Statistical characterization of seafloor roughness

Abstract

The topography of the seabed can strongly affect underwater sound propagation in the ocean. In this regard, seafloor features fall into three overlapping categories according to size: large features that block propagation, intermediate features that act primarily as sloping bottoms, and small-scale features that act as scatterers. In this paper, statistical parameters of bottom topography for the latter two categories are presented. Spatial wavenumber spectra of ocean bottom and subbottom roughness are determined from narrow-beamwidth echosounding and seismic reflection profiling. The spectra are compared to the expression <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P(K) = CK^{-b}</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P(K)</tex> is the power spectral density, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> is a proportionality constant, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</tex> is the wavenumber, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> is a constant that characterizes the class of roughness. The parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> is often assumed to be 3; however, the present study shows that <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> can range from about 1 to 5. Topographic samples were found to have probability density functions which were both non-Ganssian and Gaussian. It is suggested that a first-order roughness data base include hand-limited root mean square (RMS) roughness; <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K_{1}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K_{2}</tex> (the wavenumbers of the estimate); <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> ; sediment type; physiographic province, water depth, and location.