Note: Intro -- Preface -- Contents -- About the Editors -- Keynote -- 1 Rupture Dynamics and Seismic Radiation on Multi-scale Geometrically Complex Faults -- Abstract -- 1 Introduction -- 2 Method and Parameterization -- 3 Results -- 3.1 Dynamic Ruptures on Segmented Faults -- 3.2 Dynamic Ruptures on Rough Faults -- 3.3 Kinematic Rupture Simulations for Rough Faults -- 4 Conclusion -- References -- Applications of Gravity and Magnetic Methods -- 2 The Study of the Gravity Anomaly Maps of West and Southwestern Part of Ninawa Governorate (Iraq) -- Abstract -- 1 Introduction -- 2 Separation Methods -- 3 Results (Interpretation and Discussion) -- 3.1 Regional Gravity Anomaly Maps -- 3.2 Residual Anomaly Map -- 4 Conclusion -- References -- 3 High-Precision Gravity Measurements in Riyadh Using FGL Absolute Gravimeter -- Abstract -- 1 Introduction -- 2 Research Procedure -- 3 Adjusting ARAMCO Gravity Surveys to KSU Absolute Gravity Station -- 4 Discussion and Conclusion -- 4 Geological Evolution of the Tefedest Terrane a Recorder of a Polycyclic Pan-African Amalgamation (Central Hoggar, Algeria): Evidence from Airborne Geophysics, Remote Sensing and Field Study -- Abstract -- 1 Introduction -- 2 Data and Materials -- 3 Results -- 3.1 Remote Sensing Results -- 3.2 Airborne Geophysics Results -- 4 Discussion and Conclusion -- References -- 5 Structural Setting of Western Mali Insights from Magnetic Data Analysis -- Abstract -- 1 Introduction -- 2 Geological Setting -- 3 Methodology -- 4 Data Analysis and Interpretation -- 5 Conclusion -- References -- 6 Improved Internal Geomagnetic Field Selection Using Artificial Neural Network -- Abstract -- 1 Introduction -- 2 Methodology -- 3 Results -- 3.1 Evaluation Metrics -- 4 Discussion -- 5 Conclusion -- References. , 7 Lithospheric Structure Along a Transect from Red Sea to Arabian Shield Using a Potential Data (Gravity and Aeromagnetic Data) -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Results -- 3.1 Gravity Results -- 3.2 Aeromagnetic Results -- 4 Discussion -- 5 Conclusions -- References -- 8 Neotectonic Deformation Model of the Northern Algeria from Paleomagnetic Data: Preliminary Results from Northwestern Areas -- Abstract -- 1 Introduction -- 2 Paleomagnetic Sampling -- 3 Paleomagnetic Results -- 4 Discussion -- 5 Conclusion -- References -- 9 Geothermal Reconnaissance of Southeastern Nigeria from Analysis of Aeromagnetic Data -- Abstract -- 1 Introduction -- 2 Settings, Materials and Methods -- 3 Results -- 4 Discussion -- 5 Conclusion -- References -- Electrical and Electromagnetic Methods in Mineral and Groundwater Exploration -- 10 A Complete Solution to Self-potential Anomalies Due to 2D Inclined Sheets Using Whale Optimization -- Abstract -- 1 Introduction -- 2 Methodology -- 2.1 Problem Formulation -- 3 Results -- 3.1 Synthetic Example -- 3.2 Real Examples -- 4 Conclusions -- References -- 11 Contribution of Electrical Tomography to the Study of Landslides in Texenna Region (Northeast Algeria) -- Abstract -- 1 Introduction -- 2 Location of the Studied Area -- 3 Materials and Methods -- 4 Results and Discussion -- 5 Conclusion -- References -- 12 Effectiveness of DC Resistivity Imaging and Shallow Seismic Refraction Techniques Around El Giza-Pyramid Plateau, Egypt -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Results and Discussion -- 4 Conclusion -- References -- 13 Magnetotelluric Investigation of the Underlying Structure of Manzaz Volcanic District (Hoggar, Southern Algeria) -- Abstract -- 1 Introduction -- 2 Geological Settings -- 3 MT Data Survey, Analysis and Modeling -- 4 Discussion -- References. , 14 Characterization of Layers Saturated with Biogenic Gas Using Electromagnetic Geophysical Method -- Abstract -- 1 Introduction -- 2 Methods -- 3 Results -- 4 Discussion -- 5 Conclusion -- References -- 15 Integration of Aeromagnetic Interpretation and Induced Polarization Methods in Delineating Mineral Deposits and Basement Configuration Within Southern Bida Basin, North-West Nigeria -- Abstract -- 1 Introduction -- 2 Methodology -- 3 Results -- 4 Discussion -- 5 Summary and Conclusion -- References -- 16 Study of an Aquifer in a Semi-arid Area Using MRS, FDEM, TDEM and ERT Methods (Youssoufia and Khouribga, Morocco) -- Abstract -- 1 Introduction -- 2 Settings and Methods -- 2.1 Investigation Areas -- 2.2 Materials and Methods -- 3 Results and Discussion -- 4 Conclusion -- References -- 17 2-D Earth Resistivity Imaging for Subsurface Characterization in Srinagar, Garhwal Himalaya -- Abstract -- 1 Introduction -- 2 Methodology -- 3 Results and Discussion -- 4 Conclusions -- References -- 18 Two-Dimensional Resistivity Imaging of Migmatized Gneiss Basement Rock in Kaduna Polytechnic Main Campus, Kaduna Nigeria -- Abstract -- 1 Introduction -- 2 Data Acquisition -- 3 Results -- 4 Discussion -- 5 Conclusion -- References -- 19 2-D Resistivity Model of Magnetotelluric Inversion from M'rara Area, Algerian Sahara‏ -- Abstract -- 1 Introduction -- 2 MT Data -- 3 Dimensionality and Inversion Results -- 4 Discussion and Interpretation -- 5 Conclusions -- References -- 20 Magnetotelluric Imaging of Subsurface Structure in Rahat Volcanic Field, Madinah City (Saudi Arabia) -- Abstract -- 1 Introduction -- 2 Materials -- 3 Results -- 4 Conclusion -- References -- 21 Indices of Energy and Appraisal for Electrical Current Signal at Polarising Frequency Using Electrical Drilling: A Novel Approach -- Abstract -- 1 Introduction -- 2 Materials and Methods. , 3 Results and Discussion -- 4 Conclusion -- References -- Case Studies on Refraction and Reflection Seismic Methods -- 22 Refraction Seismic Study Over a Proposed Landfill Site in South West Bank, Palestine -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Results -- 4 Discussion -- 5 Conclusion -- References -- 23 Application of Seismic Refraction Tomography to Map Bedrock: A Case Study from Al-Amrat, Oman -- Abstract -- 1 Introduction -- 2 Methods -- 3 Results and Discussion -- 4 Conclusion -- References -- 24 Q Factor Estimation and Validation: A New Link Between VSP and Seismic Lines -- Abstract -- 1 Introduction -- 2 Method -- 3 Results -- 4 Conclusion -- References -- 25 Young's Modulus: From Core and Logging to Seismic Lines -- Abstract -- 1 Introduction -- 2 Method -- 3 Results -- 4 Conclusion -- References -- 26 Application of Varying Geometric Spreads in Seismic Refraction Studies to Characterize the Overburden Strata on the Flanks of Zaria Dam, Northwestern Nigeria -- Abstract -- 1 Introduction -- 2 Data Acquisition -- 3 Results -- 4 Discussion -- 5 Conclusion -- References -- Integrated Geoscience Applications in the Exploration of Subsurface Resources -- 27 Contribution of Tomographic Imaging in the Study of the Tabellout Dam Site, Jijel (Northeast Algeria) -- Abstract -- 1 Introduction -- 2 Geology of Tabellout Site -- 3 The Dam Site Fracturing -- 4 Geophysical Prospection -- 4.1 Equipment Used -- 4.2 At the Supports -- 4.3 