A Multiphysics approach to constrain the dynamics of the Altiplano-Puna magmatic system

A. Spang1, T. S. Baumann1, B. J. P. Kaus1,2

1Johannes Gutenberg University, Institute of Geosciences, Johann-Joachim-Becher-Weg 21, 55128 Mainz, Germany

2TeMaS, Terrestrial Magmatic Systems Research Center, temas.uni-mainz.de

Corresponding author: Arne Spang ([email protected])

This manuscript has been peer reviewed and was accepted for publication by JGR Solid Earth. DOI: 10.1029/2021JB021725 manuscript submitted to JGR: Solid Earth

A Multiphysics approach to constrain the dynamics of the Altiplano-Puna magmatic system

A. Spang 1, T. S. Baumann 1, B. J. P. Kaus 1,2

1Johannes Gutenberg University, Institute of Geosciences, Johann-Joachim-Becher-Weg 21, 55128 Mainz, Germany 2TeMaS, Terrestrial Magmatic Systems Research Center, temas.uni-mainz.de

Key Points: • 3D visco-elasto-plastic thermomechanical modelling of the Altiplano-Puna magma system, constraining density, melt content and geometry of the APMB • Joint, dynamically consistent, interpretation of seismic imaging, gravity anomalies and surface velocities, including uncertainty estimation • APMB has a central rise of about 80 km diameter, a density contrast of 90 - 130 kg/m3 to the crust and a melt content of 15 - 22 %

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Corresponding author: Arne Spang, [email protected] Accepted –1– This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1029/2021JB021725.

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This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article Dgoyai oeln,gaiymdlig aibegoer,prmtrsensitivity, parameter geometry, variable APMB modelling, inference, gravity Bayesian modelling, geodynamic 3D Keywords Terms Index studies. numerical in the techniques emphasizes modelling which surface and different system sets that magmatic data show the cen- multiple to of the including able parts in of are different body importance We to magma location, observations. sensitive Altiplano-Puna constrain surface are the observables can only discover of we using way, content can Andes, This melt we tral observations, likely. and a surface density pa- are geometry, given real combinations these size, surface, changing to and the automatically results ranges of at By parameter modelling laws make which our parameters. the would comparing geometrical obey we these and and that that observe rameters physical observations models directly of the systems (computer) to set compute magmatic numerical techniques certain by to how no controlled show us have and we allow currently study, physics fed we our are and In They them systems. beneath deposits. crust ore the of in creation the and ulation Summary Language Plain the of understanding important better most a the for are constrained two be and the to crust between need contrast upper processes. and density the the subsurface system the of the with the as rheology of constrained in well the parts be parameters as that deeper can mush shows the geometry magma analysis constrain whose the law controlled anomalies APMB scaling is Bouguer the Automated pattern while of APMB. flow observations top The InSAR the of sources. at help pressure model rise magma thermomechanical additional central m driven 3D for a buoyancy by visco-elasto-plastic need by kg Our the self-consistently 130 without deformation %. - transport surface 22 90 contrast observed - to density the 15 rock the reproduces to host constrain important fraction We surrounding most melt the system. the sociated and the identify the APMB of and estimate the dynamics APMB can geometry between the the we the Furthermore, control of between that observations. geometry relationship parameters surface the a and with create associated body to the uncertainties magma law able of mid-crustal scaling are imaging, density a modelling, we seismic and of thermomechanical inference, of geometry Bayesian modelling, interpretation 3D gravity and joint location, combining analysis a constrain By use to we body. data magma Here, magma InSAR Altiplano-Puna Andes. and the central anomalies above the gravity pattern in deformation (APMB) surface ( body concentric monitoring a (InSAR) revealed Radar has Aperture Synthetic Interferometric Continuous Abstract 49Pyisadceityo am bodies magma of chemistry and Physics 8439 quantification Uncertainty 3275 techniques of structure Integration Earth 1295 and anomalies Gravity 1219 deformation Non-tectonic 1211 pop- the of security the infrastructure, economic on impact big a have can Volcanoes aucitsbitdto submitted manuscript –2– G:SldEarth Solid JGR: − 3 (2 σ n h as- the and ) > 5years) 25

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This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article hilwk ta.(99 n ad ta.(03 nepee h eylwvlct zones melting. velocity partial low very of the zone interpreted a (2003) generally al. more identified et have or Wigger, Zandt studies APMB 1984; and of the Zeil, (V number (1999) be & large al. to Breitkreuz a et suggest 1984; Chmielowski (1999), they al., al. that et et layer, Schwarz Chmielowski a (e.g., with 1980s Starting the 1988). as back far as Surveys Imaging 2.1 perform the to creating use 2.3, on we to focus code, 2.1 2.6 thermomechanical sections to the In 2.4 on sections level. details while sea gives modelling. study to 2.7 numerical this reference Section in in setup. used are model data, study the this describe in we depth of measures All depth). km (15 part widest the its of at extent model lateral our the in shows APMB the line fitting of magenta extent best Dashed show 2012). lines Pearse, White & 2003). (Fialko al., and pattern” et reflection ”sombrero Oncken ANCORP 2002; shows al., line the et green of (Brasse dark extent profile Solid the magnetotellurics (2016). shows al. square yellow et the Comeau while of by (2017) model used al. resistivity stations et Kukarina the and denote shows (2018) stars line al. blue red et Dark dashed McFarlin extent. the APMB and maximum (2014) the al. al. of et et suggestion Zandt Ward their by by proposed used APMB, stations the denote of squares al. extent Red et the Chmielowski (2003). show and lines (2003) green al. dashed et the Zandt and by (1999) used stations the denote circles Green studies. 1. Figure h PBt easl iesrcueo esta mtikesi bu 5k depth. km 15 ambient about and in functions thickness receiver km combined V 1 (2014) a than al. develop less et to Ward of tomography of structure noise like study recent sill more a The be to APMB the ieltopeewihcicdswt o lcrclrssiiisrpre yBas tal. et Brasse on by (depending reported km resistivities 40-80 electrical (2018). to low down al. K¨uhn with km et (2002); coincides 5 is which about which V lithosphere from Uturuncu, The tire extends beneath depth. and feature isocontour) diameter different the in distinctly km a 20 present only (2017) al. the et for Kukarina the imaging suggestions Uturuncu. considering be various volcano and might the central north, study summarizes its further this S1 beneath is (2014), Figure APMB profile al. Supplementary the their et of of body. Ward as top extent the (2003); but the of V al. depth imaged edge The et km and the Zandt depth. 15 km by km to 100 suggested 8 12 x extent at about 100 layer at body’s about point thin APMB the of conversion a thick of area common km estimates an a 9 covering good presented the functions, for (2018) receiver allow of al. of not zone et stack McFarlin a does recently, imaged study Most 2016) their by al. thickness. (2015, that supported et acknowledge al. is Jay authors et zone by the Comeau ( molten proposed to by resistivity partially level, 5 s survey electrical the sea about km (MT) low of around from 2.9 magnetotellurics top (BDTZ) extend than A shallow zone lower to this (2012). transition velocity APMB of brittle-ductile any the concept shallow that suggest The the argue therefore authors depth. and The km melt 22 of km. presence 50 the of indicates depth a to tending s < mgn tde nern h rsneo am ntecnrlAda rs date crust Andean central the in magma of presence the inferring studies Imaging osdrn htteoewemn aoiyo tde,icuigtelrescale large the including studies, of majority overwhelming the that Considering inversion, time travel and (2018) al. et McFarlin as stations same the Using . ms km 1.0 oorpi a ftesuyae,icuigsimcsain sdi imaging in used stations seismic including area, study the of map Topographic − 1 nterserwv oest eprilymle n hsconclude thus and molten partially be to models wave shear their in ) < aucitsbitdto submitted manuscript m triga 4k et ntevcnt fUuuc and Uturuncu of vicinity the in depth km 14 at starting Ωm) 3 p mdlo ete l 20)soslwvlcte nteen- the in velocities low shows (2008) al. et Heit of -model s mdlcvrn nae faot40x40k,ex- km, 400 x 400 about of area an covering -model –4– p G:SldEarth Solid JGR: mdlo nkne l 20)shows (2003) al. et Oncken of -model − 1

