IS THE OCEAN-FLOOR A FRACTAL

The topographic structure of the ocean bottom is investigated at diffe rent scales of resolution to answer the question: Can the seafloor be described as a fractal process? Methods from geostatistics, the theory of regionalized variables, are used to analyze the spatial structure of the ocean floor at different scales of resolution. The key to the a nalysis is the variogram criterion: Self-similarity of a stochastic pr ocess implies self-similarity of its variogram. The criterion is deriv ed and proved here; it also is valid for special cases of self-affinit y (in a sense adequate for topography). It has been proposed that seaf loor topography can be simulated as a fractal (an object of Hausdorff dimension strictly larger than its topological dimension), having scal ing properties (self-similarity or self-affinity). The objective of th is study is to compare the implications of these concepts with observa tions of the seafloor. The analyses are based on SEABEAM bathymetric d ata from the East Pacific Rise at 13 degrees N/104 degrees W and at 9 degrees N/104 degrees W and use tracks that run both across the ridge crest and along the ridge flank. In the geostatistical evaluation, the data are considered as a stochastic process. The spatial continuity o f this process is described by variograms that are calculated for diff erent scales and directions. Applications of the variogram criterion t o scale-dependent variogram models yields the following results: Altho ugh the seafloor may be a fractal in the sense of the definition invol ving the Hausdorff dimension, it is not self-similar, nor self-affine (in the given sense). Mathematical models of scale-dependent spatial s tructures are presented, and their relationship to geologic processes such as ridge evolution, crust formation, and sedimentation is discuss ed.