Preface

Geodesy covers a broad range of applications related to the Earth and its dynamic phenomena, and it relies on well-established theories with mathematical formulations for generating solutions and models in analyzing and explaining the Earth phenomena. According to this perspective, geodesy is an applied science based on strong theoretical foundations that serves many other science and engineering disciplines for a better and sustainable future in the world. In the twenty-first century, technological developments, in particular the artificial satellites, have led the unprecedented progress in observation techniques and have expanded the possibilities in the fields of geodesy for observing and analyzing the Earth as a whole in detail with much higher precision. These developments in technology not only led to the advancement of measurement and data acquisition techniques but also to the more rigorous application of the theory through powerful computers and processors. All these developments in theory and practice influenced each field of Geodesy, and it began to provide improved outputs that would serve humanity's future.

In this collection, eight chapters provide a detailed overview of the recent developments lived in the Geodetic Science and its theory and applications, through the selected case studies and their investigation fields. In this way, a picture was depicted from the last point reached in the main fields of Geodetic Science including Earth gravity field, sea level investigations, navigation satellites' data evaluations, and continental-scale tectonic investigations. The following paragraphs refer to some of the research issues that are currently under investigation in Geodesy. The research topics mentioned are those that have been investigated and exemplified in the chapters of this book.

Gravity inversion provides a useful tool for investigating the Earth's interior, and static gravity observations are mainly used to determine the lithosphere density distribution or the Moho depth. In this manner, global geopotential models derived from the Earth gravity field satellite missions' data contribute to these investigations on a global scale, and in the regions without terrestrial data such as the polar areas. The satellite missions Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On also provide gravity observations with a high temporal resolution, which are being used to model the geophysical phenomena such as the glacial isostatic adjustment and seismic and volcanic events, and for carrying out hydrological research such as drought monitoring. However, since the gravity inversion includes numerical instability, independent data such as seismic data or GNSS-derived vertical deformations are additionally required to constrain the solutions, and the methodological contributions are essentially required for the modeling and better understanding of the Earth's interior and related processes.

Precise modeling of the regional and global static gravity field and the geoid with the high-spatial-resolution is another research issue and essential for a broad range of scientific and engineering applications. For this purpose, terrestrial, marine, and airborne gravity data, in addition to the satellite-based data, are used. In this field, the launch of dedicated satellite missions such as GRACE and GOCE and

the improvements in satellite radar altimetry are breakthrough accomplishments, and they have an essential role in the unprecedented improvement in accuracy and spatial resolutions of the calculated models. Also crucial is the information coming from digital topography/bathymetry models. The improvements of the elevation and bathymetry models make an important contribution to the precise gravity field and geoid determination, as well as the use of forward modeling techniques for estimating the realistic densities and unknown sub-ice terrains in polar areas. Although the methodologies of use and computations of the terrain effects have already been well-formulated so far, there is still a need for justifications to explain differences between the approximations and their consequences for precise cm-level geoid determination, and the computation of the high-resolution global models of the topographic or topographic-isostatic potential.

Besides the progress in the modeling of the static gravity field, it has become possible to determine its temporal variations with high accuracy and resolution related to the mass transport and the physical processes within the Earth's system such as ocean circulation, hydrological cycle, postglacial rebound, and gravity change as a result of a strong earthquake. Although the dedicated satellite gravimetry missions on estimating the time-varying gravity field continue to evolve with the successors, temporal and spatial resolutions of their observations are still currently insufficient to meet the demand of the hydrological studies. Therefore, new data evaluation strategies and algorithms are required to investigate the hydrological signals. Besides more developed algorithms, other space techniques including altimeter, GNSS, and interferometric synthetic-aperture radar are used to complement the satellite gravimetry for more detailed analyses of the consequences that stem from the hydrological mass loading or groundwater depletion, etc. Thus, the combination of various geodetic observation techniques at different spatiotemporal scales yields further opportunities for deeper and more detailed analyses of global and regional water cycling and climate change.

In addition to the satellite gravimetry, the developments in satellite altimeter techniques lead possibilities to perform more detailed investigations with improved products at global seas as well as at coastal areas and inland water bodies (SAR/SARIn altimetry). Satellite altimetry with the complementary data makes an essential contribution to monitoring the near-global ocean surface topography, thus improving the knowledge of oceanography, marine geodesy, and geophysics, as well as their roles in climate. The evaluation results of satellite altimetry data are used to clarify regional (even in very small water bodies and areas very close to the shore) and global sea-level changes, surface currents, mesoscale circulation and variability, wind speeds and wave heights, marine gravity field, geoid, mean sea surface, mean dynamic topography, seafloor topography, vertical height datum, as well as the land vertical deformations.

The experienced developments have not only been in the Earth gravity field investigations branch of geodesy but also the global navigation satellite systems and their related applications have noticeable improvements. As a consequence of the developments, new fields such as GNSS meteorology are constituted where the navigation signal has benefited different purposes. In these fields, rather than considering the atmosphere as an error source for the GNSS signals, the geodetic measurements including the GNSS, satellite altimetry, VLBI, SLR, and DORIS are considered valuable data sources for understanding and analyzing the state and dynamics of the atmosphere. From this point of view, real-time observations

**V**

have the potential to evolve for monitoring and forecasting the ionospheric state and to optimize ultrafast tropospheric products. All the developments in this area lead to improvements in all application areas where the GNSS position is used.

These are the highlights of the topics, which are currently studied in the field of geodesy. Regarding these highlights and pointed research topics, this book aims to provide a useful reference for the researchers and practitioners who are working in

> **Bihter Erol and Serdar Erol** Istanbul Technical University,

> > Istanbul, Turkey

the field of geodesy and its multidisciplinary fields.

have the potential to evolve for monitoring and forecasting the ionospheric state and to optimize ultrafast tropospheric products. All the developments in this area lead to improvements in all application areas where the GNSS position is used.