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article ie rvt aa ecmae h oge nml rd(G20,grav- (EGM2008, grid anomaly Bouguer the compared We ity data. gravity sider Data Gravity 2.3 to used 282) 2017). and Pritchard, 10 & (ERS (Henderson tracks set satellite data descending LOS similar the two create the between averages the ftevlct etrrespectively, λ vector velocity the of ihtelrergoa aasto h olbrtv eerhCne 267 Center (http://www.cms.fu- Research (1997) Collaborative Kirchner G¨otze the and berlin.de/sfb/sfb267/results/data in of presented set interest 267), data of (SFB regional area large http://icgem.gfz- the the (ICGEM, for with K¨ohler Models (2016)) and Earth Barthelmes Global potsdam.de/home, for Center International the velocity, LOS is ∆LOS where LOS into them project to need 2018 we to velocities, 1992 LOS from to: https://igppweb.ucsd.edu/ to evolved 2010 according at results has to available direction modelling velocity 1992 are our maximum from sets compare the velocities data To how (LOS) Both show sight 2). (2018) of (Figure al. line et average Lau gridded and present (2012) Pearse and Data InSAR 2.2 not are lower location the and in size the areas model. their of molten the on half partially in constraints upper of them geophysical the presence include available within The to the zone sufficient but scenario. velocity likely this low is on a crust focus image will (2000), we al. crust, et Yuan of tomography displacement 2018). vertical Total al., (b) et (Lau 7. time and over 3a uplift 1, of Figures center in the ones subsi- of the and to (inner) identical uplift are of and region (outer) the dence to correspond Circles volcano. Uturuncu around (2012) 2. Figure 15) orpouetegaiysga nalremuti etlk h ne,i sim- the precisely, is more it or Andes, crust, the like Andean al. thickened belt et the Talwani mountain forward of of large to influence approach a option for the the in an allows consider using signal provides it gravity to objects, also as the portant created and system reproduce the slices the To of 2D up (1959). anomaly drawn make Bouguer from that the objects bodies model 3D 3D gravity. of the and Bauville creation create (https://bitbucket.org/geomio/geomio, imaging the to geomIO seismic (2019)) software from Baumann source insights and aforementioned open the the with use We constrain can we cation Geometry Body’s Magma the Constraining 3a) (Figure 2.4 ICGEM the of grid the coverage. use area to larger decided and we resolution and regular 3c) its (Figure for well agree sets data sisicdneage(iloe l,20) euse We 2001). al., et (Fialko angle incidence its is anomaly ohl osri h oainadpoete fteAM,w con- we APMB, the of properties and location the constrain help To euesraedfraindt ocekterslso u owr oes Fialko models. forward our of results the check to data deformation surface use We h etro u hroehnclmdli h PB hs hp,sz n lo- and size shape, whose APMB, the is model thermomechanical our of center The g 0.05 bg, a vrg O ln fsgt eoiyfo 92t 00fo iloadPearse and Fialko from 2010 to 1992 from velocity sight) of (line LOS Average (a) ◦ eouin im asinfitrwt 5k egh from length) km 75 with filter Gaussian Sigma 6 resolution, ∆ LOS aucitsbitdto submitted manuscript U n =[ , catalogue/central U φ U n e steaiuh(ih ieto)o h aelt and satellite the of direction) (flight azimuth the is sin and ( φ ) U − z U r h ot,es n etclcomponent vertical and east north, the are –5– e cos ( andean φ G:SldEarth Solid JGR: φ )] sin = ( − λ data/gravitiy )+ 167 U . and 5 z cos ( ∼ λ λ fialko/data.html. (1) ) aahm) Both data.html). 21 = . hc are which 5

