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The location and volume change of pressurized magma chambers can be constrained by inverse modelling of the surface displacements they cause. Through a joint inversion of surface displacements and gravity changes the chamber mass change during the pressurization period can also be inferred. Such inversions often start with constraining the deformation source parameters using the deformation data alone (step 1). Using these parameters the gravity data are then corrected for the effect of mass redistribution in the host rocks and surface uplift/subsidence associated with the chamber expansion (step 2). Next, the corrected gravity changes together with the source location from the deformation inversion are used to infer the intrusion mass (step 3). Provided that the intrusion compressibility is known, the intrusion density can be estimated from the intrusion mass and source volume change from step 1 and step 3, respectively (step 4).We show that the original gravity data (only corrected for ambient effects) are directly related to the deformation source parameters through the deformation-induced gravity changes and the free-air effect. Thus, both of these effects, which have been mostly considered as nuisance, in fact can be harvested to provide better constraints on the deformation source parameters and the mass changes. We propose a Bayesian framework for the joint inversion of deformation and gravity data by which all the deformation source parameters and chamber mass change are constrained simultaneously. This way, steps 1 to 3 of the previous approach are carried out at once. The advantages of the suggested approach are: (a) this way the gravity data help constrain deformation source parameters with smaller uncertainties, (b) it leads to a smaller uncertainty for the inferred mass change, (c) the optimal relative weights of various deformation and gravity datasets can be estimated as hyper-parameters within the Bayesian inference, thus, they are estimated directly and in an objective way, (c) the gravity and deformation stations need not be co-located, (d) errors associated with interpolation of vertical displacements at gravity benchmarks are avoided, (e) the uncertainty of vertical displacements is no longer propagated into the reduced gravity changes, and thus, mass changes are estimated more accurately. We apply this approach to the deformation and gravity data associated with the 1982-1999 inflation period at Long Valley caldera. The results agree with those from earlier efforts; however, show a clear improvement in the constrained source parameters and the intrusion mass. We discuss the implications and benefits of this approach depending on the relative quality of the deformation and gravity data.

Deformation source inversions have played a substantial role in our present understanding of magma plumbing systems at active volcanoes. Such inversions mostly rely on analytical models for uniformly-pressurized cavities as idealized representations of expanding magma bodies. The most common analytical cavity models used for rapid inversions are the isotropic point-source, the finite spheroidal cavity model and tensile dislocations or cracks. All these models have very specific shapes which cannot represent potentially significant deviations of magma chambers from axisymmetric geometries; thus, this aspect of volcano deformation sources has largely remained unexplored. Potential deviations from spherical and spheroidal shapes may explain the long-wavelength systematic residuals often encountered in inversions of deformation data. Even if the biases in the inferred deformation source parameters are small, they may translate into large biases in the mass change constrained through joint inversion of deformation and gravity data.The next step to promote our understanding about volcano deformations is to explore these complexities in the source geometries and their implications. We develop a finite ellipsoidal cavity model (finite ECM) that is a solution for surface displacements and deformation-induced gravity changes caused by finite pressurized ellipsoidal cavities. The model can be used to constrain deformation source parameters and subsurface mass changes caused by magmatic intrusions and other processes pressurizing relatively shallow magma chambers. The model is in the form of a distribution of triaxial point sources with depth-dependent spacing and strengths. We systematically validate and benchmark the model by using analytical and numerical solutions. Also through these comparisons, we explore the limitations of the finite ECM. In particular, we analyze the biases in the inferred source depth, volume change and mass change due to the approximations inherent in the model. The finite ECM is computationally efficient and can be used for coupled inversions of deformation and gravity data.

