In this introductory chapter, we focus first on the description of arbitrary mass distributions in space and on the study of the gravity potential of an irregularly shaped, rotating body by means of the spherical harmonic functions. The Stokes coefficients of the gravity potential are also introduced, and the relationship between their low-degree harmonics and the moments of the mass distributions (i.e., the centre of mass and the inertia tensor) is enlightened. In the second section, we define the simplest mechanical tests in rheology, i.e., the creep, relaxation and the creep recovery test. We introduce the Hooke, Newton and Maxwell rheological laws by studying their constitutive equations. The transient Kelvin-Voigt rheological law and the generalised visco-elastic rheologies are defined, dwelling on the bi-viscous Burgers model. The correspondence principle for linear viscoelasticity is introduced and motivated, defining appropriate s-dependent complex moduli in the Laplace domain. In the third section, we study the properties of the mass distributions by defining the concepts of topography and sea level. The ice and water load are introduced, and the ocean function and its complementary continent function are defined in terms of topography and ice thickness. The surface load function and its spatio-temporal variation are introduced and discussed, imposing the fundamental constraint of mass conservation in the Earth’s system.

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Gravity, Rheology and Mass Distributions

  • Giorgio Spada,
  • Daniele Melini

摘要

In this introductory chapter, we focus first on the description of arbitrary mass distributions in space and on the study of the gravity potential of an irregularly shaped, rotating body by means of the spherical harmonic functions. The Stokes coefficients of the gravity potential are also introduced, and the relationship between their low-degree harmonics and the moments of the mass distributions (i.e., the centre of mass and the inertia tensor) is enlightened. In the second section, we define the simplest mechanical tests in rheology, i.e., the creep, relaxation and the creep recovery test. We introduce the Hooke, Newton and Maxwell rheological laws by studying their constitutive equations. The transient Kelvin-Voigt rheological law and the generalised visco-elastic rheologies are defined, dwelling on the bi-viscous Burgers model. The correspondence principle for linear viscoelasticity is introduced and motivated, defining appropriate s-dependent complex moduli in the Laplace domain. In the third section, we study the properties of the mass distributions by defining the concepts of topography and sea level. The ice and water load are introduced, and the ocean function and its complementary continent function are defined in terms of topography and ice thickness. The surface load function and its spatio-temporal variation are introduced and discussed, imposing the fundamental constraint of mass conservation in the Earth’s system.