EDP Sciences 1775429961 20260405 fre

laboutique.edpsciences.fr-R002566 03 01 01 R002566 00 ED E107 00 01 01 Seafloor Topography Estimation from Gravity: Theory and Applications 01 eng 08 142 03 22 12818780 17 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 11 00 20231226 02 01 002673 03 9782759831975 15 9782759831975 03 01 D1 EDP Sciences 45 03 laboutique.edpsciences.fr-002673 03 01 01 002673 03 9782759831975 15 9782759831975 10 EA E107 10 00 01 R002566 ED E107 1 10 01 02 Hors collection - 01 01 Seafloor Topography Estimation from Gravity: Theory and Applications 1 A01 01 A2239 Junjun YANG YANG, Junjun Junjun YANG Junjun YANG is an assistant professor at China Aero Geophysical Survey and Remote Sensing Center for Natural Resources, China Geological Survey. His research interests include seafloor topography estimation, airborne gravity measurement, and geoid determination 01 eng 08 140 03 02 24 Izibook:Subject Sciences de la Terre 24 Izibook:SubjectAndCategoryAndTags |Sciences de la Terre| 20 seafloor topography;gravity;methods;data;practical examples;airborne gravimetry;polar expedition missions 10 2011 SCI031000 01 551 06 06 05 03 00 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. 02 00 The book systematically explores the relationship between seafloor topography and gravity, establishes methods for inferring seafloor topography from gravity data, and provides practical examples demonstrating seafloor topography estimation from airborne gravimetry collected during polar expedition missions. 04 00 Preface..................................................... V<o:p></o:p>About the Author............................................ VII<o:p></o:p>CHAPTER 1<o:p></o:p>Introduction................................................. 1<o:p></o:p>1.1 Background ............................................1<o:p></o:p>1.2 Previous Studies......................................... 1<o:p></o:p>1.2.1 Global Seafloor Topography Estimation<o:p></o:p>from Altimetry-Derived Gravity ........................ 1<o:p></o:p>1.2.2 Sub-Ice-Shelf Seafloor Topography Estimation<o:p></o:p>from Airborne Gravity ............................... 5<o:p></o:p>1.3 Objective ..............................................5<o:p></o:p>CHAPTER 2<o:p></o:p>Relationship Between Topography and Gravity....................... 7<o:p></o:p>2.1 Relationship in the Frequency Domain........................ 7<o:p></o:p>2.1.1 Parker’s Theory .................................... 7<o:p></o:p>2.1.2 Forsberg’s Method ..................................10<o:p></o:p>2.1.3 Relationships of Gravity Anomaly and Gravity Gradient<o:p></o:p>to Topography ..................................... 12<o:p></o:p>2.1.4 Admittance Theory ................................. 16<o:p></o:p>2.1.5 Advantages and Limitations of Using the Gravity Gradient ... 20<o:p></o:p>2.2 Relationship in the Spatial Domain........................... 21<o:p></o:p>2.2.1 The Gravitational Gradients Due to a Right Rectangular<o:p></o:p>Prism ............................................ 22<o:p></o:p>2.2.2 The Gravity Anomalies Due to a Right Rectangular Prism... 22<o:p></o:p>2.3 Errors Associated with Gradient Inversion Techniques............. 23<o:p></o:p>2.3.1 Truncation and Resolution Errors in the Forward<o:p></o:p>Computation ...................................... 23<o:p></o:p>2.3.2 Summary of Other Error Sources .......................27<o:p></o:p>CHAPTER 3<o:p></o:p>Estimation Methodology........................................ 29<o:p></o:p>3.1 Seafloor Topography Estimation Based on Fourier Transform ....... 29<o:p></o:p>3.2 Analysis of the Nonlinear Terms............................. 30<o:p></o:p>3.2.1 Validity of the Linear Approximation.................... 30<o:p></o:p>3.2.2 Introduction to the Coherency......................... 34<o:p></o:p>3.2.3 Coherency for Finite Power Signals..................... 