This book aims to provide, with comprehensive detail, the fundamental theory of the Earth"s global elastic deformation, as well as the associated variations of the gravity field and rotation, that the readers can thoroughly understand with little reference to other books or journal papers. Its contents belong to the essential background physics of geodesy nowadays.The noteworthy style of this book is its inclusion of ample intermediate steps of mathematical derivations and physical interpretations of the mathematical formulae not found elsewhere. It is based on undergraduate mathematics and physics as usually taught to mathematics- or physics-heavy majors. No university-level Earth science knowledge is assumed; the most elementary is provided concisely to the depth required. Mathematics and physics above the level mentioned, notably, vector and tensor analysis, spherical harmonics, elasticity, and solid body rotation, are treated to sufficient depth for preparing the r
eaders to understand the relevant publications on theoretical formulation. Gravity and shape of the Earth are essential for the deformation theory. Seismology relies on the theory of the elastic deformation of the Earth; the density and elastic parameters of the Earth are determined using seismic data. Therefore, gravity and seismology are also treated adequately. Specifically, the free oscillation of the Earth, which is a kind of global elastic deformation, is treated to a depth and detail rarely found in books of seismology. After all these preparations, the elastic deformation theories of the Earth tide and surface loading are developed. The formulation of the respective Love numbers, as well as their roles in the Earth rotation theory, is emphasized. Plenty of details on the methods and implementations of numerical computations are included. The topics covered are fundamental and common for theoretical geodesists devoted to studying global geophysical processes. Besides, also
provided are many details on the applications of the Love numbers in the study of Earth system processes using space geodetic data, particularly, the mass transport in the atmosphere-hydrosphere-cryosphere system.To the author s knowledge, this is the first book in this discipline that brings mathematics, physics, theoretical modeling, methods of numerical computations, as well as applications together in such detail and depth starting from very fundamental mathematics and physics. The details of the derivations and interpretations of the mathematical formulae are expected to be valuable assets for both researchers and educators.
Chapter 1. Background Knowledge.- Chapter 2. Three-Dimensional Vector and Tensor Analysis.- Chapter 3. Physical Equations of Rotation and Elastic Deformation of the Earth.- Chapter 4. Spherical Harmonics with Applications.- Chapter 5. Gravity and Shape of the Earth.- Chapter 6. Seismology and the Spherical Elastic Earth Model.- Chapter 7. Earth Tide and Surface Loading of the Spherical Elastic Earth Model.- Chapter 8. Earth Rotation.
