Generation Of A Sea-Like Random Surface

Abstract

The concept of two-dimensional digital filtering is used to generate three-dimensional random surfaces with specified autocorrelation function. The unknown filter weights is found to be the inverse Fourier transform of the square root of the Fourier transform of the surface autocorrelation function (or the square root of the roughness spectrum). To generate the sea -like random surfaces with specification up to the second moment, ie., the correlation , accurate estimate of the two-dimensional anisotropic sea roughness spectrum must be known. A patch of sea surface with 300x300 data points obtained from stereo photography by Ocean Research and Engineering was used to estimate the sea surface autocorrelation function and roughness spectrum. The effect of both the sizes of the surface patch and the averaging of several patches on the estimate of the autocorrelation function was examined for a numerically generated surface with Gaussian correlation function . It is found that averaging different patches alone does not help in the estimation of the correlation function. However, averaging does help in the accuracy of the estimate of the correlation if the size of each patch is at least 20 times the correlation length. It is recommended that the estimation of autocorrelation function being handled in the following steps. First using the total data to estimate the correlation length of the surface. Secondly the correlation function is estimated by averaging estimates from smaller patches each with at least 20 times the correlation length in size. A sea-like random surface is generated following the above algorithm. The statistics calculated from the generated surface are in good agreement with the specifications.