36<o:p></o:p>3.2.4 Radially Symmetric Coherency .........................37<o:p></o:p>3.2.5 Coherency for Signals on the Sphere..................... 38<o:p></o:p>3.3 Seafloor Topography Estimation Using Simulated Annealing........ 43<o:p></o:p>3.3.1 Introduction to the Simulated Annealing................. 43<o:p></o:p>3.3.2 Seafloor Topography Estimation from Gravity Gradients..... 45<o:p></o:p>3.3.3 Seafloor Topography Estimation from Gravity Anomalies..... 46<o:p></o:p>3.4 Difference Between Simulated Annealing and Parker’s Method ...... 47<o:p></o:p>CHAPTER 4<o:p></o:p>Numerical Experiment......................................... 49<o:p></o:p>4.1 Study Area Description.................................... 49<o:p></o:p>4.2 Estimation Using Parker’s Formulation........................ 49<o:p></o:p>4.2.1 Data Preparation ...................................49<o:p></o:p>4.2.2 Data Filtering .....................................50<o:p></o:p>4.2.3 Determination of Topography-to-Gradient Admittance Scale . . 54<o:p></o:p>4.2.4 Results and Evaluation ..............................57<o:p></o:p>4.2.5 Results After Including Shorter Wavelengths.............. 59<o:p></o:p>4.3 Estimation Using Simulated Annealing........................ 61<o:p></o:p>4.3.1 Analysis of the Forward Computation in the SA........... 61<o:p></o:p>4.3.2 Data Preparation and SA Configuration................. 63<o:p></o:p>4.3.3 Results of the Simulated Annealing..................... 65<o:p></o:p>4.3.4 Low-Pass Filtering the Estimated Seafloor Topography...... 69<o:p></o:p>4.3.5 Evaluation ........................................ 69<o:p></o:p>4.3.6 Other Tests of the Simulated Annealing Algorithm......... 71<o:p></o:p>4.4 Comparison of the Estimation Results......................... 74<o:p></o:p>4.4.1 Comparison with the SIO Topography Model.............. 74<o:p></o:p>4.4.2 Comparison Between the Two Methods ..................75<o:p></o:p>4.5 Conclusions.............................................77<o:p></o:p>CHAPTER 5<o:p></o:p>Estimation from Airborne Gravity Gradients........................ 79<o:p></o:p>5.1 Airborne Gravity Gradients and Multibeam Bathymetry........... 80<o:p></o:p>5.2 Inversion Parameters...................................... 81<o:p></o:p>5.3 Analysis and Removal of the Non-Terrain Effects................ 81<o:p></o:p>5.4 Results, Evaluation, and Discussion.......................... 84<o:p></o:p>5.5 Conclusions.............................................86CHAPTER 6<o:p></o:p>Seafloor Topography Offshore Northeast Greenland................... 89<o:p></o:p>6.1 Introduction............................................ 89<o:p></o:p>6.2 Data and Methods .......................................90<o:p></o:p>6.2.1 Airborne Gravity ...................................90<o:p></o:p>6.2.2 Bathymetric Data .................................. 92<o:p></o:p>6.2.3 Inversion Parameters ................................92<o:p></o:p>6.3 Results and Evaluation.................................... 93<o:p></o:p>6.3.1 Accuracy Evaluation ................................93<o:p></o:p>6.3.2 Seafloor Topography ................................94<o:p></o:p>6.4 Discussion.............................................. 97<o:p></o:p>6.4.1 Topographic Steering of Ocean Currents................. 97<o:p></o:p>6.4.2 Errors Associated with Gravity Inversion Techniques........ 99<o:p></o:p>6.5 Conclusions.............................................100<o:p></o:p>CHAPTER 7<o:p></o:p>Seafloor Topography Beneath the Amery Ice Shelf, East Antarctica ....... 103<o:p></o:p>7.1 Introduction............................................ 103<o:p></o:p>7.2 Data and Methods .......................................105<o:p></o:p>7.2.1 Airborne Gravity ...................................105<o:p></o:p>7.2.2 Laser Altimeter and Ice-Penetrating Radar Data........... 105<o:p></o:p>7.2.3 Hydrographic Data .................................106<o:p></o:p>7.2.4 Inversion Parameters ................................106<o:p></o:p>7.3 Results ................................................107<o:p></o:p>7.3.1 New Bathymetric Model .............................107<o:p></o:p>7.3.2 Water Masses Arriving at the AmIS..................... 110<o:p></o:p>7.4 Discussion.............................................. 