Volcanic crises are often associated with magmatic intrusions or the pressurization of magma chambers of various shapes. These volumetric sources deform the country rocks, changing their density, and cause surface uplift. Both the net mass of intruding magmatic fluids and these deformation effects contribute to surface gravity changes. Thus, to estimate the intrusion mass from gravity changes, the deformation effects must be accounted for. We develop analytical solutions and computer codes for the gravity changes caused by triaxial sources of expansion. This establishes coupled solutions for joint inversions of deformation and gravity changes. Such inversions can constrain both the intrusion mass and the deformation source parameters more accurately., Plain Language Summary: Volcanic crises are usually associated with magmatic fluids that intrude and deform the host rocks before potentially breaching the Earth's surface. It is important to estimate how much fluid (mass and volume) is on the move. Volume can be determined from the measured surface uplift. Mass can be determined from surface gravity changes. The fluid intrusion increases the mass below the volcano, thereby increasing the gravity and pressurizing the rocks. This dilates parts of the host rock and compresses other parts, changing the rock density and redistributing the rock mass. This causes secondary gravity changes, called deformation‐induced gravity changes. The measured gravity change is always the sum of the mass and deformation‐induced contributions. Here, we develop mathematical equations for the rapid estimation of these deformation‐induced gravity changes caused by arbitrary intrusion shapes. This way we can take the mass contribution apart from the deformation contribution. We show that by using this solution not only the intrusion mass, but also other intrusion parameters, including the volume, depth, and shape can be calculated more accurately., Key Points; We develop analytical solutions for gravity changes due to the point Compound Dislocation Model simulating triaxial expansions. Rapid coupled inversions of deformation and gravity changes, accounting for deformation‐induced gravity changes are now possible. For shallow sources, estimation errors in the chamber volume change may lead to large biases in the simulated gravity changes., EU Horizon 2020 programme NEWTON‐g project, under the FETOPEN‐ Grant Agreement No., Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/501100001659, https://volcanodeformation.com/onewebmedia/pCDMgravity.zip

Lava fountains represent a common eruptive phenomenon at basaltic volcanoes, which consist of jets of fluid lava ejected into the atmosphere from active vents or fissures. They are driven by rapid formation and expansion of gas bubbles during magma ascent. The dynamics of lava fountains is thought to be controlled by the gas accumulation in the foam layer at the top of a shallow magmatic reservoir, which eventually collapses triggering the lava fountaining. Gravity measurements taken from a location close to summit of Mt. Etna during the 2011 lava fountain episodes showed a pre-fountaining decrease of the gravity signal. The interplay between gas accumulation in the foam layer and its subsequent exsolution in the conduit has been interpreted as the mechanism producing the gravity decrease and eventually leading to the foam collapse and onset of the lava fountaining activity. Gravity measurements have proved helpful in recording the earliest phases anticipating the lava fountain episodes and inferring the amount of gas involved. However, more accurate estimates of the accumulating and ascending gas volume and total magma mass require considering the possible effect of non-spherical magma chamber geometries and magma compressibility. Under task 4.4 of the H2020 NEWTON-g project, we are accomplishing a detailed study aimed to simulate the gravity signal produced in the stage prior to a lava fountain episode, through a magma chamber - conduit model. We use a prolate ellipsoidal chamber matching the inferred shape of the shallow chamber active at Mt. Etna during the lava fountain episodes, and calculate the surface gravity changes induced by inflow of new magma into the chamber-conduit system. We use a two-phase magma with fixed amount of gas mass fraction and account for magma compressibility. We find that a realistic chamber shape and magma compressibility play a key role and must be considered to produce realistic gravity changes simulations. We combine our physical model with empirical distributions of recurrence time and eruption size of the past lava fountains at Mt. Etna to stochastically simulate realistic time series of gravity changes. The final goal of this study is to develop a prediction model for the amount of magma and duration of lava fountains at Mt. Etna.

Gravity change observations at volcanoes provide information on the location and mass change of intruded magma bodies. Gravity change and surface displacement observations are often combined in order to infer the density of the intruded materials. Previous studies have highlighted that it is crucial to account for magma compressibility and the shape of the gravity change and deformation source to avoid large biases in the density estimate. Currently, an analytical model for the deformation field and gravity change due to a source of arbitrary shape is lacking, affecting our ability to perform rapid inversions and assess the nature of volcanic unrest. Here, we propose an efficient approach for rapid joint-inversions of surface displacement and gravity change observations associated with underground pressurized reservoirs. We derive analytical solutions for deformations and gravity changes due to the volume changes of triaxial point-sources in an isotropic elastic half-space. The method can be applied to volcanic reservoirs that are deep compared to their size (far field approximation). We show that the gravity changes not only allow inferring mass changes within the reservoirs, but also help better constrain location, shape and the volume change of the source. We discuss how the inherent uncertainties in the realistic shape of volcanic reservoirs are reflected in large uncertainties on the density estimates. We apply our approach to the surface displacements and gravity changes at Long Valley caldera over the 1985-1999 time period. We show that gravity changes together with only vertical displacements are sufficient to constrain the mass change and all the other source parameters. We also show that while mass change is well constrained by gravity change observations the density estimate is more uncertain even if the magma compressibility is accounted for in the model.