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This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article onsotieo h PBssga.W eeaea nta e f378(8 32768 grid of of set (CAGH) influence initial the the an of limit generate effect and We the km model, signal. exclude (NS) our APMB’s to 200 of the us and part 1, of allows (EW) not weight outside This 120 is the points axes 3a). which received semi-major (Figure 2002), anomaly with 0.5 Krause, Bouguer (G¨otze lowest ellipse of & weight the an a of inside received point location grid the every from while km 100 of model, radius a of misfit the is Φ where function: misfit RMS weighted a using data, the and model each tween km 11.1 and 8.9 (in 6f+g). describes polygons (Figure S1 control y(NS)-direction text factors 2 and Supplementary stretch use We the 4a). large and body variation. (Figure a automatically depth) a geometry model test generate of for reference we we contrast methodology drawn combinations, which density our hand parameter contrasts the our density realistic between upon and of trade-off based extent geometries al- a different the anomalies is of gravity estimate there To number the of as of nature volume. solutions geometry non-unique its of the The and range between observations. a relationship surface for the the lows investigate and to body us magma allows which account, into S2. text supplementary in topography synthetic mate- the the on on Details Details S1. 2. table exaggeration: in Vertical properties body. rial magma and root crustal for analysis gravity 5. Figure -) sn tgee rdi obnto ihamre-ncl prah(alw& (eq. (Harlow energy approach marker-in-cell and a mass momentum, with combination of conservation in the grid for staggered solves a It using 3-5), 2016). al., et (Kaus Model Thermomechanical 2.7 the shows this 5 at Figure the models. stall and as thermomechanical naturally parameters depth viscous, the to material same less for andesites the the a used the summarizes at and setup expect S1 parts upper Table 2018), we both dacitic, al., as boundary. between W¨orner viscous, buoyancy interface et boundary 2017; more crust the al., a crust/middle put into et We upper APMB Godoy part. studies the 2014; of lower of isotope split al., layer product andesitic, by we et lower the why supported Michelfelder a are is is 2010; by which which concept al., build dacites This et be evolved up Kay melting. to more with (e.g., crustal lavas APMB of extensive layer dacitic the and upper concluding reported differentiation an inclusions, and Sparks and andesitic Uturuncu S5. andesites of of Figure Tassaraintruding wt% products supplementary 2009; few eruption in al., a the summarized regional et to studied 2019) three (Prezzi (2008) al., inversion and al. et gravity 2013) et Ibarra and al., chemistry 2012; et Echaurren, rock (Laske & on 1.0 based crust models model crustal global the between compromise Structure Lithospheric 2.6 algorithm neighborhood misfit. low the of use we areas Next, in models factors. kgm 60000 stretch 250 another the and produce for 0 to 2.0 of 1999a) and range (Sambridge, 0.1 the of in range values the distributed uniformly using els and respectively anomalies ete oe h oge nml ftegoer n opt h ifi be- misfit the compute and geometry the of anomaly Bouguer the model then We o u oesw s h Dtemmcaia nt ieecscd LaMEM code differences finite thermomechanical 3D the use we models our For layered horizontally a use we APMB, the surrounding structure lithospheric the For eu o hroehnclmdl ae ncutlsrcuesuisadour and studies structure crustal on based models thermomechanical for Setup aucitsbitdto submitted manuscript w stewih ftegi on.Eeygi on niea inside point grid Every point. grid the of weight the is Sx Φ= 1 gB , Sx mod s 2 P , and Sy w i 1 ( gB gB and –7– o,i mod, obs P Sy r h oeldadosre Bouguer observed and modelled the are w G:SldEarth Solid JGR: 2 − i otasomtebd nx(EW)- in body the transform to gB b,i obs, ) 2 − 3 o ∆ for 5 nqemod- unique ) ρ n in and (2)

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article rma vrgdpol rmWr ta.(07 tbeS) eas osdrterocks the consider also We ratio S1). Poisson’s (table a (2017) 2007). use al. (Gercek, and et focus compressible Ward will be from we to profile Here averaged (2016). an al. from components. et 3 Kaus equation the to this impact referred of which is discussion parameters reader detailed material the a For the components, on its components. of rate all strain and plastic and viscous tic,  h pressure the S1. and constant gas sal creep: dislocation of relationship powerlaw rate-dependent strain and temperature- components: plastic and viscous elastic, the visco-elasto-plastic of a sum by the characterized is are rate rocks strain The the derivative. where time rheology material the is D/Dt capacity, heat specific the ulus, compression), in (positive sure τ (Kaus surface free 2012). stabilized al., the et above Crameri air 2011; sticky al., of et km allowing Duretz 10 conditions, 2010; about slip al., include free et we apply setup, we the setup, of the of boundaries velocities the Along 1965). Welch, ai okfito nlsi iie ogaie n eut sal ayaon 30 around vary usually mag- results on and research granites Most to 1978). limited (Byerlee, 1952) is law Prager, angles Byerlee’s & friction of (Drucker rock approximation criterion matic good failure Drucker-Prager a the is which to corresponds 8 Equation ae(˙ rate where oe o w ieses h rttmse sntcniee,a hr ssiliflec of body. influence magma the still the the run is onward, of only there buoyancy timestep we as the second system, by considered, the the From dominated not of resolution are is Moho. state vertical velocities timestep and day a surface first topography present as The between the well balancing in steps. as isostatic interested time 1.95, are two of we for resolution As model horizontal km. a 0.74 and of cells million 8.5 roughly ta. 08.Chso siae o natrcstpclyrneaon e P (e.g., MPa few a around use range we typically Therefore rocks intact 1997). for Brown, estimates & Cohesion Hoek 2018). al., et ˙ ij ij eoe h oa eitrcsri aetno,wie˙ while tensor, rate strain deviatoric total the denotes steCuh tesdeviator, stress Cauchy the is α  h icu opnn scaatrzdb h viscosity the by characterized is component viscous The modulus shear the by controlled is component elastic The h lsi opnn scnrle yteyedstrength yield the by controlled is component plastic The eue26clsi ahhrzna ieto n 2 el ntevria.Ti yields This vertical. the in cells 128 and direction horizontal each in cells 256 use We II B h hra xaso coefficient, expansion thermal the n ( = > stecepcntn,˙ constant, creep the is aallt h al hl etn epniua eoiist .A h top the At 0. to velocities perpendicular setting while walls the to parallel 0 p 2 1  ˙ swl stemtra aaeescohesion parameters material the as well as ij  ˙ ij ) 1 T / 2 ), h eprtr.Alvsosprmtr r umrzdi table in summarized are parameters viscous All temperature. the E λ n aucitsbitdto submitted manuscript h hra conductivity, thermal the h ciainenergy, activation the η ρ  = density, II x 2 1 ρC i ( h qaero ftescn nain ftestrain the of invariant second the of root square the ( τ i K B yield 1 p 1 = n DT ∂τ ∂x Dt Dp Dt )  ˙ − ij φ =sin( g , ij T j 2 i n =30 1 ˙ = = − , − rvttoa acceleration, gravitational (˙ )dntsteCreincoordinates, Cartesian the denotes 3) h temperature, the ν   α ∂x ij el II ∂x ∂p ∂ –8– f02fralcutlrcsadtemantle the and rocks crustal all for 0.2 of ◦ DT φ Dt ˙ + ) i ) i and n 1 p   + − ij vi +cos( λ + n ρg 1 ˙ + G:SldEarth Solid JGR: ∂x ∂T exp c ∂x ∂v h oelwexponent, powerlaw the i 0 H  0(3) =0 i ij pl 1 P o l rocks. all for MPa =10 i i   φ  ij el 0(4) =0 h ouercha oreand source heat volumetric the ) + nRT ˙ , c c E 0 0 H  ij vi n n rcinangle friction and v η i  n ˙ and hc olw the follows which , τ G h eoiyvector, velocity the yield (7) , hc ecompute we which ,  hc eed on depends which , ij pl K ersn h elas- the represent h ukmod- bulk the R φ h univer- the : p ◦ (Jang spres- is C p (6) (5) (8)

