# Principles of the Gravitational Method

**By**

- Alex Kaufman, Professor Emeritus, Colorado School of Mines, Golden, USA
- Richard Hansen, EDCON-PRJ, Inc., Lakewood, CO, USA

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.

View full description### Audience

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

### Book information

- Published: November 2007
- Imprint: ELSEVIER
- ISBN: 978-0-444-52993-0

### Table of Contents

**Introduction.**

Acknowledgements.

List of symbols.

Chapter 1: Principles of theory of attraction.

1. NewtonĂ˘Â€Â™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. LaplaceĂ˘Â€Â™s and PoissonĂ˘Â€Â™s equations.

7. The potential and its relation to masses.

8. Fundamental solution of PoissonĂ˘Â€Â™s and LaplaceĂ˘Â€Â™s equations.

9. Theorem of uniqueness and solution of the forward problem.

10. GreenĂ˘Â€Â™s formula and the relationship between potential and boundary conditions.

11. Analytical upward continuation of the field.

12. PoissonĂ˘Â€Â™s integral.

13. Behavior of the attraction field.

14. LegenderĂ˘Â€Â™s functions and solution of LaplaceĂ˘Â€Â™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. ClairautĂ˘Â€Â™s Theorem.

6. Potential of the gravitational field in terms of spherical harmonics.

7. Geoid and leveling.

8. Stokes formula.

9. MolodenskyĂ˘Â€Â™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 HookeĂ˘Â€Â™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).

**Appendix.**

References.

Index.