Analysis of spatial order in sandstones. I. Basic principles |
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| Authors: | Christopher M Prince and Robert Ehrlich |
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| Institution: | (1) Geology Department, University of South Carolina, 29208 Columbia, South Carolina |
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| Abstract: | The spatial arrangement of sedimentary rock components is a fundamental property of sedimentary rocks. If we assume that the size, shape, and composition of sedimentary rock components (mineral grains, pores) carry useful petrologic information, there is no reason to assume that their spatial arrangement does not. Spatial arrangement has been discussed in terms of  texture and fabric, but it has had little objective measurement or classification. This deficiency is primarily due to the difficulties associated with the quantification of spatial phenomena. However, using digital-imaging techniques it is possible to generate petrographic images from thin-sections and quantify the spatial arrangement of selected rock components using a two-dimensional (2D) Fourier transform. A Fourier transform creates a spectral representation of the image similar to an x-ray diffraction pattern. This paper presents the fundamental framework of 2D Fourier analysis in petrology. This type of analysis provides a means to quantify and analyze the spatial arrangement of rock components in an objective, mathematical framework. 2D Fourier power spectra can be used to characterize the type and degree of spatial order in an image, both in terms of the classical concepts of long-range and short-range order and in terms of spatial patterns characteristic of sedimentary rock. The clearly defined mathematical relationship between an image and its Fourier power spectrum provide the opportunity to define the 2D structure of an image in the same manner that x-ray diffraction patterns are used to map 3D structure in minerals. In addition, a 2D Fourier power spectrum is easily transformed into a radial power spectrum. Radial power spectra can be used to characterize the density of objects in an image. They also provide a valid means to compare and contrast images in a multivariate framework, regardless of the type of order. One of the most desirable properties of a Fourier transform is its reversibility. Using selected components of the power spectrum, the inverse transform can be used to build synthetic images, which highlight those petrologic components that most affect the power spectrum. The inverse transform provides the means to translate the results of analysis into meaningful petrologic characteristics. |
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| Keywords: | two-dimensional Fourier transform spatial analysis petrology |
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