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Stylolites from the Saudi Arabian Permian Khuff formation are characterized by a fine-grained, dark-colored, more-or-less fabric-oriented and insoluble seam material. The seams are three-dimensional; however, in the present study, only their visible cross-sectional aspects are considered for geometrical classification and fractal analysis. Detailed...
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... 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. ...
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... The development of the concept of fractals (e.g., Mandelbrot, 1967;Turcotte, 1990) has helped quantify the self-similarity of different scales of geological features. For example, several studies have shown that the planes of individual stylolites have fractal geometries (e.g., Hassan et al., 2002;Karcz and Scholz, 2003;Renard et al., 2004). Fractal behaviour is commonly expressed in terms of power-law scaling relationships, which can be given by N = c·U -D , where N = number of elements with a characteristic greater than U, c = a constant, and D = the power-law exponent (e.g., Scholz and Cowie, 1990). ...
Bed-parallel (“sedimentary”) stylolites are used as an example of a population that evolves by the addition of new components, their growth and their merger. It is shown that this style of growth controls the changes in the scaling relationships of the population. Stylolites tend to evolve in carbonate rocks through time, for example by compaction during progressive burial. The evolution of a population of stylolites, and their likely effects on porosity, are demonstrated using simple numerical models. Starting with a power-law distribution, the adding of new stylolites, the increase in their amplitudes and their merger decrease the slope of magnitude versus cumulative frequency of the population. The population changes to a non-power-law distribution as smaller stylolites merge to form larger stylolites. The results suggest that other populations can be forward- or backward-modelled, such as fault lengths, which also evolve by the addition of components, their growth and merger. Consideration of the ways in which populations change improves understanding of scaling relationships and vice versa, and would assist in the management of geofluid reservoirs.
... It even seems possible to evaluate the paleo-stress value associated with stylolites from a roughness statistical analysis ( Fig. 12a-b). Analysis of stylolite roughness shows that these structures have a fractal morphology over 4 -5 orders of magnitude in spatial bandwidth, with an average fractal dimension D (obtained by spectral and scaled windowed variance analyses) clustering at 1.5 (Karcz and Scholz, 2003), 1.3 (Drummond and Sexton, 1998) or 1-1.3 (Hassan et al., 2002). High resolution measurements at laboratory scale (Renard et al., 2004b;Schmittbuhl et al., 2004) showed an even more complex roughness (Fig. 12c). ...
Pressure solution creep is a major mechanism of ductile deformation of
the upper crust, accommodating basin compaction, folding, shear zone
development, and fault creep and interseismic healing. However, its
kinetics is strongly dependent on the composition of the rocks (mainly
the presence of clays and phyllosilicates minerals that activate
pressure solution) and on its interaction with fracturing and healing
processes (that activate and slow down pressure solution, respectively).
It is shown how fluid-rock interactions control both the slow temporal
evolution of rock composition and the fast episodic effect of fracturing
and healing processes. Observations of natural deformation show how the
initial mixing of soluble minerals (as quartz, feldspars, calcite,
serpentine) and insoluble minerals (as clay, phyllosilicates)
facilitates the pressure solution process and how the progressive
passive concentration of insoluble species associated with pervasive
pressure solution creep processes leads to the localization of the
deformation along creeping fault and shear zones. Experiments with
dynamic indenter technique show how episodic fracturing events activate
pressure solution kinetics by opening paths for diffusion and
precipitation and how the progressive healing of such fractures slow
down the pressure solution kinetics. Displacement-rate versus time
relation shows that post-fracturing displacement fit first a power law
(with an exponent of about 0.4) then the same linear evolution as before
fracturing and healing. Such displacement-rate versus time relation can
also be found in temporal evolution of post-seismic displacement.
Consequently, in natural deformation, pressure solution is likely to be
a non-steady-state creep process. - Fracturing (weakening effect)
competes with healing (strengthening effect) during earthquake cycles
and the change in shear zones, and probably also in all the deformation
processes that are triggered by human activity (fluid extraction or
geological storage). - Phyllosilicates content increase (weakening
effect) competes with vein sealing (strengthening) at all time scales
from earthquake cycles to basin compaction or mountain building leading
to tectonic segregation. This complex behaviour is true for all the
stress-driven mass transfer mechanisms including metamorphic reactions
when they imply a thin fluid phase trapped under stress.
