Sustained Uplift at a Continental Rift Caldera

Journal of Geophysical Research: Solid Earth RESEARCH ARTICLE Sustained Uplift at a Continental Rift Caldera 10.1029/2018JB015711 Special Section: Merging Geophysical, Petrochronologic and Modeling Perspectives to Understand Large Silicic Magma Systems Key Points: • Corbetti caldera, Ethiopia, has been uplifting continuously since mid-2009 at a vertical rate of ∼7 cm/year • The uplift at Corbetti can be modeled by an inflating Mogi source at depth ∼6.6 km, with a consistent volume change of 107 m3 /year • The deformation at Corbetti is likely caused by a magmatic system Supporting Information: • Supporting Information S1 Correspondence to: R. Lloyd, [email protected] Citation: Lloyd, R., Biggs, J., Birhanu, Y., Wilks, M., Gottsmann, J., Kendall, J.-M., et al. (2018). Sustained uplift at a continental rift caldera. Journal of Geophysical Research: Solid Earth, 123, 5209–5226. https://doi.org/10.1029/2018JB015711 Received 1 MAR 2018 Accepted 20 APR 2018 Accepted article online 10 MAY 2018 Published online 2 JUN 2018 ©2018. The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. LLOYD ET AL. Ryan Lloyd1 , Juliet Biggs1 , Yelebe Birhanu2 , Matthew Wilks2 , Joachim Gottsmann2 , J.-Michael Kendall2 , Atalay Ayele3 , Elias Lewi3 , and Hjálmar Eysteinsson4 1 COMET, School of Earth Sciences, University of Bristol, Bristol, UK, 2 School of Earth Sciences, University of Bristol, Bristol, UK, 3 Institute of Geophysics, Space Science, and Astronomy, Addis Ababa University, Addis Ababa, Ethiopia, 4 Reykjavik Geothermal, Reykjavik, Iceland Abstract Caldera systems are often restless and experience pulses of uplift and subsidence, with a weak, but significant link to eruption. Characterizing the spatial and temporal patterns of deformation episodes provides insight into the processes responsible for unrest and the architecture of magmatic and hydrothermal systems. Here we combine interferometric synthetic aperture radar images with data from Global Positioning System and a network of seismometers at a continental rift caldera Corbetti, Ethiopia. We document inflation that started mid-2009 and is ongoing as of 2017, with associated seismicity. We investigate the temporal evolution of the deformation source using a Hastings-Metropolis algorithm to estimate posterior probability density functions for source model parameters and use the Akaike information criterion to inform model selection. Testing rectangular dislocation and point sources, we find a point source at a depth of 6.6 km (95% confidence: 6.3 − 6.8 km) provides the statistically justified fit. The location of this source is coincident with a conductive anomaly derived from magnetotelluric measurements. We use a joint inversion of two geodetic data sets to produce a time series, which shows a volume input of 1.0 × 107 m3 /year. This is the first observation of a prolonged period of magma reservoir growth in the Main Ethiopian Rift and has implications for hazard assessment and monitoring. Corbetti is < 20 km from two major population centers and has estimated return periods of ∼500 and ∼900 years for lava flows and Plinian eruptions, respectively. Our results highlight the need for long-term geodetic monitoring and the application of statistically robust methods to characterize deformation sources. 1. Introduction 1.1. Crustal Magma and Continental Rifts Magma reservoirs in the Earth’s crust are currently thought to be interconnected crystal melt mush regions (Cashman & Sparks, 2013), and understanding the architecture and evolution of magmatic systems is a fundamental goal in volcanology. Observations or inferences of the depth, size, or temporal evolution of a magma reservoir can put constraints on, for example, how large magma reservoirs form, the temporal and spatial characteristics of magma recharge (Gudmundsson, 1990), and the size, style, and duration of potential eruptions (Becerril et al., 2013; Bower & Woods, 1998). In continental rift systems four major styles of volcanism are observed: large silicic centers along the rift axis (Abebe et al., 2007), spatially distributed fields of basaltic monogenetic volcanism (Mazzarini et al., 2004), fissure eruptions (Pagli et al., 2012), and off-rift volcanism (Maccaferri et al., 2014). Each of these styles is a product of different magma reservoir architectures and storage conditions. In continental rifts, faulting and magma throughout the crust is necessary to reduce the crustal tensile strength enough to facilitate rifting (Buck, 2006), and transport via diking has a distinctively different influence on the rifting process than storage of silicic magma at calderas. Rifting initially begins as a zone of diffuse faulting, which transitions into being driven through repeated magmatic intrusions in a narrow region along the rift axis (Beutel et al., 2010; Ebinger et al., 2017). These repeated intrusions are thought to build up along the rift axis to form crustal magma reservoirs, which then fractionate, forming the centers observed beneath the axial silicic volcanoes (Gudmundsson, 2011). Seismic evidence for aligned melt in the crust suggests that the orientation of the melt is an important factor in facilitating rifting (Keir et al., 2005; Kendall et al., 2006). InSAR (interferometric synthetic aperture radar) and GPS (Global Positioning System) are complementary techniques that are ideally suited for observing surface deformation associated with magmatic processes. InSAR observations have a high spatial resolution (typically 30 m), and GPS data can have high temporal resolution (typically up to days). However, there are limitations: GPS stations only provide a measure UPLIFT 5209 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 of the surface deformation in their location and are vulnerable to damage. InSAR, on the other hand, can lose coherence if the ground scattering properties change too much, and the temporal resolution is dependent on satellite data acquisition dates, which can be variable. In addition, geophysical signals can last longer than the observation period of some sensors or deployments, and so data from multiple sensors may need to be combined. The differing spatial and temporal resolutions of GPS and InSAR can also lead to complications in combining observations for modeling. Since the purpose of making these observations is to comment on the subsurface, we combine our data to look at the temporal evolution of the signal through the use of a source model (Biggs, Lu, et al., 2010). In this paper we focus on the surface deformation of a Main Ethiopian Rift (MER) silicic caldera, Corbetti, to investigate the magmatic storage conditions and temporal evolution, for example, pulsed versus continuous supply. We perform inversions of surface deformation, observed with InSAR and GPS, for analytical source model parameters using a Bayesian approach (e.g., González et al., 2015). This approach allows us to report our optimal model parameters with posterior probability density functions, and specifically comment on poorly constrained parameters, and parameter trade-offs. To quantitatively compare our models, we use the Akaike information criterion (AIC), which allows us to consider their complexity and likelihood. To investigate the temporal evolution of the source, we combine our data through the use of a source model to jointly invert for the cumulative volume change. 