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Geodesy and Gravity

  


by Filed under geodesy, physics

Geodesy and Gravity

File : 1.15 MB, 304 pages

TOC

1 Introduction 1
1.1 Introduction
1.2 Geodesy
1.3 Course Organization

2 Observational Techniques
2.1 Instruments
2.1.1 Gravity meters
2.1.2 Pendulums
2.1.3 Springs
2.1.4 LaCoste-Romberg Meter
2.1.5 Superconducting Gravimeter
2.2 Relative Gravity at Sea and on Planes
2.3 Free Fall Meters
2.3.1 Launch Type
2.4 Free-Fall-only Meters
2.4.1 Uncertainty in /, (Lambda)
2.4.2 Electronic counting and timing errors
2.4.3 Ground Acceleration
2.4.4 Non-gravitational forces
2.4.5 Accuracy
2.4.6 Satellites
2.5 Positioning
2.5.1 Ground Based Techniques
2.5.1.4 Distances
2.5.1.4.4 Strainmeters
2.5.2 Space Techniques
2.5.2.1 Satellites
2.5.2.1.1 Radio Ranging Satellites
2.5.2.1.1.1 Doppler Satellites
2.5.2.1.1.2 GPS (Global Positioning System)
2.5.2.1.2 Laser ranging satellites
2.5.2.1.3 Lunar Laser Ranging (LLR)
2.5.2.1.4 VLBI (very-long-baseline-interferometry)
2.5.2.2 Advantages of one space positioning technique over another
2.5.2.3 Some Results
2.5.2.4 Altimeters
2.5.2.5 Dedicated Gravity Mission

3 Potential Theory
3.1 Introductory remarks
3.2 Finding the gravitational field from knowledge of the density
3.2.4 A numerical method for arbitrary mass anomalies
3.3 Poisson’s equation
3.3.1 Derivation
3.3.1.1 Gauss’ Law
3.3.1.2 Continuity conditions
3.3.2 Laplace’s equation
3.3.2.1 Green’s Theorems
3.3.3 Solutions to Laplace’s equation
3.3.3.1 Planar boundaries
3.3.3.2 Cylindrical coordinates
3.3.3.3 Spherical boundaries
3.3.4 Properties of the Y m’s and P m’s
3.3.4.1 Parity
3.3.4.2 Recursion Relations
3.3.4.3 Speci c Results
3.3.4.4 Orthogonality
3.3.4.5 Completeness
3.3.4.6 The wavelengths of the Y m’s
3.3.4.7 The Addition Theorem
3.3.5 Applications
3.3.6 The use of Y l m’s in direct integration
3.3.6.1 Finding V outside a surface
3.3.6.2 Finding V inside a surface
3.3.6.3 A slightly non-spherical surface

4 Physical Geodesy Problems
4.1 The Figure of the Earth: The Geoid
4.1.1 Spherically Symmetric, Non-rotating Earth
4.1.2 Spherically Symmetric, Rotating Earth
4.1.3 Rotating, Elliptically Symmetric Earth
4.1.4 The ellipsoid
4.2 Clairaut’s Differential Equation
4.2.1 Example: A uniform (homogeneous) earth
4.3 A More Realistic Earth
4.3.1 The Geoid
4.3.2 Stoke’s Formula
4.4 Satellite Geoids

5 Stress/Strain Relations
5.1 Stress tensor
5.2 Stress-Induced Deformation
5.3 Response to Tij for i <> j
5.3.1 Strain Tensor
5.3.2 Relation between stress and strain
5.4 Relation between stress/strain and the displacement eld
5.5 Remarks
5.6 Putting T into F = ma
5.6.1 Example: Waves in a homogeneous, isotropic, 1 medium
5.6.2 p-waves: longitudinal or sound waves
5.6.3 s-waves: transverse waves
5.6.4 The general case
5.7 Anelasticity
5.7.1 The general linear model
5.7.2 The Frequency regime
5.7.3 Short-period behavior
5.7.4 Long-Period behavior
5.7.4.1 Maxwell solid
5.7.4.2 Kelvin-Voigt solid
5.7.4.3 Standard Linear solid

5.7.4.4 Three-dimensional Maxwell solid rheology
6 Interpretation of Observed Gravity Anomalies
6.1 Surface Gravity Anomalies
6.2 Isostasy
6.2.1 Airy compensation
6.2.2 Pratt compensation
6.2.3 Airy versus Pratt
6.3 A Better Model for Airy Compensation Effects on Gravity
6.4 A Better Model for Pratt Compensation Effects on Gravity
6.4.1 Remarks
6.5 Geoid anomalies
6.5.1 One Final Remark
6.6 Lithospheric Bending
6.6.1 Lithosphere
6.6.2 Theory of Flexure
6.6.3 Application
6.6.4 Gravity
6.6.5 Remarks
6.6.6 Examples of Pratt compensation
6.6.6.1 Basin and Range
6.6.6.2 Hot Spots
6.6.6.3 Mid-Ocean Ridges
6.6.6.3.1 Thermal Isostasy
6.7 Convergence Zones
6.8 The Long-Wavelength Geoid

7 Postglacial Rebound
7.1 Theory
7.2 Elastic Problem
7.3 Numbers
7.4 Interpretation
7.5 The Data
7.6 The Conclusions

8 Earth Tides
8.1 A Qualitative Description of the Tidal Force
8.2 Tidal Potential
8.3 Tidal Response of the Earth
8.3.1 An Example: Surface Gravity Tides
8.3.2 Numerical Results
8.3.3 What the simple model ignores
8.3.3.1 The Oceans
8.3.3.2 Local Effects
8.3.3.3 Effects of rotation and ellipticity
9 Earth Rotation
9.1 Variable Rotation Rate
9.2 Motion of the Rotation Axis
9.3 Changes in the lod
9.3.1 Linear change in the lod
9.3.2 Decadal Fluctuations in the lod
9.3.3 Short period lod fluctuations
9.4 Wobble
9.4.1 Annual Wobble
9.4.2 Chandler wobble
9.5 Nutations and Precession

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