The transport of magma and magmatic fluids is a key process behind the occurrence, duration and intensity of volcanic crises. Volcano gravimetry allows for unequivocal inference of the location and mass of accumulated or removed magmatic fluids at volcanoes. This task is best accomplished through collecting gravity time series at multiple stations simultaneously. The performance of individual gravimeters and the configuration of the gravimetric array, however, determine the threshold of detectable mass change and the ability of the array to minimize the uncertainty on the inferred quantities.We utilize numerical optimization techniques to design a network including one absolute quantum gravimeter (AQG), two superconducting relative gravimeters (iGRAVs) and several microelectromechanical system (MEMS) relative gravimeters at Mount Etna. We also develop analytical solutions for simple design problems. We show that the analytical solutions are essential for validating the numerical optimization procedure. We provide practical details and caveats that should be considered in similar gravimetric network optimizations. These include 1) specifying the target zone of the network by using the history of mass transport, 2) accounting for the relative importance of different parts of the target zone, 3) accounting for logistic and instrumental constraints in the optimizations 4) calibrating the objective functions associated with various optimizations, 5) analyzing the network sensitivities to different parts of the target zone and identifying blind zones and 6) calculating the optimal number of gravimeters as a function of the sensor sensitivity and accuracies. We show that our optimal solution for Mount Etna provides an improved detection power across the target zone as compared to an equally spaced network of gravimeters with the same existing constraints, surface topography and sensor sensitivities. Furthermore, this optimal solution ensures that a certain range of mass change anywhere in the target zone can be sensed by a given minimum number of gravimeters and at the same time minimizes the impact of random observation errors on the inferred quantities.

The largest volcanic eruptions in the geological record are typical of Large Igneous Provinces (LIPs) or of calderas. Known factors facilitating large eruptions include a large size of the feeding magma reservoir, massive vesiculation and gradual collapse of the magma reservoir roof to sustain pressure. Based on analytical models considering rock (visco)elasticity and magma compressibility, here we identify further controlling factors: the aspect ratio of the magma reservoir (equi-dimensional vs. elongated or crack-like), its orientation (vertical vs. horizontal) and its depth. We find that thin (crack-like) horizontally elongated reservoirs filled with gas-rich magma can best sustain pressure during eruptions and can thus evacuate a larger fraction of the magma they contain. In order for these melt lenses to accumulate magma without solidifying they should be located either in the lower crust or, if shallow, within large crystal mushes, where temperatures are high. All these factors are relevant for LIPs and caldera reservoirs and not for other settings. Our model predicts that eruptive volumes scale with the square of the horizontal dimension of the magma reservoir, and not with its third power, as it would be expected if reservoir volume was the main controlling factor. This scaling is supported by observations from calderas worldwide.

Gravimetry is the only method able to directly track redistributions of bulk masses. Hence, it can supply unique information on geophysical processes that involve subsurface fluids like water, hydrocarbons, and magma. Nevertheless, the high cost of currently available gravimeters and the difficulty to use them in field conditions, has limited the applicability of the gravity method, that is indeed not as widely adopted as other geophysical methods.A new system for gravity measurements is being developed in the framework of the H2020 NEWTON-g project. This system, called “gravity imager”, includes an array of MEMS gravimeters, anchored to an absolute quantum device. It will enable, for the first time, gravity measurements at high spatio-temporal resolution. After the phases of design and production of the new devices, NEWTON-g involves a 2-year phase of field tests at Mt. Etna volcano (Italy), starting in the summer of 2020.

