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NASA NTRS2011

Reconciling Simulated and Observed Views of Clouds: MODIS, ISCCP, and the Limits of Instrument Simulators in Climate Models

The properties of clouds that may be observed by satellite instruments, such as optical depth and cloud top pressure, are only loosely related to the way clouds are represented in models of the atmosphere. One way to bridge this gap is through "instrument simulators," diagnostic tools that map the model representation to synthetic observations so that differences between simulator output and observations can be interpreted unambiguously as model error. But simulators may themselves be restricted by limited information available from the host model or by internal assumptions. This work examines the extent to which instrument simulators are able to capture essential differences between MODIS and ISCCP, two similar but independent estimates of cloud properties. We focus on the stark differences between MODIS and ISCCP observations of total cloudiness and the distribution of cloud optical thickness can be traced to different approaches to marginal pixels, which MODIS excludes and ISCCP treats as homogeneous. These pixels, which likely contain broken clouds, cover about 15% of the planet and contain almost all of the optically thinnest clouds observed by either instrument. Instrument simulators can not reproduce these differences because the host model does not consider unresolved spatial scales and so can not produce broken pixels. Nonetheless, MODIS and ISCCP observation are consistent for all but the optically-thinnest clouds, and models can be robustly evaluated using instrument simulators by excluding ambiguous observations.

Pincus, Robert↗

NASA NTRS2014

The Architecture of the LkCa 15 Transitional Disk Revealed By High-Contrast Imaging

We present four new epochs of Ks-band images of the young pre-transitional disk around LkCa 15 and perform extensive forward modeling to derive the physical parameters of the disk. We find indications of strongly anisotropic scattering (Henyey-Greenstein g = 0.67 (+0.18/−0.11)) and a significantly tapered gap edge ("round wall") but see no evidence that the inner disk, whose existence is predicted by the spectral energy distribution, shadows the outer regions of the disk visible in our images.We marginally confirm the existence of an offset between the disk center and the star along the line of nodes; however, the magnitude of this offset (x = 27 (+19/−20) mas) is notably lower than that found in our earlier H-band images. Intriguingly, we also find an offset of y = 69 (+49/−25) mas perpendicular to the line of nodes at high significance. If confirmed by future observations, this would imply a highly elliptical - or otherwise asymmetric - disk gap with an effective eccentricity of e ≈ 0.3. Such asymmetry would most likely be the result of dynamical sculpting by one or more unseen planets in the system. Finally, we find that the bright arc of scattered light we see in direct imaging observations originates from the near side of the disk and appears brighter than the far side because of strong forward scattering.

dynamical sculpting↗

NASA NTRS2013

Simulation of Inflated Pahoehoe Lava Flows

A new stochastic model simulates late-stage pahoehoe lobes where random processes dominate emplacement. The model prescribes probabilistic rules for determining where and when parcels of lava move within the lobe. Unlike a classical Brownian motion random walk, the model allows individual parcels to remain dormant, but fluid, for multiple time steps. The randomness of parcel volume transfers within the lobe interior as well as at the margins qualitatively reflects inflation processes observed in the field. The fraction of inflated volume to total volume increases with the total volume, with greater than 75% of the lobe volume contributed through inflation for typical lobes. The influence on planform shape and topographic cross-sectional profiles of total volume, source area and shape, topographic confinement, and sequential breakouts at the lobe margins, are all explored with the stochastic model. Each of these factors influences the overall lobe thickness and width. The model provides a means for assessing the relative importance of these processes through comparisons with field data. For the first time, Gaussian and parabolic functions are quantitatively fit to field measurements of pahoehoe lobes. Both functional forms provide adequate description of the cross-sectional flow shapes. When comparing simulated lobes to field data, sequential breakouts at the lobe margins are found to be an important process controlling the final topographic distribution of observed pahoehoe lobes.

modeling↗

NASA NTRS2023

Impact of Design Factors for ESA CCI Satellite Soil Moisture Data Assimilation over Europe