2. Background 2.1. The East African Rift The East African Rift System (EARS) is a major continental rift separating the Nubian and Somalian tectonic plates (Figure 1). It extends from Ethiopia and Eritrea in the north, southward to Mozambique. Along the EARS spreading rates vary from ∼6.6 mm/year in the MER to less than 3 mm/year in Mozambique (Stamps et al., 2008). The presence or absence of magma within the rift is key to the distribution of hazards and strain. Since 1890 there have been 11 eruptions, from 7 volcanoes, in Ethiopia alone (Wadge et al., 2016). The causes of deformation within the EARS span a range of processes: eruptions (Pagli et al., 2012), magmatic intrusions (Biggs et al., 2009, 2016), hydrothermal activity (Hutchison et al., 2016), earthquakes (Biggs, Nissen, et al., 2010), slow-slip faulting events (Calais et al., 2008), and subsidence from cooling, crystallization, and degassing (Biggs et al., 2016). It is notable that periods of prolonged magma reservoir growth have not yet been described in this setting but are common elsewhere (e.g., Dzurisin et al., 2009; Le Mével et al., 2015). Corbetti caldera, in the southern MER, formed in a >10 km3 eruption at 182 ± 18 ka (Hutchison et al., 2015). Within the caldera are two major centers of resurgent volcanism, Urji (syn. Wendo Koshe) and Chabi, and several smaller vents and cones (Figure 1). The postcaldera volcanism is exclusively characterized by the eruption of peralkaline rhyolites in both pyroclastic sequences and aphyric obsidian flows dated between ∼20 and ∼0.5 ka (Fontijn et al., 2018; Hutchison et al., 2015; Martin-Jones et al., 2017; Rapprich et al., 2016). Martin-Jones et al. (2017) identify and analyze ∼12 ash layers from the last 10 kyr deposited in a lake ∼30 km away from Corbetti to derive a return period of explosive eruptions of 900 ± 220 years (Connor et al., 2003). Based on the four most recent lava flows, Rapprich et al. (2016) propose an effusive eruption return period of 500–550 years. Corbetti has been observed recently deforming: 1994–1996 there was >1.4 cm of uplift and 1997–2000 there was <14 cm of subsidence, as measured by InSAR (Biggs et al., 2011). This subsidence was modeled as a point source at a depth of 5.8–7.8 km. No deformation was observed between 2003 and mid-2007. Between June 2007 and November 2008 a localized region of uplift followed by subsidence was observed in the south of the caldera, the source of which is interpreted to be a shallow hydrothermal or groundwater system (Lloyd et al., 2018). A large rift oblique fault structure also crosses through the caldera (Lloyd et al., 2018). This structure is thought to have influenced initial magma reservoir formation and hydrothermal fluid and magma migration within the caldera. Magnetotelluric (MT) observations, which are sensitive to the ground resistivity (e.g., Didana et al., 2014; Samrock et al., 2015; Whaler & Hautot, 2006), have been used to image the subsurface beneath Corbetti (Gíslason et al., 2015). Gíslason et al. (2015) find a conductive anomaly <2-km-thick layer in the upper 2 km, beneath the northern half of the caldera, which is interpreted to be a layer of hydrothermally altered clays. Beneath Urji and the center of the caldera there is another conductive anomaly. The 10 Ωm contour up domes to a depth of 3 km below sea level (b.s.l). Down to 7 km b.s.l this anomaly is ∼2-km wide (north-south), below which it broadens by ∼2-km to the north. This deeper anomaly is interpreted by Gíslason et al. (2015) as a region of partial melt. Fumerole geochemistry analysis in 2011 identified high geothermal temperatures (>300 ∘ C), suggesting a heat source at depth (Gíslason et al., 2015). More than 500,000 people LLOYD ET AL. UPLIFT 5210 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 Figure 1. (a) The Main Ethiopian Rift, with northern East Africa inset (NU = Nubian plate; SO = Somalian plate). The main volcanic centers are shown by red triangles, faults by black lines (Agostini et al., 2011). (b) The Corbetti caldera. Global Positioning System stations used in this study are shown by inverted black triangles. The stations HAWA, CURG, C01G, and C03G were set up in March 2013. C01G and C03G became inoperable following vandalism (C01G: 15 April 2015 and C03G: 5 September 2014). Station CNHG was installed in October 2015 as a replacement (Figure S1). Seismic stations locations are shown by blue triangles. C01E, C02E, and C03E were deployed in January 2012, and C05E and C06E in January 2013. C03E was relocated to C04E in May 2014. In October 2013 C07E was deployed. The black cross shows the center of the caldera (Lloyd et al., 2018). live in and around the Corbetti region, primarily in the major population centers of Hawassa and Shashemene and also on the surrounding agricultural land. The caldera is a potential geothermal resource (Gíslason et al., 2015) and within 10 km of a national airport. Lake Hawassa, which supports a fishing economy, is also within 10 km. The RiftVolc and ARGOS projects have carried out temporary deployments of seismic and geodetic equipment at Corbetti, but there is no permanent or real-time monitoring network (Birhanu et al., 2018; Wilks et al., 2017). 3. Surface Deformation 3.1. Interferogram Processing InSAR uses the phase component of two synthetic aperture radar (SAR) images of the Earth’s surface to determine the change in path length that has occurred in the satellite’s line of sight (LOS). We produced ∼420 interferograms, using SAR data from four different satellites or satellite constellations, over Corbetti caldera from between October 2007 and January 2017 (Table S1 in the supporting information). ALOS, Envisat, and Cosmo-SkyMed (CSK) interferograms were processed using the ISCE software package (Rosen et al., 2012). Sentinel-1 interferograms were processed using the GAMMA software (Werner et al., 2000), within the LiCSAR facility (González et al., 2016). The topographic contribution in all interferograms were removed using the 30-m Shuttle Radar Topography Mission (SRTM) digital elevation model (Farr & Kobrick, 2000). Table S2 shows the parameters selected for each sensor made during processing. To maximize coherence in CSK data, interferograms were resampled to 60-m pixels before the removal of topographic phase contributions. Interferograms were then filtered (strength 0.6), resampled (120-m pixels), and then filtered again (strength 0.6) before unwrapping (Chen & Zebker, 2001; Goldstein & Werner, 1998). Atmospheric artifacts were investigated using ascending and descending acquisitions covering the same time period and pairwise logic using networks of interferograms (e.g., Ebmeier et al., 2013; Pritchard & Simons, 2004). We tested using weather models (e.g., Yu, Penna, & Li, 2017; Yu, Li, & Penna, 2017) to correct atmospheric delays, but as the climate is generally dry and the relief low, they showed little correspondence with the interferograms. A linear ramp was removed from each interferogram to correct for long-wavelength atmospheric or orbital delays (Biggs et al., 2007). The temporal coverage of all interferograms can be seen in Figure S1. This InSAR data set contains interferograms produced using radar data with a range of wavelengths: 3.1 (X-band), 5.6 (C-band), and 23.1 cm (L-band) (CSK, Sentinel-1 and ENVISAT, and ALOS, respectively). The