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  • 1
    Publication Date: 2019-02-01
    Description: The ocean load in glacial isostatic adjustment (GIA) modelling is represented by the so-called sea level equation (SLE). The SLE describes the mass redistribution of water between ice sheets and oceans on a deforming Earth. Despite various teams independently investigating GIA, there has been no systematic intercomparison among the numerical solvers of the SLE through which the methods may be validated. The goal of this paper is to present a series of synthetic examples designed for testing and comparing the numerical implementations of the SLE in GIA modelling. The 10 numerical codes tested combine various temporal and spatial parametrizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parametrize the GIA-related field variables spatially. The surface ice-water load and solid Earth’s topography are represented spatially either on an equiangular grid, a Gauss–Legendre or an equiarea grid with icosahedron-shaped spherical pixels. Comparisons are made in a series of five benchmark examples with an increasing degree of complexity. Due to the complexity of the SLE, there is no analytical solution to it. The accuracy of the numerical implementations is therefore assessed by the differences of the individual solutions with respect to a reference solution. While the benchmark study does not result in GIA predictions for a realistic loading scenario, we establish a set of agreed-upon results that can be extended in the future by including more complex case studies, such as solutions with realistic loading scenarios, the rotational feedback in the linear-momentum equation, and by considering a 3-D viscosity structure of the Earth’s mantle. The test computations performed so far show very good agreement between the individual results and their ability to capture the main features of sea-surface variation and the surface vertical displacement. The differences found can often be attributed to the different approximations inherent in the various algorithms. This shows the accuracy that can be expected from different implementations of the SLE, which helps to assess differences noted in the literature between predictions for realistic loading cases.
    Type: Article , PeerReviewed
    Format: text
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  • 2
    Publication Date: 2014-01-01
    Description: An underwater geomorphological survey along the coasts of six Cycladic islands (Sifnos, Antiparos, Paros, Naxos, Iraklia and Keros) revealed widespread evidence of seven submerged tidal notches. At least seven former shorelines were identified at depths between 280 ± 20 and 30 ± 5 cm below modern sea level. The vertical succession of several submerged notches suggests the occurrence of rapid subsidence events, potentially of seismic origin. Comparison with other sea-level indicators from Naxos and Delos islands indicates that these relative sea-level changes took place after 3300 BP and provides a rough estimate of the time of development of several submerged shorelines. The submergence of the uppermost notch at −30 ± 5 cm is ascribed to effects of the recent global sea-level rise occurred during the last two centuries and, at least in part, to effects of recent earthquakes. Potential effects of the 1956 Amorgos earthquake with regard to coseismic and post-seismic vertical displacement have been recently investigated using a modellistic approach. According to the above, the lower shorelines should result from repetitive subsidence events and not from gradual subsidence. ©2013 Springer-Verlag Berlin Heidelberg
    Print ISSN: 1437-3254
    Electronic ISSN: 1437-3262
    Topics: Geosciences
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  • 3
    Publication Date: 2016-05-05
    Description: We propose a procedure for uncertainty quantification in Probabilistic Tsunami Hazard Analysis (PTHA), with a special emphasis on the uncertainty related to statistical modelling of the earthquake source in Seismic PTHA (SPTHA), and on the separate treatment of subduction and crustal earthquakes (treated as background seismicity). An event tree approach and ensemble modelling are used in spite of more classical approaches, such as the hazard integral and the logic tree. This procedure consists of four steps: (1) exploration of aleatory uncertainty through an event tree, with alternative implementations for exploring epistemic uncertainty; (2) numerical computation of tsunami generation and propagation up to a given offshore isobath; (3) (optional) site-specific quantification of inundation; (4) simultaneous quantification of aleatory and epistemic uncertainty through ensemble modelling. The proposed procedure is general and independent of the kind of tsunami source considered; however, we implement step 1, the event tree, specifically for SPTHA, focusing on seismic source uncertainty. To exemplify the procedure, we develop a case study considering seismic sources in the Ionian Sea (central-eastern Mediterranean Sea), using the coasts of Southern Italy as a target zone. The results show that an efficient and complete quantification of all the uncertainties is feasible even when treating a large number of potential sources and a large set of alternative model formulations. We also find that (i) treating separately subduction and background (crustal) earthquakes allows for optimal use of available information and for avoiding significant biases; (ii) both subduction interface and crustal faults contribute to the SPTHA, with different proportions that depend on source-target position and tsunami intensity; (iii) the proposed framework allows sensitivity and deaggregation analyses, demonstrating the applicability of the method for operational assessments.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 4
    Publication Date: 2016-05-05
    Description: We review the theory of the Earth's elastic and gravitational response to a surface disk load. The solutions for displacement of the surface and the geoid are developed using expansions of Legendre polynomials, their derivatives and the load Love numbers. We provide a matlab  function called diskload that computes the solutions for both uncompensated and compensated disk loads. In order to numerically implement the Legendre expansions, it is necessary to choose a harmonic degree, n max , at which to truncate the series used to construct the solutions. We present a rule of thumb (ROT) for choosing an appropriate value of n max , describe the consequences of truncating the expansions prematurely and provide a means to judiciously violate the ROT when that becomes a practical necessity.