112<o:p></o:p>7.4.1 Topographic Steering of Ocean Currents................. 112<o:p></o:p>7.5 Conclusions.............................................113<o:p></o:p>References.................................................. 115<o:p></o:p>Appendix A: The Spherical Harmonics of the Gravity Anomaly.......... 125<o:p></o:p>Appendix B: Pseudo-Code for the Adaptive Simulated Annealing......... 127<o:p></o:p> Preface..................................................... V<o:p></o:p>About the Author............................................ VII<o:p></o:p>CHAPTER 1<o:p></o:p>Introduction................................................. 1<o:p></o:p>1.1 Background ............................................1<o:p></o:p>1.2 Previous Studies......................................... 1<o:p></o:p>1.2.1 Global Seafloor Topography Estimation<o:p></o:p>from Altimetry-Derived Gravity ........................ 1<o:p></o:p>1.2.2 Sub-Ice-Shelf Seafloor Topography Estimation<o:p></o:p>from Airborne Gravity ............................... 5<o:p></o:p>1.3 Objective ..............................................5<o:p></o:p>CHAPTER 2<o:p></o:p>Relationship Between Topography and Gravity....................... 7<o:p></o:p>2.1 Relationship in the Frequency Domain........................ 7<o:p></o:p>2.1.1 Parker’s Theory .................................... 7<o:p></o:p>2.1.2 Forsberg’s Method ..................................10<o:p></o:p>2.1.3 Relationships of Gravity Anomaly and Gravity Gradient<o:p></o:p>to Topography ..................................... 12<o:p></o:p>2.1.4 Admittance Theory ................................. 16<o:p></o:p>2.1.5 Advantages and Limitations of Using the GravityGradient ... 20<o:p></o:p>2.2 Relationship in the Spatial Domain........................... 21<o:p></o:p>2.2.1 The Gravitational Gradients Due to a Right Rectangular<o:p></o:p>Prism ............................................ 22<o:p></o:p>2.2.2 The Gravity Anomalies Due to a Right Rectangular Prism... 22<o:p></o:p>2.3 Errors Associated with Gradient InversionTechniques............. 23<o:p></o:p>2.3.1 Truncation and Resolution Errors in the Forward<o:p></o:p>Computation ...................................... 23<o:p></o:p>2.3.2 Summary of Other Error Sources .......................27<o:p></o:p>CHAPTER 3<o:p></o:p>Estimation Methodology........................................ 29<o:p></o:p>3.1 Seafloor Topography Estimation Based on FourierTransform ....... 29<o:p></o:p>3.2 Analysis of the Nonlinear Terms............................. 30<o:p></o:p>3.2.1 Validity of the Linear Approximation.................... 30<o:p></o:p>3.2.2 Introduction to the Coherency......................... 34<o:p></o:p>3.2.3 Coherency for Finite Power Signals..................... 36<o:p></o:p>3.2.4 Radially Symmetric Coherency .........................37<o:p></o:p>3.2.5 Coherency for Signals on the Sphere..................... 38<o:p></o:p>3.3 Seafloor Topography Estimation Using Simulated Annealing........ 43<o:p></o:p>3.3.1 Introduction to the Simulated Annealing................. 43<o:p></o:p>3.3.2 Seafloor Topography Estimation from Gravity Gradients..... 45<o:p></o:p>3.3.3 Seafloor Topography Estimation from GravityAnomalies..... 46<o:p></o:p>3.4 Difference Between Simulated Annealing and Parker’sMethod ...... 47<o:p></o:p>CHAPTER 4<o:p></o:p>Numerical Experiment......................................... 49<o:p></o:p>4.1 Study Area Description.................................... 49<o:p></o:p>4.2 Estimation Using Parker’s Formulation........................ 49<o:p></o:p>4.2.1 Data Preparation ...................................49<o:p></o:p>4.2.2 Data Filtering .....................................50<o:p></o:p>4.2.3 Determination of Topography-to-Gradient AdmittanceScale . . 