Quantitative methods for analyzing the roughness of the seafloor
Authors: Fox Christopher G. , Hayes Dennis E. 
Published: February 2008

The bathymetry of the world ocean has been mapped using a variety of acoustic sounding instruments and traditional contouring methods. Prior to this study, relatively few quantitative studies have been focused on the detailed morphology of the seafloor. The work of most investigators has generally dealt with the analysis of seafloor relief without regard to spatial frequency or concern for obvious morphologic anisotropies. A brief review of previous work is presented and is accompanied by an identification of the specific applications and limitations of those approaches. The availability of more precise digital sounding data coupled with the development of higher‐resolution sonar mapping instruments (e.g., DEEPTOW, SEAMARC) now make it possible to investigate quantitatively many important aspects of seafloor relief and the geological processes responsible for its formation. Typical bathymetric contour maps represent a low‐frequency deterministic model of the seafloor. To describe the higher‐frequency variability or roughness of the seafloor requires the development of an appropriate statistical method for generating a valid stochastic model. New methods are developed herein which allow valid statistical models of the variability of oceanic depths to be derived from existing digital bathymetric soundings. The smooth contoured surface (often preserved as a geographic grid of depths), when supplemented by such a roughness model, can provide an essentially complete statistical description of the relief. Statistical models of seafloor roughness are also valuable tools for predicting acoustic scattering and bottom loss and, in addition, contain a wealth of information for more comprehensive interpretations of deep‐sea, relief‐forming geological processes. To allow the variability of depths to be described as a function of scale (spatial frequency), the amplitude spectrum is employed as the fundamental statistic underlying the model. Since the validity of the amplitude spectrum depends upon the assumption of a statistically stationary sample space, a computer algorithm operating in the spatial domain was developed which delineates geographic provinces of limited statistical heterogeneity. Within each of these provinces, a spectral model is derived by fitting the amplitude estimates with one or two two‐parameter power law functions, using specialized regression techniques. The distribution of resultant model parameters is examined for a large test area adjacent to the coast of Oregon (42°–45°N, 130°–124°W) which includes several contrasting geologic environments. The distribution of roughness corresponds generally with the various physiographic provinces observed in the region. Within some provinces, additional complexities are apparent in the roughness model which cannot be inferred by simply studying the bathymetry. These patterns are related to a variety of geological processes operating in the region, such as the convergence of the continental margin and the presence of a propagating rift on the northern Gorda Rise. In contrast, a very large area of the continental margin off the east coast of the United States was found to have in common a single, distinct amplitude spectrum. This amplitude spectrum is almost identical to that found from the Tufts Abyssal Plain region off the west coast of the United States. Spectra from both of these areas can be clearly separated into two straight‐line segments of different slope. The two segments of these spectra are interpreted as reflecting two dominant relief‐forming processes, the higher‐frequency band representing a sedimentary regime and the lower‐frequency band representing an underlying tectonic/volcanogenic regime. In many cases, the calculated roughness statistics are not constant for data collected along different ship track directions; this is due to the anisotropic nature of the seafloor relief. A simple model is developed which describes the roughness statistics as a function of azimuth. The parameters of this model quantify the anistropy of the seafloor, allowing insight into the directionality of the corresponding relief‐forming processes and the physical meaning of the derived model statistical parameters. Finally, the model is used to successfully predict the roughness of a surface at scales much smaller than those resolvable by surface sonar systems. The model regression line (derived from a hull‐mounted sonar) is compared to data from deep‐towed sonars and bottom photographs. The amplitude of roughness is predicted to within half an order of magnitude over five decades of spatial frequency, and this prediction capability can probably be improved even further. The stochastic models presented also demonstrate the potential for closely approximating the full two‐dimensional nature of some areas of the seafloor, with only four statistical parameters. These parameters can be estimated from random ship track data, given a sufficient number of tracks and range of headings.