In this study, soil moisture retrievals of the combined active–passive ESA Climate Change Initiative (CCI) soil moisture product are assimilated into the Noah-MP land surface model over Europe using a one-dimensional ensemble Kalman filter and an 18-yr study period. The performance of the data assimilation (DA) system is evaluated by comparing it with a model-only experiment (at in situ sites) and by assessing statistics of innovations and increments as DA diagnostics (over the entire domain). For both assessments, we explore the impact of three design choices, resulting in the following insights. 1) The magnitude of the assumed observation errors strongly affects the skill improvements evaluated against in situ stations and internal diagnostics. 2) Choosing between climatological or monthly cumulative distribution function matching as the observation bias correction method only has a marginal effect on the in situ skill of the DA system. However, the internal diagnostics suggest a more robust system parameterization if the observations are rescaled monthly. 3) The choice of atmospheric reanalysis dataset to force the land surface model affects the model-only skill and the DA skill improvements. The model-only skill is higher with input from the MERRA-2 than with input from the ERA5 reanalysis, resulting in larger DA skill improvements for the latter. Additionally, we show that the added value of the DA strongly depends on the quality of the satellite retrievals and land cover, with the most substantial soil moisture skill improvements occurring over croplands and skill degradation occurring over densely forested areas.

Soil moisture↗

DOE OSTI2026

HFIR Steady State Heat Transfer Code (HSSHTC) Statistical Uncertainty Analysis

HSSHTC, the safety basis steady state TH code for HFIR, uses a highly conservative approach in which all input and calculation uncertainties are resolved simultaneously at their most limiting setting. This results in excessive conservatism which does not account for the high unlikelihood of such simultaneous worst-case conditions. The present study explores an alternative approach, BEPU, in which reasonable working assumptions for the probability distribution of each input uncertainty are used to determine a relationship between burnout power margin and core fuel failure probability. This was performed under a philosophy of perturbing uncertainty parameters already defined within the HSSHTC methodology while preserving the HSSHTC calculation approach and solution methodology itself. Based on the assumptions employed in this study, the BEPU approach resulted in a 0.29 increase in burnout power ratio (25 MW increase in burnout power) compared to the latest HSSHTC calculations of C-HFIR-2026-004. The study can be refined in the future by employing fuel fabrication data to provide more realistic input distributions. Future changes to the HSSHTC methodology would potentially allow a more comprehensive treatment of uncertainties which may further increase the burnout power ratio.

Wysocki, Aaron [ORNL] (ORCID:0000000222043779)↗

NASA NTRS2001

"A Richness Study of 14 Distant X-Ray Clusters from the 160 Square Degree Survey"

We have measured the surface density of galaxies toward 14 X-ray-selected cluster candidates at redshifts z(sub i) 0.46, and we show that they are associated with rich galaxy concentrations. These clusters, having X-ray luminosities of Lx(0.5-2 keV) approx. (0.5 - 2.6) x 10(exp 44) ergs/ sec are among the most distant and luminous in our 160 deg(exp 2) ROSAT Position Sensitive Proportional Counter cluster survey. We find that the clusters range between Abell richness classes 0 and 2 and have a most probable richness class of 1. We compare the richness distribution of our distant clusters to those for three samples of nearby clusters with similar X-ray luminosities. We find that the nearby and distant samples have similar richness distributions, which shows that clusters have apparently not evolved substantially in richness since redshift z=0.5. There is, however, a marginal tendency for the distant clusters to be slightly poorer than nearby clusters, although deeper multicolor data for a large sample would be required to confirm this trend. We compare the distribution of distant X-ray clusters in the L(sub X)-richness plane to the distribution of optically selected clusters from the Palomar Distant Cluster Survey. The optically selected clusters appear overly rich for their X-ray luminosities, when compared to X-ray-selected clusters. Apparently, X-ray and optical surveys do not necessarily sample identical mass concentrations at large redshifts. This may indicate the existence of a population of optically rich clusters with anomalously low X-ray emission, More likely, however, it reflects the tendency for optical surveys to select unvirialized mass concentrations, as might be expected when peering along large-scale filaments.

Jones, Christine↗

DOE OSTI2021

Redshift evolution of the underlying type Ia supernova stretch distribution

The detailed nature of type Ia supernovae (SNe Ia) remains uncertain, and as survey statistics increase, the question of astrophysical systematic uncertainties arises, notably that of the evolution of SN Ia populations. We study the dependence on redshift of the SN Ia SALT2.4 light-curve stretch, which is a purely intrinsic SN property, to probe its potential redshift drift. The SN stretch has been shown to be strongly correlated with the SN environment, notably with stellar age tracers. We modeled the underlying stretch distribution as a function of redshift, using the evolution of the fraction of young and old SNe Ia as predicted using the SNfactory dataset, and assuming a constant underlying stretch distribution for each age population consisting of Gaussian mixtures. We tested our prediction against published samples that were cut to have marginal magnitude selection effects, so that any observed change is indeed astrophysical and not observational in origin. In this first study, there are indications that the underlying SN Ia stretch distribution evolves as a function of redshift, and that the age drifting model is a better description of the data than any time-constant model, including the sample-based asymmetric distributions that are often used to correct Malmquist bias at a significance higher than 5σ. The favored underlying stretch model is a bimodal one, composed of a high-stretch mode shared by both young and old environments, and a low-stretch mode that is exclusive to old environments. The precise effect of the redshift evolution of the intrinsic properties of a SN Ia population on cosmology remains to be studied. The astrophysical drift of the SN stretch distribution does affect current Malmquist bias corrections, however, and thereby the distances that are derived based on SN that are affected by observational selection effects. We highlight that this bias will increase with surveys covering increasingly larger redshift ranges, which is particularly important for the Large Synoptic Survey Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Subsurface microbial community structure shifts along the geological features of the Central American Volcanic Arc

