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Previous work at Fernandina, the most active volcano of the Western Galápagos (Ecuador), revealed evidence for both a shallow and a deep magma reservoir, but the relative contribution of the two reservoirs to eruptions remains unclear. Here we investigate the September 2017 circumferential eruption and the June 2018 radial eruption using interferometric synthetic aperture radar data and geodetic modeling. Our results show that during the 2017 eruption magma was simultaneously withdrawn from the deep reservoir, injected upwards through the shallow reservoir, and then fed the circumferential feeder dike to the SW of the caldera. Two episodes of inflow of new magma occurred in both the deep and shallow magma reservoirs in the inter‐eruptive period from December 2017 to May 2018. During the 2018 eruption, both reservoirs fed two radial feeder dikes below the north flank, probably interacting with an underlying peripheral melt pocket, and an inclined sheet below the NW sector of the caldera. Our results highlight the primary role of the deeper reservoir which accumulates most of the magma before eruptions. Both eruptions were characterized by rapid magma transfer from the deeper to the shallower reservoir. This is similar to what is observed at the nearby Wolf volcano, but unlike nearby Sierra Negra, where a shallower reservoir accumulates higher volumes of magma before eruptions. These differences in the pre‐eruptive role of the deeper and shallower reservoirs might be related to the different evolutionary stages of Fernandina and Wolf with regard to the more mature Sierra Negra. Plain Language Summary: Fernandina is the most active volcano of the Western Galápagos (Ecuador). Two magma reservoirs at different depths below the volcano trigger eruptions both near the caldera rim (circumferential eruptions) and lower on the volcano flanks (radial eruptions). The role played by the two reservoirs in the eruptions is poorly understood. Here we studied the 2017 and the 2018 eruptions that occurred at Fernandina by using deformation data derived from radar satellites to investigate the inputs and outputs of new magma into the two reservoirs when eruptions occurred. The 2017 eruption had similar characteristics to the 2005 eruption, while the 2018 eruption had more complex mechanisms of shallow magma transfer, with magma transported in multiple directions below the north flank of Fernandina. We found that rapid magma transfer from the deep to the shallow reservoir provided most of the magma for both eruptions, similar to the nearby Wolf volcano, and unlike nearby Sierra Negra, a feature that may be due to the evolutionary stage of the volcanoes. Key Points: The 2017 circumferential eruption at Fernandina shows similar characteristics to the 2005 eruption, occurred in the same areaThe 2018 eruption is connected to the propagation of multiple dikes and sills, with most of the magma remaining intrudedBoth eruptions were characterized by rapid magma transfer from the deeper to the shallower reservoir, similar to what is observed at Wolf [ABSTRACT FROM AUTHOR]

Volcanism is one of the main mechanisms transferring mass and energy between the interior of the Earth and the Earth's surface. However, the global mass flux of lava, volcanic ash and explosive pyroclastic deposits is not well constrained. Here we review published estimates of the mass of the erupted products from 1980 to 2019 by a global compilation. We identified 1,064 magmatic eruptions that occurred between 1980 and 2019 from the Smithsonian Global Volcanism Program database. For each eruption, we reported both the total erupted mass and its partitioning into the different volcanic products. Using this data set, we quantified the temporal and spatial evolution of subaerial volcanism and its products from 1980 to 2019 at a global and regional scale. The mass of magma erupted in each analyzed decade ranged from 1.1–4.9 × 1013 kg. Lava is the main subaerial erupted product representing ∼57% of the total erupted mass of magma. The products related to the biggest eruptions (Magnitude ≥6), with long recurrence times, can temporarily make explosive products more abundant than lava (e.g., decade 1990–1999). Twenty‐three volcanoes produced ∼72% of the total mass, while two different sets of 15 volcanoes erupted >70% of the total mass of either effusive or explosive products. At a global scale, the 10 and 40‐year average eruptive rates calculated from 1980 to 2019 have the same magnitude as the long‐term average eruptive rates (from thousand to millions of years), because in both cases rates are scaled for times comparable to the recurrence time of the biggest eruptions occurred. Plain Language Summary: The impact of volcanism on the Earth system depends on how the magma is erupted at the surface. Lava effects are very strong locally, while ash emissions can impact larger areas. However, the total mass of magma erupted, as well as the mass of each volcanic product (effusive: lava; explosive: ash and pyroclastic flows) remain poorly constrained. Here we investigated the temporal and spatial evolution of global subaerial volcanism by quantifying the mass of each solid volcanic product erupted above the sea level from 1980 to 2019. Results show that at a global scale the subaerial volcanism produced 1.1–4.9 × 1013 kg of magma per decade from 1980 to 2019. Lava is the main subaerial product representing ∼57% of the total erupted mass of magma. Combined with already available datasets, our work furthers future investigations of the relationship between the erupted masses of magma and of volatiles, the variation of the eruptive rates after an earthquake, the impact of the erupted mass on the Geospheres at local and global scales. Finally, mass balancing between the erupted and intruded mass could provide information of whether a volcano or a magmatic province is accumulating magma, potentially increasing future eruptive hazards on a decadal timescale. Key Points: Global estimation of the mass and products erupted from 1980 to 2019Lava is the main subaerial product erupted from 1980 to 2019Twenty‐three volcanoes produced ∼72% of the total mass erupted from 1980 to 2019 [ABSTRACT FROM AUTHOR]

