Modeling the Earth's Gravity Field in Space and Time

Abstract:

The Earth constantly deforms as it undergoes dynamic phenomena, such as earthquakes, post-glacial rebound and water displacement in its fluid envelopes. These processes have different spatial and temporal scales and are accompanied by mass displacements, which create temporal variations of the gravity field. Since 2002, satellite missions such as GOCE and GRACE provide an unprecedented view of the spatial and temporal variations of the Earth's gravity field. Gravity models built from these data are essential to study the Earth’s dynamic processes.

The gravity field and its time variations are usually modelled using spatial spherical harmonics functions averaged over a fixed period, as 10 days or 1 month. This approach is well suited for modeling global phenomena. To better estimate gravity variations related to local and/or transient processes, such as earthquakes or floods, and take into account the trade-off between temporal and spatial resolution resulting from the satellites sampling, we propose to model the gravity field as a four-dimensional quantity using localized functions in space and time.

For that, we first design a four-dimensional multi-scale basis, well localized both in space and time, by combining spatial Poisson wavelets with an orthogonal temporal wavelet basis. In such approach, the temporal resolution can be adjusted to the spatial one. Then, we set-up the inverse problem to model potential differences between the twin GRACE satellites in 4D, and propose a regularization using prior knowledge on the water cycle signal amplitude. We validate our 4D modelling method on a synthetic test over Africa, using synthetic data on potential differences along the orbits constructed from a global hydrological model.

A perspective of this work is to apply it on real data, in order to better model and understand the non-stationnary gravity field variations and associated processes at regional scales.