... It even seems possible to evaluate the paleo-stress value associated with stylolites from a roughness statistical analysis ( Fig. 12a-b). Analysis of stylolite roughness shows that these structures have a fractal morphology over 4 -5 orders of magnitude in spatial bandwidth, with an average fractal dimension D (obtained by spectral and scaled windowed variance analyses) clustering at 1.5 (Karcz and Scholz, 2003), 1.3 (Drummond and Sexton, 1998) or 1-1.3 (Hassan et al., 2002). High resolution measurements at laboratory scale (Renard et al., 2004b;Schmittbuhl et al., 2004) showed an even more complex roughness (Fig. 12c). ...
The aim of this review is to characterize the role of pressure solution creep in the ductility of the Earth's upper crust and to describe how this creep mechanism competes and interacts with other deformation mechanisms. Pressure solution creep is a major mechanism of ductile deformation of the upper crust, accommodating basin compaction, folding, shear zone development, and fault creep and interseismic healing. However, its kinetics is strongly dependent on the composition of the rocks (mainly the presence of phyllosilicates minerals that activate pressure solution) and on its interaction with fracturing and healing processes (that activate and slow down pressure solution, respectively). The present review combines three approaches: natural observations, theoretical developments, and laboratory experiments. Natural observations can be used to identify the pressure solution markers necessary to evaluate creep law parameters, such as the nature of the material, the temperature and stress conditions, or the geometry of mass transfer domains. Theoretical developments help to investigate the thermodynamics and kinetics of the processes and to build theoretical creep laws. Laboratory experiments are implemented in order to test the models and to measure creep law parameters such as driving forces and kinetic coefficients. Finally, applications are discussed for the modeling of sedimentary basin compaction and fault creep. The sensitivity of the models to time is given particular attention: viscous versus plastic rheology during sediment compaction; steady state versus non-steady state behavior of fault and shear zones. The conclusions discuss recent advances for modeling pressure solution creep and the main questions that remain to be solved.
... Previous work on the scaling of stylolites has focused on the geometries of individual stylolite surfaces and on the spacing between stylolites. Several papers have shown that Hassan et al., 2002;Karcz and Scholz, 2003;Renard et al., 2004). Merino et al. (1983) suggest that stylolites are approximately evenly spaced in initially uniform rock. ...
The frequencies, amplitudes and insoluble residue thicknesses of 4639 stylolites have been measured from ∼674.3 m of core from four vertical wells in the Khuff Formation, a Permo-Triassic carbonate reservoir, offshore Abu Dhabi. Although there are similar numbers of stylolites per metre of core in dolomites and limestones, the stylolites in the limestones have approximately double the cumulative amplitudes and insoluble residue thicknesses than the stylolites in dolomites. This indicates that stylolites in the limestones have grown at approximately twice the speed or for twice as long as the stylolites in the dolomites. Stylolite amplitudes in dolomites and limestones together appear to obey a power-law scaling relationship over about one order of magnitude (∼20–150 mm). Stylolite amplitudes in dolomites, however, have a higher power-law exponent than those in the limestones, and appear to obey a power-law down to ∼10 mm. This indicates that stylolites in the limestones have merged more than the stylolites in the dolomites. The amount of pressure solution, and possibly the scaling of a population of stylolites, may also be controlled by location within the fold, with less pressure solution in the hinge region, into which hydrocarbons migrated earlier than in the limbs.
... Recently, Hassan et al. (2002) studied 22 stylolite samples (up to 12 cm long) from the carbonate Khuff Formation (Permian, Saudi Arabia), to determine the relationship between their morphology and their fractal properties. They obtained by the box counting method (see Feder, 1988) fractal dimension values ranging from 0.95 to 1.35. ...
