Satellite Gravimetry and the Solid Earth
Mathematical Foundations
- 1st Edition - September 15, 2020
- Imprint: Elsevier
- Author: Mehdi Eshagh
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 1 6 9 3 6 - 0
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 1 6 9 3 7 - 7
Satellite Gravimetry and the Solid Earth: Mathematical Foundations presents the theories behind satellite gravimetry data and their connections to solid Earth. It covers the theor… Read more
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Request a sales quoteSatellite Gravimetry and the Solid Earth: Mathematical Foundations presents the theories behind satellite gravimetry data and their connections to solid Earth. It covers the theory of satellite gravimetry and data analysis, presenting it in a way that is accessible across geophysical disciplines. Through a discussion of satellite measurements and the mathematical concepts behind them, the book shows how various satellite measurements, such as satellite orbit, acceleration, vector gravimetry, gravity gradiometry, and integral energy methods can contribute to an understanding of the gravity field and solid Earth geophysics.
Bridging the gap between geodesy and geophysics, this book is a valuable resource for researchers and students studying gravity, gravimetry and a variety of geophysical and Earth Science fields.
- Presents mathematical concepts in a pedagogic and straightforward way to enhance understanding across disciplines
- Explains how a variety of satellite data can be used for gravity field determination and other geophysical applications
- Covers a number of problems related to gravimetry and the gravity field, as well as the effects of atmospheric and topographic factors on the data
- Addresses the regularization method for solving integral equations, isostasy based on gravimetric and flexure methods, elastic thickness, and sub-lithospheric stress
Geodesists, Geophysicists, Geologists, Seismologists, Volcanologists, Geochemists; also students and engineers in related fields
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface
- Acknowledgements
- Chapter 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
- 1.3. Solving potential from its first-order derivatives
- 1.4. Solving the potential from its second-order derivatives
- 1.5. Spectra of the potential field
- Chapter 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
- 2.4. Satellite acceleration
- 2.5. Satellite velocity
- 2.6. Inter-satellite range rate
- 2.7. Line-of-sight measurements
- 2.8. Satellite gravity gradiometry
- 2.9. Satellite altimetry data
- Chapter 3. Integral equations for inversion of satellite gravimetry data
- 3.1. Anomalous parameters of the Earth's gravity field
- 3.2. Integral equations for inversion of temporal variations of orbital elements
- 3.3. Integral inversion of acceleration and velocity of perturbations
- 3.4. Integral equations for inversion of satellite acceleration and velocity
- 3.5. Integral equations for inversion of low–low tracking data
- 3.6. Integral equations for inversion of satellite gradiometry data
- 3.7. Integral inversion of satellite altimetry data
- Chapter 4. Numerical inversion of satellite gravimetry data
- 4.1. Discretisation of integral formulae
- 4.2. Handling spatial truncation error
- 4.3. Regularisation methods
- 4.4. Sequential Tikhonov regularisation
- 4.5. Variance component estimation in ill-conditioned systems
- 4.6. Quality of integral inversion in the presence of spatial truncation error
- Chapter 5. The effect of mass heterogeneities and structures on satellite gravimetry data
- 5.1. Gravitational potential of topographic and bathymetric masses
- 5.2. Gravitational potential of crustal layers based on CRUST1.0
- 5.3. Gravitational potential of sediments
- 5.4. Gravitational potential of atmospheric masses
- 5.5. Remove–compute–restore model of topographic and atmospheric masses
- 5.6. Topographic and atmospheric bias
- Chapter 6. Isostasy
- 6.1. Isostatic equilibrium
- 6.2. Pratt–Hayford isostasy model
- 6.3. Airy–Heiskanen model
- 6.4. Flexure isostasy and the Vening Meinesz principle
- 6.5. The effect of sediment, ice and crustal masses in isostasy
- 6.6. Non-isostatic equilibriums
- Chapter 7. Satellite gravimetry and isostasy
- 7.1. Smoothing satellite gravimetry data
- 7.2. Determination of the product of Moho depth and density contrast
- 7.3. Determination of density contrast
- 7.4. Determination of lithospheric elastic thickness and rigidity
- 7.5. Determination of oceanic bathymetry
- 7.6. Continental ice thickness determination
- 7.7. Sediment basement determination
- Chapter 8. Gravity field and lithospheric stress
- 8.1. Runcorn's theory for sub-lithospheric stress modelling
- 8.2. Hager and O'Connell theory for sub-lithospheric stress modelling
- 8.3. Stress propagation from sub-lithosphere to lithosphere
- Chapter 9. Satellite gravimetry and lithospheric stress
- 9.1. Mathematical foundation based on Runcorn's formula
- 9.2. Sub-lithospheric shear stresses from satellite gradiometry data
- 9.3. Sub-lithospheric stress from vertical-horizontal satellite gravity gradients
- 9.4. Example: application of Gravity Field and Ocean Circulation Explorer data for determining sub-lithospheric shear stresses in Iran
- 9.5. Example: application of Gravity Field and Ocean Circulation Explorer and seismic data for sub-lithospheric stress modelling over Indo-Pak region
- 9.6. Example: considering lithospheric mass and structure heterogeneities to determine sub-lithospheric shear stress
- 9.7. Satellite gradiometry data and lithospheric stress tensor
- 9.8. Inter-satellite tracking data and stress
- 9.9. Determination of lithospheric stress tensor from inter-satellite tracking data
- Chapter 10. Satellite gravimetry and applications of temporal changes of gravity field
- 10.1. Time-variable gravity field
- 10.2. Hydrological effects and equivalent water height from time-variable gravity field
- 10.3. Surface mass changes over ocean and satellite gravimetry
- 10.4. Determination of land uplift caused by postglacial rebound
- 10.5. Determination of upper mantle viscosity
- 10.6. Gravity strain tensor and epicentre points of shallow earthquakes
- Index
- Edition: 1
- Published: September 15, 2020
- No. of pages (Paperback): 500
- No. of pages (eBook): 500
- Imprint: Elsevier
- Language: English
- Paperback ISBN: 9780128169360
- eBook ISBN: 9780128169377
ME
Mehdi Eshagh
Mehdi Eshagh is a Professor of Geodesy at University West in Sweden. His field of research covers satellite gravimetry with specialisation in local gravity field determination, crustal structure recovery and stress determination using gravimetric data. The subject of this book is exactly in the research field of the author and this book will be a collection of the author’s experiences in Satellite gravimetry and its applications.
Affiliations and expertise
Mehdi Eshagh, Professor of Geodesy, University West, SwedenRead Satellite Gravimetry and the Solid Earth on ScienceDirect