Subduction of the Cocos and Nazca oceanic plates beneath the Caribbean plate drives the upward movement of deep fluids enriched in carbon, nitrogen, sulfur, and iron along the Central American Volcanic Arc (CAVA). These compounds fuel diverse subsurface microbial communities that in turn alter the distribution, redox state, and isotopic composition of these compounds. Microbial community structure and functions vary according to deep fluid delivery across the arc, but less is known about how microbial communities differ along the axis of a convergent margin as geological features (e.g., extent of volcanism and subduction geometry) shift. Here, we investigate changes in bacterial 16S rRNA gene amplicons and geochemical analysis of deeply-sourced seeps along the southern CAVA, where subduction of the Cocos Ridge alters the geological setting. We find shifts in community composition along the convergent margin, with communities in similar geological settings clustering together independently of the proximity of sample sites. Microbial community composition correlates with geological variables such as host rock type, maturity of hydrothermal fluid and slab depth along different segments of the CAVA. This reveals tight coupling between deep Earth processes and subsurface microbial activity, controlling community distribution, structure and composition along a convergent margin.

Science & Technology - Other Topics↗

NASA NTRS2010

Determining Shear Stress Distribution in a Laminate

A "simplified shear solution" method approximates the through-thickness shear stress distribution within a composite laminate based on an extension of laminated beam theory. The method does not consider the solution of a particular boundary value problem; rather, it requires only knowledge of the global shear loading, geometry, and material properties of the laminate or panel. It is thus analogous to lamination theory in that ply-level stresses can be efficiently determined from global load resultants at a given location in a structure and used to evaluate the margin of safety on a ply-by-ply basis. The simplified shear solution stress distribution is zero at free surfaces, continuous at ply boundaries, and integrates to the applied shear load. The method has been incorporated within the HyperSizer commercial structural sizing software to improve its predictive capability for designing composite structures. The HyperSizer structural sizing software is used extensively by NASA to design composite structures. In the case of through-thickness shear loading on panels, HyperSizer previously included a basic, industry-standard, method for approximating the resulting shear stress distribution in sandwich panels. However, no such method was employed for solid laminate panels. The purpose of the innovation is to provide an approximation of the through-thickness shear stresses in a solid laminate given the through-thickness shear loads (Qx and Qy) on the panel. The method was needed for implementation within the HyperSizer structural sizing software so that the approximated ply-level shear stresses could be utilized in a failure theory to assess the adequacy of a panel design. The simplified shear solution method was developed based on extending and generalizing bi-material beam theory to plate-like structures. It is assumed that the through-thickness shear stresses arise due to local bending of the laminate induced by the through-thickness shear load, and by imposing equilibrium both vertically and horizontally, the through-thickness shear stress distribution can be calculated. The resulting shear stresses integrate to the applied shear load, are continuous at the ply interfaces, and are zero at the laminate-free surfaces. If both Qx and Qy shear loads are present, it is assumed that they act independently and that their effects can be superposed. The calculated shear stresses can be rotated within each ply to the principal material coordinates for use in a ply-level failure criterion. The novelty of the simplified shear solution method is its simplicity and the fact that it does not require solution of a particular boundary value problem. The advantages of the innovation are that an approximation of the though-thickness shear stress distribution can be quickly determined for any solid laminate or solid laminate region within a stiffened panel.

