Abstract We present a new GPS velocity field covering the peri-Adriatic tectonically active belts and the entire Balkan Peninsula. From the velocities, we calculate consistent strain rate and interpolated velocity fields. Significant features of the crustal deformation include (1) the eastward motion of the northern part of the Eastern Alps together with part the Alpine foreland and Bohemian Massif toward the Pannonian Basin, (2) shortening across the Dinarides, (3) a clockwise rotation of the Albanides-Hellenides, and (4) a southward motion south of 44 ∘ N of the inner Balkan lithosphere between the rigid Apulia and Black Sea, toward the Aegean domain. Using this new velocity field, we derive the strain rate tensor to analyze the regional style of the deformation. Then, we devise a simple test based on the momentum balance equation, to investigate the role of horizontal gradients of gravitational potential energy in driving the deformation in the peri-Adriatic tectonically active mountain belts: the Eastern Alps, the Dinarides, the Albanides, and the Apennines. We show that the strain rate fields observed in the Apennines and Albanides are consistent with a fluid, with viscosity ∼ 3 × 10 21 Pa s, deforming in response to horizontal gradients of gravitational potential energy. Conversely, both the Dinarides and Eastern Alps are probably deforming in response to the North and North-East oriented motion of the Adria-Apulia indenter, respectively, and as a consequence of horizontal lithospheric heterogeneity. Introduction The surface deformation in collisional belts has challenged the plate tectonics theory for a long time. Indeed, most mountain belts and in particular the Himalayas and the Andes are characterized by broad deforming areas with multiple active faults far from the simple view of a sharp boundary between two large and rigid lithospheric plates [e.g., Molnar, 1988; Molnar and Tapponnier, 1975] . In the last decades, several attempts to model these complex deformation patterns have been conducted based on different assumptions about the rheology of the lithosphere and the forces affecting it. First, several authors proposed first-order models of mountain belt deformation considering that lithosphere can be split into small-scale rigid blocks rotating around Euler poles and bounded by active faults accommodating their relative motion [e.g., Chen et al., 2004; Meade, 2007; Thatcher, 2007] . However, alternative models assuming a continuous and viscous lithosphere deforming under kinematics boundary conditions and body forces have been shown to reproduce just as well the deformation in these areas [e.g., Flesch et al., 2000; Vergnolle et al., 2007; Copley, 2008] . Indeed, the horizontal gradients of gravitational potential energy (GPE) between mountain ranges and their forelands [e.g., Molnar and Lyon-Caen, 1988; England and Houseman, 1989; England and Molnar, 1997] , together with lateral variations in the lithosphere rheology [e.g., Robl and Stüwe, 2005; Copley, 2008] , may be controlling a significant part of the continental deformation. Based on mantle anisotropy and surface velocity measurements, it has also been proposed that astenospheric convective motions could drive surface deformation through basal shearing of the lithosphere [e.g., Le Pichon and Kreemer, 2010; Brun and Sokoutis, 2010] . Overall, determining which of these mechanisms (boundary conditions, body forces, elastic loading on active faults, and mantle-driven deformation) is dominant and controls the deformation pattern in a continental mountain belt is not a simple problem [see Thatcher, 2009 , for a review]. Here we take advantage of a new velocity field covering the deforming peri-Adriatic region and the Balkan Peninsula to assess whether the peri-Adriatic belts are deforming as a consequence of horizontal GPE gradients or if other controlling factors may play a role. Introduction Our study area, namely, the peri-Adriatic region, encompasses the Italian Peninsula, the Po Plain, a large part of the Central and Eastern Alps with their associated forelands, the Balkan Peninsula, and the Aegean domain. The Balkan Peninsula, i.e., the portion of Eurasia located in between the Adriatic Sea to the west and the Black Sea to the east and extending from the Alpine and Carpathian mountain belts to the north to the highly straining central Greece to the south, is certainly the less well-known part of this large region (Figure 1 ). F1 Indeed, it is often considered as a stable part of the Eurasian Plate. Compared to the seismically very active zones in the vicinity of structures such as the strike-slip North Anatolian Fault (NAF) and the extensional Corinth Gulf [e.g., Jolivet et al., 2013] , the Balkan Peninsula is seismically relatively quiet. However, it experienced large