.1365-246X.2007.03380.x","article-title":"Modelling of ground deformation and gravity fields using finite element method: An application to Etna volcano","volume":"169","author":"Currenti","year":"2007","journal-title":"Geophys. J. Int."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.epsl.2008.04.040","article-title":"Simultaneous inversion of deformation and gravity changes in a horizontally layered half-space: Evidences for magma intrusion during the 1982-1984 unrest at Campi Flegrei caldera (Italy)","volume":"272","author":"Amoruso","year":"2008","journal-title":"Earth Planet. Sc. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Crescentini, L., and Amoruso, A. (2007). Effects of crustal layering on the inversion of deformation and gravity data in volcanic areas: An application to the Campi Flegrei caldera, Italy. Geophys. Res. Lett., 34.","DOI":"10.1029\/2007GL029919"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1093\/gji\/ggt507","article-title":"Numerical evidence enabling reconciliation of gravity and height changes in volcanic areas","volume":"197","author":"Currenti","year":"2014","journal-title":"Geophys. J. Int."},{"key":"ref_26","first-page":"119","article-title":"Gravity changes due to overpressure sources in 3D heterogeneous media: Application to Campi Flegrei caldera, Italy","volume":"51","author":"Trasatti","year":"2008","journal-title":"Ann. Geophys."},{"key":"ref_27","first-page":"175","article-title":"On deformation sources in volcanic areas: Modeling the Campi-Flegrei (Italy) 1982-84 unrest, Earth planet","volume":"306","author":"Trasatti","year":"2011","journal-title":"Sci. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0377-0273(03)00171-9","article-title":"The mechanics of unrest at Long Valley Caldera, California: 2. Constraining the nature of the source using geodetic and micro-gravity data","volume":"127","author":"Battaglia","year":"2003","journal-title":"J. Volcanol. Geotherm. Res."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.tecto.2008.09.040","article-title":"Analytical modeling of gravity changes and crustal deformation at volcanoes: The Long Valley caldera, California, case study","volume":"471","author":"Battaglia","year":"2009","journal-title":"Tectonophysics"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1453","DOI":"10.1007\/s00024-004-2514-5","article-title":"The Interpretation of Gravity Changes and Crustal Deformation in Active Volcanic Areas","volume":"161","author":"Battaglia","year":"2004","journal-title":"Pure Appl. Geophys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1130\/G25318A.1","article-title":"Uplift and magma intrusion at Long Valley caldera from InSAR and gravity measurements","volume":"37","author":"Tizzani","year":"2009","journal-title":"Geology"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Roberts, C., Jachens, R., and Morin, R. (2021, February 15). High-precision Stations for Monitoring Gravity Changes in Long Valley Caldera, California, Available online: https:\/\/pubs.usgs.gov\/of\/1988\/0050\/report.pdf.","DOI":"10.3133\/ofr8850"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1130\/GES00570.1","article-title":"Structure of the Sierra Nevada from receiver functions and implications for lithospheric foundering","volume":"7","author":"Frassetto","year":"2011","journal-title":"Geosphere"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/S0040-1951(97)00268-0","article-title":"Thin crust and active upper mantle beneath the Southern Sierra Nevada in the western United States","volume":"286","author":"Ruppert","year":"1998","journal-title":"Tectonophysics"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Farr, T.G., Rosen, P.A., Caro, E., Crippen, R., Duren, R., Hensley, S., Kobrick, M., Paller, M., Rodriguez, E., and Roth, L. (2007). The shuttle radar topography mission. Rev. Geophys., 45.","DOI":"10.1029\/2005RG000183"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1130\/G45094.1","article-title":"Seismic evidence for significant melt beneath the Long Valley Caldera, California, USA","volume":"46","author":"Flinders","year":"2018","journal-title":"Geology"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3698","DOI":"10.1029\/2019GL082254","article-title":"Snowmelt-triggered earthquake swarms at the margin of Long Valley Caldera, California","volume":"46","author":"Shelly","year":"2019","journal-title":"Geophys. Res. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2018","DOI":"10.1130\/GES02093.1","article-title":"A multicomponent Isabella anomaly: Resolving the physical state of the Sierra Nevada upper mantle from Vp\/Vs anisotropy tomography","volume":"15","author":"Bernardino","year":"2019","journal-title":"Geosphere"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2081","DOI":"10.1785\/0120050077","article-title":"Empirical relations between elastic wavespeeds and density in the Earth\u2019s crust","volume":"95","author":"Brocher","year":"2005","journal-title":"Bull. Seismol. Soc. Am."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1029\/GL008i001p00039","article-title":"Dynamic and static moduli","volume":"8","author":"Cheng","year":"1981","journal-title":"Geophys. Res. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1111\/j.1365-246X.2004.02213.x","article-title":"Differences between static and dynamic elastic moduli of a typical seismogenic rock","volume":"157","author":"Ciccotti","year":"2004","journal-title":"Geophys. J. Int."