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article rvt oes d D o est otat∆ contrast density the for resampling PDF from (d) resulting gridded models. (PDF) regular gravity functions the density to probability due Posterior space (d-e) parameter models. 2-dimensional initial this in (8 projected 512 are of they model when fitting dinate best the is misfit high of areas 6. Figure for httegoer ftelwrpr fteAM ( APMB the of part lower the of geometry the that Dve frfrneAM.Eeyhn eo oto oyo rd saetdby affected (g) is new). (red) = 1 solid polygon original, control = below (dashed Everything polygon APMB. single reference a of affect view ( Sy 3D part and upper Sx how the show for to case Sketch the (f) is opposite The distributions. Gaussian by described oyo hwn elcredsrbto u r nta on ihnteetr ag with range entire the within found instead are but distribution curve Sy bell no show polygon and ( deviation standard a and ∆ by controlled being models misfit low of range the with spread large Sy cie nmr eali upeetr etS n iue desmaieteresults. de- the is summarize algorithm 6d+e polygon resampling Figures m The and ∆ S4 priors. kg for text our 250 samples supplementary as to accepted in parameters 0 The detail stretch of more all (1999b). ranges in for Sambridge the scribed 2.0 by in to described numbers 0.1 approach random and rejection distributed the uniformly with use We space space parameter parameter the the sample reduce the to of thickness (2014) investigation. thickness the al. our km keep et for 9 Ward to size by of decided reasonable suggested body therefore a extent We magma to the a (2018). to with al. fixed anomaly et ∆ APMB McFarlin Bouguer a by the set that proposed fit independent show as to an and necessary performed S3a be also Figure poorly would We supplementary is in body. ∆ APMB displayed varying magma the are only the of models, extent of 1000 lateral part of the upper that the demonstrates for good This constrained a 6c). is (Figure the There entirely of S2. m selection Figure a kg in show 130 found 6a-c to be Figure 80 can tween parameters. overview ∆ 5 full between the a correlation of while out ones 2 important of most dependence in model Inversion Gravity 3.1 Results 3 sets. both by affected 2 1 Sx hl vrtigaoecnrlplgn2(le saetdby affected is (blue) 2 polygon control above everything while , rnigtwrstelwrand lower the towards trending σ ooti oeqatttv eut eflo aeinivrinsrtg n re- and strategy inversion Bayesian a follow we result, quantitative more a obtain To individual each of misfit the plot we inversion, gravity the of results the visualize To 1 nsldred, solid in 0 = Sx 1 and . ac ifi Φ ndpnec fst f2prmtr.Nt htec o nthe in dot each that Note parameters. 2 of sets of dependence in (Φ) Misfit (a-c) 8ad01.Smlsfor Samples 0.12. and 08 Sy 1 Sy − ρ r lonral itiue with distributed normally also are 1 , 3 Sx ndse red, dashed in n . o13 epciey(iue6a,b). (Figure respectively 1.3, to 0.8 and σ aucitsbitdto submitted manuscript 1 ρ f97k m kg 9.7 of ) and hwanra itiuinwt en( mean a with distribution normal a show ρ n h etcletn fteAM ( APMB the of extent vertical the and Sy 1 Sx ihtebs tigmdl en osrie be- constrained being models fitting best the with 2 Sx Sx oad h pe end. upper the towards − 2 2 3 nsldbu and blue solid in and h tec atr o h oe control lower the for factors stretch The . –9– ρ hwn tt e111 be to it showing , Sy Sx 2 G:SldEarth Solid JGR: 3 hc r eae oteuprcontrol upper the to related are which 1 esosta l lto h aecoor- same the on plot all that versions ) and µ Sy 1 = Sy ρ 1 swl osrie n a be can and constrained well is ) 2 fruhy20k m kg 200 roughly of ndse le hsshows This blue. dashed in . Sx 4ad12 respectively 1.23 and 04 Sx 2 2 ± ρ and µ S , and f11k m kg 111 of ) . gm kg 9.7 z Sx .Teresults The ). Sy 1 Sy and 2 − 2 eta atis part Central . 3 Sx show o ∆ for Sy − 2 − 3 Sx 1 e PDF (e) . and 3 1 ρ − 3 and Sy 2 ).

