## Earth’s Gravity Field Modelling

The study of the external Earth’s gravity field is one of the key pillars of modern geodesy. Knowledge of the Earth’s gravity field plays an important role in geosciences, e.g. in the study of the structure and dynamics of lithosphere, interpretation of tectonics, changes in sea levels and ocean currents, variations of hydrological conditions in larger streams, melting of icebergs in polar areas and implementation of position-reference systems.

Determining the absolute value of gravity, astronomical measurements of plumb line variations and measuring of equipotential surface curvatures using torsion balances on the Earth’s surface are considered traditional methods for determining gravity field parameters. Full spectrum of the gravity field hereby determined is the clear advantage of these traditional methods. However, their use is limited to areas offering sufficiently developed infrastructure. On local or global level, the gravity field can be determined by means of sensors placed onto airplanes and satellites. Dozens of aerial observation campaigns in polar and mountain regions and three satellite missions – CHAMP (CHAllenging Minisatellite Payload, 2000-2010), GRACE (GRAvity field and Climate Experiment, on the orbit since 2002) and GOCE (Gravity field and steady-state Ocean Circulation Explorer, 2009-2013) – have taken place so far. At the beginning of the new millennium, especially the satellite missions marked an important milestone in geodesy, leading to considerable progress in geosciences, in the global-level study of physical phenomena with 100-km spatial resolution.

The current priorities in the study of the external gravity field of the Earth are as follows:

**1. Development of Mathematical Apparatus for Gravity Field Modelling **

Until 1990s, geoid determination represented a traditional problem in geodesy, i.e. determination of the basic equipotential surface to determine heights above sea level. Theoretically, this task is based on the so-called Stokes’ integral (Stokes, 1849) to transform terrestrial scalar gravity values to geoid height above an ellipsoid. Aerial, and namely satellite data, such as scalar, vector and tensor gravitational field quantities that have become available after 2000, greatly enhance the current gravity field modelling options. Precise modelling requires new mathematical relations between gravitational field parameters.

One of the tasks of the research team is to develop a theoretical apparatus for gravity field modelling. Research team members derive new mathematical relations in the form of integral transformations (Šprlák et al., 2014, Šprlák and Novák, 2014a, b, Šprlák et al., 2015). Integral transformations enable mutual conversion of terrestrial, aerial and satellite data in the form of scalar, vector or tensor gravitational field quantities. The research efforts also include generalization of the mathematical apparatus for gravity field modelling.

**2. Utilization of Terrestrial, Aerial and Satellite Data to Model Gravity Field **

Databases of terrestrial, aerial and satellite measurements are freely available and contain dozens of millions of values. These measurements and their combinations are namely used to derive the Earth’s gravity field parameters in the form of harmonic coefficients or a digital raster. Alternatively, individual measurements or available models of the gravity field as well as other products are used to calibrate and validate aerial and satellite data.

Members of the research team namely focus on the use of satellite data for the purpose of gravity field modelling (Sebera et al., 2014, 2015). This task is solved by means of mathematical methods designed for inverse problems. Options for the validation of satellite data using the Earth’s crustal structure models (Novák and Tenzer, 2013) and measurements of sea levels (Šprlák et al., 2015) are also studied.

**3. Alternative Options of Gravity Field Mapping**

Despite considerable progress in the field of global gravity field modelling that has been seen over the past few years, new options are still being tested. One of the possible alternatives is measuring of the so-called gravitational curvatures, or third derivatives of gravitational potential. So far, observations of this kind have been carried out on the Earth’s surface as part of the Dulkyn (http://www.dulkyn.ru, Balakin et al. 1997) and Magia (Rosi et al. 2015) experiments. The first initiative for a satellite mission that would measure gravitational curvatures occurred in 2010 (Brieden et al. 2010).

Members of the research team are currently focusing on the study of properties of gravitational curvatures and development of a theoretical apparatus for the Earth’s gravity field modelling using gravitational curvatures (Šprlák and Novák 2015). Possibility of a new satellite mission is also being studied; the mission would measure gravitational curvatures on the orbit and requirements for sensor accuracy (Šprlák et al. 2015).