1,721,194 research outputs found
Love Numbers of a Generalized Maxwell Sphere
No full textBy elementary methods, we study the Love numbers of a homogeneous, incom-
pressible, self–gravitating sphere characterized by a generalized Maxwell rheology,
whose mechanical analogue is represented by a finite or infinite system of classical
Maxwell elements disposed in parallel. Analytical, previously unknown forms of the
complex shear modulus for the generalized Maxwell body are found by algebraic
manipulation, and studied in the particular case of systems of springs and dash-
pots whose strength follows a power–law distribution. It will be shown that the
sphere is asymptotically stable for any choice of the mechanical parameters that
define the generalized Maxwell body and analytical forms of the Love numbers are
always available for generalized bodies composed by less than five classical Maxwell
bodies. For the homogeneous sphere, real Laplace inversion methods based on the
Post–Widder formula can be applied without performing a numerical discretization
of the n–th derivative, which can be computed in a closed–form with the aid of the
Fa`a di Bruno formula
Why are earthquakes nudging the pole towards 140 E?
No full textEarthquakes have collectively the tendency to displace the pole of rotation of the earth towards a preferred direction (∼140°E). This trend, which is still unexplained on quantitative grounds, has been revealed by computations of earthquake‐induced inertia variations on both a secular and a decade time‐scale. Purpose of this letter is to show that the above trend results from the combined effects of the geographical distribution of hypocenters and of the prevailing dip‐slip nature of large earthquakes in this century. Our findings are based on the static dislocation theory and on simple geometrical arguments
ALMA: a program for computing tidal and loading Love numbers of a spherically symmetric planet
No full textALMA is a Fortran 90 program for computing the tidal and the loading “Love numbers” of a spherically symmetric, incompressible, viscoelastic planet, using the Post–Widder Laplace inversion formula. Knowledge of the Love numbers is required in various geophysical applications, ranging from modeling of glacial-isostatic adjustment to the study of the response of the Earth to the gravitational pull exerted by external bodies. ALMA requires modest computing resources and can be employed to compute the Love numbers for very detailed radial rheological profiles and linear viscoelastic rheologies, including those characterized by a large number of simple mechanical elements, such as the generalized Maxwell rheology. A brief account of the theory, a description of the code and a few basic applications is provided
Changes in the Earth inertia tensor: the role of boundary conditions at the core-mantle interface
No full textIn the early seventies, a broad scientific debate began upon the nature of the conditions to be applied at the core‐mantle interface in order to study the static deformations of the Earth. This controversy, which first arose in the context of post‐seismic deformations, has also affected later investigations on inertia perturbations driven by surface or internal density contrasts. The aim of this communication is not to readdress the long‐standing question about the appropriate set of boundary conditions to be imposed at the core‐mantle boundary, but rather to show how the choice of these conditions may affect the calculation of inertia changes. When applied to glacially‐induced inertia perturbations, our results demonstrate that the pitfall of the core‐mantle boundary conditions has been acting for a long time after the scientific discussion mentioned above came to an end
True polar wander and long-wavelength dynamic topography
No full textWe analyze the potential influence of True Polar Wander, the global motion of the Earth's mantle with respect to the rotation axis, on the long-wavelength pattern of the Earth's dynamic topography. Internal mass redistributions, related to mantle convection, subduction episodes and thermal processes associated to plate formation, produce two main effects. First, they induce both a geoidal and topographic signal at the Earth's surface. Second, they change the Earth's inertia tensor. As a consequence, the Earth's rotation axis may be subject to excursions with respect to the whole mantle. Since the integrated effect of the internal heterogeneities defines the equator of the Earth, the present-day pattern of both long-wavelength geoid and dynamic topography are therefore expected to be affected to some extent by True Polar Wander (TPW). Our results suggest that the observed presence of maxima and minima for the non-hydrostatic geoid and dynamic topography in the equatorial region is due to a global readjustment of the Earth's shape caused by True Polar Wander
Glacial Isostatic Adjustment and Contemporary Sea Level Rise: An Overview
