Directional wavelet analysis on the sphere: Application to gravity and topography of the terrestrial planets
Abstract
The spectral relations (admittance and correlation) between gravity and topography are often used to obtain information on the density structure, flexural support, and heat flow of planetary lithospheres. Mapping spatial variations in these quantities requires spatiospectral analysis techniques. Here we describe the application of a directional, continuous spherical wavelet transform using a wavelet basis constructed from the superposition of azimuthally adjacent complex Morlet wavelets, in a manner similar to the “fan” wavelet developed in the plane. The method is applied to gravity and topography of the Earth, Venus, Mars, and the Moon. The wavelet coefficients are used to compute isotropic and directional wavelet autospectra and cross spectra, which are then combined to form the admittance and correlation functions. The resulting maps offer insights into lithospheric structure of the terrestrial planets. In particular we show that the Earth and Venus have uniformly low positive admittance and high correlation, whereas Mars and the Moon display hemispherical contrasts with large negative and anisotropic coefficients coinciding with lowlands. As has long been known, the two largest impact basins in the inner solar system, the South Pole–Aitken basin on the Moon and the Hellas basin on Mars, display low positive admittance and high correlation, indicating isostatic compensation. In contrast, most other impact basins, particularly the Martian and lunar mascons, show negative coefficients at low wavelet degrees suggesting flexural support by a strong lithosphere. These results imply that, although simple isotropic flexural models can account for most observations, future models may need to incorporate anisotropy as an additional parameter.