MER is densely vegetated, with primarily agricultural land in the Corbetti region. As is commonly seen in InSAR data, we found this repeated resurfacing of the ground surface resulted in a loss of coherence, especially so for our X-band and long temporal baseline C-band interferograms. All coherent interferograms with temporal baselines greater than ∼1 month and after March 2009 showed concentric fringes of a decrease in range change, LLOYD ET AL. UPLIFT 5211 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 Figure 2. East (E), north (N), up (U), ascending (LOS asc), and descending (LOS desc) LOS displacements for C01G (left) and CURG (right). A time series of ascending (green) and descending (red) Sentinel-1 displacements for the location CURG is presented with the CURG Global Positioning System data projected into the respective LOS. LOS = line of sight. consistent with uplift. Due to a loss of coherence in agricultural areas, the extent of the deformation is unconstrained in several C- and X-band interferograms. For coherent interferograms longer than ∼1 year, however, low rates of deformation can be seen to extend <4 km outside the caldera. 3.2. Global Positioning System Five continuous GPS stations were operational during the observation period, four on the volcano (CURG, C01G, C03G, and CNHG), and one in Hawassa (HAWA; see Figure 1b for locations and Figure S1 for temporal coverage). Station positions, delays, and ambiguities were solved for using the GAMIT/GLOBK software package (Herring et al., 2010). International Global Navigation Satellite System reference sites were used to constrain the solution in the International Terrestrial Reference Frame 2014 (Altamimi et al., 2016). The station location and time series for the volcano GPS sites are calculated relative to HAWA. Daily GPS solutions were resampled to weekly solutions for analysis and modeling. The GPS station C01G is the closest to the center of the caldera. The maximum vertical deformation at C01G was 6.5 ± 1.3 cm between 22 March 2013 and 15 April 2015, whereas there was only 0.6 ± 0.6 cm of northward and 2.3 ± 0.7 cm eastward motion during the same period (Figure 2). CURG is the longest running GPS station: 31 March 2013 to 31 December 2016. This station was moving 2.9 ± 0.3 cm/year SWW (azimuth of 206 ± 005∘ ) and up at 3.9 ± 0.7 cm/year (Figure 2). C03G, east of the caldera, was moving 1.9 ± 0.6 cm/year east (108 ± 014∘ ), and up at 1.8 ± 1.7 cm/year (22 March 2013 to 5 September 2014). CNHG, located at the southern caldera rim, was moving 1.5 ± 0.3 cm/year SE (156 ± 023∘ ) and up at 2.2 ± 2.1 cm/year (7 October 2015 to 31 December 2016). 4. Time Series Analysis We produce time series of the LOS range change using ALOS and Sentinel-1 data independently, using the short baseline subset approach methodology (Berardino et al., 2002). The uncertainty in the InSAR time series is determined by the mean standard deviation of the range change for each data set, calculated for the region LLOYD ET AL. UPLIFT 5212 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 Figure 3. Left: Maximum LOS displacement from (a) ALOS ascending, (b) Cosmo-SkyMed ascending, (c) Sentinel-1 ascending, (d) ENVISAT descending, (e) Cosmo-SkyMed descending, and (f ) Sentinel-1 descending time series analysis or interferograms (connecting lines on b and e). Right: Cumulative displacement during the observation period of each satellite (top-bottom: ALOS: 23 December 2007 to 30 September 2010, ENVISAT: 17 October 2007 to 28 July 2010, Sentinel-1 ascending: 29 September 2015 to 17 October 2016, Sentinel-1 descending: 19 August 2015 to 24 October 2016) for the point marked with an X relative to Global Positioning System station HAWA or the open circle if HAWA is incoherent (d). The gray regions correspond to the time periods used in the source inversion in section 5.1. LOS = line of sight. outside of 10 km from the center of the caldera. Seasonal hydrological contributions to deformation in this area have been shown to be more than an order of magnitude (<2 mm) smaller than the uplift at Corbetti (Birhanu et al., 2018), demonstrating no seasonal corrections need to be applied to the GPS time series. Time series analysis using ENVISAT and ALOS interferograms indicates that there is no edifice centric deformation at Corbetti between October 2007 and March 2009 (Figures 3a and 3d). Uplift followed by subsidence localized to the southern half of the caldera is observed, however, previously described and interpreted by Lloyd et al. (2018) to be associated with a hydrothermal system. Between March 2009 and September 2009 deformation begins, at a peak rate of 4.0 ± 1.2 cm/year (maximum ascending LOS) until September 2010 (Figures 3a and 3d). Any displacement during the time period September 2010 to March 2012 is unconstrained by our data set (Figure S1). After March 2012 individual CSK interferograms show that uplift occurred at a rate of 7.5–14.8 cm/year relative to HAWA, but the InSAR coherence is too poor to produce a displacement time series between HAWA and CURG. Individual interferograms are included on Figure 3. The consistent location and spatial extent of the signal before and after our data gap suggest that the displacement is continuous. The GPS data at CURG show a variation in vertical rate from 2.2 ± 3.6 cm/year between March 2013 and November 2013, to 4.3 ± 0.9 cm/year from November 2013 to December 2016 (Figure 2). Between August 2015 and December 2016 the ascending and descending Sentinel-1 time series show continuous linear uplift at 5.5 ± 1.0 cm/year and 5.0 ± 0.7 cm/year, respectively (maximum LOS). We compare the InSAR time series to the three-component monthly GPS time series projected into the satellite LOS. The location of CURG does not correspond to the maximum deformation but was selected as it is the longest running GPS station and to facilitate a comparison between the GPS and InSAR data. The ascending and descending Sentinel-1 data agree within error with the GPS displacement measurements projected into LOS at CURG between August 2015 and October 2016 (Figure 2). A comparison between the InSAR and GPS values for CURG and C01G can be found in Table S3. LLOYD ET AL. UPLIFT 5213 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 5. Inverse Modeling 5.1. Bayesian Inversion for Analytical Source Models Preeruptive surface deformation in volcanic settings can be caused by a volume or pressure change in the subsurface. In volcanic settings, the source of this change could be magmatic, hydrothermal, or a combination. We choose to explore two analytical source models embedded in a homogeneous elastic half-space to describe the deformation: a point source (Mogi, 1958, hereafter named “Mogi source”) and a rectangular dislocation (Okada, 1985, hereafter named “Okada source”). We discount a possible dike intrusion as the deformation at Corbetti is radially symmetric, rather than the three lobed pattern characteristic of diking observed using InSAR (e.g., Keir et al., 2011). For all our models we selected a Poison’s ratio of 0.25 and a shear modulus of 16.5 GPa, which are typical values for similar caldera systems (e.g., Coco et al., 2016; Masterlark, 2007). Corbetti has low relief; the elevation of the caldera rim and resurgent volcanism is <400 m higher than the rift valley floor. As such, we consider the effects of