54<o:p></o:p>4.2.4 Results and Evaluation ..............................57<o:p></o:p>4.2.5 Results After Including Shorter Wavelengths.............. 59<o:p></o:p>4.3 Estimation Using Simulated Annealing........................ 61<o:p></o:p>4.3.1 Analysis of the Forward Computation in the SA........... 61<o:p></o:p>4.3.2 Data Preparation and SA Configuration................. 63<o:p></o:p>4.3.3 Results of the Simulated Annealing..................... 65<o:p></o:p>4.3.4 Low-Pass Filtering the Estimated Seafloor Topography...... 69<o:p></o:p>4.3.5 Evaluation ........................................ 69<o:p></o:p>4.3.6 Other Tests of the Simulated Annealing Algorithm......... 71<o:p></o:p>4.4 Comparison of the EstimationResults......................... 74<o:p></o:p>4.4.1 Comparison with the SIO Topography Model.............. 74<o:p></o:p>4.4.2 Comparison Between the Two Methods ..................75<o:p></o:p>4.5 Conclusions.............................................77<o:p></o:p>CHAPTER 5<o:p></o:p>Estimation from Airborne Gravity Gradients........................ 79<o:p></o:p>5.1 Airborne Gravity Gradients and Multibeam Bathymetry........... 80<o:p></o:p>5.2 InversionParameters...................................... 81<o:p></o:p>5.3 Analysis and Removal of the Non-Terrain Effects................ 81<o:p></o:p>5.4 Results, Evaluation, and Discussion.......................... 84<o:p></o:p>5.5 Conclusions.............................................86CHAPTER 6<o:p></o:p>Seafloor Topography Offshore Northeast Greenland................... 89<o:p></o:p>6.1 Introduction............................................ 89<o:p></o:p>6.2 Data and Methods .......................................90<o:p></o:p>6.2.1 Airborne Gravity ...................................90<o:p></o:p>6.2.2 Bathymetric Data .................................. 92<o:p></o:p>6.2.3 Inversion Parameters ................................92<o:p></o:p>6.3 Results and Evaluation.................................... 93<o:p></o:p>6.3.1 Accuracy Evaluation ................................93<o:p></o:p>6.3.2 Seafloor Topography ................................94<o:p></o:p>6.4 Discussion.............................................. 97<o:p></o:p>6.4.1 Topographic Steering of Ocean Currents................. 97<o:p></o:p>6.4.2 Errors Associated with Gravity Inversion Techniques........ 99<o:p></o:p>6.5 Conclusions.............................................100<o:p></o:p>CHAPTER 7<o:p></o:p>Seafloor Topography Beneath the Amery Ice Shelf, EastAntarctica ....... 103<o:p></o:p>7.1 Introduction............................................ 103<o:p></o:p>7.2 Data and Methods .......................................105<o:p></o:p>7.2.1 Airborne Gravity ...................................105<o:p></o:p>7.2.2 Laser Altimeter and Ice-Penetrating Radar Data........... 105<o:p></o:p>7.2.3 Hydrographic Data .................................106<o:p></o:p>7.2.4 Inversion Parameters ................................106<o:p></o:p>7.3 Results ................................................107<o:p></o:p>7.3.1 New Bathymetric Model .............................107<o:p></o:p>7.3.2 Water Masses Arriving at the AmIS..................... 110<o:p></o:p>7.4 Discussion.............................................. 112<o:p></o:p>7.4.1 Topographic Steering of Ocean Currents................. 112<o:p></o:p>7.5 Conclusions.............................................113<o:p></o:p>References.................................................. 115<o:p></o:p>Appendix A: The Spherical Harmonics of the Gravity Anomaly.......... 125<o:p></o:p>Appendix B: Pseudo-Code for the Adaptive Simulated Annealing......... 