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1016\/S1365-1609(99)00120-3","article-title":"Triaxial compression tests on a granite at different strain rates and confining pressures","volume":"36","author":"Li","year":"1999","journal-title":"Int. J. Rock Mech. Min. Sci."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"4249","DOI":"10.1029\/JB093iB05p04249","article-title":"Deformation from inflation of a dipping finite prolate spheroid in an Elastic Half-Space as a model for volcanic stressing","volume":"93","author":"Yang","year":"1988","journal-title":"J. Geophys. Res."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1093\/comjnl\/7.4.308","article-title":"A simplex method for function minimization","volume":"7","author":"Nelder","year":"1965","journal-title":"Comput. J."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Hickey, J., Gottsmann, J., and Mothes, P. (2015). Estimating volcanic deformation source parameters with a finite element inversion: The 2001\u20132002 unrest at Cotopaxi volcano. Ecuad. J. Geophys. Res. Solid Earth, 120.","DOI":"10.1002\/2014JB011731"},{"key":"ref_46","first-page":"105","article-title":"Finite element modeling of ground deformation and gravity field at Mt Etna","volume":"51","author":"Currenti","year":"2008","journal-title":"Ann. Geophys."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Nikkhoo, M., and Rivalta, E. (2021). Analytical solutions for gravity changes caused by triaxial volumetric sources. Earth Space Sci. Open Arch., 2.","DOI":"10.1002\/essoar.10507706.1"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Rivalta, E., and Segall, P. (2008). Magma compressibility and the missing source for some dike intrusions. Geophys. Res. Lett., 35.","DOI":"10.1029\/2007GL032521"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1016\/j.tecto.2008.10.006","article-title":"Analytical models of deformation and residual gravity changes due to a Mogi source in a viscoelastic medium","volume":"471","author":"Bonafede","year":"2009","journal-title":"Tectonophysics"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1856","DOI":"10.1002\/2017JB014990","article-title":"Mass addition at Mount St. Helens, Washington, inferred from repeated gravity surveys","volume":"123","author":"Battaglia","year":"2018","journal-title":"J. Geophys. Res."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Mastin, L.G., Lisowski, M., Roeloffs, E., and Beeler, N. (2009). Improved constraints on the estimated size and volatile content of the Mount St. Helens magma system from the 2004\u20132008 history of dome growth and deformation. Geophys. Res. Lett., 36.","DOI":"10.1029\/2009GL039863"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00410-017-1391-8","article-title":"The geochemical and petrological characteristics of prenatal caldera volcano: A case of the newly formed small dacitic caldera, Hijiori, Northeast Japan","volume":"172","author":"Miyagi","year":"2017","journal-title":"Contrib. Miner. Pet."},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Anderson, K., and Segall, P. (2011). Physics-based models of ground deformation and extrusion rate at effusively erupting volcanoes. J. Geophys. Res., 116.","DOI":"10.1029\/2010JB007939"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Snieder, R. (1998). The role of nonlinearity in inverse problems. Inverse Probl., 14.","DOI":"10.1088\/0266-5611\/14\/3\/003"},{"key":"ref_55","unstructured":"Cervelli, P.F., Langbein, J.O., Perkins, J.P., Svarc, J.L., and Owen, S.E. (2010, January 13\u201317). Campaign GPS Measurements from 2000-2010 in the Sierra Block South of Long Valley Caldera, CA, USA. Proceedings of the American Geophysical Union Fall Meeting, San Francisco, CA, USA."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1402","DOI":"10.2138\/am.2011.3718","article-title":"Amorphous Materials: Properties, Structure, and Durability: Compositional dependent compressibility of dissolved water in silicate glasses","volume":"96","author":"Malfait","year":"2011","journal-title":"Am. Mineral."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1016\/j.jvolgeores.2009.05.021","article-title":"Modeling the effect of layered volcanic material on magma reservoir failure and associated deformation, with application to Long Valley caldera, California","volume":"186","author":"Long","year":"2009","journal-title":"J. Volcanol. Geoth. Res."},{"key":"ref_58","unstructured":"Magni, V., Battaglia, M., Tizzani, P., Manconi, A., and Walter, T. (2008, January 4\u20136). Axial symmetric crustal deformation model for Long Valley Caldera, California. Proceedings of the COMSOL Conference 2008, Hannover, Germany."},{"key":"ref_59","unstructured":"Pepe, S., Tizzani, P., and Manconi, A. (2010, January 17\u201319). Numerical inversion of surface deformation at Long Valley Caldera (California) by using 3D mechanical models. Proceedings of the COMSOL Conference 2010, Paris, France."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1071\/EG986189","article-title":"Magnetic and gravity anomalies of a triaxial ellipsoid","volume":"17","author":"Clark","year":"1986","journal-title":"Explor. Geophys."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/20\/4054\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:11:30Z","timestamp":1760166690000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/13\/20\/4054"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,11]]},"references-count":60,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["rs13204054"],"URL":"https:\/\/doi.org\/10.3390\/rs13204054","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2021,10,11]]}}}