Spectral and wavelet analysis of gilgai patterns from air photography

Abstract

Gilgais form repeating patterns that seem to be regular to some degree. We have analysed the patterns of gilgais as they appear on aerial photographs of the Bland Plain of New South Wales to discover to what degree they exhibit regularity and to estimate the spatial frequencies of the repeating patterns. We digitised rectangular sections of the photographs to produce grids of pixels at 0.063-mm intervals, equivalent to 1.3 m on the ground, with the optical density of each pixel recorded as a level of grey in the range 0 (black) to 255 (white). From the data we computed autocorrelograms and power spectra in both 1 and 2 dimensions and wavelet coefficients and wavelet packet coefficients and their variances. Spectra of many of the individual rows of the grids contained peaks corresponding to wavelengths of ≈32 m (at Caragabal) and ≈52 m (at Back Creek). The 2-dimensional spectra have rings of relatively large power corresponding to these wavelengths in addition to their central peaks. The 1-dimensional wavelet variances have pronounced peaks at the 16–32 pixel scale, corresponding to 20–40 m on the ground. The 2-dimensional wavelet analyses revealed peaks in the variances in the same range. Back Creek has in addition a low-frequency feature caused by the much darker than average gilgais in one corner of the digitised rectangle, and this is equally evident in the 1-dimensional analyses of rows that cross this corner, where the largest contribution to wavelet packet variation is at wavelength 84–167 m. Where this feature is absent, the best wavelet packet basis indicates that variation at frequencies at or below the repeating pattern is consistent with an underlying stationary random variable, while higher-frequency components show more complex (non-stationary) behaviour. We conclude that the gilgai patterns we have examined have a regularity with wavelengths in the range 30–50 m.