topography in our modeling or associated atmospheric artifacts to be negligible (Masterlark, 2007; Parker et al., 2015). The time series analysis indicates a negative range change, consistent with uplift, from between March and September 2009 to the end of our observations in January 2017, where constrained by InSAR data (Figure 3). To investigate any changes through time, such as variations in the driving behavior (e.g., injection rate; Hickey et al., 2016; Parks et al., 2015) or source location (Biggs et al., 2016; Bignami et al., 2014), we model the rate of range change from the InSAR and GPS data for three ∼1 yearlong time periods: the onset of the signal (November 2008 to June 2010), after ∼5 years (January 2014 to January 2015), and after ∼6 years (October 2015 to October 2016; Table S4). We also perform a combined inversion, using all of the data together. For the years where GPS stations did not run continuously, we use the available data within that year to calculate the rate of deformation, which we assume is constant for that time period. The three periods were selected because (1) ∼1 year of observations provides a high signal-to-noise ratio, (2) over ∼1 year C-band interferograms do not decorrelate significantly, and (3) during these time periods there are observations of the signal from ascending and descending satellite viewing geometries. We search for the best model of the deformation using a Bayesian inverse modeling approach, incorporating Monte Carlo algorithms (Hastings, 1970; Mosegaard & Tarantola, 1995), that estimates the posterior probability density function for the best fitting parameters of each analytical source model, using the open source software (Geodetic Bayesian Inversion Software; Hooper et al., 2013; González et al., 2015). We assume that all measurement errors are Gaussian. For each interferogram we calculate the 1-D exponential covariance function and subsample using the quadtree method, based on the data variance away from the signal (Jonsson et al., 2002). Iterative sensitivity tests are conducted throughout the Bayesian inversion to ensure fast convergence and that all parameters contribute equally to changes in likelihood. We also solve for a constant offset in each interferogram. To qualitatively compare Bayesian models, one would use the Bayes factor (Brunetti et al., 2017; Jeffreys, 1935). However, the marginal likelihood, which is the likelihood function integrated over the model parameters, is challenging to calculate analytically (Kass & Raftery, 2008), and the results of approximation methods are generally unstable (see Raftery et al., 2007). As such, we use the AIC (Akaike, 1974). AIC considers the trade-off between goodness of fit (represented by the model likelihood) and model complexity, and is described by equation (1), where k is the number of model parameters and l is the maximum value of the likelihood function. AIC’s applicability in comparing nonnested models also supports its suitability over other methods (e.g., the F test). AIC = 2k − 2 ln(l). (1) Two AIC values can be compared to determine a model’s relative likelihood, L. The relative likelihood is how likely one model is, compared to a reference model with a smaller AIC value, to minimize the information loss (Burnham & Anderson, 2002). The relative likelihood is calculated using equation (2), where AICmin is the minimum AIC value and AICi is the model for comparison. ln(L) = (AICmin − AICi )∕2. LLOYD ET AL. UPLIFT (2) 5214 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 Figure 4. Joint probability density functions for key model parameters for the Mogi and Okada models using the combined, 2008–2010, 2014–2015, and 2015–2016 data sets, plotted together. In all subplots grayscale contours correspond to individual time period inversions, and colored contours represent the combined inversion. Colored circles denote the optimal values. (a) Mogi X against Y position, (b) Mogi volume change per year against depth, (c) Okada X against Y position, (d) Okada opening per year against depth, (e) Okada length against width. (f ) The location of the combined inversion Mogi (yellow star) and Okada (red rectangle) sources with the caldera outline. The dashed region represents the extent shown by (a) and (b). The model inputs are detailed in Table S4, initial conditions and range in Table S5, model results are summarized in Table S6, and root-mean-square (rms) residuals and AIC values in Table S7. The location (0,0) in our models is the center of the caldera: 38.381∘ E, 7.192∘ N (Lloyd et al., 2018; see Figure 1b). In our inversion we allowed the parameters to explore the full parameter space, for example, for a strike between 0 and 360∘ . The table of results are presented in this way (Table S6), but in the interest of visual LLOYD ET AL. UPLIFT 5215 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 Figure 5. Mogi model data-model-residual plots (wrapped) for an interferogram from each time period used in the combined inversion. The caldera outline is shown on each subplot, which corresponds to that in Figure 1. The yellow star denotes the location of the Mogi source. comparisons we reframe some of the model parameters, that is, a 10 × 10 km Okada model with strike 90∘ would plot in the same place as a 10 × 10-km Okada model with a strike of 180∘ in Figure 4c. 5.1.1. Model Results For the Mogi model the joint posterior probability density functions for the 2008–2010, 2015–2016, and combined (which uses all of the data) inversions, overlap near 0 km north and 2.0 km east of the center of the caldera (Figure 4a), between Urji and Chabi (Figure 4f ). Their marginal probability density functions for the depth also overlap between ∼6.4 and 6.6 km (Figure 4b). This qualitatively suggests that the source is similar during these time periods. In contrast, the 2014–2015 source sits away from the other models in both the X -Y and depth-opening rate parameter spaces (Figures 4a and 4b). The optimal rates of volume change are 0.5 × 107 to 1.2 × 107 m3 /year for 2008–2010 and 2015–2016, respectively, and 0.9 × 107 m3 /year (combined) (Figures 4b and S2). The 2014–2015 Mogi model inversion produces a clearly different solution: a source that sits 0.9 km further to the north (0.6–1.1 km, 95% confidence), deeper (7.2–8.2 km, 95% confidence), and with a significantly greater rate of volume change (2.4 × 107 m3 /year, 95% confidence: 2.1 − 2.8 × 107 m3 /year). However, although a Mogi source is able to model each time period relatively well and the inferred locations are consistent within error, a joint inversion using a single Mogi source for all the time periods combined fits the data less well. A source at 6.6 km with a rate of volume change of 0.9 × 107 m3 /year overpredicts the uplift between 2008 and 2010 but underpredicts the uplift between 2014–2015 and 2015–2016 (Figure 5). The 2008–2010 and 2015–2016 time periods are more similar, and a single Mogi source fits the combined LLOYD ET AL. UPLIFT 5216 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 Figure 6. (a) Cumulative volume change at Corbetti 9 November 2008 to 30 September 2010. (b) Minimum root-mean-square source locations from grid search (0.015∘ spacings) for optimal source location. Source is fixed at 6.6-km depth. The black cross denotes the center of the caldera (Lloyd et al., 2018), and yellow star shows the best