Principles of the Gravitational Method - 1st Edition - ISBN: 9780444529930, 9780080553870

Principles of the Gravitational Method, Volume 41

1st Edition

Authors: Alex Kaufman Richard Hansen
eBook ISBN: 9780080553870
Hardcover ISBN: 9780444529930
Imprint: Elsevier Science
Published Date: 7th November 2007
Page Count: 258
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Table of Contents

List of symbols.
Chapter 1: Principles of theory of attraction.

1. Newton’s law of attraction.
2. The field of attraction and solution of the forward problem.
3. Different types of masses and their densities.
4. Two fundamental features of the attraction field.
5. System of equations of the field of attraction.
6. Laplace’s and Poisson’s equations.
7. The potential and its relation to masses.
8. Fundamental solution of Poisson’s and Laplace’s equations.
9. Theorem of uniqueness and solution of the forward problem.
10. Green’s formula and the relationship between potential and boundary conditions.
11. Analytical upward continuation of the field.
12. Poisson’s integral.
13. Behavior of the attraction field.
14. Legender’s functions and solution of Laplace’s equation.
Chapter 2: Gravitational field of the earth.
1. Forces acting on an elementary volume of the rotating earth and the gravitational field.
2. Gravitational field of the earth.
3. Potential of the gravitational field of the earth.
4. Potential and the gravitational field due to an ellipsoid of rotation.
5. Clairaut’s Theorem.
6. Potential of the gravitational field in terms of spherical harmonics.
7. Geoid and leveling.
8. Stokes formula.
9. Molodensky’s problem.
10. Attraction field of the spheroid.
11. Spheroid and equilibrium of rotating fluid.
12. Development of the theory of the figure of the earth.
Chapter 3: Principles of measurements of the gravitational field.
1. History of measurements of the gravitational field.
2. Principles of ballistic gravimeter.
3. Pendulum devices.
4. Influence of Coriolis force on particle motion.
5. Vertical spring mass-system.
6. Spring with an initial compression and Hooke’s law.
7. Torsion spring-mass system.
8. Lever spring-mass system.
9. Measurements of second derivatives of the potential of gravitational field.
Chapter 4: Uniqueness and the solution of the inverse problem in gravity.
1. Concept of uniqueness and solution of the inverse problem.
2. Solution of inverse problem and influence of noise.
3. Solution of the forward problem (calculation of the field of attraction).


This self-contained monograph gives a thorough introduction to the theory of gravity which is used as the basis for developing applications in exploration and geodesy. In addition, a survey of gravity instrumentation is given, with emphasis on the theory of underlying these instruments. The book finishes with an exposition of forward modeling and inverston, again emphasizing fundamental principles.

Key Features

Surveys gravity instrumentation with emphasis on the theory of why certain instrumentation is used Presents thorough developments of the theory of gravity to aid in creating applications in exploration and geodesy *Emphasizes the fundamental principles of forward modeling and inversion in the gravitational method


Researchers interested in gravimetry, geodesy, tectonophysics, applied geophysics, and geothermics


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Elsevier Science
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About the Authors

Alex Kaufman Author

Emeritus Professor A.Kaufman has 28 years’ experience of teaching at the geophysical department in Colorado School of Mines He received his PhD. in Institute of Physics of the Earth (Moscow) and degree of Doctor of Science from the Russian Academy of Science . From 1981 to 20015 he published 14 monographs by Academic Press and Elsevier, describing different geophysical methods. Most of them are translated and published in Russia and China. He also holds three patents, which found application in the surface and borehole geophysics. A. Kaufman is a honorary member of SEG.

Affiliations and Expertise

Professor Emeritus, Colorado School of Mines, Golden, USA

Richard Hansen Author

Affiliations and Expertise

EDCON-PRJ, Inc., Lakewood, CO, USA