Elsevier S & T

Principles of the Gravitational Method

Kaufman, Alex A.; Hansen, Richard O.

In stock
No reviews
68.500 KD inc. VAT
License
Table of contents
  • Cover
  • Contentsv
  • Introductionix
  • List of Symbolsxi
  • Chapter 1. Principles of Theory of Attraction1
  • 1.1. Newton’s Law of Attraction1
  • 1.2. The Field of Attraction and Solution of the Forward Problem6
  • 1.3. Different Types of Masses and their Densities9
  • 1.4. Two Fundamental Features of the Attraction Field10
  • 1.5. System of Equations of the Field of Attraction14
  • 1.6. Laplace’s and Poisson’s Equations18
  • 1.7. The Potential and its Relation to Masses20
  • 1.8. Fundamental Solution of Poisson’s and Laplace’s Equations21
  • 1.9. Theorem of Uniqueness and Solution of the Forward Problem25
  • 1.10. Green’s Formula and the Relationship Between Potential and Boundary Conditions33
  • 1.11. Analytical Upward Continuation of the Field37
  • 1.12. Poisson’s Integral40
  • 1.13. Behavior of the Attraction Field42
  • 1.14. Legendre’s Functions and a Solution of Laplace’s Equation54
  • Chapter 2. Gravitational Field of the Earth59
  • 2.1. Forces Acting on an Elementary Volume of the Rotating Earth and the Gravitational Field59
  • 2.2. Gravitational Field of the Earth72
  • 2.3. Potential of the Gravitational Field of the Earth75
  • 2.4. Potential and the Gravitational Field due to an Ellipsoid of Rotation84
  • 2.5. Clairaut’s Theorem100
  • 2.6. Potential of the Gravitational Field in Terms of Spherical Harmonics106
  • 2.7. Geoid and Leveling114
  • 2.8. Stokes’s Formula120
  • 2.9. Molodensky’s Boundary Problem128
  • 2.10. Attraction Field of the Spheroid135
  • 2.11. Spheroid and Equilibrium of a Rotating Fluid143
  • 2.12. Development of the Theory of the Figure of the Earth (Brief Historic Review)149
  • Chapter 3. Principles of Measurements of the Gravitational Field161
  • 3.1. History of Measurement of the Gravitational Field161
  • 3.2. Principles of Ballistic Gravimeter163
  • 3.3. Pendulum Devices169
  • 3.4. Influence of Coriolis Force on Particle Motion180
  • 3.5. Vertical Spring–Mass System187
  • 3.6. Spring with an Initial Compression and Hooke’s Law197
  • 3.7. Torsion Spring–Mass System201
  • 3.8. Lever Spring–Mass System206
  • 3.9. Measurement of Second Derivatives of the Potential of Gravitational Field210
  • Chapter 4. Uniqueness and the Solution of the Inverse Problem in Gravity217
  • 4.1. Concept of Uniqueness and the Solution of the Inverse Problem217
  • 4.2. Solution of the Inverse Problem and the Influence of Noise225
  • 4.3. Solution of the Forward Problem (A Calculation of the Field of Attraction)229
  • Bibliography237
  • Appendix239
  • Subject Index243
Book details
  • Vendor Elsevier S & T
  • SKU 9780444529930
  • ISBN-13 9780080553870
  • Author Kaufman, Alex A.; Hansen, Richard O.
  • Category Science
  • Subject Geophysics

Do you have questions about this book?

Ask an expert!

Description eBook delivery & access Reviews
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