fitting source location from the combined Bayesian inversion. (c) Cumulative volume change at Corbetti 3 May 2012 to 28 January 2017. The black dashed line shows the volume change estimates from the Bayesian inversion for the 2015–2016 time period. The blue line represents the best linear fit to the data 13 April 2013 to 27 January 2017. (d–f ) Interpolated minimum root-mean-square source locations from grid search (0.015∘ spacings) for optimal source location using (d) GPS, (e) InSAR, and (f ) InSAR and GPS, for a source fixed at 6.6-km depth. The black cross denotes the center of the caldera (Lloyd et al., 2018). The yellow star shows the best fitting source location from the combined Bayesian inversion. GPS = Global Positioning System; InSAR = interferometric synthetic aperture radar. data from these time periods well (Figure 5). This location is able to explain the 2014–2015 signal in most of the caldera, but there are residuals in the north (Figure 5). The inversion for an Okada model yields similar ranges of estimated model parameters (Figures 4c–4e and S3). Figure 4c shows the X and Y locations for the center of the Okada model. Depth against opening per year shows a trade-off that is the same shape for the 2008–2010, 2015–2016, and combined models, suggesting that the source is between 6- and 8-km deep, with an opening between 0.07 and 0.19 m/year (Figure 4d). The 2014–2015 trade-off has the same trend but greater opening per year. Figure 4e shows the optimal Okada models are ∼7 × 11 km in size, (aspect ratios of 1.47 [2008–2010], 1.57 [2014–2015], 1.1 [2015–2016], and 1.53 [combined]) indicating a slight elongation. The Okada models are all orientated with long axis ∼097∘ –112∘ (Table S6) and coincide with the surface expressions of Urji and Chabi. We find the rate of volume change of the combined Okada model (Figure S3) is comparable to the volume change of the combined Mogi model but lower by ∼10%. The residuals to the GPS data used in the combined inversion also reflect the pattern seen in the InSAR. For both the Mogi and Okada models, deformation at station CO1G, 1.4 km away from the source, is underpredicted (Figure S5). At distal stations, the vertical component of the deformation is consistent with the observations, but the amplitude and orientation of the horizontal components are not. This suggests that our models do not completely capture the source geometry, which in reality may be more vertically ellipsoidal to produce a higher vertical to horizontal deformation ratio. 5.1.2. Statistical Model Selection For the 2008–2010, 2014–2015, and combined inversions the Okada source fits the data better than the Mogi source (Table S7). However, in all cases the AIC values indicate that the increase in fit cannot be statistically justified given the increase in the number of model parameters, and therefore, there is a preference for the more simple Mogi model (Table S7). For the combined inversion, the Okada model is 0.7 times as probable to minimize the information loss (fit the data) as well as the Mogi model. The offset in the joint posterior probability density functions for both the Mogi and Okada models suggests qualitatively that the source during 2014–2015 is different to during 2008–2010 and 2015–2016. To test this, we compared three Mogi model situations using AIC: one where a single set of parameters describes all of the data (the combined model), one where the parameters in each time step are independent, and one where the parameters during 2014–2015 are independent of 2008–2011 and 2015–2016, which are the same. LLOYD ET AL. UPLIFT 5217 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 In the former case l in equation (1) is the product of the maximum likelihood function values of the three models, and k is the sum of the number of parameters in each model. The AIC value for the independent parameters model is −12.7, for the constant parameters model AIC = 2.5, and for the independent 2014–2015 model AIC = −5.4. These AIC values indicate that the data are best modeled using separate model parameters through time. We also test whether the residuals to the models can be explained by the inclusion of a second, shallower source (e.g., Lloyd et al., 2018), but find that it cannot be justified over the 2014–2015 time interval (supporting information). 5.2. Volume Change Time Series Since the individual models suggest that the source varies throughout 2008–2017 (Figures 5 and S4), we investigate whether the temporal evolution can be explained by a varying volume change of a fixed source through time using the methodology of Biggs, Lu, et al. (2010), (e.g., Hutchison et al. (2016) and Parks et al. (2015)). The inversion is based on the small baseline subset time series approach to produce a time series of deformation for each data point independently and can combine networks of unconnected interferograms through singular value decomposition (Berardino et al., 2002) with campaign and continuous GPS. The use of a simple analytical source model allows us to combine data sets with different three-component observation vectors, since the observed surface displacement can be predicted through the scalar product of the three-component observation vectors and the predicted deformation caused by the source. Furthermore, the use of a fixed source does not require data points to be present in all time periods, allowing the incorporation of interferometric data sets with spatially variable coherence. A full explanation of the method can be found in Biggs, Lu, et al. (2010). We use a Mogi source as the AIC values are lower than those for the Okada model. The exact nature of the source is unimportant, since it acts as a Green’s function to represent the shape of the surface deformation, and the goal here is to investigate temporal changes in the location or volume change of the source. We invert for the location and volume change of the Mogi source at a fixed depth, using the same material properties for the subsurface as before. We use the latitude, longitude, and depth from the optimal combined source inversion to act as a guide for a grid search to find the best fitting location within a 0.1∘ × 0.1∘ region at depth slices between 4.6 and 8.6 km (Figures 6b, 6d–6f, and S6). Each interferogram is downsampled by a factor of 2 within 8 km of the surface projection of the source and a factor of 8 outside of 8 km. The error in each interferogram is based on the standard deviation outside of this 8-km radius and is propagated through the inversion. We perform an inversion for the cumulative volume change between 9 November 2008 and 30 September 2010 (ALOS data, 13 interferograms), and 3 March 2012 and 28 January 2017 (CSK: 42 ascending and 38 descending interferograms, Sentinel: 32 ascending and 34 descending interferograms, and the three-component GPS from all four stations within the caldera). We chose to exclude the ENVISAT data from this inversion as most interferograms were too incoherent, too noisy, or covered the period with no deformation. For the 2012–2017 period we repeat the inversion using GPS data only, InSAR data only, and GPS and InSAR data together (Figure 6). In all inversions we use the weekly three-component GPS solutions at each station. 