Testing fractal and multifractal concepts for seafloor topography.

Abstract

Scattering and reverberation properties of the seafloor depend on the high-resolution spatial structure of submarine topography. Whether concepts of fractal geometry, scaling properties, and multifractal theory provide possibilities to describe the seafloor across several scales of resolution is investigated. In an attempt to predict the spatial structure of the seafloor beyond the scale resolved by survey systems, it has been proposed that the seafloor can be simulated using the self-similarity property of a fractal. (By definition, a fractal is an object of Hausdorff dimension strictly exceeding its topological dimension.) However, results from analyses of bathymetric data from the East Pacific Rise at 13° N/104° W and from the Juan de Fuca Ridge at 45° N/130° W show scale-dependent spatial structures, contradicting a simple self-similarity or self-affinity. Consequently, the seafloor probably has noninteger (fractal) dimension, but with different geologic processes dominating specific ranges of scale (rather than scale invariance). To capture the complexity of seafloor generating processes, the more versatile concept of multifractals is introduced and explored for seafloor topography description.