The dynamics of magma deep in the Earth’s crust are difficult to capture by geophysical monitoring. Since May 2018, a seismically quiet area offshore of Mayotte in the western Indian Ocean has been affected by complex seismic activity, including long-duration, very-long-period signals detected globally. Global Navigation Satellite System stations on Mayotte have also recorded a large surface deflation offshore. Here we analyse regional and global seismic and deformation data to provide a one-year-long detailed picture of a deep, rare magmatic process. We identify about 7,000 volcano-tectonic earthquakes and 407 very-long-period seismic signals. Early earthquakes migrated upward in response to a magmatic dyke propagating from Moho depth to the surface, whereas later events marked the progressive failure of the roof of a magma reservoir, triggering its resonance. An analysis of the very-long-period seismicity and deformation suggests that at least 1.3 km3 of magma drained from a reservoir of 10 to 15 km diameter at 25 to 35 km depth. We demonstrate that such deep offshore magmatic activity can be captured without any on-site monitoring. Recent seismicity near Mayotte in the Indian Ocean is due to dyke propagation from and drainage of a 25–35 km deep magma reservoir, according to an analysis of earthquake and deformation data.

Copahue volcano straddling the edge of the Agrio-Caviahue caldera along the Chile-Argentina border in the southern Andes has been in unrest since inflation began in late 2011. We constrain Copahue's source models with satellite and airborne interferometric synthetic aperture radar (InSAR) deformation observations. InSAR time series from descending track RADARSAT-2 and COSMO-SkyMed data span the entire inflation period from 2011 to 2016, with their initially high rates of 12 and 15 cm/yr, respectively, slowing only slightly despite ongoing small eruptions through 2016. InSAR ascending and descending track time series for the 2013–2016 time period constrain a two-source compound dislocation model, with a rate of volume increase of 13 × 106 m3/yr. They consist of a shallow, near-vertical, elongated source centered at 2.5 km beneath the summit and a deeper, shallowly plunging source centered at 7 km depth connecting the shallow source to the deeper caldera. The deeper source is located directly beneath the volcano tectonic seismicity with the lower bounds of the seismicity parallel to the plunge of the deep source. InSAR time series also show normal fault offsets on the NE flank Copahue faults. Coulomb stress change calculations for right-lateral strike slip (RLSS), thrust, and normal receiver faults show positive values in the north caldera for both RLSS and normal faults, suggesting that northward trending seismicity and Copahue fault motion within the caldera are caused by the modeled sources. Together, the InSAR-constrained source model and the seismicity suggest a deep conduit or transfer zone where magma moves from the central caldera to Copahue's upper edifice.

The three-dimensional assessment of ring-fault geometries and kinematics at active caldera volcanoes is typically limited by sparse field, geodetic or seismological data, or by only partial ring-fault rupture or slip. Here we use a novel combination of spatially dense InSAR time-series data, numerical models and sand-box experiments to determine the three-dimensional geometry and kinematics of a sub-surface ring-fault at Tendurek volcano in Turkey. The InSAR data reveal that the area within the ring-fault not only subsides, but also shows substantial westward-directed lateral movement. The models and experiments explain this as a consequence of a ‘sliding-trapdoor’ ring-fault architecture that is mostly composed of outward-inclined reverse segments, most markedly so on the volcano's western flanks but includes inward-inclined normal segments on its eastern flanks. Furthermore, the model ring-fault exhibits dextral and sinistral strike-slip components that are roughly bilaterally distributed onto its northern and southern segments, respectively. Our more complex numerical model describes the deformation at Tendurek better than an analytical solution for a single rectangular dislocation in a half-space. Comparison to ring-faults defined at Glen Coe, Fernandina and Barðarbunga calderas suggests that ‘sliding-trapdoor’ ring-fault geometries may be common in nature and should therefore be considered in geological and geophysical interpretations of ring-faults at different scales worldwide.

