Preface |
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1 Gravitational attraction |
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1 | (9) |
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1.1 Universal gravitational attraction |
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1 | (2) |
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1.2 Gravitational acceleration |
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3 | (1) |
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1.3 Gravitational potential of a point mass |
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4 | (1) |
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1.4 Gravitational potential of a solid body |
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5 | (2) |
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7 | (1) |
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1.6 Attraction of a sphere |
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8 | (1) |
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1.7 Units of acceleration |
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9 | (1) |
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2 Instruments and data reduction |
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10 | (31) |
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2.1 The gravitational constant |
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10 | (1) |
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2.2 Absolute measurements |
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11 | (2) |
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2.3 Relative measurements |
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13 | (3) |
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2.4 Instruments for gravity-gradient measurements |
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16 | (1) |
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17 | (4) |
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2.6 Variation with latitude |
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21 | (3) |
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2.7 Atmospheric correction |
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24 | (1) |
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24 | (3) |
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2.9 The simple Bouguer correction |
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27 | (2) |
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29 | (3) |
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32 | (6) |
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2.12 Characteristics of the different reductions |
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38 | (3) |
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3 Field acquisition of gravity data |
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41 | (7) |
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41 | (1) |
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42 | (1) |
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3.3 Suggested documentation |
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43 | (1) |
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44 | (1) |
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3.5 Monitoring meter drift |
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45 | (1) |
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3.6 Same-day data reduction |
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46 | (2) |
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4 Graphical representation of the anomalous field |
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48 | (21) |
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4.1 Map scale and implied accuracy |
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48 | (3) |
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51 | (1) |
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4.3 The accuracy of gravity data measurements |
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52 | (2) |
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4.4 Observational determination of precision |
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54 | (1) |
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4.5 Linear interpolation of gravity data |
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55 | (2) |
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4.6 Accuracy of linear interpolation |
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57 | (3) |
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4.7 Optimal linear interpolation |
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60 | (2) |
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4.8 Accuracy of the gravity gradient |
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62 | (1) |
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4.9 Precision of a gravity map |
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63 | (1) |
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4.10 The correlation and covariance functions |
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63 | (3) |
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4.11 Computation of the autocovariance function |
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66 | (3) |
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5 Manipulation of the gravity field |
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69 | (30) |
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5.1 Objective of gravity field manipulation |
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69 | (1) |
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5.2 Anomalies: regional, local, and noise |
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70 | (1) |
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71 | (3) |
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5.4 Examination of a three-point smoothing operator |
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74 | (2) |
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5.5 Orthogonal function decomposition |
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76 | (2) |
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5.6 The discrete Fourier transform |
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78 | (8) |
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5.7 Least squares criteria for fitting data |
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86 | (1) |
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87 | (1) |
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87 | (4) |
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5.10 Numerical integration of upward continuation |
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91 | (1) |
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5.11 Fourier transform continuation |
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92 | (1) |
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5.12 Finite-difference methods |
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93 | (1) |
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5.13 Analytical continuation |
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94 | (5) |
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6 Interpretation of density structure |
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99 | (30) |
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99 | (1) |
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100 | (4) |
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6.3 Nettleton's method for determination of reduction density |
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104 | (2) |
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6.4 Seismic velocity as a constraint for rock density |
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106 | (1) |
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6.5 Gravity anomalies from spherical density structures |
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107 | (5) |
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6.6 The attraction of a thin rod |
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112 | (2) |
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6.7 Attraction of a horizontal cylinder of finite length |
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114 | (2) |
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6.8 The two-dimensional potential |
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116 | (1) |
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117 | (2) |
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6.10 Horizontal half-sheet |
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119 | (2) |
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6.11 Two-dimensional polygonal-shaped bodies |
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121 | (4) |
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6.12 Polygons of attracting mass in a horizontal sheet |
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125 | (4) |
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7 The inversion of gravity data |
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129 | (20) |
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129 | (2) |
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7.2 Depth of a basin as layer thicknesses |
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131 | (2) |
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7.3 Depth in a basin as an overdetermined inverse problem |
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133 | (3) |
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136 | (2) |
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7.5 Formulation of an underdetermined inverse problem |
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138 | (1) |
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7.6 The minimum length solution of the underdetermined inverse problem |
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138 | (4) |
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7.7 Seismic velocity as a constraint |
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142 | (1) |
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7.8 Maximum likelihood inversion |
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143 | (6) |
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149 | (12) |
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8.1 The isostatic reduction |
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149 | (1) |
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8.2 The isostatic response function |
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149 | (2) |
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8.3 Determination of the isostatic response function |
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151 | (4) |
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8.4 Interpretation of the isostatic response function |
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155 | (1) |
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8.5 Example computation of the admittance and isostatic response functions |
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156 | (2) |
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8.6 Isostasy in coastal plain sediments |
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158 | (3) |
Appendix A Common definitions and equations in potential theory |
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161 | (4) |
Appendix B Glossary of symbols |
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165 | (2) |
References |
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167 | (3) |
Index |
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170 | |