Quantifying the transition between tectonic trend and meso‐scale texture in topographic data

Topographic elevation is considered to be governed by a large‐scale trend generated by tectonics and by a meso‐scale texture described by fractal parameters. We investigate the scale threshold of this transition. A scalar parameter called vertical aspect ratio or mean slope r ( d ), where d is an horizontal distance, is shown to be sensitive to both components; r ( d ) is derived from the variograms. An application to selected windows in a Digital Elevation Model has detected a scale threshold called d i 1 such that one observes: (i) a strongly anisotropic trend for d > d i 1 , (ii) for d < d i 1 , a slight reversed anisotropic fractal signature or a complete isotropic signature when the mean topographic drift increases, (iii) a power law r ( d ) ∝ d −1 in the horizontal direction orthogonal to the trend, possibly related to a 1/ k noise, k being wavenumber. The anisotropies detected reveal the relation of the vertical distribution of topography to the underlying drainage network. Depending on geographical location, we have observed 5 km < d i 1 < 25 km.