Applications of the H-Principle of Mathematical Modelling

Traditional statistical test procedures are briefly reviewed. It is pointed out that significance testing may not always be reliable. The author has formulated a modelling procedure, the H-principle, for how mathematical modelling should be carried out in the case of uncertain data. Here it is applied to linear regression. Using this procedure, the author has developed a common framework for carrying out linear regression. Six regression methods are analysed by this framework, two stepwise methods: principal component regression, ridge regression, PLS regression and an H-method. The same algorithm is used for all methods. It is shown how model validation and graphic analysis, which is popular in chemometrics, apply to all the methods. Validation of the methods is carried out by using numerical measures, cross-validation and test sets. Furthermore, the methods are tested by a blind test, where 40 samples have been excluded. It is shown how procedures in applied statistics and in chemometrics both apply to the present framework

Pre-Holocene volcanic ash in sediments near Jan Mayen

Poster presentation at the conference Nordic Geological winter meeting, 11.05.22 - 13.05.22, Reykjavik, Icelan

Formation and elimination of segmentation and transform faults on the Reykjanes Ridge

The objectives of R/V Neil Armstrong cruise AR35-04 (Fig. 1) were to survey the flanks of the Reykjanes Ridge and determine the timing, geometry and associated geophysical characteristics of the large-scale tectonic reorganizations that occurred there in the Paleogene and continue to the present (Fig. 2). The North Atlantic plate boundary between what is today the Bight Fracture Zone and Iceland, a distance of nearly 1000 km, was originally a linear orthogonally-spreading ridge that became abruptly fragmented in a stair-step fashion following a change in plate motion [Smallwood and White, 2002]. Its subsequent evolution involved the systematic and progressive removal of offsets from north to south to re-establish its original linear configuration [Hey et al., 2016; Martinez and Hey, 2017], even though this required the ridge to then spread obliquely, since the new spreading direction remained stable. These tectonic reorganizations took place within the region of influence of the Iceland “hotspot” which creates a strong gradient in mantle melting along the ridge, increasing crustal thicknesses by ~3-4 km and decreasing ridge axis depths by ~ 3000 m between the Bight Fracture Zone and Iceland [Louden et al., 2004]. A mantle gradient in melting properties (compositional and/or thermal) is presumably what results in the regional residual basement depth anomaly that extends throughout this region of the North Atlantic from the Greenland-Iceland-Faroe Ridge to south of the Bight Fracture Zone. This gradient in mantle properties with distance from the Iceland hotspot apparently had strong modulating effects on the tectonic reorganizations: the initial segment lengths and offsets appear in regional magnetic anomaly and satellite-derived gravity maps to be smaller toward Iceland and the segments evolved to re-establish the linear ridge configuration more quickly to the north [Hey et al., 2016]. As both kinematic and “hotspot” effects influence their development, the Reykjanes ridge flanks are key areas for investigating lithospheric and mantle controls on ridge segmentation, formation and elimination of transform faults and the mechanisms controlling their evolution.This work was funded by NSF grant OCE-1756760. The Marine Advanced Technology and Education program supported the participation of the MATE interns. An InterRidge Cruise Bursary supported the participation of Dr. Dominik Palgan

Mapping and Assessing Surface Morphology of Holocene Lava Field in Krafla (NE Iceland) Using Hyperspectral Remote Sensing

Iceland is well known for its volcanic activity due to its location on the spreading Mid Atlantic Ridge and one of the earth’s hot spot. In the past 1000 years there were about 200 eruptions occurring in Iceland, meaning volcanic eruptions occurred every four to five years, on average. Iceland currently has 30 active volcano systems, distributed evenly throughout the socalled Neovolcanic Zone. One of these volcanic systems is the Krafla central volcano, which is located in the northern Iceland at latitude 65°42'53'' N and longitude 16°43'40'' W. Krafla has produced two volcanic events in historic times: 1724-1729 (Myvatn Fires) and 1975-1984 (Krafla Fires). The Krafla Fires began in December 1975 and lasted until September 1984. This event covered about 36-km2 surrounding area with lava, having a total volume of 0.25-0.3 km3 . Previous studies of lava surface morphology at Krafla focused on an open channel area by remote sensing are essential as a complementary tool to the previous investigations and to extend the area of mapping. Using Spectral Angle Mapper (SAM) classification approach by selecting spectral reflectance end members, this study has successfully produced a detailed map of the surface morphology in Krafla lava field EO-1 Hyperion (Hyperspectral) satellite images. The overall accuracy of lava morphology map is 61.33% (EO-1 Hyperion). These results show that hyperspectral remote sensing is an acceptable alternative to field mapping and assessing the lava surface morphology in the Krafla lava field. In order to get validation of the satellite image’s spectral reflectance, in-situ measurements of the lava field’s spectral reflectance using ASD FieldSpec3 is essential.LPDP scholarship (Indonesia Endowment Fund for Education