127<o:p></o:p> 21 00 06 01 https://laboutique.edpsciences.fr/produit/1387/9782759831975/seafloor-topography-estimation-from-gravity-theory-and-applications 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/983/071/original/9782759831968-Seafloor_Topography_Estimation_from_Gravity_couv-sofedis.jpg 17 14 20240913T173334+0200 01 P15 EDP Sciences & Science Press 01 01 P15 EDP Sciences & Science Press 04 11 00 20231226 01 00 20231226 19 00 20231226 2026 06 3052868830012 01 WORLD 13 03 9782759831968 15 9782759831968 06 03 9782759831982 15 9782759831982 WORLD 08 EDP Sciences & Science Press 04 01 00 20231226 03 01 D1 EDP Sciences 20 04 05 01 02 1 00 65.99 01 5.50 3.44 EUR 04 06 01 02 1 00 231.99 01 5.50 3.44 EUR 01 04 06 01 02 1 00 255.99 01 5.50 13.35 USD 01 laboutique.edpsciences.fr-002674 03 01 01 002674 03 9782759831982 15 9782759831982 10 EA 10 10 01 02 Hors collection - 01 01 Seafloor Topography Estimation from Gravity: Theory and Applications 1 A01 01 A2239 Junjun YANG YANG, Junjun Junjun YANG Junjun YANG is an assistant professor at China Aero Geophysical Survey and Remote Sensing Center for Natural Resources, China Geological Survey. His research interests include seafloor topography estimation, airborne gravity measurement, and geoid determination 01 eng 08 140 03 02 24 Izibook:Subject Sciences de la Terre 24 Izibook:SubjectAndCategoryAndTags |Sciences de la Terre| 20 seafloor topography;gravity;methods;data;practical examples;airborne gravimetry;polar expedition missions 10 2011 SCI031000 01 551 06 06 05 03 00 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. 02 00 The book systematically explores the relationship between seafloor topography and gravity, establishes methods for inferring seafloor topography from gravity data, and provides practical examples demonstrating seafloor topography estimation from airborne gravimetry collected during polar expedition missions. 04 00 Preface..................................................... V<o:p></o:p>About the Author............................................ VII<o:p></o:p>CHAPTER 1<o:p></o:p>Introduction................................................. 1<o:p></o:p>1.1 Background ............................................1<o:p></o:p>1.2 Previous Studies......................................... 1<o:p></o:p>1.2.1 Global Seafloor Topography Estimation<o:p></o:p>from Altimetry-Derived Gravity ........................ 1<o:p></o:p>1.2.2 Sub-Ice-Shelf Seafloor Topography Estimation<o:p></o:p>from Airborne Gravity ............................... 5<o:p></o:p>1.3 Objective ..............................................5<o:p></o:p>CHAPTER 2<o:p></o:p>Relationship Between Topography and Gravity....................... 7<o:p></o:p>2.1 Relationship in the Frequency Domain........................ 7<o:p></o:p>2.1.1 Parker’s Theory .................................... 7<o:p></o:p>2.1.2 Forsberg’s Method ..................................10<o:p></o:p>2.1.3 Relationships of Gravity Anomaly and Gravity Gradient<o:p></o:p>to Topography ..................................... 12<o:p></o:p>2.1.4 Admittance Theory ................................. 16<o:p></o:p>2.1.5 Advantages and Limitations of Using the Gravity Gradient ... 20<o:p></o:p>2.2 Relationship in the Spatial Domain........................... 21<o:p></o:p>2.2.1 The Gravitational Gradients Due to a Right Rectangular<o:p></o:p>Prism ............................................ 22<o:p></o:p>2.2.2 The Gravity Anomalies Due to a Right Rectangular Prism... 22<o:p></o:p>2.3 Errors Associated with Gradient Inversion Techniques............. 23<o:p></o:p>2.3.1 Truncation and Resolution Errors in the Forward<o:p></o:p>Computation ...................................... 23<o:p></o:p>2.3.2 Summary of Other Error Sources .......................27<o:p></o:p>CHAPTER 3<o:p></o:p>Estimation Methodology........................................ 29<o:p></o:p>3.1 Seafloor Topography Estimation Based on Fourier Transform ....... 29<o:p></o:p>3.2 Analysis of the Nonlinear Terms............................. 30<o:p></o:p>3.2.1 Validity of the Linear Approximation.................... 30<o:p></o:p>3.2.2 Introduction to the Coherency......................... 