and destructive earthquakes in the past, mainly in the vicinity of the Dinarides and Albanides mountain belts. More than eight M w > 6 shallow crustal earthquakes occurred since the beginning of the twentieth century, including the 1904, M s 7.2 Krupnik, the 1963, M w 6.2 Skopje, and the 1979, M w 6.9 Montenegro earthquakes [Ambraseys and Jackson, 1998; Shanov and Dobrev, 2000; Petrovski, 2004; Galasso et al., 2013] . Introduction Over the past few years, several GPS studies brought new insights on the deformation pattern around the Adriatic Sea. First, the nearly rigid rotation of the Adria and Apulia microplates forming the core of the Adriatic domain generates a 2 to 4 mm/yr northeastward motion into the Eastern and Central Alps [e.g., D'Agostino et al., 2008; Cheloni et al., 2014] and into the Dinarides [e.g., Serpelloni et al., 2005; D'Agostino et al., 2008; Nocquet, 2012] . Furthermore, the eastward motion of the Eastern Alps toward the Pannonian Basin has been extensively discussed and analyzed [e.g., Robl and Stüwe, 2005; Selverstone, 2004; Ratschbacher et al., 1991] . Second, very dense measurements available over the Italian Peninsula have confirmed that the Apennines are extending in a roughly SW-NE direction along their topographic crest [e.g., D'Agostino et al., 2008 [e.g., D'Agostino et al., , 2014 . Finally, in the Balkan Peninsula, the NS extension observed in Northern Greece and the Aegean Sea continues MÉTOIS ET AL. Introduction DYNAMICS OF THE PERI-ADRIATIC BELTS 2 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth 10.1002/2015JB012023 at ∼5 mm/yr into the inner Balkans and the southern margin of the Pannonian Basin [Matev, 2011; Burchfiel et al., 2006; Perouse et al., 2012] . Moreover, northwestern Greece and Albania are rotating clockwise [Reilinger et al., 2010; Nocquet, 2012; Perouse et al., 2012; Jouanne et al., 2012] . Therefore, the peri-Adriatic area including the Balkans is slowly but actively deforming ( Figure 1 ). The lack of sufficiently dense GPS measurements has prevented so far the determination of a consistent image of the peri-Adriatic domain deformation and of the transition from the SW-NE compression across the Dinarides to the NE-SW extension pattern documented in Southern Balkans [e.g., Burchfiel et al., 2006; Perouse et al., 2012; Nocquet, 7785587195/2015JB012023 Since the beginning of the 21st century, new GPS networks have been developed for scientific research but also for civilian applications (e.g., cadastral and telecommunications), in particular in the Balkans area. Here we take advantage of these continuous GPS data coming from academic and nonacademic networks to obtain a new interseismic velocity field. We calculate an interpolated velocity field and compute the homogeneous strain rate distribution over the entire area using the method described by Haines and Holt [1993] . The derived strain rate map brings new insights into the deformation pattern within the continental collision systems around the Adriatic Sea. Finally, we propose a simple method to test the role of gravity on the dynamics of the peri-Adriatic mountain belts. We take advantage of the new velocity field to carry out simple tests that allow us to discuss whether the deformation of the lithosphere in the region of interest is mainly controlled by forces applied at its edges, by gravitational forces or strength heterogeneities arising from horizontal heterogeneities in crustal and lithospheric structures. GPS Data and Processing In this study, we gather data from 711 permanent stations coming from scientific and civilian GPS networks distributed over the Eurasian plate, Balkan Peninsula, Greece, Italy, Turkey, and Austria together with more widely distributed stations for reference frame realization (additional supporting information). All networks made the receiver-independent exchange files directly available to us, allowing for a consistent processing for Q3 all the stations, except the Austrian network that only provides only provides solution independent exchange Q4 (SINEX) solutions (i.e., coordinates and their covariances, see section 2.3). Data Processing GPS data were reduced using the Jet Propulsion Laboratory (JPL) GPS Inferred Positioning System (GIPSY)-Orbit Analysis Simulation Software (OASIS) II software (version 6.2) in a precise point positioning mode applied to ionospheric-free carrier phase and pseudorange data [Zumberge et al., 1997] and using JPL's final fiducialfree GPS orbit products [Bertiger et al., 2010] . We apply the Global Mapping Function [Böhm et al., 2006] and estimate tropospheric wet zenith delay and horizontal gradients as stochastic random walk parameters every 5 min [Bar-Sever et al., 1998] , to model tropospheric refractivity. We compute the ocean loading from the FES2004 tidal model