Bednarcyk, Brett A.↗

NASA NTRS2003

Mineralogy and Petrology of Amoeboid Olivine Inclusions in CO3 Chondrites: Relationship to Parent-Body Aqueous Alteration

Petrographic and mineralogic studies of amoeboid olivine inclusions (AOIs) in CO3 carbonaceous chondrites reveal that they are sensitive indicators of parent-body aqueous and thermal alteration. As the petrologic subtype increases from 3.0 to 3.8, forsteritic olivine (Fa(sub 0-1)) is systematically converted into ferroan olivine (Fa(sub 60-75)). We infer that the Fe, Si and O entered the assemblage along grain boundaries, forming ferroan olivine that filled fractures and voids. As temperatures increased, Fe(+2) from the new olivine exchanged with Mg(+2) from the original AOI to form diffusive haloes around low-FeO cores. Cations of Mn(+2), Ca(+2) and Cr(+3) were also mobilized. The systematic changes in AOI textures and olivine compositional distributions can be used to refine the classification of CO3 chondrites into subtypes. In subtype 3.0, olivine occurs as small forsterite grains (Fa(sub 0-1)), free of ferroan olivine. In petrologic subtype 3.2, narrow veins of FeO-rich olivine have formed at forsterite grain boundaries. With increasing alteration, these veins thicken to form zones of ferroan olivine at the outside AOI margin and within the AOI interior. By subtype 3.7, there is a fairly broad olivine compositional distribution in the range Fa(sub 63-70), and by subtype 3.8, no forsterite remains and the high-Fa peak has narrowed, Fa(sub 64-67). Even at this stage, there is incomplete equilibration in the chondrite as a whole (e.g., data for coarse olivine grains in Isna (CO3.8) chondrules and lithic clasts show a peak at Fa(sub39)). We infer that the mineral changes in A01 identified in the low petrologic types required aqueous or hydrothermal fluids whereas those in subtypes greater than or equal to 3.3 largely reflect diffusive exchange within and between mineral grains without the aid of fluids.

Chizmadia, Lysa J.↗

DOE OSTI2020

Electronic structure and optical properties of quantum crystals from first principles calculations in the Born–Oppenheimer approximation

In this work, we develop a formalism to accurately account for the renormalization of the electronic structure due to quantum and thermal nuclear motions within the Born–Oppenheimer approximation. We focus on the fundamental energy gap obtained from electronic addition and removal energies from quantum Monte Carlo calculations in either the canonical or grand-canonical ensembles. The formalism applies as well to effective single electron theories such as those based on density functional theory. We show that the electronic (Bloch) crystal momentum can be restored by marginalizing the total electron–ion wave function with respect to the nuclear equilibrium distribution, and we describe an explicit procedure to establish the band structure of electronic excitations for quantum crystals within the Born–Oppenheimer approximation. Based on the Kubo–Greenwood equation, we discuss the effects of nuclear motion on optical conductivity. Our methodology applies to the low temperature regime where nuclear motion is quantized and, in general, differs from the semi-classical approximation. We apply our method to study the electronic structure of C2/c-24 crystalline hydrogen at 200 K and 250 GPa and discuss the optical absorption profile of hydrogen crystals at 200 K and carbon diamond at 297 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Acoustic Impedance Inversions for Offshore CO 2 Storage: South Georgia Embayment, United States

This study builds and expands on previous CO 2 storage resource assessment studies of the southeastern offshore Atlantic margin by providing a detailed evaluation on how rock porosities and permeabilities are distributed across the Upper Cretaceous strata restricted to the South Georgia Embayment (SGE). Using legacy industry two-dimensional seismic reflection and well data, this assessment is the first application of multiple seismic inversion techniques in this area. This workflow provides a reliable and repeatable model-based inversion which gives an improved image to discriminate lithology and predict porosity. The workflow is applicable to future CO 2 storage resource assessment studies elsewhere. The inversion results indicate that distinct porosity and permeability regimes are present and distributed in the Upper Cretaceous strata within the SGE. The impedance and porosity relationships show well-founded and reliable correlation. These relationships reveal low impedance coincident to the high porosity intervals which are proposed as potential reservoir intervals for CO 2 storage. In addition, the result shows that the Upper Cretaceous strata have two main potential reservoirs in the lower part. These are overlain by a thick impermeable interval, mostly shale, which has high impedance, low porosity, and low permeability and extends within the SGE. This result is in agreement with a previous study that also proposed two significant storage reservoirs for CO 2 in the Upper Cretaceous strata. Since porosity distribution is estimated using multiple methods, it follows the trends of seismic signature and structures of the Upper Cretaceous strata. The extracted values of porosity, ranging from 15 to 36%, and permeability, ranging from 1 to 100 mD, are close to the measured values from the well core data at the Upper Cretaceous strata interval.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1993

Some deformation trends and topographic characteristics of tesserae on Venus

Mapping of dominant trends of deformation and topographic analysis of tesserae reveal that (1) consistant patterns of deformation exist between individual tesserae; (2) regional deformation associated with coronae and rifts commonly overprints tesserae fabrics; (3) normalized area frequency plots of tesserae display a strongly bimodal distribution between -70 to 70 degrees latitude; and (4) the relief at tessera margins is relatively constant and independent of tessera elevation. We are continuing to expand these observations and test their implications for the formation of tesserae and for global models of deformation on Venus.

