Seafloor Topography Estimation from Gravity: Theory and Applications, livre ebook

Seafloor topography data are essential for a multitude of Earth science studies. Among various seafloor mapping technologies, gravity inversion is the dominant approach to achieve rapid global coverage at low resolution and to obtain the bathymetry at places covered by ice shelves, icebergs, or ice mélange. The present book systematically discusses the relationship between topography and gravity, establishes methods of inferring seafloor topography from gravity, and gives practical examples showing seafloor topography estimation from airborne gravities measured in polar expedition missions.

Preface..................................................... V

About the Author............................................ VII

CHAPTER 1

Introduction................................................. 1

1.1 Background ............................................1

1.2 Previous Studies......................................... 1

1.2.1 Global Seafloor Topography Estimation

from Altimetry-Derived Gravity ........................ 1

1.2.2 Sub-Ice-Shelf Seafloor Topography Estimation

from Airborne Gravity ............................... 5

1.3 Objective ..............................................5

CHAPTER 2

Relationship Between Topography and Gravity....................... 7

2.1 Relationship in the Frequency Domain........................ 7

2.1.1 Parker’s Theory .................................... 7

2.1.2 Forsberg’s Method ..................................10

2.1.3 Relationships of Gravity Anomaly and Gravity Gradient

to Topography ..................................... 12

2.1.4 Admittance Theory ................................. 16

2.1.5 Advantages and Limitations of Using the GravityGradient ... 20

2.2 Relationship in the Spatial Domain........................... 21

2.2.1 The Gravitational Gradients Due to a Right Rectangular

Prism ............................................ 22

2.2.2 The Gravity Anomalies Due to a Right Rectangular Prism... 22

2.3 Errors Associated with Gradient InversionTechniques............. 23

2.3.1 Truncation and Resolution Errors in the Forward

Computation ...................................... 23

2.3.2 Summary of Other Error Sources .......................27

CHAPTER 3

Estimation Methodology........................................ 29

3.1 Seafloor Topography Estimation Based on FourierTransform ....... 29

3.2 Analysis of the Nonlinear Terms............................. 30

3.2.1 Validity of the Linear Approximation.................... 30

3.2.2 Introduction to the Coherency......................... 34

3.2.3 Coherency for Finite Power Signals..................... 36

3.2.4 Radially Symmetric Coherency .........................37

3.2.5 Coherency for Signals on the Sphere..................... 38

3.3 Seafloor Topography Estimation Using Simulated Annealing........ 43

3.3.1 Introduction to the Simulated Annealing................. 43

3.3.2 Seafloor Topography Estimation from Gravity Gradients..... 45

3.3.3 Seafloor Topography Estimation from GravityAnomalies..... 46

3.4 Difference Between Simulated Annealing and Parker’sMethod ...... 47

CHAPTER 4

Numerical Experiment......................................... 49

4.1 Study Area Description.................................... 49

4.2 Estimation Using Parker’s Formulation........................ 49

4.2.1 Data Preparation ...................................49

4.2.2 Data Filtering .....................................50

4.2.3 Determination of Topography-to-Gradient AdmittanceScale . . 54

4.2.4 Results and Evaluation ..............................57

4.2.5 Results After Including Shorter Wavelengths.............. 59

4.3 Estimation Using Simulated Annealing........................ 61

4.3.1 Analysis of the Forward Computation in the SA........... 61

4.3.2 Data Preparation and SA Configuration................. 63

4.3.3 Results of the Simulated Annealing..................... 65

4.3.4 Low-Pass Filtering the Estimated Seafloor Topography...... 69

4.3.5 Evaluation ........................................ 69

4.3.6 Other Tests of the Simulated Annealing Algorithm......... 71

4.4 Comparison of the EstimationResults......................... 74

4.4.1 Comparison with the SIO Topography Model.............. 74

4.4.2 Comparison Between the Two Methods ..................75

4.5 Conclusions.............................................77

CHAPTER 5

Estimation from Airborne Gravity Gradients........................ 79

5.1 Airborne Gravity Gradients and Multibeam Bathymetry........... 80

5.2 InversionParameters...................................... 81

5.3 Analysis and Removal of the Non-Terrain Effects................ 81

5.4 Results, Evaluation, and Discussion.......................... 84

5.5 Conclusions.............................................86

CHAPTER 6

Seafloor Topography Offshore Northeast Greenland................... 89

6.1 Introduction............................................ 89

6.2 Data and Methods .......................................90

6.2.1 Airborne Gravity ...................................90

6.2.2 Bathymetric Data .................................. 92

6.2.3 Inversion Parameters ................................92

6.3 Results and Evaluation.................................... 93

6.3.1 Accuracy Evaluation ................................93

6.3.2 Seafloor Topography ................................94

6.4 Discussion.............................................. 97

6.4.1 Topographic Steering of Ocean Currents................. 97

6.4.2 Errors Associated with Gravity Inversion Techniques........ 99

6.5 Conclusions.............................................100

CHAPTER 7

Seafloor Topography Beneath the Amery Ice Shelf, EastAntarctica ....... 103

7.1 Introduction............................................ 103

7.2 Data and Methods .......................................105

7.2.1 Airborne Gravity ...................................105

7.2.2 Laser Altimeter and Ice-Penetrating Radar Data........... 105

7.2.3 Hydrographic Data .................................106

7.2.4 Inversion Parameters ................................106

7.3 Results ................................................107

7.3.1 New Bathymetric Model .............................107

7.3.2 Water Masses Arriving at the AmIS..................... 110

7.4 Discussion.............................................. 112

7.4.1 Topographic Steering of Ocean Currents................. 112

7.5 Conclusions.............................................113

References.................................................. 115

Appendix A: The Spherical Harmonics of the Gravity Anomaly.......... 125

Appendix B: Pseudo-Code for the Adaptive Simulated Annealing......... 127