Topography measurement of scale-model representations of the rough ocean bottom by touch-trigger probe and its implications for spectral characterization

Scale models of the ocean bottom exhibiting multiscale roughness having power-law form power-spectral density are useful for validation of deterministic and stochastic rough-surface scattering theories. Such scattering theories require accurate knowledge of the topography of the scale-model surface, which, at acoustic scales, can be measured on a two-dimensional grid using a kinematic-resistive touch-trigger probe and represented by a digital elevation model. Both the discrete representation and the physical measurement process introduce spectral artifacts. While the theoretical relationship describing spectral effects of the discrete representation is well known, this relationship is more complex for the physical measurement process. In the later case, spectral effects result from a combination of random measurement errors and fundamental limitations of probe measurement. Here, a numerical model of the physical measurement process is presented, which is used to simulate spectral effects of probe measurement. While random measurement errors can be controlled for and tend to introduce only an additive white-noise component into the measured power-spectral density, limitations of probe measurement are due to the finite size of the probe stylus and result in a systematic error in the measured power-spectral density for spatial wavenumbers above a critical wavenumber