New Mathematical Tool For Icy Moon Exploration: Spherical Iterative Filtering For Gravimetric Data And The Study Case Of Ganymede

The gravitational field of a planetary body is a direct manifestation of its internal mass distribution, and the ability to decompose this signal into contributions from individual internal layers is crucial for accurate interior characterization. This is particularly relevant for icy moons, where the internal structure is thought to consist of a dense, rocky core overlain by a hydrosphere composed of a subsurface ocean and icy shells. Due to this layered configuration, large-scale gravitational anomalies are typically attributed to the deeper rocky components, while finer-scale features are often linked to the upper hydrosphere and ice shell. Through the expansion of the gravitational potential into spherical harmonics [1], the field can be interpreted as a combination of spatial frequencies, making it analysable to signal processing techniques. In this framework, the gravitational field can be viewed as a two-dimensional oscillatory signal distributed over the spherical surface of the planetary body. However, traditional signal decomposition tools, such as Fourier or wavelet transforms, are often inadequate for non-stationary, non-linear signals on spherical domains, which is where our proposed approach comes into play.

In this work, we present a novel mathematical tool called Spherical Iterative Filtering (SIF), designed specifically for the decomposition of non-stationary signals defined on spherical surfaces. The method extends the well-established Iterative Filtering (IF) algorithm, originally developed for one-dimensional time series [2], into the spherical domain. IF works by iteratively removing local averages to isolate intrinsic mode functions (IMFs), each representing a dominant oscillatory mode in the signal. Its value has been demonstrated across various disciplines [3], and its performance has been significantly enhanced via the Fast Iterative Filtering (FIF) approach, which can be guaranteed a priori convergent and whose acceleration is obtained via the so called Fast Fourier Transform [4]. SIF generalizes this decomposition strategy to spherical data, yielding what we term Intrinsic Mode Surfaces (IMSs). Unlike other techniques, SIF does not require any a priori assumptions or predefined basis functions, allowing it to adaptively separate components while preserving the inherent non-stationary characteristics of the data. This algorithm has also addressed the convergence properties of the method on the sphere in discrete settings, by leveraging the Generalized Locally Toeplitz (GLT) matrix theory, laying a solid theoretical foundation for its application in planetary sciences [5].

As a case study, we apply SIF to simulated gravimetric data of Ganymede, Jupiter’s largest moon and a prime target of ESA’s upcoming JUICE mission. This mission is expected to return high-resolution gravitational data that will be critical for probing Ganymede’s internal structure. Using an interior model of Ganymede based on current knowledge [6], we apply SIF to decompose the moon’s synthetic gravitational field and demonstrate its ability to separate contributions from the rocky core and the overlying hydrosphere. Remarkably, this decomposition is achieved in a blind fashion without any external constraints or prior information about the internal layers. Although the results presented here are based on simulated data and are subject to uncertainty, they provide a strong proof of concept. The outputs from SIF can serve as a first-order tool to constrain parameter spaces for more computationally intensive inverse methods, offering a valuable pre-processing step in planetary gravity inversion pipelines.

In summary, Spherical Iterative Filtering emerges as a powerful and flexible tool for the analysis of gravitational signals on planetary bodies, particularly those with complex, layered interiors like Ganymede. Its ability to decompose spherical, non-stationary signals in a fully data-driven way, with minimal assumptions, makes it a strong candidate for future geophysical applications in icy moon exploration and beyond.

 

Acknowledgements:
E.S.M. and G.M. acknowledge support from the Italian Space Agency (project 2023-6-HH.0). This research has been conducted within the framework of the Italian national inter-university PhD programme in Space Science and Technology.

 

References:

[1] M. A. Wieczorek, ‘Gravity and Topography of the Terrestrial Planets’, in Treatise on Geophysics, Elsevier, 2015.

[2] L. Lin, Y. Wang, and H. Zhou. Iterative filtering as an alternative algorithm for empirical mode decomposition. Adv. in Adap. Data An., 2009, 1.04, 543-560.

[3] G. Barbarino, A. Cicone. Conjectures on spectral properties of ALIF algorithm. Linear Algebra and its Applications, 2022, 647, 127-152.

[4] A. Cicone, H. Zhou. Numerical Analysis for Iterative Filtering with New Efficient Implementations Based on FFT. Num. Math., 2021, 147 (1),1-28.

[5] G. Barbarino, R. Cavassi, A. Cicone. Extension and convergence analysis of Iterative Filtering to spherical data. Lin. Alg. and its Applications, 2024.

[6] D. M. Fabrizio et al., ‘Observability of Ganymede’s gravity anomalies related to surface features by the 3GM experiment onboard ESA’s JUpiter ICy moons Explorer (JUICE) mission’, Icarus, 2021.