Contrasting mechanisms of magma fragmentation during coeval magmatic and hydromagmatic activity: the Hverfjall Fires fissure eruption, Iceland

Growing evidence for significant magmatic vesiculation prior to magma-water interaction (MWI) has brought into question the use of ‘diagnostic’ features, such as low vesicularities and blocky morphologies, to identify hydromagmatic pyroclasts. We address this question by quantifying co-variations in particle size, shape and texture in both magmatic and hydromagmatic deposits from the Hverfjall Fires fissure eruption, Iceland. Overlapping vesicularity and bubble number density distributions measured in rapidly quenched magmatic and hydromagmatic pyroclasts indicate a shared initial history of bubble nucleation and growth, with substantial vesiculation prior to MWI. Hydromagmatic fragmentation occurred principally by brittle mechanisms, where the length scale and geometry of fracturing was controlled by the bubble population. This suggests that the elevated fragmentation efficiency of hydromagmatic deposits is driven, at least in part, by brittle disintegration of vesicular pyroclasts due to high thermal stress generated during rapid cooling. In this way, the shape and size distributions of hydromagmatic pyroclasts, both critical input parameters for ash dispersion models, are strongly influenced by the dynamics of vesiculation prior to MWI. This result underlines the need to analyse multiple grain-size fractions to characterise the balance between magmatic and hydromagmatic processes. During the Hverfjall Fires eruption, the external water supply was sufficient to maintain MWI throughout the eruption, with no evidence for progressive exhaustion of a water reservoir. We suggest that both the longevity and the spatial distribution of MWI were determined by the pre-existing regional hydrology and represent continuous interaction between a propagating dike and a strong groundwater flow system hosted within permeable basalt lavas

New Insights for Detecting and Deriving Thermal Properties of Lava Flow Using Infrared Satellite during 2014–2015 Effusive Eruption at Holuhraun, Iceland

A new lava field was formed at Holuhraun in the Icelandic Highlands, north of Vatnajökull glacier, in 2014–2015. It was the largest effusive eruption in Iceland for 230 years, with an estimated lava bulk volume of ~1.44 km3 covering an area of ~84 km2. Satellite-based remote sensing is commonly used as preliminary assessment of large scale eruptions since it is relatively efficient for collecting and processing the data. Landsat-8 infrared datasets were used in this study, and we used dual-band technique to determine the subpixel temperature (Th) of the lava. We developed a new spectral index called the thermal eruption index (TEI) based on the shortwave infrared (SWIR) and thermal infrared (TIR) bands allowing us to differentiate thermal domain within the lava flow field. Lava surface roughness effects are accounted by using the Hurst coefficient (H) for deriving the radiant flux (Φrad) and the crust thickness (Δh). Here, we compare the results derived from satellite images with field measurements. The result from 2 December 2014 shows that a temperature estimate (1096 °C; occupying area of 3.05 m2) from a lava breakout has a close correspondence with a thermal camera measurement (1047 °C; occupying area of 4.52 m2). We also found that the crust thickness estimate in the lava channel during 6 September 2014 (~3.4–7.7 m) compares closely with the lava height measurement from the field (~2.6–6.6 m); meanwhile, the total radiant flux peak is underestimated (~8 GW) compared to other studies (~25 GW), although the trend shows good agreement with both field observation and other studies. This study provides new insights for monitoring future effusive eruption using infrared satellite imagesThe first author has been supported by the Indonesia Endowment Fund for Education (LPDP), Institute of Earth Science and Vinir Vatnajökuls during his Ph.D. project. Authors also would also like to thank anonymous reviewers for their constructive comments for the manuscript.Peer Reviewe

Contrasting mechanisms of magma fragmentation during coeval magmatic and hydromagmatic activity: the Hverfjall Fires fissure eruption, Iceland

Growing evidence for significant magmatic vesiculation prior to magma-water interaction (MWI) has brought into question the use of ‘diagnostic’ features, such as low vesicularities and blocky morphologies, to identify hydromagmatic pyroclasts. We address this question by quantifying co-variations in particle size, shape and texture in both magmatic and hydromagmatic deposits from the Hverfjall Fires fissure eruption, Iceland. Overlapping vesicularity and bubble number density distributions measured in rapidly quenched magmatic and hydromagmatic pyroclasts indicate a shared initial history of bubble nucleation and growth, with substantial vesiculation prior to MWI. Hydromagmatic fragmentation occurred principally by brittle mechanisms, where the length scale and geometry of fracturing was controlled by the bubble population. This suggests that the elevated fragmentation efficiency of hydromagmatic deposits is driven, at least in part, by brittle disintegration of vesicular pyroclasts due to high thermal stress generated during rapid cooling. In this way, the shape and size distributions of hydromagmatic pyroclasts, both critical input parameters for ash dispersion models, are strongly influenced by the dynamics of vesiculation prior to MWI. This result underlines the need to analyse multiple grain-size fractions to characterise the balance between magmatic and hydromagmatic processes. During the Hverfjall Fires eruption, the external water supply was sufficient to maintain MWI throughout the eruption, with no evidence for progressive exhaustion of a water reservoir. We suggest that both the longevity and the spatial distribution of MWI were determined by the pre-existing regional hydrology and represent continuous interaction between a propagating dike and a strong groundwater flow system hosted within permeable basalt lavas

