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Moving random surfaces and correlation analysis
Author(s) -
Burke M. J.
Publication year - 1987
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs022i004p00607
Subject(s) - autocorrelation , correlation function (quantum field theory) , correlation , spatial correlation , mathematics , decorrelation , mathematical analysis , correlation coefficient , geometry , physics , optics , statistics , spectral density
Two models of moving random surfaces with known velocity and known correlation function are described. The random surfaces are formed from an infinite set of plane waves with decorrelation arising from random temporal and spatial changes. For model 1 the random changes are independent of the wave frequency. For model 2 they increase with frequency. It is shown that if there are random spatial changes in the direction of motion, then speeds derived by the full correlation method will be less than the true speed of the surface. If temporal series based on the models are subjected to a high‐pass filter before correlation analysis, the correlation speeds increase in value. Correlation functions from one of these models (model 2) fail the requirements for full correlation analysis because the half widths of the cross‐correlation functions are greater than the half width of the autocorrelation function. However, from a survey of experimental ionospheric drift measurements it is argued that radio interference patterns appear to have the form of this model. For this model, (1) correlation speeds increase with increasing antenna spacing, (2) the correlation ellipse tends to line up with that antenna pair with the greatest spacing, (3) the straight line of the straight‐line method will not be straight, and as stated above, (4) the speeds will be low. These features have been found experimentally and are contrary to the assumptions of the correlation method. It is shown that an alternate analysis, the “similar fades average velocity method,” gives a better estimate of the surface speed than does the correlation method.