    Keywords: Gravity, Geodesy and Tides
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 5
    Publication Date: 2013-07-05
    Description: The identification of a source model for the catastrophic 1908 December 28 Messina earthquake ( M w  = 7.2) has been the subject of many papers in the last decades. Several authors proposed different models on the basis of seismological, macroseismic and geodetic data sets; among these models, remarkable differences exist with regard to almost all parameters. We selected a subset of six models among those most cited in literature and used them to model the post-seismic sea level variation recorded at the tide gauge station of Messina (until 1923), to attempt an independent discrimination among them. For each model, we assumed a simple rheological structure and carried out a direct-search inversion of upper crust thickness and lower crust viscosity to fit the post-seismic sea level signal. This approach enabled us to identify a class of fault geometries which is consistent with the post-seismic signal at the Messina tide gauge and with the known structural and rheological features of the Messina strait.
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 6
    Publication Date: 2019
    Description: 〈span〉〈div〉SUMMARY〈/div〉Glacial Isostatic Adjustment (GIA) modelling has recently seen a significant development, stimulated by the need of understanding past, current and future sea level variations and geodetic signals associated with climate change. Our main motivation is that albeit its importance is well recognized within the climate science community, the problem of classifying and quantifying GIA modelling uncertainties has so far received little attention. Here, we consider two possible ways of defining and evaluating these uncertainties. The first is associated with limited knowledge of input model parameters (e.g. the viscosity profile of the Earth’s mantle or the deglaciation history), once it is assumed that the ice margins are known and a unique set of relative sea level (RSL) data are used to constrain the model. We also discuss a second and more problematic source of uncertainty, associated with structural differences in GIA models, stemming from distinct eustatic curves and ice margins geometries, different RSL constraints, non-identical input parameters and different numerical solution schemes. By analysing the present-day ‘GIA fingerprints’ of relative and absolute sea level change, and exploring the GIA contribution to secular sea level rise and to the time-variations of the Earth’s gravity field, here we evaluate the two types of uncertainty showing that they are (i) of significant amplitude and (ii) of comparable importance.〈/span〉
    Print ISSN: 2051-1965
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 7
    Publication Date: 2019
    Description: 〈span〉〈div〉Summary〈/div〉Glacial Isostatic Adjustment (GIA) modelling has recently seen a significant development, stimulated by the need of understanding past, current and future sea-level variations and geodetic signals associated with climate change. Our main motivation is that albeit its importance is well recognised within the climate science community, the problem of classifying and quantifying GIA modelling uncertainties has so far received little attention. Here we consider two possible ways of defining and evaluating these uncertainties. The first is associated with limited knowledge of input model parameters (〈span〉e.g.〈/span〉, the viscosity profile of the Earth’s mantle or the deglaciation history), once it is assumed that the ice margins are known and a unique set of Relative Sea Level (RSL) data is used to constrain the model. We also discuss a second and more problematic source of uncertainty, associated with structural differences in GIA models, stemming from distinct eustatic curves and ice margins geometries, different RSL constraints, non-identical input parameters and different numerical solution schemes. By analysing the present-day “GIA fingerprints” of relative and absolute sea-level change, and exploring the GIA contribution to secular sea-level rise and to the time-variations of the Earth’s gravity field, here we evaluate the two types of uncertainty showing that they are 〈span〉i)〈/span〉 of significant amplitude and 〈span〉ii)〈/span〉 of comparable importance.〈/span〉
    Print ISSN: 2051-1965
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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