Surface topography as a nonstationary random process

Details Surface topography as a nonstationary random process Surface topography as a nonstationary random process

Feb 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978natur.271..431s&link_type=abstract

Nature, vol. 271, Feb. 2, 1978, p. 431-434.

Statistics

75

Power Spectra, Random Processes, Surface Roughness, Topography, Bandwidth, Root-Mean-Square Errors

Scientific paper

The topography of physical objects is considered in terms of the underlying random structure where undulations in surface height continue over as broad a bandwidth as the surface size will allow. The central limit theorem is applied to show through Gaussian statistics that the variance of the height distribution of such a structure is linearly related to the length of sample involved. In a graph, the experimental points show the increase in normalized root mean square roughness with cut-off wavelength observed from two different topographies. A log-log plot of the variation of normalized power spectral density with wavelength shows that many different surface topographies (e.g., motorway, grit blasted surface, periphery of ground disk) have a similar form of power spectrum, over several decades of surface wavelength. The root mean square power increases, to a good approximation, as the square of the wavelength.

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