Principles of the Gravitational Method (eBook)

Richard O. Hansen, Alex Kaufman (Autoren)

eBook Download: PDF

2007 | 1. Auflage
258 Seiten
Elsevier Science (Verlag)
978-0-08-055387-0 (ISBN)

Infos

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.

*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

Inhalt

Cover 1
Contents 6
Introduction 10
List of Symbols 12
Chapter 1. Principles of Theory of Attraction 14
1.1. Newton’s Law of Attraction 14
1.2. The Field of Attraction and Solution of the Forward Problem 19
1.3. Different Types of Masses and their Densities 22
1.4. Two Fundamental Features of the Attraction Field 23
1.5. System of Equations of the Field of Attraction 27
1.6. Laplace’s and Poisson’s Equations 31
1.7. The Potential and its Relation to Masses 33
1.8. Fundamental Solution of Poisson’s and Laplace’s Equations 34
1.9. Theorem of Uniqueness and Solution of the Forward Problem 38
1.10. Green’s Formula and the Relationship Between Potential and Boundary Conditions 46
1.11. Analytical Upward Continuation of the Field 50
1.12. Poisson’s Integral 53
1.13. Behavior of the Attraction Field 55
1.14. Legendre’s Functions and a Solution of Laplace’s Equation 67
Chapter 2. Gravitational Field of the Earth 72
2.1. Forces Acting on an Elementary Volume of the Rotating Earth and the Gravitational Field 72
2.2. Gravitational Field of the Earth 85
2.3. Potential of the Gravitational Field of the Earth 88
2.4. Potential and the Gravitational Field due to an Ellipsoid of Rotation 97
2.5. Clairaut’s Theorem 113
2.6. Potential of the Gravitational Field in Terms of Spherical Harmonics 119
2.7. Geoid and Leveling 127
2.8. Stokes’s Formula 133
2.9. Molodensky’s Boundary Problem 141
2.10. Attraction Field of the Spheroid 148
2.11. Spheroid and Equilibrium of a Rotating Fluid 156
2.12. Development of the Theory of the Figure of the Earth (Brief Historic Review) 162
Chapter 3. Principles of Measurements of the Gravitational Field 174
3.1. History of Measurement of the Gravitational Field 174
3.2. Principles of Ballistic Gravimeter 176
3.3. Pendulum Devices 182
3.4. Influence of Coriolis Force on Particle Motion 193
3.5. Vertical Spring–Mass System 200
3.6. Spring with an Initial Compression and Hooke’s Law 210
3.7. Torsion Spring–Mass System 214
3.8. Lever Spring–Mass System 219
3.9. Measurement of Second Derivatives of the Potential of Gravitational Field 223
Chapter 4. Uniqueness and the Solution of the Inverse Problem in Gravity 230
4.1. Concept of Uniqueness and the Solution of the Inverse Problem 230
4.2. Solution of the Inverse Problem and the Influence of Noise 238
4.3. Solution of the Forward Problem (A Calculation of the Field of Attraction) 242
Bibliography 250
Appendix 252
Subject Index 256

Produkt-Details

• Erscheint lt. Verlag: 21.11.2007
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geologie
• Themenwelt: Naturwissenschaften ► Geowissenschaften ► Geophysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik
• ISBN-10: 0-08-055387-7 / 0080553877
• ISBN-13: 978-0-08-055387-0 / 9780080553870