34<o:p></o:p>3.2.3 Coherency for Finite Power Signals..................... 36<o:p></o:p>3.2.4 Radially Symmetric Coherency .........................37<o:p></o:p>3.2.5 Coherency for Signals on the Sphere..................... 38<o:p></o:p>3.3 Seafloor Topography Estimation Using Simulated Annealing........ 43<o:p></o:p>3.3.1 Introduction to the Simulated Annealing................. 43<o:p></o:p>3.3.2 Seafloor Topography Estimation from Gravity Gradients..... 45<o:p></o:p>3.3.3 Seafloor Topography Estimation from Gravity Anomalies..... 46<o:p></o:p>3.4 Difference Between Simulated Annealing and Parker’s Method ...... 47<o:p></o:p>CHAPTER 4<o:p></o:p>Numerical Experiment......................................... 49<o:p></o:p>4.1 Study Area Description.................................... 49<o:p></o:p>4.2 Estimation Using Parker’s Formulation........................ 49<o:p></o:p>4.2.1 Data Preparation ...................................49<o:p></o:p>4.2.2 Data Filtering .....................................50<o:p></o:p>4.2.3 Determination of Topography-to-Gradient Admittance Scale . . 54<o:p></o:p>4.2.4 Results and Evaluation ..............................57<o:p></o:p>4.2.5 Results After Including Shorter Wavelengths.............. 59<o:p></o:p>4.3 Estimation Using Simulated Annealing........................ 61<o:p></o:p>4.3.1 Analysis of the Forward Computation in the SA........... 61<o:p></o:p>4.3.2 Data Preparation and SA Configuration................. 63<o:p></o:p>4.3.3 Results of the Simulated Annealing..................... 65<o:p></o:p>4.3.4 Low-Pass Filtering the Estimated Seafloor Topography...... 69<o:p></o:p>4.3.5 Evaluation ........................................ 69<o:p></o:p>4.3.6 Other Tests of the Simulated Annealing Algorithm......... 71<o:p></o:p>4.4 Comparison of the Estimation Results......................... 74<o:p></o:p>4.4.1 Comparison with the SIO Topography Model.............. 74<o:p></o:p>4.4.2 Comparison Between the Two Methods ..................75<o:p></o:p>4.5 Conclusions.............................................77<o:p></o:p>CHAPTER 5<o:p></o:p>Estimation from Airborne Gravity Gradients........................ 79<o:p></o:p>5.1 Airborne Gravity Gradients and Multibeam Bathymetry........... 80<o:p></o:p>5.2 Inversion Parameters...................................... 81<o:p></o:p>5.3 Analysis and Removal of the Non-Terrain Effects................ 81<o:p></o:p>5.4 Results, Evaluation, and Discussion.......................... 84<o:p></o:p>5.5 Conclusions.............................................86CHAPTER 6<o:p></o:p>Seafloor Topography Offshore Northeast Greenland................... 89<o:p></o:p>6.1 Introduction............................................ 89<o:p></o:p>6.2 Data and Methods .......................................90<o:p></o:p>6.2.1 Airborne Gravity ...................................90<o:p></o:p>6.2.2 Bathymetric Data .................................. 92<o:p></o:p>6.2.3 Inversion Parameters ................................92<o:p></o:p>6.3 Results and Evaluation.................................... 93<o:p></o:p>6.3.1 Accuracy Evaluation ................................93<o:p></o:p>6.3.2 Seafloor Topography ................................94<o:p></o:p>6.4 Discussion.............................................. 97<o:p></o:p>6.4.1 Topographic Steering of Ocean Currents................. 97<o:p></o:p>6.4.2 Errors Associated with Gravity Inversion Techniques........ 99<o:p></o:p>6.5 Conclusions.............................................100<o:p></o:p>CHAPTER 7<o:p></o:p>Seafloor Topography Beneath the Amery Ice Shelf, East Antarctica ....... 103<o:p></o:p>7.1 Introduction............................................ 