coefficients provided by the Ocean Tide Loading Provider [http://holt.oso.chalmers.se/ loading & Scherneck, 1991] and apply it as a station motion model. Ambiguity resolution is applied using the wide lane and phase bias method [Bertiger et al., 2010] . Finally, station coordinates obtained in the loose frame of JPL fiducial-free GPS orbits are transformed into the IGS08 reference frame [Rebischung et al., 2012] using daily seven parameter transformations provided by JPL. Eurasian Reference Frame Because we aim at resolving small interseismic velocities (∼1 mm/yr), we take a special care in realizing an accurate continental-scale reference frame. To analyze and interpret station velocities relative to the Eurasia plate with the largest possible accuracy, we have specifically built a new terrestrial reference frame for studying deformation in and around that plate following the approach of Blewitt et al. [2013] . This frame is defined by six Cartesian coordinates and velocities of each of 174 stations selected by specific quality criteria ( Figure 2 and additional supporting information). Our frame is based on GPS time series from 2000.0 to 2014.1 F2 obtained from daily coordinates of over 1000 GPS stations regularly processed at INGV-Rome with the GIPSY software, following the strategy presented in section 2.1. Our Eurasian frame is aligned in origin and scale with International GNSS Service 2008 (IGS08) [Rebischung et al., 2012] , a GPS-based realization of International Terrestrial Reference Frame 2008 (ITRF2008) [Altamimi et al., 2011] . It is implemented to have no-net rotation with respect to the stable interior of the Eurasian plate, realized by a core of 69 stations (Figure 2 ). The Eurasia Euler pole relative to ITRF08 defined by these core stations (with a normalized root-mean-square nRMS lower DYNAMICS OF THE PERI-ADRIATIC BELTS 3 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth 10.1002/2015JB012023 Figure 2. Permanent stations used for reference frame building. Red dots: position of permanent GPS stations used for Eurasia-fixed reference frame building; blue dots: core stations defining its no-net rotation condition. 10.1002/2015JB012023 their frame-predicted positions, the 174 frame stations have a daily RMS scatter of 1.1 mm in the north, 0.9 mm east, and 3.8 mm in the vertical ( Figure S1 ). 10.1002/2015JB012023 This reference frame realization method transforms the station time series into a plate-fixed frame and effectively applies a continental-scale spatial filter to the station coordinates, leading to a reduction of the common-mode errors [Wdowinski et al., 1997] , and to an increase of the signal-to-noise ratio ( Figure S2 ). Integration of Austrian Coordinate Solutions In this study we integrate our daily solutions with the ones calculated by the Space Research Institute (Austrian Academy of Sciences) and distributed by OLG (Observatory Lustbuehel Graz) at ftp://olggps.oeaw. ac.at [Haslinger et al., 2007] . These solutions include the stations of the Austrian permanent GPS network APOS (http://www.bev.gv.at), together with additional stations from EUREF and IGS networks. We used the "GP5yyddd0" solutions provided in SINEX format. The original solutions are obtained using the Bernese software [Hugentobler et al., 2006] following the standards of the EUREF-EUREF Permanent Network Analysis Q6 Centers (http://www.epncb.oma.be/_productsservices/analysiscentres). To align the Austrian solutions in our realization of the Eurasian frame, we select 13 stations common to our and OLG solutions. We combine the daily OLG solutions in the period 2008.0-2014.44 of these 13 stations (BODO, BRBZ, KOE2, GRAZ, LINZ, WTZR, STBZ, PFA2, PENC, SPRN, ZIMM, STPO, and VLCH), constraining a priori their linear velocities to follow our Eurasia plate-fixed estimates. Before the combination, the covariance matrix of each daily OLG solution is augmented (i.e., "loosened") assuming large variances in the seven transformation parameters. Blewitt [1998] showed that this covariance augmentation procedure is equivalent to estimating a daily seven parameter transformation simultaneously with the velocities and epoch positions. We then align the original, complete OLG daily solutions to the newly calculated solution, using a seven parameters Helmert transformation. An average number of 12.6 stations were used to calculate the daily alignment of the OLG solutions. After the Helmert transformation the 13 stations have a daily RMS scatter about their frame-predicted positions of 1.1 mm in the north, 1.0 mm east, and 2.9 mm in the vertical. These values are very similar to the daily RMS scatter of the 174 stations used to realize the Eurasian reference about their frame-predicted positions (see previous section), suggesting a similar level of noise shared by