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article aaeesa ela cln a htdsrbshwifleta niiulprmtr are parameters individual influential all how of set describes gradients parameter that finite-difference and law the model scaling compute a a can Utu- With as we of well (2018a). well, summit as observations al. the parameters the et at match Reuber velocity can of vertical that approach the the for following testing runcu sensitivity the automated weakens an and formed APMB the inside flow thinning the how restricts illustrates diameter 8b rise, pattern. its Figure central (Figure deformation half APMB’s NW- system. uplift surface to the the the minor rise of towards impacted of central flow geometry it areas the minor the two changing creat- some in how the down, uncertainty investigated also to sinks aforementioned we is corresponding same from the There body, the drained Given magma surface. At are 7c). the the that 8a). of at APMB (Figure NE-edge pushing subsidence the uplift upwards, and of of of and ring parts area rise the the concentric central ing overlying the the crust creating towards the and APMB time, up the crust of overlying outskirts the the from flowing is LSwe rjcigtesraevlcte noteacnigstlietakENVISAT peak track of satellite north- shift ascending the westwards the in km into broken 6 velocities is the surface ( ring ∆LOS reproduce the 89 The with also (∆LOS projecting We subsidence km. minor when noticeably. of 150 of ∆LOS move ring roughly areas of not diffuse of find velocities does a we diameter peak surface is where a with 7c). there east and ∆LOS, (Figure area, and cm/yr positive data uplifting west 0 of InSAR the to area and the Around -0.3 wide location to of km cm/yr. the fit 80 1.2 do improved altered circular, - gravity we an a 1.1 and achieved APMB, produces imaging and the model seismic rise APMB of The of central the features resolution the of scale spatial of rise smaller It the geometry central constrain and 7b). As the to uplift (Figure overlying shallowest). allow of observations was was not areas InSAR area it show to the uplifting where did 1 match the (i.e. result not that eq. the did apparent used While however pattern and was the direction. velocities subsidence, sight surface of of predict areas line to into LaMEM them in project models forward performed we Models Thermomechanical 3.2 7. surface Figure corresponding of the colorbar show completely the Insets made using features. were deformation, relevant cm/yr the 0.3 of and visibility -0.1 better velocity between vertical for Areas show transparent body. areas magma Shaded the (b). above diameter crust its the of in 50% to narrowed was rise central the 8. them. Figure between that changed APMB was the rise of central slices modulus the 2D-EW shear of exaggerated higher shape vertically a the are with how c c illustrate, and pow- of b Variation higher above a (f) Sketches with crust. mantle. c upper the of the Variation in of (e) law mush. flow density the lower for in a basis exponent with erlaw and c rise of central Variation of seismic (d) geometry by row. and constrained 2nd solely location the geometry, altering the after of Results Result in (c) (b) gravity. ones and the data. imaging to InSAR identical (a) are 3. and and orientation 2 for 1, are Figures circles dashed and Solid LOS. into projected 7. Figure φ = ogi oeisgtit h aaeesta h oe ssniiet,w per- we to, sensitive is model the that parameters the into insight more gain To material that shows APMB the around and inside field velocity the at look a Taking sn h am oy osrie ysimciaigadgaiymodelling, gravity and imaging seismic by constrained body, magma the Using − 3and 13 eoiyfil nieadaon PBfrterfrnecs a n aewhere case a and (a) case reference the for APMB around and inside field Velocity models different of velocities surface the and data InSAR between Comparison λ =41 . ) srpre y(ilo&Pas,2012). Pearse, & (Fialko by reported as 1), aucitsbitdto submitted manuscript –10– < G:SldEarth Solid JGR: . my)ulf n h remaining the and uplift cm/yr) 0.3

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article eta ie( rise central in increase an to lead will sms hra aaees(hra expansivity (thermal parameters components thermal elastic most followed the as is crust, It upper deformation. and mush surface maximum dacitic modulus between the (shear contrast on density influential the most by is mush) dacitic the energy vation and oetmt t netite.Teaayi lospot h ocp famgabd of body magma a of concept us have the allows could supports also set also interpretations data analysis different neither The 90’000 which than uncertainties. APMB more its the Computing estimate of to own. geometry its scale on large provided the of picture bust Gravity and Imaging Seismic 4.1 Discussion 4 and model. Fialko diapir uplifted. their equi- has in isostatic it observation be reach elevation same eventually to surface the will is the report system which and (2012) the time, mush Pearse over magma, buoyant decreases of the velocities between supply the librium new of without amplitude as the expected Only the pattern. affects mation 20% Figure by displacement. mush the surface and of the crust modulus on between shear contrast effect is the density no which 7f, the to 20% system. Figure changing little by In how with crust shows velocities. 20% upper 7d LOS by the Figure the in increased of as from increase was exponent results conclusions mantle strong powerlaw simulation the a the forward that with of our shows associated increase with 7 an consistent Figure represents are of 7e analysis row exponent lower law The scaling velocity. surface the on ductivity would parameter respective the to shows in corresponding 9 change triangles Figure relative observable. a the strongly change how describes exponent law where nteosrainpit thsteform: the has It point. observation the on material. one any with associated not therefore are They model. Parameters rock. host associated its and and magma the between contrast characterized density is the Dacite instance, (for parameters viscosity same Utu- linear the of by use summit materials the all at not velocity that vertical Note the case, runcu). this (in observation the change would parameter ( value 9. Figure Sx b 1 h cln a ugssta h hooyo h pe rs cnrle yteacti- the by (controlled crust upper the of rheology the that suggests law scaling The h on nepeaino esi mgn tde n rvt aapoie ro- a provides data gravity and studies imaging seismic of interpretation joint The defor- surface the affect not does time of amount longer a for model the Running u | 2 to b obs | r emti aaeeso h PBand APMB the of parameters geometric are fteepnn faprmtri esr fhwsrnl eaiecag nthat in change relative a strongly how of measure a is parameter a of exponent the of ) k b htaentascae ihteuprcuto aii uhhv iteeffect little have mush dacitic or crust upper the with associated not are that ) n steosre velocity, observed the is Sx r h epciesaiglwepnns If exponents. law scaling respective the are uoaial optdsaiglwepnnsfralprmtr.Teabsolute The parameters. all for exponents law scaling computed Automatically En 2 G and h oelwexponent powerlaw the , η n oso ratio poisson and hl h pe rs’ hooyi endb n nadn.∆ n). and En Bn, by defined is rheology crust’s upper the while Sy 2 .Tepatcprmtr cohesion parameters plastic The ). u b> aucitsbitdto submitted manuscript obs n onadpitn rage orsodn to corresponding triangles pointing downward and 0 n ievrafor versa vice and A ν ftedctcms swl stegoer fthe of geometry the as well as mush dacitic the of ) sapre-factor, a is u | b obs | o l oe aaees ihuwrspointing upwards with parameters, model all for n = n nietyb h nta temperature initial the by indirectly and Ap –11– 1 b 1 p b α 2 b i etcapacity heat , 2 G:SldEarth Solid JGR: < ...p T p bot 1 .Teaslt au ftescaling the of value absolute The 0. n b to b n h eprtr ttebto fthe of bottom the at temperature the i > p n c ,a nraei parameter in increase an 0, 0 r h oe parameters model the are n rcinangle friction and Cp n hra con- thermal and φ Sx b< swell as ρ 1 , 0. T describes Sy of p 1 i , Sx (9) 2