These are the highlights of the topics, which are currently studied in the field of geodesy. Regarding these highlights and pointed research topics, this book aims to provide a useful reference for the researchers and practitioners who are working in the field of geodesy and its multidisciplinary fields.

> **Bihter Erol and Serdar Erol** Istanbul Technical University, Istanbul, Turkey

**IV**

the improvements in satellite radar altimetry are breakthrough accomplishments, and they have an essential role in the unprecedented improvement in accuracy and spatial resolutions of the calculated models. Also crucial is the information coming from digital topography/bathymetry models. The improvements of the elevation and bathymetry models make an important contribution to the precise gravity field and geoid determination, as well as the use of forward modeling techniques for estimating the realistic densities and unknown sub-ice terrains in polar areas. Although the methodologies of use and computations of the terrain effects have already been well-formulated so far, there is still a need for justifications to explain differences between the approximations and their consequences for precise cm-level geoid determination, and the computation of the high-resolution global

Besides the progress in the modeling of the static gravity field, it has become possible to determine its temporal variations with high accuracy and resolution related to the mass transport and the physical processes within the Earth's system such as ocean circulation, hydrological cycle, postglacial rebound, and gravity change as a result of a strong earthquake. Although the dedicated satellite gravimetry missions on estimating the time-varying gravity field continue to evolve with the successors, temporal and spatial resolutions of their observations are still currently insufficient to meet the demand of the hydrological studies. Therefore, new data evaluation strategies and algorithms are required to investigate the hydrological signals. Besides more developed algorithms, other space techniques including altimeter, GNSS, and interferometric synthetic-aperture radar are used to complement the satellite gravimetry for more detailed analyses of the consequences that stem from the hydrological mass loading or groundwater depletion, etc. Thus, the combination of various geodetic observation techniques at different spatiotemporal scales yields further opportunities for deeper and more detailed analyses of global and regional

In addition to the satellite gravimetry, the developments in satellite altimeter techniques lead possibilities to perform more detailed investigations with improved products at global seas as well as at coastal areas and inland water bodies (SAR/SARIn altimetry). Satellite altimetry with the complementary data makes an essential contribution to monitoring the near-global ocean surface topography, thus improving the knowledge of oceanography, marine geodesy, and geophysics, as well as their roles in climate. The evaluation results of satellite altimetry data are used to clarify regional (even in very small water bodies and areas very close to the shore) and global sea-level changes, surface currents, mesoscale circulation and variability, wind speeds and wave heights, marine gravity field, geoid, mean sea surface, mean dynamic topography, seafloor topography, vertical height datum, as well as the land vertical deformations.

The experienced developments have not only been in the Earth gravity field investigations branch of geodesy but also the global navigation satellite systems and their related applications have noticeable improvements. As a consequence of the developments, new fields such as GNSS meteorology are constituted where the navigation signal has benefited different purposes. In these fields, rather than considering the atmosphere as an error source for the GNSS signals, the geodetic measurements including the GNSS, satellite altimetry, VLBI, SLR, and DORIS are considered valuable data sources for understanding and analyzing the state and dynamics of the atmosphere. From this point of view, real-time observations

models of the topographic or topographic-isostatic potential.

water cycling and climate change.

**Chapter 1**

Geophysics

*Mehdi Eshagh*

**Abstract**

change, viscosity

**1. Introduction**

**1**

The Earth's Gravity Field Role in

The Earth gravity field is a signature of the Earth's mass heterogeneities and structures and applied in Geodesy and Geophysics for different purposes. One of the main goals of Geodesy is to determine the physical shape of the Earth, geoid, as a reference for heights, but Geophysics aims to understand the Earth's interior. In this chapter, the general principles of geoid determination using the well-known methods of Remove-Compute-Restore, Stokes-Helmert and least-squares modification of Stokes' formula with additive corrections are shortly discussed. Later, some Geophysical applications like modelling the Mohorovičić discontinuity and density contrast between crust and uppermantle, elastic thickness, ocean depth, sediment and ice thicknesses, sub-lithospheric and lithospheric stress, Earthquakes and epicentres, post-glacial rebound, groundwater storage are discussed. The goal of

this chapter is to briefly present the roll of gravity in these subjects.

formula with addition corrections (LSMSF) [3] are presented.

**Keywords:** bathymetry, earthquake, geoid height, groundwater, ice thickness, Moho discontinuity, post-glacial rebound, sediment basement, stress, sea level

The Earth's gravity field reflects of the Earth's interior and is an interesting subject in Geodesy and Geophysics with various applications. Geodesy aims to determine three types of the shape and size of the Earth, the Earth's surface, geoid as the physical shape, reference ellipsoid as the mathematical one. Physical Geodesy deals with determination of the physical shape of the Earth or the geoid, which is a reference for heights, from gravimetric data. In this chapter, short descriptions of three known methods of geoid determination such as Remove-Compute-Restore (RCR) [1], Stokes-Helmert (SH) [2] and least-squares modification of the Stokes

In Geophysics, understanding the Earth's physics, dynamics and interior geometry is of interest using such data. Gravity measurements can be analysed over small or large area depending on the geophysical purpose. For instance, in exploration Geophysics they are used to detect or discover near surface resources and for such a goal precision and accuracy of these data should be high. Here, such applications are named small-scale Geophysics. However, understanding or studying the deep Earth's interior physics, dynamics or geometry does not require high spatial

Geodesy and Large-Scale