No full textGlacial isostatic adjustment (GIA) encompasses a suite of geophysical phenomena accompanying the waxing and waning of continental-scale ice sheets. These involve the solid Earth, the oceans and the cryosphere both on short (decade to century) and on long (millennia) timescales. In the framework of contemporary sea-level change, the role of GIA is particular. In fact, among the processes significantly contributing to contemporary sea-level change, GIA is the only one for which deformational, gravitational and rotational effects are simultaneously operating, and for which the rheology of the solid Earth is essential. Here, I review the basic elements of the GIA theory, emphasizing the connections with current sea-level changes observed by tide gauges and altimetry. This purpose is met discussing the nature of the “sea-level equation” (SLE), which represents the basis for modeling the sea-level variations of glacial isostatic origin, also giving access to a full set of geodetic variations associated with GIA. Here, the SLE is employed to characterize the remarkable geographical variability of the GIA-induced sea-level variations, which are often expressed in terms of “fingerprints”. Using harmonic analysis, the spatial variability of the GIA fingerprints is compared to that of other components of contemporary sea-level change. In closing, some attention is devoted to the importance of the “GIA corrections” in the context of modern sea-level observations, based on tide gauges or satellite altimeters. © 2016 Springer Science+Business Media Dordrech
Spectral analysis of sea level during the altimetry era, and evidence for GIA and glacial melting fingerprints
No full textWe study the spatial patterns of the mass and steric components of sea-level change during the "altimetry era" (1992-today), and we characterize them at different scales by the orthonormal functions method. The spectrum of the altimetry-derived rate of sea-level rise is red and decays with increasing wavenumber nearly following a power law with exponent ≈. 2. By analyzing the degree correlation and the admittance function, we find that the altimetric rate of sea-level change is coherent with the total steric field in the whole range of wavelengths considered (down to ≈. 1000 km), but particularly for wavelengths exceeding ≈. 2000 km. Thermosteric and halosteric components are moderately anti-correlated within the range of wavelengths 1000-4000 km. Their power spectrum varies significantly with the wavelength and, for ≈. 2000 km, it is equally partitioned between the two components. The power of regional sea-level variations driven by Glacial Isostatic Adjustment and the melting of continental ice sheets is small compared to that held by the steric component, which explains most of the regional variability shown by the altimetry record. This causes the elusiveness of the "static" sea-level fingerprints, which at present are hidden in the pattern of the residual sea-level (i.e., the altimetry-derived sea-level minus the steric component). However, we find that at harmonic degree 2, mainly associated with rotational variations, the power of glacial melting is significant and it will progressively increase during next century in response to global warming. We also estimate that at the end of the Mid-Holocene the strength of the glacial isostatic readjustment fingerprints was ≈. 10 times larger than today, well above the long-wavelength component of residual sea-level. © 2016 Elsevier B.V
SELEN User Manual - Version 2.9
No full textThe open source program SELEN solves numerically the so–called “Sea Level Equation” (SLE) for a spherical, layered, non–rotating Earth with Maxwell viscoelastic rheology.
The SLE is an integral equation that was introduced in the 70s to model the sea level variations in response to the melting of late–Pleistocene ice–sheets, but it can also be employed for predictions of geodetic quantities in response to present-day melting of continental ice-sheets. SELEN can compute vertical and horizontal surface displacements, gravity variations and sea level changes on a global and regional scale.
SELEN (acronym of SEa Level EquatioN solver) is particularly oriented to scientists at their first approach to the glacial isostatic adjustment (GIA) problem and, according to our experience, it can be successfully used in teaching. The current release (2.9) considerably improves the previous version of the code in terms of computational efficiency, portability and versatility. As far as we know, SELEN is the only open source program designed for solving the SLE.
SELEN 2.9 solves the SLE following the classical theory of ?. In the future release of SELEN (SELEN 3.0), which is under development, two important new features will be introduced: the rotational feedback on sea level and the horizontal migration of shorelines in response to sea level change.
This User guide describes the essentials of the theory behind the SLE, and provides instructions for the configuration and execution of SELEN
TABOO - User guide
Full text linkIn this manual we describe the general purpose of TABOO, its structure, and
its applications. A very basic knowledge of the Fortran 90 language and
of Unix is required. The mathematical theory behind TABOO is given in a
separate theory document (hereafter referred as to TD) which is released
with these instructions
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