Toward mapping the effective elastic thickness of planetary lithospheres from a spherical wavelet analysis of gravity and topography

• Reviews developments in elastic thickness estimation using gravity and topography.
• Shows that planar and spherical formulations are equivalent.
• Proposes to use fully spherical techniques to avoid edge effects.
• Presents a preliminary analysis of terrestrial planets.
• Discusses limitations and future directions of research in this field.

The effective elastic thickness (Te)(Te) of the lithosphere controls the flexural response to transverse loading and can be used in conjunction with rheological models to remotely estimate surface heat flux of terrestrial planets. In the vast majority of studies, TeTe estimation is carried out in a two-step process: (1) the joint spectra (admittance and/or coherency) of gravity anomalies (free air and/or Bouguer) and topography are calculated within finite-size windows, and (2) the spectra are inverted using a model for the loading of an infinite elastic plate or shell. In recent years, research in the spatio-spectral analysis of Cartesian grids and improvements in lithospheric loading models have allowed the mapping of TeTe on the Earth at unprecedented resolution. Nevertheless, the limitations imposed by working with Cartesian data and models are hampering further advances in terrestrial TeTe studies. The planetary community, on the other hand, has traditionally used spatio-spectral methods that work directly on the sphere, thereby avoiding the undesirable distortions and biases inherent in Cartesian studies. However, the models and methods developed for the Earth have never been applied to planetary data, therefore also limiting further advances in the mapping of planetary TeTe. This paper reviews the latest developments in TeTe studies and proposes to combine advances in both terrestrial and planetary studies to allow the mapping of TeTe of terrestrial planets using a spherical wavelet analysis of gravity and topography data. We begin with a review of the recent literature on the challenges and debates concerning TeTe estimation from joint gravity and topography spectra. We then briefly review the implementation of the continuous planar and spherical wavelet transforms (CPWT and CSWT) and demonstrate that both transforms possess exactly the same resolving power, however the CSWT does not suffer from effects associated with non-periodic boundaries. We further re-derive, in a consistent manner, the expressions for the admittance and coherency from flexural equations for the loading of thin elastic plates and shells and show that they result in similar spectra, except at the longest wavelengths where the shell membrane stresses dominate. We then estimate global grids of Earth’s continentalTeTe by inverting the planar and spherical admittance and coherency functions, both separately and jointly, using either free air or Bouguer gravity anomalies. The correspondence between the Cartesian and spherical approaches and the similarity of TeTe results for the Earth’s continents indicate that the spherical methods are robust. Results obtained from the joint inversion of admittance and coherency show that simple lithospheric loading models fail to capture the complexity of the data, with adverse effects on the estimated parameters. Finally, we extend the analysis to the Moon and other terrestrial planets and discuss limitations and future applications of the fully spherical techniques.