At the Plate -- 4.3.1 Seismic Imaging -- 4.3.2 Electric Imaging -- 5 Conclusion -- References -- 28 Integrated Studies to Elucidate the Subsurface Structures and Groundwater at Moghra Oasis, Northwestern Desert, Egypt -- Abstract -- 1 Introduction -- 2 Geologic Setting of Moghra Lake Area -- 3 Methodology -- 4 Results -- 4.1 Stratigraphic Results -- 4.2 Results of Land Magnetic Data. , 4.3 Geoelectric Results -- 4.4 Water Quality Results -- 5 Discussion and Conclusion -- Acknowledgements -- Acknowledgements -- References -- 29 The Way to a Clearer Seismic Image: An Integrated Approach in South Tunisia Ghadames Basin -- Abstract -- 1 Introduction -- 2 Geological Settings -- 3 Major Issue -- 4 Approach and Results -- 5 Conclusion -- References -- 30 Geophysical Modeling of Contact Area Between Outer and Inner Western Carpathians (Slovakia) -- Abstract -- 1 Introduction -- 2 Geological Setting and Methods -- 3 Interpretation of Geophysical Models -- 4 Conclusion -- Acknowledgements -- References -- 31 Geothermal Resources Database in Saudi Arabia (GRDiSA) -- Abstract -- 1 Introduction -- 2 Materials -- 3 Results -- 4 Conclusion -- References -- Non-listed references -- 32 Hydrogeochemical and Geophysical Studies on the Shallow Groundwater Aquifer at New Galala City, Northern Galala Plateau, Egypt -- Abstract -- 1 Introduction -- 2 Geomorphological and Geological Setting -- 3 Geophysical and Geochemical Results -- 3.1 Aeromagnetic Data Analysis -- 3.2 Geochemical Properties of the Shallow Aquifer -- 3.3 Classification of Groundwater -- 4 Discussion -- 5 Conclusion -- References -- 33 Geophysical and Geochemical Exploration of the Gold Bearing Placer Deposits in the Southern Blue Nile (Sudan) -- Abstract -- 1 Introduction -- 2 Electrical Resistivity Tomography Survey -- 2.1 ERT Fieldwork -- 2.2 ERT Results and Interpretation -- 3 Geochemical Survey -- 4 Discussion of Results -- 5 Conclusion -- Acknowledgements -- References -- Hydrocarbon and Petrophysical Studies -- 34 Halokinetic Activities and Structural Style in the Jeffara Basin (Tunisia): Implication for Hydrocarbon Prospectivity -- Abstract -- 1 Introduction -- 2 Geodynamic Evolution -- 3 Methodology -- 4 Results -- 5 Discussion -- 6 Conclusion -- References. , 35 Gas Hydrates Potential of Makran Area, Offshore Pakistan.

Note: Intro -- About the 2nd Springer Conference of the Arabian Journal of Geosciences (CAJG-2), Tunisia 2019 -- Proceedings Volume 1: New Prospects in Environmental Geosciences and Hydrogeosciences -- Proceedings Volume 2: Advances in Geophysics, Tectonics and Petroleum Geosciences -- Proceedings Volume 3: Recent Research on Geomorphology, Sedimentology and Geochemistry -- Proceedings Volume 4: Research developments in Geotechnics, Geo-Informatics and Remote Sensing -- About the Conference Steering Committee -- Preface -- Contents -- About the Editors -- Earthquake Seismology and Geodesy (T3): IGCP-659 Meeting-Seismic Hazard and Risk Assessment in Africa -- 1 Tsunami Hazard Along the Eastern African Coast from Mega-Earthquake Sources in the Indian Ocean -- Abstract -- 1 Introduction -- 2 Earthquake Sources and Hydrodynamic Simulations -- 3 Results -- 4 Conclusions -- References -- 2 Preliminary Tsunami Hazard Map for Africa -- Abstract -- 1 Introduction -- 2 Methodology -- 3 Results -- 4 Discussion -- 5 Conclusions -- References -- 3 The AD 365 Crete Earthquake/Tsunami Submarine Impact on the Mediterranean Region -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Results -- 4 Discussion -- 5 Conclusions -- References -- 4 The AD 365 Alexandria (Egypt) Tsunami, Revisited -- Abstract -- 1 Introduction -- 2 Evaluation of the Tsunami Model Predictions -- 3 Revisiting Historical Sources -- 3.1 Alexandria -- 3.2 Methoni -- 4 Discussion -- Acknowledgements -- References -- 5 Seismotectonics of the Easternmost Cyprus Arc: Implications for Tsunami Hazard Assessment -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Results -- 4 Discussion -- 5 Conclusions -- References -- 6 Seismic Hazard and Risk in Africa, a Hidden Hazard in an Extreme Vulnerable Context -- Abstract -- 1 Introduction -- 2 The SEISMOSHAF Project. , 3 Implementation Strategy -- References -- 7 Seismotectonics of the Khurutse Region, Botswana -- Abstract -- 1 Introduction -- 2 Results -- 3 Discussion and Conclusion -- References -- 8 Kinematic and Elastic Modeling of Fault-Related Folds: Examples from Active Structures of the Tell Atlas (Northern Algeria) -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Analysis and Results -- 4 Discussion and Conclusion -- References -- 9 Magmatic Rifting and Seismicity in Afar and Northern Main Ethiopian Rift (MER) -- Abstract -- 1 Introduction -- 2 Methods -- 3 Results -- 3.1 Results (Earthquake Swarms) -- 3.2 Results (Frequency Time Analysis) -- 4 Discussion -- 5 Conclusions -- References -- 10 Architecture and Evolution of the Kivu Rift Within the Western Branch of the East African Rift System: Implications for Seismic Hazard Assessment -- Abstract -- 1 Introduction -- 2 Geological and Neotectonic Evolution -- 3 Seismic Hazard Evaluation -- 4 Discussion/Conclusion -- References -- 11 Stress Transfer and Poroelasticity Associated to Major Earthquakes: From the East African Rift to the African-Eurasian Plate Boundary -- Abstract -- 1 Introduction -- 2 Stress Modeling and Fault Interaction -- 3 Results -- 4 Conclusion -- References -- 12 Seismic Risk in Ghana: Efforts and Challenges -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Discussions -- 4 Conclusions -- References -- 13 Toward an African Seismological Data Center -- Abstract -- 1 Introduction -- 2 Methodology -- 3 Discussion -- References -- 14 An Overview of the Seismic Hazard in Sudan -- Abstract -- 1 Introduction -- 2 Method -- 3 Results -- 4 Discussion and Conclusion -- References -- 15 Seismic Hazard Assessment in Kenya and Its Vicinity -- Abstract -- 1 Introduction -- 2 Material and Method -- 3 Results and Discussion -- 4 Conclusion -- References. , 16 Probabilistic Seismic Hazard Assessment for the Main Cities Along the Continental Section of the Cameroon Volcanic Line -- Abstract -- 1 Introduction -- 2 Data and Methods -- 3 Results -- 3.1 Earthquake Catalogue of CVL -- 3.2 Seismic Source Zones and Seismicity Models -- 3.3 Ground Motion Prediction Equations (GMPE) -- 3.4 Seismic Hazard Along the CVL -- 4 Discussion -- 5 Conclusions -- References -- 17 Assessing Seismic Hazard for the Democratic Republic of Congo and Its Vicinity Based on New Seismic Zoning Source Model -- Abstract -- 1 Introduction -- 2 Methodology -- 2.1 Declustering and Assessment of the Completeness of the Earthquake Catalogue -- 2.2 Seismic Source Zoning and Seismicity Analysis -- 2.3 Ground Motion Prediction Equations and Hazard Computation -- 3 Results -- 4 Discussion, Conclusion and Recommendations -- References -- 19 AEON Transdisciplinary Natural Baseline in the Karoo (South Africa) -- Abstract -- 1 Introduction -- 2 