Determination of mechanical properties of historical paper based on NIR spectroscopy and chemometrics - a new instrument

Due to sampling restrictions in the analysis of cultural heritage materials, non-destructive approaches are intensively sought for. While NIR spectrometry has rarely been used for this purpose due to the complexity of the spectra, chemometric methods can be used to extract the necessary information. For the purpose of determination of mechanical properties of historical paper, partial least squares approach was used and it is shown that tensile strength, and tensile strength after folding, can be estimated based on NIR spectra. As the mechanical properties of paper-based objects define their accessibility, a new dispersive portable instrument was built, which will enable us to rapidly survey the condition of library and archival collections

A multi-scale risk assessment for tephra fallout and airborne concentration from multiple Icelandic volcanoes – Part 1: Hazard assessment

This is the final version of the article. Available from EGU via the DOI in this record.In order to assist the elaboration of proactive measures for the management of future volcanic eruptions in Iceland, we developed a new scenario-based approach to assess the hazard associated with tephra dispersal and sedimentation at various scales and for multiple sources. The target volcanoes are Hekla, Katla, Eyjafjallajökull and Askja, selected either for their high probabilities of eruption and/or their high potential impact. By coupling tephrostratigraphic studies, probabilistic techniques and modelling, we developed comprehensive eruption scenarios for both short- and long-lasting eruptions and compiled hazard maps for tephra ground deposition at a national scale and air concentration at a European scale using the TEPHRA2 and FALL3D models, respectively. New algorithms for the identification of realistic sets of eruptive source parameters are investigated, which assist the generation of probability density functions of eruption source parameters for the selected scenarios. Aggregation processes were accounted for using various empirical models. Outcomes, i.e. probabilities conditioned to the occurrence of an eruption, help the assessment and comparison of hazard levels at different scales. For example, at a national scale Askja has a 5–10% probability of blanketing the easternmost half of the country with a tephra accumulation of at least 1 kg m−2. At a continental scale, Katla has a 5–10% probability of producing ash clouds with concentrations of 2 mg m−3 over the UK, Scandinavia and northern Europe with a mean arrival time of 48–72 h and a mean persistence time of 6–18 h. In a companion paper, Scaini et al. (2014) present a vulnerability assessment for Iceland to ground deposition of tephra and for the European air traffic to airborne ash which, combined with the outcomes of the present paper, constitute one of the first comprehensive multi-scale risk assessment associated with tephra dispersal and sedimentation.S. Biass is supported by SNF (#200021-129997) and ESF/MemoVolc (#5193) subsides. C. Scaini is partly supported by the Spanish Research Project ATMOST (CGL2009-10244) and by the SNF (IZK0Z2_ 142343)

Ash-plume dynamics and eruption source parameters by infrasound and thermal imagery: The 2010 Eyjafjallajökull eruption

During operational ash-cloud forecasting, prediction of ash concentration and total erupted mass directly depends on the determination of mass eruption rate (MER), which is typically inferred from plume height. Uncertainties for plume heights are large, especially for bent-over plumes in which the ascent dynamics are strongly affected by the surrounding wind field. Here we show how uncertainties can be reduced if MER is derived directly from geophysical observations of source dynamics. The combination of infrasound measurements and thermal camera imagery allows for the infrasonic type of source to be constrained (a dipole in this case) and for the plume exit velocity to be calculated (54–142 m/s) based on the acoustic signal recorded during the 2010 Eyjafjallajökull eruption from 4 to 21 May. Exit velocities are converted into MER using additional information on vent diameter (50±10 m) and mixture density (5.4±1.1 kg/m3), resulting in an average ∼9×105 kg/s MER during the considered period of the eruption. We validate our acoustic-derived MER by using independent measurements of plume heights (Icelandic Meteorological Office radar observations). Acoustically derived MER are converted into plume heights using field-based relationships and a 1D radially averaged buoyant plume theory model using a reconstructed total grain size distribution. We conclude that the use of infrasonic monitoring may lead to important understanding of the plume dynamics and allows for real-time determination of eruption source parameters. This could improve substantially the forecasting of volcano-related hazards, with important implications for civil aviation safety