5.2.1. Volume Change Time Series Results: 2012–2017 The total volume change using the InSAR and GPS data between 3 March 2012 and 28 January 2017 is 4.2 ± 0.5 × 107 m3 (Figure 6c). From 22 March 2013, when the GPS data become available, the rate of volume change is 1.1 ± 0.1 × 107 m3 /year. Between 3 March 2012 and 14 April 2013 this rate is low: 0.9 ± 1.0 × 106 m3 /year. This result is likely to be because any displacement during this period is only observed in the CSK interferograms, which at this time have poor coherence and are thus unable to constrain the full spatial extent and temporal evolution of any displacement. The low volume change estimates before April 2013 are therefore probably related to the data availability. This result is included for completeness, but we do not discuss it further. According to the grid search the best fitting location of the Mogi source for 3 May 2012 to 28 January 2017 is situated ∼1.5 km NE of the center of the caldera (Figure 6f ). For the GPS data alone (Figure 6d) there is a corridor of preferred locations, which traverses NW-SE through the caldera, between the GPS stations. The InSAR only inversion is able to constrain that the source is not east of the caldera, as many of the interferograms used in the inversion are only coherent in this region, over the Chabi basalts (Figure 6e). LLOYD ET AL. UPLIFT 5218 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 By combining the data sets though, the inversion is able to constrain the source location well, to near the center of the caldera (Figure 6f ), consistent with the Bayesian inversion. For this inversion we selected to use the model depth result from section 5.1, as the methodology and more coherent data used in that inversion have greater sensitivity to source depth. Next, we perform a curve fitting analysis to investigate temporal changes in the rate of volume change after April 2013. This volume change can be described well by a linear function with time, with gradient of 1.12 × 107 m3 /year (95% confidence bounds: 1.09 − 1.15 × 107 m3 /year; solid blue line, Figure 6c). The coefficient of determination (r2 ) of this fit is 0.96, and the rms to the data is 1.9 × 106 m3 , smaller than the mean uncertainty (3.5 × 106 m3 ). The dashed line on Figure 6c shows the optimal rate from the previous inversion for the 2015–2016 time period for comparison (Table S6). This rate agrees well with the linear function calculated here. Although the volume change for a single model is, within error, constant with time during 2013–2017, the model residuals (section 5.1) suggest source variation during 2014–2015. To test this, we investigate temporal variations in the model residuals using the rms to each interferogram in the time series analysis and find that they do increase 2014–2015, compared to outside this time period (see supporting information Figure S7a). The increase is small, however, and not discussed further. 5.2.2. Volume Change Time Series Results: 2008–2010 We apply the same method to the inversion of ALOS data and find a 14 ± 0.08 × 106 m3 volume increase from the start of the data, 9 November 2008 to 30 September 2010. However, the data are unable to explicitly constrain the deformation onset (Figure 3d), so we calculate a rate of volume change for when individual interferograms show deformation: 26 September 2009 to 30 September 2010. The best fitting rate is 1.0 × 107 m3 /year (95% confidence intervals 0.6−1.4×107 m3 /year; solid line, Figure 6a), which is consistent with the rate of volume change derived from the nonlinear source inversion for individual interferograms. By assuming that the volume change began and continued to behave linearly before 29 September 2009 we can extrapolate back to find the date at which the volume change began. This date is the 19 May 2009. The 95% confidence range of this date, 13 April 2009 and 18 July 2009, is consistent with the independent constraints on the onset of the surface deformation using ENVISAT data (after 5 March 2009). The best fitting source location is in the northeast of the caldera, away from the main resurgent centers of volcanism (Chabi: ∼4 km and Urji: ∼7 km) and ∼3 km NE of the optimal location from the combined source inversion (Figure 6b, yellow star). The depth with minimum rms is 6.6 km (Figure S6a), coincident with the combined source inversion. All of the inversions agree on a source with a rate of volume change of ∼1.0 × 107 m3 /year and a depth of ∼6.6 km. However, residuals to the inversions for a source model suggest that there is a variation in the rate of volume change, depth, or both, specifically during 2014–2015 (Figures 5, S4, and S7). The inversion for the time series of volume change allows us to test whether variations in rate of volume change are able to describe the data, by fixing the depth. The time series using a fixed depth shows a strikingly linear increase in volume change between 2013 and 2017, and the total volume of 4.2 ± 0.5 × 107 m3 (Figure 6c) is within error of the total volume change estimated using the rate from the source model inversion (section 5.1) over the same duration of time (4.9 years): 4.4 ± 0.4 × 107 m3 . This therefore suggests that either the source depth or depth and volume change may vary during 2014–2015. The location of the model residuals indicates a preference for this deeper source to be in the north, or, more likely, a northward deeper continuation of the primary source. 6. New and Existing Subsurface Geophysics Volcanic-tectonic seismicity is an indicator of brittle rock failure, caused by subsurface stress changes in a volcanic setting. Between January 2012 and January 2014 an array of seven seismic stations were deployed at Corbetti (Figure 1b and Table S8), with up to five working at any given time. C01E, C02E, and C03E were deployed in January 2012, and C05E and C06E in January 2013. C03E was relocated to C04E in May 2014. C07E was deployed in October 2013 (Wilks, 2016). P and S wave first breaks were picked manually, with weightings based on their quality. These weightings (given values of 0 to 3) are related to P wave arrival time uncertainties of 0.05, 0.1, 0.2, and 0.5 s and S wave uncertainties of 0.1, 0.2, 0.3, and 0.5 s (Wilks, 2016). We use the probabilistic, nonlinear earthquake location software NONLINLOC to locate the seismicity (Lomax et al., 2000), using seismic arrival times and a 1-D velocity model from Daly et al. (2008), derived from seismic tomography in the northern MER. For the larger events, additional constraints on the seismicity at Corbetti were made, where possible, from a nearby seismic deployment at Aluto (Wilks et al., 2017). LLOYD ET AL. UPLIFT 5219 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 Figure 7. (a) Seismicity at Corbetti January 2012 to January 2014, colored by depth and sized by magnitude (Wilks, 2016). Blue triangles are seismic stations. The yellow star is the optimal Mogi source location from the combined Bayesian inversion, and the red rectangle is the optimal Okada model using the same data. The blue star is the optimal Mogi location from the 2014–2015 Bayesian inversion. Profile A–A′ is a profile through the magnetotelluric data, shown in (b). Dashed line shows orientation of cross-rift structure that intersects Corbetti (Lloyd et al., 2018). (b) Ground resistivity at Corbetti along the north-south profile A–A′ in a (Gíslason et al., 2015), with optimal sources the Mogi models overlain. Black dots represent earthquakes that occurred within 5 km of the profiles, with <2 km X, Y, Z uncertainty. Histogram on the left of the profile shows the relative number of earthquakes with depth. The network detected 224 earthquakes within 15 km of the caldera center, between local magnitudes 0.22 and 2.77. Of the events with <2-km uncertainty there is a cluster of seismicity located between Chabi and Urji (Figure 7a). Peaks in the number of events at Corbetti occur primarily in the shallow subsurface (above sea level) and at depths between 3 and 5 km (Figure 7b). Some seismicity also extends down to ∼9 km. The shallow seismicity is likely within a hydrothermal system (Wilks et al., 2017), but earthquakes with depths 3–5 km are consistent with brittle fracture above a source ∼6.5 km below the surface. Figure 7b shows these earthquakes projected onto an MT profile (Gíslason et al., 2015), where it can be seen they occur around the conductive anomaly in regions of higher resistivity. This location is also along the large fault structure that crosscuts the caldera (Lloyd et al., 2018; Figure 7). 