The first section of this chapter is devoted to the Surface Response Functions (SRFs), having a central role in the theory of the Sea Level Equation further on. By suitably defining a 3-D convolution, expressions are given for the SRFs corresponding to a general surface load, also providing their expansions in series of CSHs in the geographical reference frame. A special vector representation is obtained for the horizontal displacements SRFs. Furthermore, due to its relevance for the Sea Level Equation in later chapters, emphasis is placed on the study of the so-called “sea level SRF”. The “simplified surface loading problem” is discussed in the second section. Closed-form solutions are given for the surface displacements and the geoid height variations, assuming that the surface ice loads are compensated by a uniform ocean load in order to conserve the total mass of the system. Various geometries for the surface loads are considered, including the disc, the quasi-parabolic cap and the (non axis-symmetric) rectangular load, also illustrating some applications to complex loads. In the third and last section, a simple Post Glacial Rebound (PGR) simulation is performed by means of the open source program TABOO, using a realistic model for the viscoelastic Earth’s structure, which includes five layers (an elastic lithosphere, a three layer mantle and a homogeneous core). A number of geophysical variables are presented and discussed, adopting a simple deglaciation chronology and a quasi-parabolic axis-symmetric surface load. An account of the present-day isostatic disequilibrium across deglaciated regions and in the surroundings is also given, in terms of vertical and horizontal rates of displacement and of geoid height variations.

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The Earth’s Response to  Surface  Loads

  • Giorgio Spada,
  • Daniele Melini

摘要

The first section of this chapter is devoted to the Surface Response Functions (SRFs), having a central role in the theory of the Sea Level Equation further on. By suitably defining a 3-D convolution, expressions are given for the SRFs corresponding to a general surface load, also providing their expansions in series of CSHs in the geographical reference frame. A special vector representation is obtained for the horizontal displacements SRFs. Furthermore, due to its relevance for the Sea Level Equation in later chapters, emphasis is placed on the study of the so-called “sea level SRF”. The “simplified surface loading problem” is discussed in the second section. Closed-form solutions are given for the surface displacements and the geoid height variations, assuming that the surface ice loads are compensated by a uniform ocean load in order to conserve the total mass of the system. Various geometries for the surface loads are considered, including the disc, the quasi-parabolic cap and the (non axis-symmetric) rectangular load, also illustrating some applications to complex loads. In the third and last section, a simple Post Glacial Rebound (PGR) simulation is performed by means of the open source program TABOO, using a realistic model for the viscoelastic Earth’s structure, which includes five layers (an elastic lithosphere, a three layer mantle and a homogeneous core). A number of geophysical variables are presented and discussed, adopting a simple deglaciation chronology and a quasi-parabolic axis-symmetric surface load. An account of the present-day isostatic disequilibrium across deglaciated regions and in the surroundings is also given, in terms of vertical and horizontal rates of displacement and of geoid height variations.