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article oiin(al 2,icuigvltl opnnsa ela eprtr n pressure. and and com- temperature material, H its as crustal on proposes well and (2017) depends as melt density al. components of Melt et volatile mix Laumonier including components. a S2), both be (table between to position balance APMB mass the the assuming computing by APMB the within Content Melt 4.2 parame- these of influence small the signal. shows Bouguer range the parameter for entire ters the within samples find well anomalies Bouguer the fits model reference our of size the ( EW-direction depth by In same fraction. (defined the lies. melt depth at highest km roughly the 11 is contains below it body that the S3a Bouguer likely of observed Figure is center the in it the trend reproduce et scenarios, As the to Zandt three layer. but enough 1999; suggested all thin range, be al., as in a that not et zone such to would Chmielowski melt with calculations melt (e.g., thin anomalies our pure 2000s km even extend early 1 that not and a suggests did 90s for ( We late worse range 2003). even the thickness a al., is of the that case studies fit shows The the to S3a by necessary (2018). Figure be al. (2014). would et al. McFarlin 10) et (Figure Ward 40% by of proposed ∆ as high thickness, quite in km 15 about the on Details S3. content. text melt supplementary show in Planes found projections). are 2D calculations are ellipses (gray study this in sumed H and contrast density density, crustal of 10. Figure u suigasmlrrne ewudepc bu %mr eti h pe atof part upper the in content melt water more for 5% estimates about lack expect we would part we dacitic APMB. range, the the similar For a study. assuming this but than melt of tribution of density contrast, density between correlation the shows 10 H Figure crust, the body. magma the of It APMB. the of signal lower overall the the surface, on be the influence cannot to little body why closer too magma clear being has the not Despite rise of is they central part data. layer the gravity upper velocity within of The the low mass help APMB. with thin the the coincides the with of edge that constrained edge northern suggesting the Its 2003), represents al., geometry. imaged, et fitting (Oncken best profile our ANCORP of extent lateral maximum 21)(-5)bsdo h euto fserwv eoiyadwt h rfre model al. preferred et the Ward with of and estimation velocity the ( wave several of (2013) shear on range al. of based upper et reduction % the Potro the et 14-27 on with of on Comeau of be coincides based 2006; estimation should also (4-25%) al., the APMB It (2014) et with the Schilling 2016). line Kr¨uger, of 1997; 2015, in & part al., (Schwarz is andesitic studies which the H conductivity et vol-%, in and electrical Prezzi 15-22 content 2019) 2006; of melt al., al., order the et et the ranges, Ibarra (Tassara these 2013; crust on al., middle Based et the Laske of 2009; density al., study), (this contrast density µ Sx 1 1 = h osrit egie n∆ on gained we constraints The APMB the of extent the that shows 6e) (Figure data gravity the of resampling The . 4 hl tsol eetne nN-ieto ( NS-direction in extended be should it while 04) 2 ρ otn n etfato.Terdelpoddsly ieyrne o the for ranges likely displays ellipsoid red The fraction. melt and content O of siaino neii etcneto h oe afo h PBi dependence in APMB the of half lower the of content melt andesitic of Estimation Sx ∼ 2 0 gm kg 200 rnstwrshg and high towards trends ∼ 5)wihi ae ngaiydt u rpssadffrn dis- different a proposes but data gravity on based is which 25%) aucitsbitdto submitted manuscript − 3 Sx n,ascae ihta,aml otn nterange the in content melt a that, with associated and, 1 2 otnso pt 0%frtelwradstcpart andesitic lower the for % 10 to up of contents O and ρ lo st aeetmtoso h etfraction melt the on estimations make to us allow 2 Sy otn.Rdelpodidctstedt ag,as- range, data the indicates ellipsoid Red content. O 1 swl osrie yteBuuranoma- Bouguer the by constrained well is ) –12– Sy 2 oad o ausbttefc htwe that fact the but values low towards G:SldEarth Solid JGR: 2 otn Luoire l,2017). al., et (Laumonier content O µ Sx 1 1 = ≈ . 3.Fgr hw the shows 1 Figure 23). m rpsdby proposed km) 8

