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variability, or roughness, of the seafloor requires the development of 

 an appropriate statistical method for generating a valid stochastic 

 model. The smooth contoured surface (often preserved as a geographic 

 grid of depths), when supplemented by such a roughness model, provides a 

 complete description of the relief. The statistical model of seafloor 

 roughness is also a valuable tool for predicting acoustic scattering and 

 bottom loss, and in addition contains a wealth of geological information 

 for interpreting deep-sea 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 sta- 

 tionary sample space, a computer algorithm operating in the spatial 

 domain was developed which delineates geographic provinces of limited 

 statistical heterogeneity. Within these provinces, the spectral model 

 is derived by fitting the amplitude estimates within the province with 

 one or several two-parameter power law functions, using standard regression 

 techniques. 



The distribution of the model parameters is examined for a test area 

 adjacent to the coast of Oregon (42''N-45''N, 130'W-124''W) , which includes 

 a variety of 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 many cases, the roughness statistics are not constant when observed 

 in different directions, 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 anisotropy of the seafloor, allowing insight into the 

 directionality of the corresponding relief -forming processes. Finally, 

 the model is used to successfully predict the roughness of a surface at 

 scales 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. 



S/N 0102- LF-014-6401 



SeCURITV CLASUPICATION Or THIS PAOEIimM Oalm Eiit9—4i 



