Preface This booklet is devoted to the study of some theoretical and practical aspects of the so–called ”Sea Level Equation” (SLE), an integral equation that predicts the time–dependent shape of the equipotential surface of a deformable body subject to surface forces. In the field of global geodynamics, the SLE serves as a tool for computing the postglacial sealevel variations and other observable quantities, taking as an input the shapes and chronology of the Pleistocene ice–sheets. Our first purpose was simply to collect various sparse notes and to translate in simple words the theory of the SLE for the PhD students attending my lessons of ”Global Geodynamics” at the University of Bologna. However, in Part II we also provide details on the numerical discretization of the SLE and a freely available Fortran 90 code (SELEN) that anyone can use to solve the SLE on his own computer. We hope that the material presented will facilitate the work of colleagues at their first approach to Glacial Isostatic Adjustment (GIA), and perhaps also more experienced geophysicists willing to benchmark their own codes. As far as we know, this is the first time that a sealevel equation solver is made freely publically available. The development of the theory of the SLE is based on a number of approximations. First, the Earth is assumed to be radially stratified and incompressible, and the various layers are characterized by a linear viscoelastic rheology. This is a widely diffused approximation, but recent work has been done to include non–Newtonian rheologies and lateral viscosity variations in spherical Earth models (see e. g. [4, 26]). Second, it is assumed that the ocean function is constant, that implies fixed shorelines. Third, we totally neglect the effects of rotation on the GIA–induced sealevel variations. The reader is referred to [7] for the theoretical details concerning the rotational feedback and for the numerical evaluation of its consequences. In view of the approximations listed above, this booklet provides a zeroth–order model for the postglacial sealevel changes, that can be considerably refined in the future, hopefully with the aid and the contribution of other investigators. The future releases of this document will benefit from the feedback of the readers of this first edition. Please feel free to write to spada@fis.uniurb.it for questions, comments, and suggestions. GS, February 8, 2005.

Solving the sea level equation, part I, theory

SPADA, GIORGIO;
2005

Abstract

Preface This booklet is devoted to the study of some theoretical and practical aspects of the so–called ”Sea Level Equation” (SLE), an integral equation that predicts the time–dependent shape of the equipotential surface of a deformable body subject to surface forces. In the field of global geodynamics, the SLE serves as a tool for computing the postglacial sealevel variations and other observable quantities, taking as an input the shapes and chronology of the Pleistocene ice–sheets. Our first purpose was simply to collect various sparse notes and to translate in simple words the theory of the SLE for the PhD students attending my lessons of ”Global Geodynamics” at the University of Bologna. However, in Part II we also provide details on the numerical discretization of the SLE and a freely available Fortran 90 code (SELEN) that anyone can use to solve the SLE on his own computer. We hope that the material presented will facilitate the work of colleagues at their first approach to Glacial Isostatic Adjustment (GIA), and perhaps also more experienced geophysicists willing to benchmark their own codes. As far as we know, this is the first time that a sealevel equation solver is made freely publically available. The development of the theory of the SLE is based on a number of approximations. First, the Earth is assumed to be radially stratified and incompressible, and the various layers are characterized by a linear viscoelastic rheology. This is a widely diffused approximation, but recent work has been done to include non–Newtonian rheologies and lateral viscosity variations in spherical Earth models (see e. g. [4, 26]). Second, it is assumed that the ocean function is constant, that implies fixed shorelines. Third, we totally neglect the effects of rotation on the GIA–induced sealevel variations. The reader is referred to [7] for the theoretical details concerning the rotational feedback and for the numerical evaluation of its consequences. In view of the approximations listed above, this booklet provides a zeroth–order model for the postglacial sealevel changes, that can be considerably refined in the future, hopefully with the aid and the contribution of other investigators. The future releases of this document will benefit from the feedback of the readers of this first edition. Please feel free to write to spada@fis.uniurb.it for questions, comments, and suggestions. GS, February 8, 2005.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11576/1891473
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