Universal multifractal Martian topography

Landais, F.; Schmidt, Frédéric; Lovejoy, S.

doi:10.5194/npg-22-713-2015

Cited by 15 publications

(19 citation statements)

References 23 publications

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“…Multifractality Scaling allows us to introduce two distinct statistical processes : monofractal and multifractal. For a detailed description of the formalism we apply in this study, the readers can refer to Lovejoy and Shertzer (2013) briefly summed up in Landais et al (2015) . We now quickly recall the main notions here after.…”

Section: Statistical Momentsmentioning

confidence: 99%

Multifractal topography of several planetary bodies in the solar system

Landais

Schmidt

Lovejoy

2019

Icarus

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Topography is the expression of both internal and external processes of a planetary body.Thus hypsometry (the study of topography) is a way to decipher the dynamic of a planet.For that purpose, the statistics of height and slopes may be described by different tools, at local and global scale. We propose here to use the multifractal approach to describe fields of topography. This theory both encompass height and slopes and other statistical moment of the field, tacking into account the scale invariance. Contrary to the widely used fractal formalism, multifractal is able to describe the intermittency of the topography field. As we commonly observe the juxtapostion of rough and smooth at given scale, the multifractal framework seems to be appropriate for hypsometric studies. Here we analyze the data at global scale of the Earth, Mars, Mercury and the Moon and find that the statistics are in good agreement with the multifractal theory for scale larger than ∼ 10km. Surprisingly, the analysis shows that all bodies have the same fractal behavior for scale smaller than ∼ 10km. We hypothesized that dynamic topography of the mantle may be the explanation at large scale, whereas the smaller scales behavior may be related to elastic thickness.

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Section: Statistical Momentsmentioning

confidence: 99%

Multifractal topography of several planetary bodies in the solar system

Landais

Schmidt

Lovejoy

2019

Icarus

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“…In our previous analysis (Landais et al, 2015), we performed the same kind of global analysis on the topographic data from Mars, from MOLA laser altimeter measurement (Smith et al, 2001). This analysis also find a good agreement with universal multifractal but on a restricted range of scale (Landais et al, 2015). Indeed the statistical structure has been found to be different at small scale (monofractal) and large scale (multifractal) with a transition occurring around 10 km.…”

Section: Universal Multifractalsmentioning

confidence: 67%

“…Multifractality M q allows us to introduce two distinct statistical structures of interest: monofractal and multifractal. For a detailed description of the formalism we apply in this study, the readers can refer to Lovejoy and Shertzer (2013) briefly summed in Landais et al (2015). We quickly recall the main notions here :…”

Section: Universal Multifractalsmentioning

confidence: 99%

Topography of (exo)planets

Landais

Schmidt

Lovejoy

2019

Monthly Notices of the Royal Astronomical Society

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Current technology is not able to map the topography of rocky exoplanets, simply because the objects are too faint and far away to resolve them. Nevertheless, indirect effect of topography should be soon observable thanks to photometry techniques, and the possibility of detecting specular reflections. In addition, topography may have a strong effect on Earth-like exoplanet climates because oceans and mountains affect the distribution of clouds (Houze, 2012). Also topography is critical for evaluating surface habitability (Dohm and Maruyama, 2015).We propose here a general statistical theory to describe and generate realistic synthetic topographies of rocky exoplanetary bodies. In the solar system, we have examined the bestknown bodies: the Earth, Moon, Mars and Mercury. It turns out that despite their differences, they all can be described by multifractral statistics, although with different parameters. Assuming that this property is universal, we propose here a model to simulate 2D spherical random field that mimics a rocky planetary body in a stellar system. We also propose to 1 arXiv:1902.00047v1 [astro-ph.EP] 31 Jan 2019 apply this model to estimate the statistics of oceans and continents to help to better assess the habitability of distant worlds.

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“…Previous studies often found that a power law with an exponent −2.5 < b < −2 approximates the variance spectrum of topography well (Bills & Kobrick 1985;Balmino 1993;Ermakov et al 2018). At smaller scales, however, it is uncertain if a single power law can be an appropriate representation of topography (Landais et al 2015). Global data sets have limited resolution and the distribution of morphologies over the surface is inhomogeneous.…”

Section: Simulation Of Measurementsmentioning

confidence: 99%

Prospects for measuring Mercury’s tidal Love numberh₂with the BepiColombo Laser Altimeter

Thor

Kallenbach²,

Christensen

et al. 2020

A&A

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Context. The Love number h2 describes the radial tidal displacements of Mercury’s surface and allows constraints to be set on the inner core size when combined with the potential Love number k2. Knowledge of Mercury’s inner core size is fundamental to gaining insights into the planet’s thermal evolution and dynamo working principle. The BepiColombo Laser Altimeter (BELA) is currently cruising to Mercury as part of the BepiColombo mission and once it is in orbit around Mercury, it will acquire precise measurements of the planet’s surface topography, potentially including variability that is due to tidal deformation. Aims. We use synthetic measurements acquired using BELA to assess how accurately Mercury’s tidal Love number h2 can be determined by laser altimetry. Methods. We generated realistic, synthetic BELA measurements, including instrument performance, orbit determination, as well as uncertainties in spacecraft attitude and Mercury’s libration. We then retrieved Mercury’s h2 and global topography from the synthetic data through a joint inversion. Results. Our results suggest that h2 can be determined with an absolute accuracy of ± 0.012, enabling a determination of Mercury’s inner core size to ± 150 km given the inner core is sufficiently large (>800 km). We also show that the uncertainty of h2 depends strongly on the assumed scaling behavior of the topography at small scales and on the periodic misalignment of the instrument.

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Universal multifractal Martian topography

Cited by 15 publications

References 23 publications

Multifractal topography of several planetary bodies in the solar system

Multifractal topography of several planetary bodies in the solar system

Topography of (exo)planets

Prospects for measuring Mercury’s tidal Love numberh₂with the BepiColombo Laser Altimeter

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Universal multifractal Martian topography

Cited by 15 publications

References 23 publications

Multifractal topography of several planetary bodies in the solar system

Multifractal topography of several planetary bodies in the solar system

Topography of (exo)planets

Prospects for measuring Mercury’s tidal Love numberh2with the BepiColombo Laser Altimeter

Contact Info

Product

Resources

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Prospects for measuring Mercury’s tidal Love numberh₂with the BepiColombo Laser Altimeter