Fractals and Ocean Floor Topography: A Review and a Model

Abstract

The topography of the Earth’s surface, as many other geophysical variables, can be separated into two components: a large-scale, long-wavelength component that can be predicted by simple models of physical processes, and that we may call deterministic; and a small-scale, random component that is very difficult to predict in a deterministic fashion (Mandelbrot, 1975). An example is the overall topography of the ocean floor (Bell, 1979; Gilbert and Malinverno, 1988; Goff and Jordan, 1988; Mareschal, 1989). As the oceanic lithosphere moves away from the midocean ridge axis, it thickens by cooling and subsides isostatically. The overall depth of the ocean floor is proportional to the square root of its age, following the predictions of simple thermal models (Davis and Lister, 1974; Langseth and others, 1966; McKenzie, 1967; Oldenburg, 1975; Parsons and Sclater, 1977). While the cooling model explains the overall deepening of the ocean floor away from the ridge axis, it is also obvious that there are a number of apparently random residual features on the ridge flank that are not accounted for (see Fig. 6.1). These ridge-and-trough features or abyssal hills (Heezen and others, 1959), are elongated in a direction parallel to the ridge axis (i.e., perpendicular to the page in Fig. 6.1). These volcanic constructions and/or fault-bounded blocks formed near the ridge axis and were subsequently transported onto the ridge flanks (Dietz, 1961; Kappel and Ryan, 1986; Larson, 1971; Lewis, 1979; Lonsdale, 1977; Macdonald and Atwater, 1978; Macdonald and Luyendyk, 1985; Menard and Mammerickx, 1967; Pockalny and others, 1987; Pockalny and others, 1988; Rea, 1975; Searle and Laughton, 1977).