103<o:p></o:p>7.2 Data and Methods .......................................105<o:p></o:p>7.2.1 Airborne Gravity ...................................105<o:p></o:p>7.2.2 Laser Altimeter and Ice-Penetrating Radar Data........... 105<o:p></o:p>7.2.3 Hydrographic Data .................................106<o:p></o:p>7.2.4 Inversion Parameters ................................106<o:p></o:p>7.3 Results ................................................107<o:p></o:p>7.3.1 New Bathymetric Model .............................107<o:p></o:p>7.3.2 Water Masses Arriving at the AmIS..................... 110<o:p></o:p>7.4 Discussion.............................................. 112<o:p></o:p>7.4.1 Topographic Steering of Ocean Currents................. 112<o:p></o:p>7.5 Conclusions.............................................113<o:p></o:p>References.................................................. 115<o:p></o:p>Appendix A: The Spherical Harmonics of the Gravity Anomaly.......... 125<o:p></o:p>Appendix B: Pseudo-Code for the Adaptive Simulated Annealing......... 127<o:p></o:p> Preface..................................................... V<o:p></o:p>About the Author............................................ VII<o:p></o:p>CHAPTER 1<o:p></o:p>Introduction................................................. 1<o:p></o:p>1.1 Background ............................................1<o:p></o:p>1.2 Previous Studies......................................... 1<o:p></o:p>1.2.1 Global Seafloor Topography Estimation<o:p></o:p>from Altimetry-Derived Gravity ........................ 1<o:p></o:p>1.2.2 Sub-Ice-Shelf Seafloor Topography Estimation<o:p></o:p>from Airborne Gravity ............................... 5<o:p></o:p>1.3 Objective ..............................................5<o:p></o:p>CHAPTER 2<o:p></o:p>Relationship Between Topography and Gravity....................... 7<o:p></o:p>2.1 Relationship in the Frequency Domain........................ 7<o:p></o:p>2.1.1 Parker’s Theory .................................... 7<o:p></o:p>2.1.2 Forsberg’s Method ..................................10<o:p></o:p>2.1.3 Relationships of Gravity Anomaly and Gravity Gradient<o:p></o:p>to Topography ..................................... 12<o:p></o:p>2.1.4 Admittance Theory ................................. 16<o:p></o:p>2.1.5 Advantages and Limitations of Using the GravityGradient ... 20<o:p></o:p>2.2 Relationship in the Spatial Domain........................... 21<o:p></o:p>2.2.1 The Gravitational Gradients Due to a Right Rectangular<o:p></o:p>Prism ............................................ 22<o:p></o:p>2.2.2 The Gravity Anomalies Due to a Right Rectangular Prism... 22<o:p></o:p>2.3 Errors Associated with Gradient InversionTechniques............. 23<o:p></o:p>2.3.1 Truncation and Resolution Errors in the Forward<o:p></o:p>Computation ...................................... 23<o:p></o:p>2.3.2 Summary of Other Error Sources .......................27<o:p></o:p>CHAPTER 3<o:p></o:p>Estimation Methodology........................................ 29<o:p></o:p>3.1 Seafloor Topography Estimation Based on FourierTransform ....... 29<o:p></o:p>3.2 Analysis of the Nonlinear Terms............................. 30<o:p></o:p>3.2.1 Validity of the Linear Approximation.................... 30<o:p></o:p>3.2.2 Introduction to the Coherency......................... 34<o:p></o:p>3.2.3 Coherency for Finite Power Signals..................... 36<o:p></o:p>3.2.4 Radially Symmetric Coherency .........................37<o:p></o:p>3.2.5 Coherency for Signals on the Sphere..................... 38<o:p></o:p>3.3 Seafloor Topography Estimation Using Simulated Annealing........ 43<o:p></o:p>3.3.1 Introduction to the Simulated Annealing................. 43<o:p></o:p>3.3.2 Seafloor Topography Estimation from Gravity Gradients..... 45<o:p></o:p>3.3.3 Seafloor Topography Estimation from GravityAnomalies..... 46<o:p></o:p>3.4 Difference Between Simulated Annealing and Parker’sMethod ...... 47<o:p></o:p>CHAPTER 4<o:p></o:p>Numerical Experiment......................................... 49<o:p></o:p>4.1 Study Area Description.................................... 49<o:p></o:p>4.2 Estimation Using Parker’s Formulation........................ 