Transdisciplinary Baseline in the Karoo -- 3 Deep and Shallow Aquifer Connectivity as Early Warning Systems -- 4 Geophysical Probing of the Critical Zone -- 4.1 Airborne Magnetic Mapping of Subsurface Structures -- 4.2 Ambient Noise Imaging and Micro-Earthquake Monitoring -- 4.3 Deep Conductive Horizons Imaging Using Natural Earth's Electrical Currents and Magnetism -- 5 Discussion and Conclusions -- References -- Earthquake Geodesy -- 20 Active Deformation in Tunisia from Continuous GPS Data -- Abstract -- 1 Introduction -- 2 Neotectonic Setting -- 3 Results -- 4 Discussion and Conclusion -- References -- 21 Active Deformation in Northern Algeria from Continuous GPS Measurements and Recent Seismic Data -- Abstract -- 1 Introduction -- 2 Data Acquisition and Processing -- 3 Results -- 4 Implication to Seismic Hazard Assessment -- 5 Discussion-Conclusion -- References. , 22 How InSAR Can Help on the Seismic Hazard Assessment -- Abstract -- 1 Introduction -- 2 Methods -- 3 Results -- 4 Discussion and Conclusions -- References -- 23 Surface Deformation Monitoring from SAR Interferometry for Seismic Hazard Assessment Around Major Active Faults: Case of Zemmouri Earthquake (Algeria) -- Abstract -- 1 Introduction -- 2 Data Analysis and Processing -- 3 Results and Discussion -- 4 Conclusions -- References -- 24 The Use of an ELMI for Measuring the Movement of the Trougout and the Ajdir-Imzouren Faults-(North East of the RIF) MOROCCO-Between 2017 and 2019 -- Abstract -- 1 Introduction -- 2 Study Area -- 3 Methodology -- 4 Result and Discussion -- 5 Conclusion -- Acknowledgements -- References -- 25 Land and Sea Earthquakes Triggered by Groundwater Fluctuation Due to the Hydrologic Cycle in South Korea -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Results -- 3.1 Comparison of Earthquakes Between Lands and Seas -- 3.2 Rainfall, Groundwater and Earthquakes -- 4 Conclusions -- Acknowledgements -- References -- Seismotectonics, Archeoseismology and Active Faulting -- 26 Advances in Archaeoseismology -- Abstract -- 1 Introduction -- 2 Concept and Methods -- 3 Examples -- 3.1 Precariously Balanced Archaeological Structures -- 3.2 Adapted Building Techniques -- 3.3 Earthquake Source Parameters -- 4 Discussion -- 5 Conclusions -- References -- 27 Possible Tectonic Styles of Future Earthquakes from Seismic Moment Tensors of Previous Events: An Example in Italy -- Abstract -- 1 Introduction -- 2 Computational Method -- 3 Discussion and Conclusions -- References -- 28 Stress Transferred by the May 2010 Beni-Ilmane Seismic Sequence -- Abstract -- 1 Introduction -- 2 Coulomb Stress Changes -- 3 Stress Change Following the First Shock -- 4 Stress Change Following the First and Second Shocks. , 5 Coulomb Stress Change and Aftershocks' Sequence -- 5.1 Aftershocks' Sequence Between the Second Shock and the Third Shock -- 6 Discussion and Conclusion -- References -- 29 Contribution of the Pleiade Satellite Image Processing in the Characterization of the Active and Seismogenic Structures in the Tell Atlas (Northern Algeria) -- Abstract -- 1 Introduction -- 2 Materials and Methods -- 3 Results (Presentation of Some Examples) -- 4 Discussion and Conclusion -- References -- 30 Historical and Archeoseismic Investigations in Kairouan Region (Central Tunisia): Evidence for the 9 October 859 AD Large Earthquake -- Abstract -- 1 Introduction -- 2 The 9th of October, 859 Earthquake -- 3 Results -- 4 Conclusions -- References -- Old References -- Recent References -- 31 Algerian's Seismic Catalogue Completeness from Historical Instrumental Monitoring, Archeoseismological and Paleoseismological Studies -- Abstract -- 1 Introduction -- 2 Historical and Archeoseismological Investigations -- 3 Results -- 3.1 New Historical Seismic Events -- 3.2 Damage Observed on Archeological Structures -- 3.3 Paleoseismological Observations -- 4 Conclusion -- References -- 32 Analysis of the Bejaia Seismic Sequence of 2012-2013, Northeastern, Algeria -- Abstract -- 1 Introduction -- 2 Seismotectonic Settings -- 3 Aftershocks Relocation and Focal Mechanisms' Determination -- 4 Discussion -- 5 Conclusions -- References -- 33 The Hammam Melouane Seismic Sequences (North Algeria) 2014-2016 -- Abstract -- 1 Introduction -- 2 Data Acquisition and Processing -- 2.1 Aftershocks' Analysis of the Sub-sequences -- 3 Results and Discussion -- 4 Conclusions -- References -- 34 Statistical Study of Earthquake Swarms in Northeastern Algeria with Special Reference to the Ain Azel Swarm -- Hodna Chain, 2015 -- Abstract -- 1 Introduction -- 2 Scientific Background, Data and Methodology. , 3 Analysis and Results.

Note: Front Cover -- SATELLITE GRAVIMETRY AND THE SOLID EARTH -- SATELLITE GRAVIMETRY AND THE SOLID EARTH -- Copyright -- Contents -- Preface -- Acknowledgements -- 1 - Spherical harmonics and potential theory -- 1.1 General solution of Laplace equation in spherical coordinates -- 1.2 Solving potential from potential outside the earth -- 1.2.1 Spectral solution -- 1.2.2 Solving Dirichlet's problem -- 1.3 Solving potential from its first-order derivatives -- 1.3.1 Solving potential from its radial derivative -- 1.3.1.1 Spectral solution -- 1.3.1.2 Spatial solution -- 1.3.1.3 Integral equation -- 1.3.1.4 Solving the potential from a linear combination of the potential and its radial derivative -- 1.3.1.5 Spectral solution -- 1.3.1.6 Spatial solutions -- 1.3.1.7 Integral equation -- 1.3.2 Solving the potential from its gradients -- 1.3.2.1 Vector spherical harmonics -- 1.3.2.2 Spectral solutions -- 1.3.2.3 Spatial solutions -- 1.3.2.4 Integral equations -- 1.4 Solving the potential from its second-order derivatives -- 1.4.1 Tensor spherical harmonics -- 1.4.2 Spectral solutions -- 1.4.3 Spatial solutions -- 1.4.4 Integral equations -- 1.4.5 Product of a spherical harmonic series -- 1.5 Spectra of the potential field -- 1.5.1 Global spectra of the potential -- 1.5.1.1 Global first- and second-order radial derivatives of the potential -- 1.5.1.2 Global horizontal derivatives and vertical-horizontal derivatives of the potential -- 1.5.1.3 Global spectra of horizontal-horizontal derivatives of the potential -- 1.5.2 Local spectra of the potential -- 1.5.2.1 Local spectra of the potential based on the product of spherical harmonics and the Gaunt coefficient -- 1.5.2.2 Local spectra of the potential based on SjOberg's approach -- References -- 2 - Satellite gravimetry observables -- 2.1 Satellite orbit and the Earth's gravitational potential. , 2.2 Geometry of orbit and geopotential perturbation -- 2.3 Orbital elements -- 2.3.1 Lagrange equations -- 2.3.2 Gaussian equations -- 2.3.3 Velocity and acceleration of the perturbations -- 2.4 Satellite acceleration -- 2.5 Satellite velocity -- 2.6 Inter-satellite range rate -- 2.6.1 Approach 1 -- 2.6.2 Approach 2 -- 2.7 Line-of-sight measurements -- 2.8 Satellite gravity gradiometry -- 2.9 Satellite altimetry data -- References -- 3 - Integral equations for inversion of satellite