... Combined with Hurst coefficient values obtained by R/ S analysis, they present a positive correlation between the fractal dimension and the stylolite complexity, as defined qualitatively by Park and Schot (1968), i.e. the more complex the stylolite the higher its fractal dimension. The Calcare Massiccio stylolites studied here are 'seismogramlike', and are classified as 'complex', thus their high fractal dimension agrees with the Hassan et al. (2002) assertion. Railsback (1993) studied the relationship between stylolite geometry and rock fabric in Paleozoic carbonates. ...
Stylolites are serrated surfaces that form by stress enhanced dissolution. Though their geometry and morphology reflects their formation and evolution, only a few studies have attempted to quantify them. Here we present results indicating that stylolites in limestone of the Calcare Massiccio Formation (Jurassic, Italy) are fractal over 4.5 orders of magnitude in spatial bandwidth, with an average fractal dimension (obtained by spectral and scaled windowed variance analyses) clustering at 1.47. Some stylolites from the Skene (Cambrian, USA) and Tamar (Cenomanian, Israel) formations are fractal over 3 orders of magnitude, with fractal dimensions of 1.26 and 1.43. These values are high relative to other natural surfaces, and reflect the jagged topography of the stylolites. Preliminary results indicate that the fractal dimension and power are constant throughout the stylolite surface, and are not orientation dependent. Furthermore, we show that stylolite contours are fractal too. The grain size does not register in our analyses, implying that the grain is not a cutoff between processes. Rather, stylolite generating processes operate similarly below and above the grain size. Our results suggest that the geometry of these stylolites, especially at long wavelengths, may not be sensitive to the immediate fabric surrounding them.
... It even seems possible to evaluate the paleo-stress value associated with stylolites from a roughness statistical analysis ( Fig. 12a-b). Analysis of stylolite roughness shows that these structures have a fractal morphology over 4 -5 orders of magnitude in spatial bandwidth, with an average fractal dimension D (obtained by spectral and scaled windowed variance analyses) clustering at 1.5 (Karcz and Scholz, 2003), 1.3 (Drummond and Sexton, 1998) or 1-1.3 (Hassan et al., 2002). High resolution measurements at laboratory scale (Renard et al., 2004b;Schmittbuhl et al., 2004) showed an even more complex roughness (Fig. 12c). ...
Experimental deformation and chemical analyses on naturally deformed samples were used to test models of deformation of rocks by pressure solution-crystallization, with mass transfer by diffusion through a fluid phase or by infiltration of fluid. Observations of the changes in shape of fluid inclusions in crystals heated under a microscope allow the relationship to be established between the strain-rate epsilon and various parameters such as shape of cavities and internal P: thus epsilon = f(P)n where n = 3-3.5. -R.A.H.
The aim of this review is to characterize the role of pressure solution creep in the ductility of the Earth’s upper crust and to describe how this creep mechanism competes and interacts with other deformation mechanisms. Pressure solution creep is a major mechanism of ductile deformation of the upper crust, accommodating basin compaction, folding, shear zone development, and fault creep and interseismic healing. However, its kinetics is strongly dependent on the composition of the rocks (mainly the presence of phyllosilicates minerals that activate pressure solution) and on its interaction with fracturing and healing processes (that activate and slow down pressure solution, respectively). The present review combines three approaches: natural observations, theoretical developments, and laboratory experiments. Natural observations can be used to identify the pressure solution markers necessary to evaluate creep law parameters, such as the nature of the material, the temperature and stress conditions or the geometry of mass transfer domains. Theoretical developments help to investigate the thermodynamics and kinetics of the processes and to build theoretical creep laws. Laboratory experiments are implemented in order to test the models and to measure creep law parameters such as driving forces and kinetic coefficients. Finally, applications are discussed for the modelling of sedimentary basin compaction and fault creep. The sensitivity of the models to time is given particular attention: viscous versus plastic rheology during sediment compaction; steady state versus non-steady state behaviour of fault and shear zones. The conclusions discuss recent advances for modelling pressure solution creep and the main questions that remain to be solved.