Cerro Azul is one of the most active volcanoes in the western Galápagos Islands, but its unrest episodes are poorly studied. Unrest, which started in 2007, culminated in two eruptive phases from 29 May to 11 June 2008. We investigate this unrest and the associated eruptions using interferometric synthetic aperture radar (InSAR) data and geodetic modelling. To overcome the unwrapping errors affecting some of our InSAR data, we invert the wrapped phase directly by estimating the integer ambiguities simultaneously with the geophysical parameters. Our results highlight how the eruption was preceded by long-term pre-eruptive inflation (October 2007-April 2008). During the first eruptive phase, most of the magma responsible for the inflation fed the lateral propagation of a radial dike, which caused a first deflation of the magmatic reservoir. During the second eruptive phase, the further lateral propagation of the dike fed a radial eruptive fissure at the base of the edifice, causing further deflation of the magmatic reservoir. From the first to the second eruptive phase, the radial dike changed its strike propagating toward a topographic low between Cerro Azul and Sierra Negra. [ABSTRACT FROM AUTHOR]

We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this family admits an initial ideal which has linear quotients. As a corollary, we compute the Hilbert series and h -vector for all the toric ideals of graphs in this family. [ABSTRACT FROM AUTHOR]

Understanding volcanic unrest is crucial to forecasting eruptions. At active mafic calderas unrest culminates in eruption more frequently than at felsic calderas. However, the mafic caldera of Alcedo Volcano (Ecuador) has experienced repeated episodes of unrest without erupting, since at least 1992, when geodetic monitoring began. Here we investigate the unrest that occurred between 2007 and 2011 using interferometric synthetic aperture radar (InSAR) data and geodetic modeling. We observe an initial asymmetric uplift of the southern caldera floor (~30 cm of vertical motion) from 2007 to 2009, followed by subsidence of the uplifted area and contemporary uplift of the northwestern caldera rim between January and June 2010. Finally, from June 2010 through March 2011, caldera uplift resumed. The first uplift episode is best explained by inflation of a sill and the activation of an inner ring fault. Successive caldera subsidence and rim uplift are compatible with the withdrawal of magma from the previously inflated sill and its northwestern migration. The resumption of uplift is consistent with the repressurization of the sill. This evolution suggests episodic magma emplacement in a shallow reservoir beneath the caldera, with aborted lateral magma migration, probably due to the discontinuous supply from depth. This short‐term deformation pattern matches well geological observations showing a longer‐term (hundreds of years at least) asymmetric uplift of the caldera floor, culminating in a weak resurgence of ~30 m. We propose that the monitored episodes of uplift represent short‐term stages of the rarely observed incremental growth of a resurgent basaltic caldera. Key Points: The 2007‐2011 noneruptive unrest at Alcedo was caused by shallow emplacement of new magma with limited lateral intrusionUplift during unrest is similar in location and shape to the longer‐term weak resurgence of the calderaThis unrest provides the rare opportunity to document the incremental growth of a basaltic resurgent caldera [ABSTRACT FROM AUTHOR]

We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these ideals and describe formulas for the graded characters of the corresponding quotient rings. [ABSTRACT FROM AUTHOR]

Calderas are impressive volcanic depressions commonly produced by major eruptions. Equally impressive is the uplift of the caldera floor that may follow, dubbed caldera resurgence, resulting from magma accumulation and accompanied by minor eruptions. Why magma accumulates, driving resurgence instead of feeding large eruptions, is one of the least understood processes in volcanology. Here we use thermal and experimental models to define the conditions promoting resurgence. Thermal modelling suggests that a magma reservoir develops a growing transition zone with relatively low viscosity contrast with respect to any newly injected magma. Experiments show that this viscosity contrast provides a rheological barrier, impeding the propagation through dikes of the new injected magma, which stagnates and promotes resurgence. In explaining resurgence and its related features, we provide the theoretical background to account for the transition from magma eruption to accumulation, which is essential not only to develop resurgence, but also large magma reservoirs. [ABSTRACT FROM AUTHOR]

Understanding volcanic unrest is crucial to forecasting eruptions. At active mafic calderas, unrest usually culminates in eruption, and does so more frequently than at felsic calderas. However, the mafic caldera of Alcedo Volcano (Ecuador) has experienced repeated episodes of unrest without erupting, since at least 1992, when geodetic monitoring began. Here, we investigate the unrest occurred between 2007 and 2011 performing a multi-temporal InSAR analysis of ENVISAT and ALOS-1 data, using the Small Baseline method. Then, we inverted ALOS-1 data to constrain the sources of deformation, using the GBIS software. We observe an initial asymmetric uplift of the caldera (~30 cm of vertical motion) from 2007 to 2009, followed by subsidence of the uplifted area and contemporary uplift of the north-western caldera rim between January and June 2010. Finally, from June 2010 through March 2011, caldera uplift resumed. The first uplift episode is best explained by inflation of a sill and the activation of an inner ring fault. Successive caldera subsidence and rim uplift are compatible with the withdrawal of magma from the previously inflated sill and its north-western migration. The resumption of uplift is consistent with the re-pressurization of the sill. This evolution suggests episodic magma emplacement in a shallow reservoir beneath the caldera, with aborted lateral magma migration, probably due to the discontinuous supply from depth. This short-term deformation pattern matches well geological observations showing a longer-term (hundreds of years at least) asymmetric uplift of the caldera floor, culminating in a weak resurgence of ~30 m. We propose that the monitored episodes of uplift represent short-term stages of the rarely observed incremental growth of a resurgent basaltic caldera. [ABSTRACT FROM AUTHOR]

We introduce a new class of monomial ideals which we call symmetric shifted ideals. Symmetric shifted ideals are fixed by the natural action of the symmetric group and, within the class of monomial ideals fixed by this action, they can be considered as an analogue of stable monomial ideals within the class of monomial ideals. We show that a symmetric shifted ideal has linear quotients and compute its (equivariant) graded Betti numbers. As an application of this result, we obtain several consequences for graded Betti numbers of symbolic powers of defining ideals of star configurations. [ABSTRACT FROM AUTHOR]