Price, Maribeth↗

NASA NTRS2014

The Architecture of the LkCa 15 Transitional Disk Revealed by High-contrast Imaging

We present four new epochs of Ks-band images of the young pre-transitional disk around LkCa 15, and perform extensive forward modeling to derive the physical parameters of the disk. We find indications of strongly anisotropic scattering (Henyey-Greenstein g = 0.67+0.18 −0.11) and a significantly tapered gap edge ('round wall'), but see no evidence that the inner disk, whose existence is predicted by the spectral energy distribution, shadows the outer regions of the disk visible in our images. We marginally confirm the existence of an offset between the disk center and the star along the line of nodes; however, the magnitude of this offset (x = 27+19 −20 mas) is notably lower than that found in our earlier H-band images (Thalmann et al. 2010). Intriguingly, we also find, at high significance, an offset of y = 69+49 −25 mas perpendicular to the line of nodes. If confirmed by future observations, this would imply a highly elliptical- or otherwise asymmetric-disk gap with an effective eccentricity of e ≈ 0.3. Such asymmetry would most likely be the result of dynamical sculpting by one or more unseen planets in the system. Finally, we find that the bright arc of scattered light we see in direct imaging observations originates from the near side of the disk, and appears brighter than the far side because of strong forward scattering.

anisotropic scattering↗

NASA NTRS2019

Uncertainty Quantification of Modeled Electron Backstreaming Failure for the NEXT Ion Thruster

Excessive electron back streaming is one of the primary life-limiting failure modes for gridded ion thrusters. Physics-based modeling of the optics grid erosion and electron back streaming margins is augmented with statistical uncertainty quantification techniques to generate a life expectancy distribution of this particular failure mechanism for the NEXT ion thruster. Generation of distributions instead of a single point estimate provide a more comprehensive picture of thruster failure probabilities and life expectation for various mission applications.

Yim, John T.↗

NASA NTRSDate not supplied

Porosity Model Parameter Effects on Metal Additive Manufacturing Simulations

This work investigates the effects of model parameters on thermomechanical simulations of a metal additive manufacturing process. The first half of this work explores the sensitivity and effects of the two porosity parameters used in the evolving constitutive model of the simulation. Varying the two parameters of the model show that for the simulations conducted here, the linear coefficient drives the predicted residual stress results while the constant term has little impact. The second half of the work considers the size, order, and the number of element layers in the finite element mesh. The stress distribution plots show that second-order elements along with a dense mesh marginally improve mesh convergence at a significant cost.

Additive Manufacturing↗

NASA NTRS2017

Imaging a Free-Geometry Magma Reservoir Using FEM-Based Linear Inverse Modeling of InSAR Data: Application to Rabaul Caldera, Papua New Guinea

We test an innovative inversion scheme using Green’s functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green’s function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluidfilled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green’s functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the east side and of the past Vulcan volcano eruptions of more evolved materials on the west side. The interconnection and spatial distributions of sources correspond to the petrography of the volcanic products described in the literature and to the dynamics of the single and twin eruptions that characterize the caldera. The ability to image the complex geometry of deformation sources in both space and time can improve our ability to monitor active volcanoes, widen our understanding of the dynamics of active volcanic systems and improve the predictions of eruptions.

Inverse theory↗

NASA NTRS2017

Imaging the Complex Geometry of a Magma Reservoir Using Fem-Based Linear Inverse Modeling of InSAR Data: Application to Rabaul Caldera, Papua New Guinea

We test an innovative inversion scheme using Green’s functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green’s function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluid-filled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green’s functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the east side and of the past Vulcan volcano eruptions of more evolved materials on the west side. The interconnection and spatial distributions of sources correspond to the petrography of the volcanic products described in the literature and to the dynamics of the single and twin eruptions that characterize the caldera. The ability to image the complex geometry of deformation sources in both space and time can improve our ability to monitor active volcanoes, widen our understanding of the dynamics of active volcanic systems and improve the predictions of eruptions.

Inverse theory↗