gravimetry data -- 3.1 Anomalous parameters of the Earth's gravity field -- 3.1.1 Normal gravity field and disturbing potential -- 3.1.2 Geoid height, gravity disturbance and anomaly as anomalous quantities -- 3.1.3 Deflections of the vertical -- 3.1.4 From geoid height to other anomalous parameters -- 3.1.5 From gravity disturbance/anomaly and deflections of the vertical to geoid height -- 3.1.6 Integral relations amongst gravity disturbance/anomaly and deflections of the vertical -- 3.2 Integral equations for inversion of temporal variations of orbital elements -- 3.2.1 Integral equations for recovering gravity anomaly/disturbance from temporal variations of orbital elements -- 3.2.2 Integral equations for inverting combination of Gaussian equations for gravity disturbance/anomaly recovery -- 3.3 Integral inversion of acceleration and velocity of perturbations -- 3.4 Integral equations for inversion of satellite acceleration and velocity -- 3.4.1 Inversion of satellite acceleration in the terrestrial reference frame -- 3.4.2 Inversion of satellite velocity in the terrestrial reference frame -- 3.5 Integral equations for inversion of low-low tracking data -- 3.5.1 Integral equations for inversion of range rates -- 3.5.2 Integral equations for inversion of line-of-sight measurements -- 3.6 Integral equations for inversion of satellite gradiometry data. , 3.6.1 Integral equations for inversion of gravity gradients in the local north-oriented frame -- 3.6.2 Integral equations for inversion of gravity gradients in the track-oriented frame -- 3.7 Integral inversion of satellite altimetry data -- 3.7.1 Determination of gravity anomaly/disturbance from altimetry geoid heights and deflections of the vertical -- 3.7.2 Determination of gravity anomaly/disturbance from altimetry-derived deflections of the vertical -- 3.7.3 Integral inversion of geoid and deflections of the vertical -- 3.7.3.1 Integral equations for inversion of altimetry geoid heights -- 3.7.3.2 Integral equations for inversion of altimetry deflections of the vertical -- References -- 4 - Numerical inversion of satellite gravimetry data -- 4.1 Discretisation of integral formulae -- 4.1.1 Numerical solution of integrals -- 4.1.2 Kernels of integrals -- 4.1.2.1 Well-behaving kernels -- 4.1.2.2 Bell-shaped kernels -- 4.1.3 Numerical inverse solution of integrals -- 4.2 Handling spatial truncation error -- 4.2.1 Estimation of spatial truncation error based on the integral and spherical harmonics -- 4.2.2 Estimation of spatial truncation error based on spherical harmonics -- 4.2.3 Size of the inversion area and spatial truncation error -- 4.2.4 Example: spatial truncation error of satellite gradiometry data -- 4.2.5 Example: spatial truncation error in the results of inversion of satellite inter-satellite tracking data -- 4.2.6 Example: inversion of Trr to Δg -- 4.2.7 Example: inversion of orbital data to gravity anomaly -- 4.3 Regularisation methods -- 4.3.1 Gauss-Markov model -- 4.3.2 A conceptual overview of regularisation methods -- 4.3.2.1 Iterative methods -- 4.3.2.1.1 Classical iterative methods -- 4.3.2.1.1.1 The ν method -- 4.3.2.1.1.2 Algebraic reconstruction technique -- 4.3.2.1.2 Krylov subspaces-based methods. , 4.3.2.1.2.1 Range-restricted generalised minimum residual method -- 4.3.2.1.2.2 Conjugate gradient -- 4.3.2.2 Estimation of the optimal iteration number by L-curve -- 4.3.2.3 Example: application of the iterative methods for determining equivalent