Advanced InSAR atmospheric correction: MERIS/MODIS combination and stacked water vapour models

A major source of error for repeat-pass Interferometric Synthetic Aperture Radar (InSAR) is the phase delay in radio signal propagation through the atmosphere (especially the part due to tropospheric water vapour). Based on experience with the Global Positioning System (GPS)/Moderate Resolution Imaging Spectroradiometer (MODIS) integrated model and the Medium Resolution Imaging Spectrometer (MERIS) correction model, two new advanced InSAR water vapour correction models are demonstrated using both MERIS and MODIS data: (1) the MERIS/MODIS combination correction model (MMCC); and (2) the MERIS/MODIS stacked correction model (MMSC). The applications of both the MMCC and MMSC models to ENVISAT Advanced Synthetic Aperture Radar (ASAR) data over the Southern California Integrated GPS Network (SCIGN) region showed a significant reduction in water vapour effects on ASAR interferograms, with the root mean square (RMS) differences between GPS- and InSAR-derived range changes in the line-of-sight (LOS) direction decreasing from ,10mm before correction to ,5mm after correction, which is similar to the GPS/MODIS integrated and MERIS correction models. It is expected that these two advanced water vapour correction models can expand the application of MERIS and MODIS data for InSAR atmospheric correction. A simple but effective approach has been developed to destripe Terra MODIS images contaminated by radiometric calibration errors. Another two limiting factors on the MMCC and MMSC models have also been investigated in this paper: (1) the impact of the time difference between MODIS and SAR data; and (2) the frequency of cloud-free conditions at the global scale

The ups and downs of volcanic unrest: Insights from integrated geodesy and numerical modelling

Part of the Advances in Volcanology book seriesThis is the final version of the chapter. Available from the publisher via the DOI in this record.Volcanic eruptions are often preceded by small changes in the shape of the volcano. Such volcanic deformation may be measured using precise surveying techniques and analysed to better understand volcanic processes. Complicating the matter is the fact that deformation events (e.g., inflation or deflation) may result from magmatic, non-magmatic or mixed/hybrid sources. Using spatial and temporal patterns in volcanic deformation data and mathematical models it is possible to infer the location and strength of the subsurface driving mechanism. This can provide essential information to inform hazard assessment, risk mitigation and eruption forecasting. However, most generic models over-simplify their representation of the crustal conditions in which the deformation source resides. We present work from a selection of studies that employ advanced numerical models to interpret deformation and gravity data. These incorporate crustal heterogeneity, topography, viscoelastic rheology and the influence of temperature, to constrain unrest source parameters at Uturuncu (Bolivia), Cotopaxi (Ecuador), Soufrière Hills (Montserrat), and Teide (Tenerife) volcanoes. Such model complexities are justified by geophysical, geological, and petrological constraints. Results highlight how more realistic crustal mechanical conditions alter the way stress and strain are partitioned in the subsurface. This impacts inferred source locations and magmatic pressures, and demonstrates how generic models may produce misleading interpretations due to their simplified assumptions. Further model results are used to infer quantitative and qualitative estimates of magma supply rate and mechanism, respectively. The simultaneous inclusion of gravity data alongside deformation measurements may additionally allow the magmatic or non-magmatic nature of the source to be characterised. Together, these results highlight how models with more realistic, and geophysically consistent, components can improve our understanding of the mechanical processes affecting volcanic unrest and geodetic eruption precursors, to aid eruption forecasting, hazard assessment and risk mitigation.s Work presented herein has received funding by the European Commission (FP7; Theme: ENV.2011.1.3.3-1; Grant 282759: VUELCO)

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Repeated magmatic intrusions at El Hierro Island following the 2011–2012 submarine eruption

After more than 200 years of quiescence, in July 2011 an intense seismic swarm was detected beneath the center of El Hierro Island (Canary Islands), culminating on 10 October 2011 in a submarine eruption, 2 km off the southern coast. Although the eruption officially ended on 5 March 2012, magmatic activity continued in the area. From June 2012 to March 2014, six earthquake swarms, indicative of magmatic intrusions, were detected underneath the island. We have studied these post-eruption intrusive events using GPS and InSAR techniques to characterize the ground surface deformation produced by each of these intrusions, and to determine the optimal source parameters (geometry, location, depth, volume change). Source inversions provide insight into the depth of the intrusions (~ 11–16 km) and the volume change associated with each of them (between 0.02 and 0.13 km3). During this period, > 20 cm of uplift was detected in the central-western part of the island, corresponding to approximately 0.32–0.38 km3 of magma intruded beneath the volcano. We suggest that these intrusions result from deep magma migrating from the mantle, trapped at the mantle/lower crust discontinuity in the form of sill-like bodies. This study, using joint inversion of GPS and InSAR data in a post-eruption period, provides important insight into the characteristics of the magmatic plumbing system of El Hierro, an oceanic intraplate volcanic island

Unexpected large eruptions from buoyant magma bodies within viscoelastic crust

Large volume effusive eruptions with relatively minor observed precursory signals are at odds with widely used models to interpret volcano deformation. Here we propose a new modelling framework that resolves this discrepancy by accounting for magma buoyancy, viscoelastic crustal properties, and sustained magma channels. At low magma accumulation rates, the stability of deep magma bodies is governed by the magma-host rock density contrast and the magma body thickness. During eruptions, inelastic processes including magma mush erosion and thermal effects, can form a sustained channel that supports magma flow, driven by the pressure difference between the magma body and surface vents. At failure onset, it may be difficult to forecast the final eruption volume; pressure in a magma body may drop well below the lithostatic load, create under-pressure and initiate a caldera collapse, despite only modest precursors