Abstract
Many geophysical records are in the form of time or spatial series, where a parameter is observed sequentially at discrete intervals in time or space. Examples include the roughness of natural fractures in rock, land and seafloor topography, the spatial series comprising geophysical well logs, and some geophysical time series (some hydrologic records, for example). A description of the geometry of these functions is essential to studies of the mechanical and transport properties of fractures in rock (Brown and Scholz, 1986; Brown, 1989; scattering of acoustic waves from the sea floor (Fox and Hayes, 1985), detecting fractures by acoustic methods (deBilly and others, 1980); characterizing the spatial variation of permeability in oil and gas reservoirs and aquifers (Hewett, 1986); and evaluating the persistence of some time-dependent geophysical phenomena, including stream flows (Mandelbrot and Wallis, 1969). In each of the examples just cited, a class of fractals known as self-affine have been used to describe the spatial or time series. The distinction between self-affine fractals and the more familiar self-similar fractals is discussed in a subsequent section.
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