Statistics of the Earth’s Topography

Abstract

The so-called “typical” values for the Earth’s topography are often used in the literature, such as the mean continental altitude (MCA), the Moho depth for “normal” continental crust, or “typical” depth of mid-oceanic ridges. However, the statistical relevance of those values is hardly discussed. Focussed on data for the global topography, this paper presents statistical analyses regarding various environments. It is shown in particular that the definition of the mid-oceanic ridge is not straightforward, and varies considerably according to what is actually considered: the ridge “inner-rift”, the ridge “crest”, or the “virtual ridge” at spreading centre. This definition is also a function of the spreading rate and has strong implications for the rationale on the age-depth relationship of the sea-floor. In addition, the latter relationship is highly dependent on how the topographic data are corrected from sediment load. The correction itself implies numerous aspects that relies on the precision and associated uncertainties of, in particular, the sediment thickness, sediment porosity, and the mantle, water and sediment densities. In this respect, the analysis carried out here favours a plate cooling model (PCM) for the age-depth dependence of the sea-floor. The topographic elevation at trench proves also to be related to the age of the sea-floor through a different PCM equation. Away from the trench, the oceanic lithosphere is affected by flexuration, for which equations can be defined assuming that the end-load position is not located at trench. On the other hand, the elevation of magmatic arc does not appear to be related to sea-floor age or spreading rate. However, the correlation between the arc-trench distance and the topographic elevation of arc for continental crust seems to be an indicator of slab dip and therefore the existence of slab roll-back processes. Along intra-oceanic magmatic arc, a periodicity in topographic elevation suggests a periodicity in the occurrence of magma chambers, and therefore magmatic processes that need to be further studied. At passive margin, the transition between continental and oceanic crust seems to be relatively sharp in average. Subdivision of the datasets according to the age of the continent-ocean boundary (COB) indicates that rift and passive margin shoulders are found within a couple of degree away from the COB and for ages younger than ca. 20 Ma. Finally, the statistical analysis of continental data assumed to be free of thinning or thickening effects suggests that the MCA should rather be considered in terms of “lowlands” and “highlands”. Relying on model of Moho depth, the “normal” crustal depth might be thinner than commonly accepted. In any case, the filtering of reduced topography can help to determine the impact of dynamic topography.