the OLG solution and ours. This procedure allows us to have daily coordinates and associated covariance matrix in a Eurasian plate reference realization equivalent to the one used for our own solutions. Velocities Estimate We estimate interseismic long-term velocities together with annual and semiannual constituents from the continuous GPS time series using the Customer Analysis and Targeting System software [Williams, 2008] . We Q7 use an error model dominated by white noise plus flicker noise to estimate the associated uncertainties and remove outliers. Every time series covering more than 2.5 years ( Figure S3 ) has been manually scrutinized to detect anomalous behavior (instrumental drifts or oscillations associated to bedrock or building instabilities) or unreferenced jumps, before estimating long-term velocities. The standard deviation is 0.61 mm for both east and north components on average. We combine our new velocity field with previously published interseismic velocities in areas where our data is sparse, i.e., in Albania , in Macedonia [Matev, 2011] , in the Aegean domain, and along the Adriatic-Dinaric coast [Nocquet, 2012] after a rotation in our Eurasia-fixed reference frame. Residuals between our data set and the velocities from Jouanne et al. [2012] and Nocquet [2012] once rotated in our reference frame are lower than 0.6 mm/yr on each component (see Table S1 ). The final velocity field presented in Figures 1, 3 , and 4 shows velocities both from campaign surveys and permanent F3 F4 stations, and it captures the overall consistent deformation pattern of the region. Some regions are relatively undersampled (i.e., Croatia and Bosnia), but our velocity field is sufficiently dense in Slovenia, Serbia, and Austria (SIGNAL, AGROS, and APOS networks, respectively, see additional supporting information) to display the main deformational features. The complete velocity field is available as supporting information. U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Deformation Pattern Velocity Field Analysis We observe in Figure 1 the main features of central Mediterranean tectonics: (i) the 2-4 mm/yr NE directed motion of the Adriatic region and the extension across the Apennines at about 3 mm/yr; (ii) the ∼2 mm/yr shortening across the southern front of the Eastern Alps and the progressive eastward rotation of velocities toward the Pannonian Basin; (iii) the ∼4 mm/yr shortening across the Dinarides; and (iv) the southward increasing motion of the Aegean domain and the Southern Balkans toward the Hellenic trench. The novelty of this velocity field described in details in the following (Figures 1, 3 , and 4) lies in particular in the dense velocity fields in Serbia, Slovenia, Austria, and Macedonia illuminating the deformational features located along the actively deforming belts circling the Adriatic Sea, so far neglected in regional kinematic studies. Velocity Field Analysis We image a ∼4 mm/yr gradient in horizontal velocity across the Dinarides (Figure 1 ), but available velocities are too sparse to conclude whether this NW-SE compression is taken up by a single front or by several active structures (see profile B on Figure 5 ). However, it appears that this shortening is accommodated within less F5 U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth 10.1002/2015JB012023 than ∼400 km from the Adriatic coast and therefore barely propagates into the Pannonian Basin. East of the Dinarides, the north-south motion significantly increases southwards from the inner Balkans to the Aegean extensional area (see profile C in Figure 5 ). This overall motion of material toward the south is maximal near 23 ∘ E and decreases toward the Black Sea on the east and the Adriatic Sea on the west. U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth Together, the compression across the Dinarides and the extension of the southern Balkans form a clockwise rotation motion around Northern Albania ( Figure 4 ). This rotation has been partly described by Nocquet [2012] and Perouse et al. [2012] , but the lack of data in the inner Balkans prevented from a precise determination of the northward extent of the rotation cell. Our results show that the rotation propagates up to the southwestern portion of the Pannonian Basin, in Serbia (44.5 ∘ N), and develops around the Albania-Montenegro border, i.e., at the transition from the Dinarides to the Albanides mountain belts corresponding to the Scutari-Peck area ( Figures 1 and 4 ). U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth The lack of data in Croatia and Bosnia prevents from obtaining the details of the deformation across the Northern Dinarides and the Istria Peninsula. However, comparison between the horizontal velocity at the station ZADA (15.228 ∘ E, 44.113 ∘ N) near the Velebit coastal