Neural network-based framework for gravity signal separation

Signal separation is a general problem in many geodetic datasets representing the superposition of various sources. We investigate global, temporal gravity data such as measured by the satellite missions Gravity Recovery and Climate Experiment (GRACE) and GRACE-Follow on (GRACE-FO). As gravity is an integral quantity, these data include signal components related to all kinds of geophysical processes involving a redistribution of masses in the Earth’s system. Examples for the latter are water mass redistribution processes such as seasonal hydrological variations or extreme events, as e.g. floods and droughts, but also Earthquakes or mass changes of ice sheets.

For optimally exploiting temporal gravity data regarding geophysical downstream applications, algorithms splitting up the data into the contained sub-signals are required. We attempt solving this signal separation task by training a neural network-based algorithm to recognize the individual signal components based on their typical patterns in space and time. Thereby, prior knowledge on the spatio-temporal behavior of the individual signals is introduced via forward-modeled time-variable gravity data for each of the components, as well as additional constraints.

Our algorithm is based on a multi-channel U-Net architecture which takes the sum of several signals as input and gives the retrieved individual sub-components as output. For the supervised training and subsequent testing of our software, we use a closed-loop simulation environment, working with the time-variable gravity signals given by the Updated ESA Earth System Model. The latter includes separate datasets for temporal gravity signals caused by mass change processes in the atmosphere and oceans (AO), the continental hydrosphere (H), the cryosphere (I) and the solid Earth domain (S).

For converting the global, temporal gravity data depending on the axes latitude, longitude and time to a 2-d image data format fitting the input and output layers of the U-Net, we split the data along one of its three axes to obtain latitude-longitude, latitude-time or time-longitude samples.

In a test example, we investigate the task of separating the above-mentioned AO, H, I and S components from their sum. The resulting relative RMS test errors being between 19% and 67% demonstrate that our network successfully separates the four considered signals from their sum at signal-to-noise ratios larger than 1.

In our contribution, we describe the functionalities of our software and possibilities to adapt it to any task of interest, including methods for introducing additional physical knowledge on the behavior of specific signals. In general, the described framework is applicable for signal separation in any dataset that depends on three axes (e.g., two spatial and one temporal, or three spatial axes). For the real data application of the framework, we suggest to use representative forward-modeled signals for training, and to subsequently test the trained separation model on real observational data.