Elsevier - Principles of the Gravitational Method, Volume 41 (Methods in Geochemistry and Geophysics).pdf

Introduction
The subject of this monograph is physical and mathematical principles of
gravitational method. The first chapter is devoted entirely to the field of attraction
caused by masses. Proceeding from Newton’s law of attraction we introduce the
concept of this field and describe its fundamental features. Special attention is paid
to the system of equations of the attraction field at regular points and interfaces
where a density is discontinuous function. Then after introduction of the potential
we perform transition from the system of equations to Poisson’s and Laplace’s
equations and discuss their fundamental solutions. Also the theorem of uniqueness
and different boundary value problems are studied in detail. As illustration, we
consider two examples, which play an important role in the exploration and global
geophysics, namely, analytical upward continuation of the field and Poisson’s
integral. At the end of this chapter there are several examples, which characterize
a field behavior inside and outside masses. The second chapter considers the
gravitational field of the earth. At the beginning, we study forces acting on
elementary volume of the rotating Earth in an inertial frame. Then, considering
the second Newton’s law in non-inertial system, we introduce the centrifugal force
and gravitational field, as well as its potential. Special attention is paid to the
gravitational field and potential, caused by an ellipsoid of rotation. This study
allows us to describe Clairaut’s theorem. Also, taking into account results derived in
Chapter 1, we represent the potential of the gravitational field in terms of spherical
harmonics. This chapter also discusses such concepts as geoid, Stokes formula, and
Molodensky’s boundary problem which play an important role in studying Earth’s
figure. In conclusion, we briefly consider equilibrium of rotating fluid and history of
development of the theory of the earth’s figure.
Principles of measurement of the gravit