range and the stations along the Slovenia-Croatia border shows that limited shortening is occurring ( Figure 3 ). This suggests that the NE oriented Adriatic oblique motion can only be partially accommodated along the coast and may be more significantly absorbed to the North in the Sava fault area [e.g., Vrabec and Fodor, 2006] . Indeed, North of the Istria Peninsula, the shortening is taken up by the eastward extension in Slovenia of the Eastern Alps thrust front. Together with this small N-S gradient of horizontal velocity, we image for the first time a regional eastward rotation of the entire Slovenia which cannot be fully explained by local strike-slip motion of the easternmost sections of the peri-Adriatic fault (PAF in Figure 3 ). U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth Thanks to the dense velocity field in Austria, we image with great details the motion of the inner Eastern Alps. It clearly appears on Figure 3 that north of the Eastern Alps front and of the peri-Adriatic fault zone that experiences a ∼1 mm/yr right-lateral gradient, the crust is moving eastward together with part of the Alpine foreland and the Bohemian Massif. This motion comes without any clear velocity gradient across the northern front of the Alps nor across the Salzach-Ennstal strike-slip fault that is supposed to accommodate part of the Alps escape toward the Pannonian Basin [Selverstone, 2004; Ratschbacher et al., 1991] . In other words, there is no evidence in the GPS measurements that this strike-slip fault has a significant slip rate nor that the northern front is an active structure. U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth 10.1002/2015JB012023 a systematic ∼1 mm/yr eastward motion relative to stable Eurasia, which affects the Eastern Alps and their foreland ( Figure 3 ). U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth The flow of crustal material with respect to stable Eurasia observed both in the southwestern Balkans and in the Eastern Alps can be described as a clockwise rotation around the Albanides and Slovenia. However, this rotations fundamentally differs from a rigid block motion, which would produce increasing velocities away from the Euler pole and constant velocities along small circles around the axis of rotation. None of these features applies to the velocity field of Figure 1 in these two regions ( Figure S8 ). Strain Rates Analysis To compute a continuous spatial distribution of the deformation, we use the principles of continuum mechanics to analyze the strain rate tensor field. We used the SPARSE code provided by Haines and Holt [1993] to derive a continuous velocity gradient tensor field from our GPS observations, using a velocity and strain rate bicubic Bessel spline interpolation technique [Beavan and Haines, 2001] . SPARSE provides also estimates of strain rate and interpolated velocity for any point in our model grid. This regular grid consists in 3120 0.4 ∘ × 0.4 ∘ cells covering the area going from 8 ∘ E to 34 ∘ E and from 32.5 ∘ N to 52 ∘ N, thus including the Hellenic subduction zone and the North Anatolian Fault. We require there be no deformation inside the northernmost cells located on the stable European craton in order to mimic rigid plate behavior of the Eurasian plate ( Figure S4 ). To avoid patchy strain rate distribution due to contradictory velocities or to observational density contrasts, we impose a smoothing parameter controlling the maximal change in slip rate values between two grid cells and fix it to 1 mm/yr since it provides a good compromise between the fit to the observed GPS velocities and the spatial consistency of the strain rate distribution. Following Perouse et al. [2012] , we allow cells located in the vicinity of the NAF and the Hellenic backstop to deform at higher strain rates than elsewhere in order to better retrieve the deformation associated to elastic loading on these structures. U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F We constrain the direction of the strain rate field to be consistent with the principal axis of deformation derived from seismic moment tensors of the Harvard centroid moment tensor (CMT) and regional CMT catalogs Q8 [Pondrelli et al., 2006 [Pondrelli et al., , 2011 (Figure 6 ), thus introducing strength anisotropy ( Figure S5 ). Note that the sign and F6 amplitude of the strain rate are left free in the inversion and that a homogeneous uniform calculation, and a more realistic model including weak zones and strength anisotropy do not significantly differ in the fit to the data in the peri-Adriatic area (nRMS is 1.46 and 1.26, respectively, Figure S7 ). This is probably due to the fact that this region is far from the zones under high strain and that few focal mechanisms are available there ( Figure 6 ). U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F In Figure 6 we plot the second invariant of the strain rate tensor defined aṡE= √ (̇2 xx +̇2 yy + 2̇2 xy ),̇i j being the ijth horizontal component of the strain rate tensoṙ, to highlight the areas of highest strain rates. To picture the deformation patterns, Figure 7a shows the first invariant of the strain rate tensor d = 1∕2(̇x x +̇y y ) F7 (for dilatation d > 0 and for compression d <0). Figure 7b shows the vorticity of the interpolated velocity field ( U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Overall, the pattern of strain around Northern Albania shown on Figures 1 and 5 is clearly delineated in Figure 6 , where we observe a strain rate of ∼ 15 × 10 −9 /yr in Serbia and inner Bosnia and up to 25 × 10 −9 /yr on the Montenegro coast ( Figure 6 ). Strain rate increases by a factor of 2 going from Albania and Macedonia to Northern Greece, while there is little or no straining in the Carpathians and the main part of the Pannonian Basin. In Italy, as previously shown by D' Agostino et al. [2014] , the strain rate is the most important in the center of the Apennines mountain belt where extension is oriented SW-NE. In Slovenia, north-south compression is dominant and reaches 20 to 30 × 10 −9 /yr. U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F The Adria and Apulia regions exhibit very low strain rates and opposite signs of vorticity, in agreement with the hypothesis of an Adriatic promontory fragmented into two rigid blocks rotating in opposite sense [D'Agostino et al., 2008] . From the interpolated velocity field, we derive Euler poles best reproducing the rigid blocks motions (nRMS < 0.6). We find that the Euler poles obtained for Adria (45. studies [D'Agostino et al., 2008; Cheloni et al., 2014] . The Adria-Apulia Euler pole (43.02 ∘ N, 16.60 ∘ E, 0.422 ∘ /Myr) is located on the eastern Adriatic coast, in front of the diffuse boundary between the two blocks, where relatively high seismicity rates are observed offshore Adriatic Sea (Figures 6 and 7b) . Furthermore, as previously underlined in section 3.1, very little compression is required in Croatia. Even if we lack dense measurements there, it seems that the western part of Croatia and the Istria Peninsula is moving together with the Adria microplate. High strain rates (∼25×10 −9 /yr) are observed across the Eastern Alps thrust front and the peri-Adriatic fault. U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth 10.1002/2015JB012023 The calculated dilatation rate and principal strain components give new insights into the regional style of deformation ( Figure 7a ). As expected, dilatation is dominant in the Apennines and the Aegean Sea, while compression is occurring all along the Hellenic subduction backstop, along the northern flank of the Apennines [Bennett et al., 2012] and across the active Eastern Alpine front [Cheloni et al., 2014] . On the Balkan Peninsula, the transition from the Dinarides compression area to the South Bulgaria, Northern Greece, and Macedonia dilatation zones appears clearly: the zero-dilatation contour splits Albania into two, consistently with the change in tectonic style observed there [e.g., Copley et al., 2009] and extends up to 44.5 ∘ N with a ∼N-S orientation. There, it rotates toward a more E-W direction and roughly follows the orientation of the Balkan mountain belt (Figure 4 ). We observe a rotation of the principal dilatation strain axis from a ∼N120 ∘ E orientation in the Albanian mountains to a nearly N-S orientation in Macedonia and southwestern Bulgaria and a ∼N10 ∘ E direction in Central Bulgaria (Figure 7a ). Insights on Lithosphere Dynamics From the Strain Rate Field The deformation of the continental lithosphere could be driven by several forces [e.g., Thatcher, 2009]: kinematic conditions applied to major plate boundaries, dragging effects from underneath the lithosphere due to convective motions of the astenospheric mantle [Faccenna et al., 2013; Le Pichon and Kreemer, 2010] , body forces generated by rheological variations within the lithosphere, and horizontal gradients of gravitational potential energy (GPE). The latter contribution can be quantified within the framework of the "thin viscous sheet" approach (TVS) [England and McKenzie, 1982] or using the "density moment" law [Fleitout and Froidevaux, 1982] , and its physical formulation provides a relationship between spatial gradients of vertically averaged deviatoric stresses and GPE. In the following, we use the estimated strain rate field obtained from observed GPS velocities to assess the role of gravitational forces in driving the deformation of the lithosphere following the approach described by England and Molnar [1997] . Testing the Fluid Lithosphere Hypothesis Assuming that spatial gradients of GPE are the main factors driving