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article oes h oe u-iue hwpoaiiydniyfrtesrthfcosi 11( 11.1 in factors stretch the for density probability show sub-Figures lower The models. 11. Figure cetd200 h pe u-iue hwterslso h eapigo h thermomechani- the of resampling only the where of models results cal the show sub-Figures upper The 20000. accepted Sy r hrceie by characterized are for 2a). distribution (Figure probability data a InSAR get the to and models 1) size models. the the (eq. thermomechanical resampled reduce expensive we to more data, and Sx gravity computationally gravity the the from to for constrained Similarly space well parameter already the are of they as constant rameters varying h emtyo h eta iew a 00fradmdl 40iiil+60i ra of areas in 600 + initial (400 models for forward constrain been 1.23 To 1000 have and ran 6e). not 1.04 we (Figure and would using rise data shape which misfit) central gravity the its like, low the and on on look of imaging deformation depends areas geometry seismic of shallow uplift the considering magnitude APMB’s surface only and the of the by how center pattern shows possible constrain the the also reproduce can As and It to we rise body. 8). crucial size, central the and is the in 7 APMB of rise (Figures the location pronounced InSAR of a by center for observed the necessity pattern to deformation outskirts surface the the from material mush of Rise Central The 4.3.1 modelling Thermomechanical 4.3 way the of sketch polygon. another single shows side Right green. in resampling gravity eta iestpare elwt h o fti etr Fgr 2.Wr ta.(2014) al. et Uturuncu. Ward beneath 12). the shallowest (Figure of body feature width magma this and the of location see top depth, they the that melt The that with Provided represents likely. state well (2017) most below. also agrees al. the from top et be emplaced rise’s Kukarina would are central by scenario melt Lastly, imaged (and last of there. anomaly hottest the batches ascent pathways, tooth-shaped is new magma rooted, crust where facilitating et deeply the area APMB, Muir the that the the 2008; fact be of al., the may center et is this the (Sparks shal- explanation above eruptions small, possible weakest) to to Another therefore prior melt 2014b). old level of initiated 2014a, of sea transport been al., reactivation around the have the reservoirs must suggest is magma it studies explanation low Consequently, geochemical reasonable own. multiple One its as pathways, perturbation. on system. initial APMB magmatic some topped the through flat the of a of approaches part from half two lower lower rise the the the Combining and of upper extent velocities. the the surface both time, the on same on sensitive constraints the effect thermome- very useful At negligible the are yields a rise. velocities incorporating has central surface but only the the APMB APMB of as the geometry that of the provides for parts to curves) compensate upper resam- (green can the gravity anomalies simulations on the Bouguer chanical constraints of the no representation analyzing to interpolated that little an demonstrates with This results pling. these combines 11 Figure 1 2 n . mdph( depth km 8.9 and ) and h eapigrsle nna-asindsrbtosfrbt tec atr which factors stretch both for distributions near-gaussian in resulted resampling The oeln h hroehncldnmc ftesse ihihsta transport that highlights system the of dynamics thermomechanical the Modelling hl h oe a hwtencsiyfrtecnrlrs,i a o eeo the develop not can it rise, central the for necessity the show can model the While Sx Sy 2 2 sn h ifi ewe h oeldsraevlcte rjce noLOS into projected velocities surface modelled the between misfit the using , and obndrslsfo h eapigo rvt n hroehnclforward thermomechanical and gravity of resampling the from results Combined Sy 2 µ nteetr ag ewe . n ..W etteohrtrepa- three other the kept We 2.0. and 0.1 between range entire the in Sx2 Sx Sx 2 0 = and 2 aucitsbitdto submitted manuscript and . 0and 70 Sy Sy 2 Sx eevre nbakaogtePFof PDF the along black in varied were 2 .Wieaesddntrcr igesml mn the among sample single a record not did areas White ). 1 µ Sy2 and 1 = Sy –13– 1 . 4a elas well as 04 epciey n 1 kgm 110 and respectively, G:SldEarth Solid JGR: σ Sx2 0 = . 3and 03 Sx − Sx and 3 2 o ∆ for σ and Sy2 Sy ρ Sy nunea influence 0 = while 2 Sx . rmthe from 05. 1 and

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article oeo uynya h rvn oc ftesse.Btisedo 0k iediapir wide km 10 a of instead But system. the of melt(∆ force pure driving almost the of as buoyancy of are role as forces simulate source buoyancy to pressure model, body prescribed our the a In of without consistently, column. rest force. self the the driving material to in the the of there source sink in flow from pressure pressure degree this moving a a lesser developing mush and prescribe a of 12) (2017) to effects (Figure al. however, and the the column et is, feature of vertical Gottsmann There central part importantly, the the material. active more in of attracts an But geometry that as body. the feature APMB main in central entire difference a the notable of of a presence consideration the the and notably system most (2017), al. et geometries different depressurization, the for shows source 12 studies. previous a Figure aforementioned only as the column. the it by extending is using or proposed vertically (2017) body, elastic a al. magma purely create pressurizing et entire a and while Gottsmann the in forces considered 1958)) crust. buoyancy that Hickey (Kiyoo, 2013) neglect study (2004), Model al., (2017) Simons (Mogi et Pritchard (Hickey and sources and Pritchard linear-visco-elastic point Henderson density inflating crust). as by through denser well caused stresses a as temperature- are in (2013) the stresses rising al. in (2012), mush et As Pearse light and rocks. (i.e. Fialko real instabilities of for model observed including visco-elastic rheology, are dependent visco-elasto-plastic that mechanisms rate-dependent deformation strain all and temperature- a with Models other to Comparison local 4.4 of bulk the with detected coincides (2017) This al. MPa). et plastic Kukarina 10 observe and and we (2012) 1 where 12). al. both area (Figure et of only earthquakes Jay cohesion the where rock is domain (for which the simulations level, our sea in and yielding surface uplift. between by rise generated isostatic tral it aforementioned elevation the the is with scale) uplift reaches 1965, (century long-term magma since long-term of buoyant uplifting no absence the for been the that that evidence has for paradox equilibrium geomorphic Uturuncu reason the show that Another solve (2016) show to uplift. al. to help et able even de- Perkins are could velocities while (2018) velocities surface several al. surface the by et of on viscosity Gottsmann slowdown effect its decades) relevant shift volatiles to a can have years of which also loss magma for could includes the paths This scenario spite in exit possible magnitude. content developing Another of crystal or orders candidate. in supply increase good magma an a waning or through be would possibly fluids, heat, the hot of over loss velocities 2b). a surface con- (Figure however, ture, in (2018) can, decrease trade We al. the mush et solution. explain and Lau unique can crust by a them upper reported find of the as any to of decade, in impossible rheology quantities. past change is multiple the a it of as that so well function clude other, as a each rise is against central turn off the in of which geometry APMB, The the within transport material Parameters Key 4.3.2 isadcntandb rvt saboatbd ihadniycnrs faot110 about of contrast density a with body buoyant a m as gravity kg by constrained and mics η neeetta u td hrswt h oko iloadPas 21)i the is (2012) Pearse and Fialko of work the with shares study our that element An Gottsmann of work the and study our between similarities important some are There system magma Altiplano-Puna the of model 3D first the present we study, this In cen- the above highest are they that show crust the in stresses deviatoric at look A tempera- on depend mush magma the of and crust upper the of rheology both, As of magnitude the by controlled is pattern deformation surface the of amplitude The − Dacite 3 otesronigcrust. surrounding the to o akn ihi iue9 h osblt o udn(ntmsae of timescales (on sudden a for possibility The 9. Figure in high ranking not ρ 0k m 400kg = aucitsbitdto submitted manuscript − 3 ,w osdrteetr PBa mgdb seis- by imaged as APMB entire the consider we ), –14– G:SldEarth Solid JGR:

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article ansGtnegUiest an hcuimizd) hc samme fteAHRP the Jo- of by member offered a services is research advisory which this and/or (hpc.uni-mainz.de), of uni- Parts II Mainz using perceptually University Mogon 2018). created used Gutenberg supercomputer were (Crameri, We hannes the 4 distortion 2013). using and data al., conducted 3 optical et were prevent 1, (Wessel project, to Figures 5.4.3 MAGMA colormaps in version the form maps Tool, through The Mapping Council Generic 771143. Research the # European Grant the Consolidator by ERC funded was study This a Acknowledgments as geometry treating recommend influence and the density. solution quantify forward or and the rheology demonstrate quantify like on we also parameter Lastly, geometries and model include. and parameters initial data sets more of the data constrain that different to of uncertainties Combining us parts the allows unconstrained. to techniques parts sensitive modelling other only different leaving are while observables system most the as models, thermomechanical consistent deformation as surface well the as slowing volatiles currently or uplift. be our heat long-term improve to of preventing to candidates of Loss and likely necessary understanding down are is systems. better well mush crystals magmatic a as of Consequently, especially of rise growth and dynamics mush. the crust the and of of upper crust width demon- understanding of upper the and properties the on pattern rheological of mainly deformation the rheology depends (i.e. link surface the deformation intrusions the the on of large show and as amplitude for also rise We the need central is that no the deformation. from, strate is of surface drained there observed geometry being model, the the areas overlying between our reproduce the the In to overlying pushing sources) crust, pattern. rise, pressure ring-like the central a time, a mush in same towards of subsiding the APMB transport At the buoyancy-driven upwards. of the crust outskirts by the caused from be material can of deformation part lower surface the observed in fraction melt vol-%. the 15-22 estimate be can to we APMB products, the eruption of chemistry the nteetn fteAM n oetmt t est otatt h urudn crust surrounding the to contrast m density its kg estimate constraints 130 to joint the - and a optimize 90 APMB use to be the We anomalies to of data. Bouguer grav- extent InSAR and imaging, the and velocities seismic on wave locations by shear earthquake made of models, observations interpretation density with crustal consistent surveys, is ity which system, magma Puna Conclusions 5 exaggeration. vertical Bottom the (2017). Note al. body. et full Kukarina cover from to Fig- isocontour out the 1.9 Zoomed of = outside right: Vp/Vs plots the which shows depth, line km black Pritchard 65 Dashed and at Henderson ure. source circle. pressure one deflating in a summarized Simons postulate are and also they Pritchard (2017) other, of each models of the top of and on most magma plot As between (2004) (2017). transition al. the et shows Gottsmann line from red material Dotted earthquake hybrid of (2012). bulk al. shows et line Jay purple by dotted reported and earth- locations (2017) show al. stars et Black Kukarina sources. from pressure locations line inflating quake Solid are lines pattern. dashed InSAR driven, observed density the are reproduce models that models various the top, On Uturuncu. 12. Figure u eut lal hwteavnae fuigjititrrttosadphysically and interpretations joint using of advantages the show clearly results Our the that show LaMEM code stokes thermomechanical the with models Forward epeeta3 olna ic-lsopatcnmrclmdlo h Altiplano- the of model numerical visco-elasto-plastic nonlinear 3D a present We Wsietruhteserwv eoiymdlfo ade l 21)beneath (2014) al. et Ward from model velocity wave shear the through slice EW − 3 (2 σ aucitsbitdto submitted manuscript .Bsdo ht n sn rsa est oesa elas well as models density crustal using and that, on Based ). –15– G:SldEarth Solid JGR:

This article is protected by copyright. All rights reserved. ThisAllarticleis rights by copyright. reserved. protected Accepted Article avle . amn,T .(09.goi:A pnsuc ALBtoolbox MATLAB open-source An geomio: (2019). S. T. Baumann, & A., Bauville, non- the constrain to inversion Geodynamic (2015). P. J. B. Kaus, & T., Baumann, mod- earth global for centre International (2016). K¨ohler, W. & F., Barthelmes, ash volcanic The (2010). G. M. Oprea, & C., L. Stoian, S¸tef˘anie, I., N., H. Ajtai, References otaefrti eerhi vial nznd at: zenodo on available is research this for Software references: citation data in-text these in available are research this for Datasets Section Research Open suggestions. their and with www.ahrp.info) manuscript Palatinate, the e.V Rhineland Alliance in Gauss Computing the Performance High for (Alliance • • • • • 6517.Rtivdfrom Retrieved doi/abs/10.1029/2018GC008057 1665–1675. drawings. vector simulations 2-D thermo-mechanical from 2D/3D of configuration initial the create to 1289–1316. lithosphere. the of rheology linear 2016. 90 handbook geodesists The in: (ICGEM), els 2010. Sciences April 21st and North- 14th over between plume de- Europe ash Eyjafjallaj¨okullWestern the volcanic the on the study of case impact A industry. and transport tection air European on impact its and ucinlslcin gravity selection: Functional EGM2008, selection: Model K¨ohler, 2016), & http://icgem.gfz-potsdam.de/home (Barthelmes anomalies: Bouguer emO Buil amn,2019), http://doi.org/10.5281/zenodo.4339050 Baumann, & (Bauville geomIO: 2016), http://doi.org/10.5281/zenodo.4419782 al., et (Kaus LaMEM: 2012), https://igppweb.ucsd.edu/ Pearse, & (Fialko InSAR: https://ds.iris.edu/ds/products/emc-apvcpunaantrfward2017/ 2017), 2014, al., https://ds.iris.edu/ds/products/emc-apvcantrfward2014/, et m (Ward 75000 Vs-model: Sigma, 6 Filter: Gaussian 0.05 Step: Grid 1) 907–1205. (10), , 2 1,57–68. (1), ◦ ‥ , eas hn nnmu eiwr o mrvn h ult of quality the improving for reviewers anonymous 2 thank also We aucitsbitdto submitted manuscript ∼ fialko/data.html anomaly https://agupubs.onlinelibrary.wiley.com/ eceity epyis Geosystems Geophysics, Geochemistry, o:10.1029/2018GC008057 doi: bg, epyia ora International Journal Geophysical –16– G:SldEarth Solid JGR: dacsi Environmental in Advances ora fGoey(2016) Geodesy of Journal , , 202 20 (3), (2), ,

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