7. Discussion We have modeled the uplift at Corbetti by mathematically approximating the source as a point source and the subsurface as an elastic half-space. Simple analytical approaches are important to understand systems where subsurface conditions are poorly constrained, but the inherent assumptions usually oversimplify natural systems. In this section we discuss what our model might physically represent and the implications for reservoir architecture, magma flux, and eruption potential. We also discuss the limitations that simplified assumptions of the subsurface physical properties, such as magma compressibility and viscoelastic behavior, may have on our interpretations. 7.1. Reservoir Architecture The best fitting source model is a point source at a depth of ∼6–7 km beneath Corbetti, which has been inflating for over 8 years. The source is located between the two major centers of resurgent volcanism (Chabi and Urji), which are considered to be geochemically homogeneous but exhibit contrasting styles LLOYD ET AL. UPLIFT 5220 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 of volcanism (Rapprich et al., 2016). The chemical homogeneity suggests that the eruptive products from both volcanoes have a common long-lasting (103 − 104 years) source. The Mogi source from the combined inversion (yellow star, Figure 7b) is colocated with a region of elevated conductivity. The depth and duration of the deformation, in addition to the coincident elevated conductivities, and occurrence of seismicity suggest that the source is magmatic (Cardona et al., 2018; Heise et al., 2010; Lu et al., 2010). In Figure 7a we also show the location of the optimal Mogi model from the 2014–2015 source inversion (blue star), which is located 7.6-km deep and ∼1 km north of the combined Mogi source. This hints at a deeper source or deeper northward extension of the source, which is consistent with the shape of the conductive anomaly. Our observations and comparisons to other systems suggest that the geophysical data likely represent a large interconnected storage network (e.g., Biggs et al., 2016; Greenfield & White, 2015; Tarasewicz et al., 2012), such as a series of vertically stacked sills (e.g., Field et al., 2012). The analytical model solutions assume an elastic half-space rheology for the crust such that volume changes within the source produce an instantaneous response at the surface. Hot or fractured rocks may behave viscoelastically, however. At long-lived volcanic systems like Corbetti, where the crust has likely been repeatedly thermally primed by numerous earlier intrusions (Rapprich et al., 2016), the viscoelastic response may have a significant influence on the location, amplitude, and temporal evolution of the observed surface deformation (e.g., Hickey et al., 2016; Masterlark, 2007). At the Aira and Santorini calderas sustained uplift is thought to be driven by pulses of magma injection accompanied by seismicity, which is separated by aseismic gaps where uplift is sustained by the viscoelastic response (Hickey et al., 2016; Parks et al., 2015). At Corbetti the rate of volume change is constant through time for the two studied time intervals (Figure 6). For a source in a viscoelastic medium, this could be explained in one of three ways: (1) through continuous magma injection, (2) a single magma injection pulse followed by viscoelastic relaxation over a time period much greater than the continuously observed time period (>5 years), or (3) pulsed magma injections, where the time between pulses is much shorter than the relaxation time. The single injection case requires a relaxation time of greater than 5 years, which is more than an order of magnitude greater than Campi Flegrei, for example (approximately months, Bonafede & Ferrari, 2009). Campi Flegrei has been modeled previously as a source embedded in a viscoelastic shell (Dragoni & Magnanensi, 1989). Corbetti would therefore require a relatively thicker shell or higher viscosity in comparison (Dragoni & Magnanensi, 1989; Newman et al., 2001). On the other hand, regular pulsed injections are not supported by the observed seismicity. Therefore, we conclude that the system is likely being fed by a continuous phase of magma injection. 7.2. Magma Flux In the period 2009–2017, the inversion of the observed surface deformation indicates a volume addition of 0.9 − 1.1 × 107 m3 /year. Geological observations show that postcaldera eruptive products are dominantly peralkaline rhyolites (Di Paola, 1971; Fontijn et al., 2018; Rapprich et al., 2016), which are produced following extreme fractional crystallization of mafic material (Peccerillo et al., 2007; Rapprich et al., 2016). Analysis using trace elements from Pantelleria and Aluto suggests 90%–96% fractional crystallization of the parental alkali basalts is required to fractionate pantellerite melts (Gleeson et al., 2017; Neave et al., 2012). At Corbetti magmas of intermediate chemical composition are absent in the postcaldera eruptive record and the pantellerites have low crystallinity (Rapprich et al., 2016). This implies that a high proportion of the mafic input material is still within a subsurface reservoir and that much of the long-term intruded volume is not erupted. Observations of erupted volcanic products at Corbetti suggest that “typical” eruptions have a volume of up to ∼5 × 108 m3 Dense Rock Equivalent (DRE) (Rapprich et al., 2016). Taking an ∼900-year recurrence interval (over the last 10 kyr, Martin-Jones et al., 2017), and assuming ∼5×108 m3 per eruption, gives a long-term eruption rate of ∼ 6 × 105 m3 /year. Fractionation of 90%–96% implies that the peralkaline eruption rate should be ∼4%–10% of the basaltic magma supply rate. Assuming all of the fractionated, peralkaline material is erupted this would give an estimated supply rate of 0.5−1.4×107 m3 /year. We discuss two plausible end-member scenarios to explain the inflation episode we observe at Corbetti: (1) the input of parental alkali basalts or (2) the transportation of fractionated peralkaline rhyolite. In the following calculations for both scenarios we assume that all of the fractionated material is eruptible. In the first scenario, at the observed rate of volume addition (107 m3 /year) of parental basalt it would take 500–1,500 years to accumulate enough material to fractionate ∼ 5×108 m3 of peralkaline magma (from ∼ 1.25×1010 m3 of intruded basalt; see Figure S2 for the distribution of peralkaline volumes and timescales given 90% and 96% fractionation and the volume change confidence thresholds). This time period encompasses the recurrence interval estimated by Martin-Jones et al. (2017). LLOYD ET AL. UPLIFT 5221 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 However, this implies that the current rate of volume change is continuous, which contrasts with previously observed periods of no deformation or subsidence (Biggs et al., 2011; Lloyd et al., 2018). Alternatively, the observed deformation may represent the transport of peralkaline rhyolites. The reservoir is likely to be a laterally and vertically extensive mush zone, with multiple melt-rich lenses. A broad zone of subsidence has been observed around uplift caused by vertical magma migration (Henderson & Pritchard, 2017), but these observations are rare, and coherence outside the volcanic center at Corbetti is likely too poor for any such signal to be detected. A volume addition of 107 m3 /year would take ∼50 years to produce 5 × 108 m3 of peralkaline magma. The flux period is much shorter than the recurrence interval and may suggest that eruptible magma reservoirs form through pulsed magma fluxes, a conclusion supported by thermal models (e.g., Menand et al., 2015). This volume of fractionated material (107 m3 /year), assuming that it is 4%–10% of the parental basalt supply rate, implies a large long-term basaltic supply rate of ∼108 m3 /year (Figure S2). This rate is larger than our estimate from erupted products, but this discrepancy may come from eruptions missing in the geological record (Martin-Jones et al., 2017, only consider the largest events) or a noncontinuous basalt supply rate. Based on our discussion above, the magma flux beneath Corbetti is between 107 m3 /year (assuming direct observation of parental basaltic magma input) and 108 m3 /year (derived basaltic flux, assuming that we are observing the vertical movement of the evolved component). Estimates of the flux required for magma to remain unfrozen in the crust vary depending on magma composition, the state of the intruded crust, and tectonic environment, but relevant estimates are between 105 and 107 m3 /year (e.g., Annen, 2009; Karakas & Dufek, 2015; Menand et al., 2015). At Corbetti our estimated flux is greater than this limit and so, if continuous, would be more than sufficient to sustain a long-lived reservoir. The flux is also in line with estimates from other caldera systems (e.g., Jellinek & DePaolo, 2003). 7.3. Eruption Potential One purpose of observing volcano deformation is to understand the current volcanic system and/or the societal impact activity may have. Numerous factors influence the hazard potential of a volcano, but quantification of where, how much, and how quickly magma is stored is critical to understanding the magnitude of a possible eruption. This is especially true at volcanoes with no previously observed eruptions close to large population centers, like Corbetti. A magmatic reservoir will fail when a critical overpressure is reached, resulting in either eruption or lateral magma movement over a variety of scales (e.g., Gudmundsson, 2012; Gudmundsson & Nilsen, 2006). Reservoir failure can be triggered internally, or externally, for example, via roof failure or sector collapse (e.g., Biggs et al., 2016; Gregg et al., 2012; Lipman et al., 1981; Voight et al., 2006). External triggers represent a source of unpredictability of potential eruptions and are not considered here. At Corbetti, there is no evidence of an eruption in recent decades, or major form of reservoir failure, meaning that the reservoir must be large and/or compressible enough to accommodate the strain associated with the intruding magma (Degruyter et al., 2016; Gottsmann & Odbert, 2014). External evidence for a large (∼102 km3 ) magma reservoir comes from the MT observations and the high degree of fractionation required to produce the peralkaline, aphyric erupted products. Whether the reservoir at Corbetti will fail following this deformation event will depend on many currently unconstrained factors, including the magma compressibility and the thermal maturity of the system (Karakas et al., 2017; Schópa & Annen, 2013). Although there is a statistically significant link between volcano deformation and eruption, this link is weaker in rift settings and calderas (Biggs et al., 2014). At many volcanoes, periods of deformation associated with magma occur in the absence of eruptions (e.g., Amelung et al., 2000; Biggs et al., 2009; Ebmeier et al., 2018; Le Mével et al., 2015; Pedersen & Sigmundsson, 2004). These episodes are usually attributed to magma reservoir growth or reorganization and could represent the processes currently ongoing at Corbetti should no eruption occur. 8. Conclusions From a combination of data from four SAR satellites/constellations and a network of continuous GPS sites we observe 7 cm/year of uplift at Corbetti directly above the source, which has been ongoing since 2009, in response to a subsurface volume change of ∼ 107 m3 /year. Evidence from the depth, duration, rate, and modeling of this deformation, as well as seismic and MT data, strongly suggests that the origin of this source is a pulse of magma intruding into a preexisting reservoir. From an analysis of Bayesian posterior probably density functions as well as the temporal and spatial analysis of model residuals, we identify that the primary magmatic reservoir is at ∼6.6-km depth, with perhaps a deeper northward protrusion (∼7.6-km deep). LLOYD ET AL. UPLIFT 5222 Journal of Geophysical Research: Solid Earth 10.1029/2018JB015711 This is supported by the MT observations and presumably represents a large interconnected magma network. The deformation could be precursory to a reservoir failure and potential subsequent eruption or represent a period of noneruptive reservoir growth beneath the volcano. This work highlights the importance of a framework within which one can combine different geodetic data sets to investigate long-term deformation signals and a statistically robust method to compare source models. Acknowledgments R. L. was supported by a NERC studentship tied to the LiCS (Looking inside the Continents from Space) consortium (NE/K010956/1). J. B., Y. B., and J. G. were supported by the Natural Environment Research Council (NERC) funded RiftVolc project (NE/L013932/1, Rift volcanism: past, present, and future). J. B. was also supported by the NERC Centre for the Observation and Modelling of Earthquakes, Volcanoes, and Tectonics (COMET). M. W. was funded by an EPSRC studentship. The Bristol University Microseismic ProjectS (BUMPS) provided funding for the seismic experiment and fieldwork. Seismic equipment was loaned from SEIS-UK (GEF loan 962). The seismic network is XM, and the data set is open access and available on IRIS. ALOS data were provided through ESA third-party mission. We thank the European Space Agency (ESA) for the ENVISAT and Sentinel-1 data. Cosmo-SkyMed data were made available through an Italian Space Agency (ASI) open call. The loan of GPS equipment was provided by the NERC Geophysical Equipment Facility. Natural Environment Research Council grants: NE/K010956/1 and NE/L013932/1. 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