Volcanic crises are often preceded and accompanied by volcano deformation caused by magmatic and hydrothermal processes. Fast and efficient model identification and parameter estimation techniques for various sources of deformation are crucial for process understanding, volcano hazard assessment and early warning purposes. As a simple model that can be a basis for rapid inversion techniques, we present a compound dislocation model (CDM) that is composed of three mutually orthogonal rectangular dislocations (RDs). We present new RD solutions, which are free of artefact singularities and that also possess full rotational degrees of freedom. The CDM can represent both planar intrusions in the near field and volumetric sources of inflation and deflation in the far field. Therefore, this source model can be applied to shallow dikes and sills, as well as to deep planar and equidimensional sources of any geometry, including oblate, prolate and other triaxial ellipsoidal shapes. In either case the sources may possess any arbitrary orientation in space. After systematically evaluating the CDM, we apply it to the co-eruptive displacements of the 2015 Calbuco eruption observed by the Sentinel-1A satellite in both ascending and descending orbits. The results show that the deformation source is a deflating vertical lens-shaped source at an approximate depth of 8 km centred beneath Calbuco volcano. The parameters of the optimal source model clearly show that it is signicantly different from an isotropic point source or a single dislocation model. The Calbuco example reflects the convenience of using the CDM for a rapid inter- pretation of deformation data.

The effective elastic thickness of the lithosphere has an important role in constraining compositional structure, geothermal gradient and tectonic forces within the lithosphere and the thickness of this layer can be used to evaluate the earthquakes’ focal depth. Hence, assessment of the elastic thickness of the lithosphere by gravitational admittance method in Iran is the main objective of this paper. Although the global geopotential models estimated from the satellite missions and surface data can portray the Earth’s gravity field in high precision and resolution, there are some debates about using them for lithosphere investigations. We used both the terrestrial data which have been provided by NCC (National Cartographic Center of Iran) and BGI (Bureau Gravimetrique International), and the satellite-derived gravity and topography which are generated by EIGEN-GL04C and ETOPO5, respectively. Finally, it is concluded that signal content of the satellite-derived data is as rich as the terrestrial one and it can be used for the determination of the lithosphere bending.

This paper presents results of the Sentinel-1 sensor in the interferometric wide-swath (IW) mode encompassing the first two years of operation of the mission. The paper focuses on persistent scatterer interferometric results and their validation. Further applications and investigations are also addressed, e.g., earthquakes, volcanoes and tomography.

Surveillance of clandestine nuclear tests relies on a global seismic network, but the potential of spaceborne monitoring has been underexploited. We used satellite radar imagery to determine the complete surface displacement field of up to 3.5 meters of divergent horizontal motion with 0.5 meters of subsidence associated with North Korea’s largest underground nuclear test. Combining insight from geodetic and seismological remote sensing, we found that the aftermath of the initial explosive deformation involved subsidence associated with subsurface collapse and aseismic compaction of the damaged rocks of the test site. The explosive yield from the nuclear detonation with best-fitting source parameters for 450-meter depth was 191 kilotonnes of TNT equivalent. Our results demonstrate the capability of spaceborne remote sensing to help characterize large underground nuclear tests. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Accepted version

S U M M A R Y Displacements and stress-field changes associated with earthquakes, volcanoes, landslides and human activity are often simulated using numerical models in an attempt to understand the underlying processes and their governing physics. The application of elastic dislocation theory to these problems, however, may be biased because of numerical instabilities in the calculations. Here, we present a new method that is free of artefact singularities and numerical instabilities in analytical solutions for triangular dislocations (TDs) in both full-space and half-space. We apply the method to both the displacement and the stress fields. The entire 3-D Euclidean space R3 is divided into two complementary subspaces, in the sense that in each one, a particular analytical formulation fulfils the requirements for the ideal, artefact-free solution for a TD. The primary advantage of the presented method is that the development of our solutions involves neither numerical approximations nor series expansion methods. As a result, the final outputs are independent of the scale of the input parameters, including the size and position of the dislocation as well as its corresponding slip vector components. Our solutions are therefore well suited for application at various scales in geoscience, physics and engineering. We validate the solutions through comparison to other well-known analytical methods and provide the MATLAB codes.