49<o:p></o:p>4.2.1 Data Preparation ...................................49<o:p></o:p>4.2.2 Data Filtering .....................................50<o:p></o:p>4.2.3 Determination of Topography-to-Gradient AdmittanceScale . . 54<o:p></o:p>4.2.4 Results and Evaluation ..............................57<o:p></o:p>4.2.5 Results After Including Shorter Wavelengths.............. 59<o:p></o:p>4.3 Estimation Using Simulated Annealing........................ 61<o:p></o:p>4.3.1 Analysis of the Forward Computation in the SA........... 61<o:p></o:p>4.3.2 Data Preparation and SA Configuration................. 63<o:p></o:p>4.3.3 Results of the Simulated Annealing..................... 65<o:p></o:p>4.3.4 Low-Pass Filtering the Estimated Seafloor Topography...... 69<o:p></o:p>4.3.5 Evaluation ........................................ 69<o:p></o:p>4.3.6 Other Tests of the Simulated Annealing Algorithm......... 71<o:p></o:p>4.4 Comparison of the EstimationResults......................... 74<o:p></o:p>4.4.1 Comparison with the SIO Topography Model.............. 74<o:p></o:p>4.4.2 Comparison Between the Two Methods ..................75<o:p></o:p>4.5 Conclusions.............................................77<o:p></o:p>CHAPTER 5<o:p></o:p>Estimation from Airborne Gravity Gradients........................ 79<o:p></o:p>5.1 Airborne Gravity Gradients and Multibeam Bathymetry........... 80<o:p></o:p>5.2 InversionParameters...................................... 81<o:p></o:p>5.3 Analysis and Removal of the Non-Terrain Effects................ 81<o:p></o:p>5.4 Results, Evaluation, and Discussion.......................... 84<o:p></o:p>5.5 Conclusions.............................................86CHAPTER 6<o:p></o:p>Seafloor Topography Offshore Northeast Greenland................... 89<o:p></o:p>6.1 Introduction............................................ 89<o:p></o:p>6.2 Data and Methods .......................................90<o:p></o:p>6.2.1 Airborne Gravity ...................................90<o:p></o:p>6.2.2 Bathymetric Data .................................. 92<o:p></o:p>6.2.3 Inversion Parameters ................................92<o:p></o:p>6.3 Results and Evaluation.................................... 93<o:p></o:p>6.3.1 Accuracy Evaluation ................................93<o:p></o:p>6.3.2 Seafloor Topography ................................94<o:p></o:p>6.4 Discussion.............................................. 97<o:p></o:p>6.4.1 Topographic Steering of Ocean Currents................. 97<o:p></o:p>6.4.2 Errors Associated with Gravity Inversion Techniques........ 99<o:p></o:p>6.5 Conclusions.............................................100<o:p></o:p>CHAPTER 7<o:p></o:p>Seafloor Topography Beneath the Amery Ice Shelf, EastAntarctica ....... 103<o:p></o:p>7.1 Introduction............................................ 103<o:p></o:p>7.2 Data and Methods .......................................105<o:p></o:p>7.2.1 Airborne Gravity ...................................105<o:p></o:p>7.2.2 Laser Altimeter and Ice-Penetrating Radar Data........... 105<o:p></o:p>7.2.3 Hydrographic Data .................................106<o:p></o:p>7.2.4 Inversion Parameters ................................106<o:p></o:p>7.3 Results ................................................107<o:p></o:p>7.3.1 New Bathymetric Model .............................107<o:p></o:p>7.3.2 Water Masses Arriving at the AmIS..................... 110<o:p></o:p>7.4 Discussion.............................................. 112<o:p></o:p>7.4.1 Topographic Steering of Ocean Currents................. 112<o:p></o:p>7.5 Conclusions.............................................113<o:p></o:p>References.................................................. 115<o:p></o:p>Appendix A: The Spherical Harmonics of the Gravity Anomaly.......... 125<o:p></o:p>Appendix B: Pseudo-Code for the Adaptive Simulated 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