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Two‐dimensional discrete Fourier transform analysis of karst and coral reef morphologies
Author(s) -
Davis Jerry D.,
Chojnacki Joseph D.
Publication year - 2017
Publication title -
transactions in gis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.721
H-Index - 63
eISSN - 1467-9671
pISSN - 1361-1682
DOI - 10.1111/tgis.12277
Subject(s) - bathymetry , frequency domain , landform , geology , coral reef , fourier transform , discrete fourier transform (general) , karst , fourier analysis , geography , remote sensing , geomorphology , short time fourier transform , computer science , mathematics , oceanography , mathematical analysis , computer vision , paleontology
Fourier transforms have been used in the analysis of landscapes that exhibit the influence of cyclic structures or other morphogenetic controls. Two‐dimensional Fourier transforms have been most successful when modeling features with a high frequency over the sample space. This research focuses on applications of 2D discrete Fourier transforms for karst and spur and groove coral reefs, using ArcGIS geoprocessing tools extended with Python NumPy numerical methods. Ten‐meter digital elevation data from Puerto Rico and Kentucky holokarst landscapes and five‐meter bathymetry from more unidirectional spur and groove coral reefs at Midway Atoll were analyzed. Our method identifies the dominant contributing waves in frequency space, and analyzed power contributions by 5° and 15° azimuth bins. A limiting factor in this analysis is the spatial extent of consistent morphology in the landscape. In contrast to time‐domain Fourier analysis, dominant landform frequencies can thus be of low magnitude, creating an imprecise estimate of wave morphometry and direction since this is derived from the combination of inverted x and y frequency values, and the limited frequency grain inherent in the discrete model degrades precision in the solution. Simulated karst and spur & groove landscapes were used to evaluate the grain of waveform orientation solutions.