surface deformation, we consider the lithosphere as a continuous medium that deforms as a fluid submitted to gravitational forces only. Neglecting inertial terms, the stress balance (or Stokes) equation for a steady state fluid-like lithosphere is Testing the Fluid Lithosphere Hypothesis where ij is the ijth component of the stress tensor, x j is the jth direction, is the density, and g i is the ith component of gravity acceleration [Malvern, 1969] . Considering that shear tractions are negligible at the bottom and top of the lithosphere and that isostasy applies, equation (1) can be written as Testing the Fluid Lithosphere Hypothesis wherēi j is the ijth component of the deviatoric stress tensor averaged on the entire column of lithosphere [England and Jackson, 1989] . Γ is the gravitational potential energy (GPE) defined as Testing the Fluid Lithosphere Hypothesis where L is the thickness of the lithosphere (supposed constant), (z) is density, and zz (z) is the vertical component of the stress tensor ij . Testing the Fluid Lithosphere Hypothesis If we have a complete knowledge of the spatial distribution of the vertically averaged deviatoric stress tensor ij , we can estimate spatial gradients of gravitational potential energy Γ from the left-hand side of equations (2) and (3). We choose to describe the rheology of the lithosphere with a "power law" defined by Sonder and England [1986] as U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth 10.1002/2015JB012023 in whichĖ is the second invariant of the strain rate tensor defined in section 3.2, and 1∕2BĖ 10.1002/2015JB012023 1 n −1 is the effective viscosity of the lithosphere. Knowinġi j at any grid point and assuming that B is constant over the entire area, we calculate the left member of equations (2) and (3) and integrate over the entire region to get the dimensionless GPE, denoted by Γ * or GPE * as defined by England and Molnar [1997] as 10.1002/2015JB012023 On the other hand, to independently calculate the right member of equations (2) and (3), we must calculate Γ from equation (4), which would require the unknown lithospheric density structure. Fortunately, a proxy for Γ can be obtained from topography if its supporting mechanism is specified. Here we assume that the Airy crustal isostasy controls topography through lateral crustal thickness variations, rather than the mantle-supported mechanism suggested for the Apennines [D' Agostino et al., 1999 Agostino et al., , 2001 . In both cases, however, we get a relatively simple relationship between Γ and h (see also D'Agostino et al. [2014] , for a discussion on alternative mechanisms of support). In the case of Airy isostasy, considering a column of lithosphere composed of a mantle of density m under a crust of density c and altitude h, we can use the following relation [England and Houseman, 1989] : 10.1002/2015JB012023 where S 0 is the crustal thickness for a column of lithosphere whose surface height is zero. Following D'Agostino et al. [2014] , we take a L =100 km thick column of lithosphere in which the crustal thickness S 0 is 30 km as a reference for the GPE calculation. We can therefore derive the GPE relative to the reference column of lithosphere directly from the ETOPO1 filtered topography (we used a 100 km width Gaussian filter), assuming c is 2800 kg.m 3 and m is 3300 kg.m 3 over the entire region ( Figure 9 ). In order to test whether isostatic compensation is achieved in our study area, we calculate the theoretical depth of the Moho from topography assuming Airy isostasy and compare it to the Moho depth estimated from seismic wave velocities in the EPcrust model for Europe (see Figure S10 and Molinari and Morelli, 2011) . Discrepancies between both Moho depths are not more than 5 km, in general, except in the Po Plain, the Pannonian Basin, and Macedonia where up to 20 km discrepancies are observed. Therefore, we are confident that, over the largest part of our study area (in particular in Central Apeninnes, Albanides, Dinarides, and Eastern Alps), Airy isostasy is a reasonable first-order assumption and that application of equation (7) is warranted (see section 4.3 for further discussion). 10.1002/2015JB012023 If the TVS hypothesis is valid and the lithosphere effectively behaves as a homogeneous fluid forced by gravity, equations (2), (3), and (6) apply, and there must be a linear relationship between the strain-derived GPE* and the topography-derived GPE. In Figure 8 , we plot the numerically calculated GPE* contours together with the GPE* gradients x Γ * and y Γ * and the filtered ETOPO1 topography. Where equation (2) is verified, the gradients of GPE* should be similar to the gradients of topography. In other words, they should be pointing toward the highlands, following the belt orientation [e.g., England and Molnar, 1997] . This is clearly the case along the Central and Southern Apennines mountain belt, where the highest values of GPE* are observed along the regional topographic culmination (the correlation coefficient r between GPE* and GPE calculated from topography is 0.71, see Figure 9 ). This result supports the earlier analyses from D'Agostino et al. [2014] obtained from 2-D sections across the Apennines and strengthens their conclusion. 