The geometry of the volcanic conduit is a main parameter controlling the dynamics and the style of volcanic eruptions and their precursors, but also one of the main unknowns. Pre-eruptive signals that originate in the upper conduit region include seismicity and deformation of different types and scales. However, the locality of the source of these signals and thus the conduit geometry often remain unconstrained at steep sloped and explosive volcanoes due to the sparse instrumental coverage in the summit region and difficult access. Here we infer the shallow conduit system geometry of Volcán de Colima, Mexico, based on ground displacements detected in high resolution satellite radar data up to 7 h prior to an explosion in January 2013. We use Boundary Element Method modeling to reproduce the data synthetically and constrain the parameters of the deformation source, in combination with an analysis of photographs of the summit. We favor a two-source model, indicative of distinct regions of pressurization at very shallow levels. The horizontal location of the upper pressurization source coincides with that of post-explosive extrusion. The pattern and degree of deformation reverses again during the eruption; we therefore attribute the displacements to transient (elastic) pre-explosive pressurization of the conduit system. Our results highlight the geometrical complexity of shallow conduit systems at explosive volcanoes and its effect on the distribution of pre-eruptive deformation signals. An apparent absence of such signals at many explosive volcanoes may relate to its small temporal and spatial extent, partly controlled by upper conduit structures. Modern satellite radar instruments allow observations at high spatial and temporal resolution that may be the key for detecting and improving our understanding of the generation of precursors at explosive volcanoes.

The Caspian Sea has displayed considerable fluctuations in its water level during the past century. Knowledge of such fluctuation is vital for understanding the local hydrological cycles, climate of the region, and construction activities within the sea and along its shorelines. This study established a point-wise satellite altimetry approach to monitor the fluctuations of the Caspian Sea using a complete dataset of TOPEX/Poseidon for the period 1993 to the middle of 2002, and its follow-on Jason-1 for the period 2002 to August 2009. Therefore, 280 virtual time-series were constructed to monitor the fluctuations. The least squares spectral analysis (LSSA) method is, then employed to find the most significant frequencies of the time-series, while the statistical method of principle component analysis (PCA) is applied to extract the dominant variability of level variations. The study also used the observations of TOPEX/Poseidon and Jason-1 over the Volga River along with 5 years of Volga’s water discharge to study its influence on the Caspian Sea level changes. The LSSA results indicate that the lunar semidiurnal (M2) and the Sun semidiurnal (S2) frequencies are the main tidal frequencies of the Caspian Sea with the mean amplitude of 4.2 and 2.8 cm, respectively. A statistically significant long-term frequency (12.5-years period) is also found from altimetry and tide gauge observations. A phase lag, related to the inter-annual frequencies of the Volga River was detected from the point-wise time-series showing level propagation from the northwest to the southeast of the sea. The cross-correlation between the power spectrum of Volga and that of the northern-most, middle, and southern-most points within the Caspian Sea were respectively 0.63, 0.51 and 0.4 of zero-lag correlation, corroborating the influence of the Volga River. The result of PCA also shows that different parts of the Caspian Sea exhibit different amplitudes of level variations, indicating that the point-wise approach, when employing all available satellite measurements could be a suitable method for a preliminary monitoring of this inland water resource as it gives accurate local fluctuations.

SUMMARY We develop quasi-analytical solutions for the surface deformation field and gravity changes due to the pressurization of a finite (triaxial) ellipsoidal cavity in a half-space. The solution is in the form of a non-uniform distribution of triaxial point sources within the cavity. The point sources have the same aspect ratio, determined by the cavity shape, while their strengths and spacing are determined in an adaptive manner, such that the net point-source potency per unit volume is uniform. We validate and compare our solution with analytical and numerical solutions. We provide computationally efficient MATLAB codes tailored for source inversions. This solution opens the possibility of exploring the geometry of shallow magma chambers for potential deviations from axial symmetry.

The gravity imager, which will be developed under NEWTON-g and field-tested at Mt. Etna volcano, is composed by an array of microelectromechanical system (MEMS) pixels and an absolute quantum gravimeter (AQG). The main aim of the present document is to define the final configuration of the gravity imager, taking into account the environmental constraints and the gravimetric signature of volcanic processes highlighted in Deliverable 4.1, especially in terms of magnitude, timescale, detection zone and probability of occurrence of these processes.