water height from the GRACE mission -- 4.3.3 Direct methods -- 4.3.3.1 Truncated singular value decomposition -- 4.3.3.2 Tikhonov regularisation -- 4.3.3.3 Generalised cross validation -- 4.3.3.4 Example: application of the TSVD and Tikhonov regularisation methods for determining equivalent water height from the GRACE ... -- 4.3.3.5 Example: inversion of on-orbit satellite gradiometry data in the local north-oriented frame and orbital reference frame -- 4.3.3.6 Example for bias corrections and estimation of a posteriori variance factor -- 4.4 Sequential Tikhonov regularisation -- 4.4.1 Example: application of sequential Tikhonov regularisation -- 4.5 Variance component estimation in ill-conditioned systems -- 4.5.1 Best quadratic unbiased estimator of variance component in ordinary systems -- 4.5.2 Best quadratic unbiased estimator of variance component in a system solved by truncated singular value decomposition -- 4.5.3 Best quadratic unbiased estimator of the variance components in systems solved by Tikhonov regularisation -- 4.5.4 Example: variance component estimation for inverting satellite gravity gradients -- 4.6 Quality of integral inversion in the presence of spatial truncation error -- 4.6.1 Reduction of spatial truncation error from the a posteriori variance factor -- 4.6.2 Reduction of spatial truncation error from variance components -- References -- 5 - The effect of mass heterogeneities and structures on satellite gravimetry data -- 5.1 Gravitational potential of topographic and bathymetric masses -- 5.1.1 Gravitational potential of topographic masses. , 5.1.1.1 Approach 1 to consider lateral density variation of topographic masses -- 5.1.1.2 Approach 2 to consider lateral density variation of topographic masses -- 5.1.1.3 Gravitational potential of the bathymetric masses (water) -- 5.2 Gravitational potential of crustal layers based on CRUST1.0 -- 5.3 Gravitational potential of sediments -- 5.3.1 Gravitational potential of sediments based on the CRUST1.0 model -- 5.3.2 Gravitational potential of sediments based on density models -- 5.3.3 Sediments' gravitational potential based on the exponential density contrast model -- 5.3.3.1 Approach 1 -- 5.3.3.2 Approach 2 -- 5.3.4 Sediments' gravitational potential based on the hyperbolic density contrast model -- 5.3.5 Sediments' gravitational potential based on the exponential compaction density model -- 5.3.6 Example: the effect of upper sediments based on different density models on satellite gradiometry data -- 5.4 Gravitational potential of atmospheric masses -- 5.4.1 Gravitational potential of atmospheric masses according to the exponential density model -- 5.4.2 Gravitational potential of atmospheric masses according to the power density model -- 5.4.3 Gravitational potential of atmospheric masses according to the polynomial density model -- 5.4.4 Gravitational potential of atmospheric masses according to a combination of the polynomial and power density models -- 5.4.5 Example: atmospheric effect on satellite gradiometry data -- 5.5 Remove-compute-restore model of topographic and atmospheric masses -- 5.5.1 Restoring the topographic effect -- 5.5.2 Restoring the atmospheric effect -- 5.6 Topographic and atmospheric bias -- References -- 6 - Isostasy -- 6.1 Isostatic equilibrium -- 6.2 Pratt-Hayford isostasy model -- 6.2.1 Pratt-Hayford isostatic model based on gravitational potential in the spherical domain. , 6.2.2 Approximate solution in spherical harmonics.