10.1002/2015JB012023 An even clearer correlation (r = 0.89) between GPE* and the GPE derived from the topography is observed over the Albanides (Figures 8 and 9 ). This result argues for a dominant control of gravity on the current-day deformation of Albania as previously suggested by Copley et al. [2009] . 10.1002/2015JB012023 On the contrary, no correlation is observed between the strain-derived GPE* and the topography in the Eastern Alps and the Dinarides. In these regions, we observe a decrease of the GPE* in the vicinity of the active fronts (the Eastern Alps thrust and the offshore western Dinarides thrust, respectively) followed by an increase of the GPE* away from this fault line. This pattern is roughly consistent with the one predicted by elastic deformation theory on active thrusts ( Figure S11) . Therefore, the deformation occurring in these regions is at least partly governed by elastic loading on what could be considered as Adria-Apulia rigid blocks boundaries. 10.1002/2015JB012023 In the Northern Apennines where the correlation between GPE* and topography is relatively low, our assumption of Airy isostasy is debatable (see Figure S10 and section 4.3 for further discussion) and elastic loading effect on the Ferrara thrust could drive part of the deformation. U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F Journal of Geophysical Research: Solid Earth 10.1002/2015JB012023 Figure 8. Strain-derived gravitational potential energy. Arrows show gradients of dimensionless gravitational potential energy (GPE * ), derived by assuming a power law rheology for the lithosphere with n = 3 (see equation (5)). Values of GPE * integrated from GPE gradients and multiplied by a factor of 10 6 are contoured and plotted together with the filtered topography from ETOPO1. Same labels as in Figures 1 and 5. in Macedonia, and across the Balkan mountain belt where GPE gradients seem to have a minor influence on the surface deformation pattern (Figure 8 ). The Eurasia-Anatolia plate boundary along the North Anatolian Fault is a zone of localized weakness, and our analysis of the lithosphere as a continuous medium is not applicable. Lithosphere Effective Viscosity Estimates We now consider the two mountain belts in which the correlation between the dimensionless GPE* and the GPE calculated from topography is significant (r > 0.5), i.e., the Apennines and Albanides (Figure 9 ). The slope of the linear correlation obtained in Figure 9 gives us an estimate of BL × (1 s) 1∕n for each region (equation (6)) and therefore allows us to calculate the lithosphere effective viscosity for a given strain rate and a value of the exponent n. Assuming L ∼100 km and n = 3 as derived from laboratory studies [e.g., Sonder and England, 1986] Agostino et al. [2014] and other studies in distinct T1 mountain belts [e.g., England and Molnar, 1997; Vergnolle et al., 2007] . Assuming a Newtonian rheology, i.e., n = 1, gives values for the lithosphere viscosity between 3.0 × 10 21 Pa s and 3.4 × 10 21 Pa s (see additional supporting information and Figure S12 ). Main Limitations By testing the fluid lithosphere hypothesis using the method presented in section 4.1, we aim at testing how far we can go in the understanding of the lithosphere dynamics using very simple assumptions. On the other hand, several limitations can affect our test [e.g., England and Molnar, 1997] : (i) we consider no lateral change in rheological properties of the lithosphere over the entire region, therefore considering that B is constant in equation (5); (ii) we assume crustal Airy isostasy as the compensation mechanism over the entire region; and (iii) basal shear traction is supposed to be negligible in equations (2) and (3). This latter assumption is probably reasonable in our study area except for regions where significant basal traction may arise from lithospheric scale thrusts like the Eastern Alps front, the Dinarides, and the Northern Apennines under which a dipping slab has been detected [Bennett et al., 2008] . As previously discussed and shown in Figure S10, U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E C T E D P R O O F U N C O R R E
{'paper_id': '131285145', 'title': 'Insights on continental collisional processes from GPS data: Dynamics of the peri-Adriatic belts', 's2_url': 'https://api.semanticscholar.org/CorpusID:131285145', 'source': 'S2ORC'}