Mathematical Considerations

It has been my intention in this book to give a coordinated treatment of the whole of theoretical geophysics. The book assumes a mathematical back ground through calculus and differential equations. It also assumes a reason able background in physics and in elementary vector analysis. The level of the book is commensurate with that of a senior undergraduate or first year graduate course. Its aim is to provide the reader with a survey of the whole of theoretical geophysics. The emphasis has been on the basic and the elementary. The expert in any one of the several disciplines covered here will find much lacking from his particular area of investigation; no apology is made for that. In order to treat all aspects in a coordinated manner, the simplest type of mathematical nota tion for the various physical problems has been used, namely, that of scalars, three-dimensional vectors, and the vector operators, gradient, curl, divergence, etc. It is appreciated that this elementary notation often may not be the most conducive to the solution of some of the more complex geophysical problems. The derivations are, in almost every case, carried through in considerable detail. Sometimes the particulars of the algebra and calculus have been omitted and relegated to one of the problems following the section. The emphasis has been on the physics of the derivations and on explaining the various physical principles important in geophysics, such as continuity, mixing, diffusion, conduction, convection, precession, wobble, rays, waves, dispersion, and potential theory.