Stylolite classification on the basis of pure geometry. (Modified, after [14]). 

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... stylolites discussed in this study come from the Permian Khuff formation, Eastern Saudi Arabia. The Khuff formation underlies every Gulf State, and major gas reserves have already been found or are expected in it. The Khuff formation represents the earliest major transgressive carbonate deposited on a shallow continental shelf in the region [43]. The formation was deposited during a widespread Late Permian marine transgression over the Arabian foreland [43, 44]. The Khuff formation in the subsurface of Central and Eastern Saudi Arabia consists of alternating limestone, dolomite, and anhydrite deposits. The thickness of the formation increases basinward, from west to east and northeast. Stylolites are abundant in the subsurface Khuff formation where their frequency in some cases reaches one stylolite per one foot of depth. In this study some of these Khuff formation stylolites were evaluated. A total of 22 stylolites were considered. Although stylolites are three dimensional features, only their two-dimensional projection normal to the bedding plane has been taken into consideration. The samples were ground and polished to get a clear view of the stylolite. The styolite in sample N is referred to as ST N , if there are more than one stylolites in the same sample N, they will be distinguished with an additional alphabetic code (as ST 10A ). Each stylolite was classified according to Park and Schot’s [14] geometric scheme (Figure 3); its orientation was checked; its column height, column width, seam material thickness were measured; the adjacent lithologies (above and below) were identified; and two kinds of fractal characteristics namely the Hausdorff– Besicovitch fractal dimension and the Hurst exponent determined (Figures 7( a – t ...

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... in sedimentary rocks are irregular planes of discontinuity between two rock units which appear to be interlocked or mutually interpenetrating. They are characterized by a fine-grained, dark in color, more-or-less foliated, and relatively insoluble seam material. The thickness of the seam material ranges from a microscopic inter-granular layer to a macroscopic (centimeters thick) residual parting ( Figure 1). Stylolites are common in limestones and dolomites; however, they were reported in almost all types of sedimentary rocks such as sandstone [1–3], shale [4], and evaporites [4, 5]. Stylolites have been reported since the middle of the eighteenth century, when Klöden [6] considered them to be a distinct organic species (“ Stylolithes sulcatus ”, see [7]). Many theories, in the past, have attempted to explain stylolites. The early theories include the organic theory [8], the crystallization theory [9], the erosion theory [10], the gas theory [11], and the bitumen theory [12]. In the early twentieth century, two schools of thought emerged to explain the nature and genesis of stylolites: the pressure solution theory (Stockdale [13]) and the contraction pressure theory (Shaub [7]). The pressure solution theory claims that stylolites were postdiagenetically created in consolidated sediments which have experienced differential solution due to non-uniform pressure or unequal solubility of minerals (Figure 2). In contrast, the contraction pressure theory proposes that stylolites had developed in an unconsolidated sediment (prediagenesis) by readjustment and rearrangement of minerals through differential squeezing. Although the pressure solution theory is widely accepted, it has its own shortcomings. Based on detailed field and laboratory studies, Park and Schot [14] have concluded that stylolites are syndiagenetic features. The disagreement on the origin of stylolites hindered attempts to establish any classification scheme based on their genesis. Rather, the classification schemes reported in the literature are based on the geometry of the seam material. Stylolites are three-dimensional features, however only their visible cross-sectional (two-dimensional) aspects are considered in the geometrical classification schemes. There are two types of geometrical classification: (1) that which considers only the geometry of the seam material (Figure 3); and (2) that which is based on the geometrical relation of the stylolites and the bedding plane (Figure 4). According to Mandelbrot [15], a fractal is a mathematical set or object whose form is extremely irregular and/or fragmented at all scales. A characteristic property of fractals is their self-similarity : any small detail of a fractal pattern can be magnified by a suitable constant λ to make it statistically similar to another part of the whole image. A practical consequence of self- similarity is that if we place the image of a fractal (embedded in the 2D Euclidean plane) on a series of grids of decreasing spacing ε → 0, the number of “boxes” (“pixels”) N ε containing elements of the image will increase with ε → 0 as an inverse power of ε ...