Theory of self‐similar network structures in sedimentary and igneous rocks and their investigation with microscopical and physical methods

Pape, H.; Riepe, Lutz; Schopper, J. R.

doi:10.1111/j.1365-2818.1987.tb02861.x

Cited by 79 publications

(65 citation statements)

References 19 publications

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“…However, this assumption has to be discussed very carefully in many practical cases. Are the borders of carbon particles or the cracks in rocks (Flook, 1978;Pape et al, 1987) really images of self-similar sets or at least good approximations? Are fractals really everywhere (Barnsley, 1988;Murray, 1995)?…”

Section: Theoretical Considerations and Practical Aspectsmentioning

confidence: 99%

Measuring fractal dimension and complexity — an alternative approach with an application

Sandau¹,

Kurz

1997

Journal of Microscopy

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SummaryFractal dimension has often been applied as a parameter of complexity, related to, for example, surface roughness, or for classifying textures or line patterns. Fractal dimension can be estimated statistically, if the pattern is known to be self-similar. However, the fractal dimension of more general patterns cannot be estimated, even though the concept may be retained to characterize complexity. We here show that the usual statistical methods, e.g. the box counting method, are not appropriate to measure complexity. A recently developed approach, the extended counting method, whose properties are closer to what fractal dimension means, is considered here in more detail. The methods are applied to geometric and to blood vessel patterns. The weak assumptions about the structure, and the lower variance of the estimate, suggest that the extended counting method has beneficial properties for comparing complexity of naturally occurring patterns.

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Section: Theoretical Considerations and Practical Aspectsmentioning

confidence: 99%

Measuring fractal dimension and complexity — an alternative approach with an application

Sandau¹,

Kurz

1997

Journal of Microscopy

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“…This opens up the possibility of considering influences resulting from an enlarged rough surface, such as surface conductivity, induced polarization [Pape et al, 1987b;Ruffet et al, 1991], and mechanical contact properties. The assumption of a fractal geometry of the pore space is in accordance with the experimental finding that the internal surface area depends on the resolution of the method of measurement used [Pape et al, 1987a]. The purpose of this paper is to explain this conceptual model and to show how it can be applied to the elastic properties of rock.…”

Section: Introductionmentioning

confidence: 56%

“…The internal surface area of a rock can by described as a fractal according to Mandelbrot [Mandelbrot, 1987;Pape et al, 1987a]. That means the apparent internal surface area depends on the resolution of the measuring technique and diverges with increasing resolution.…”

Section: Specific Internal Surface Areamentioning

confidence: 99%

A fractal model for physical properties of porous rock: Theoretical formulations and application to elastic properties

Spangenberg¹

1998

J. Geophys. Res.

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Abstract. Besides the mineralogical composition and porosity the elastic properties of porous rock are strongly influenced by the rock microstructure (pore shapes, pore size distribution, grain-to-grain contacts, ½t½.).Quantitativ½ microstructural models can provide an important contribution to achieve a fundamental understanding of the relationship between microscopic rock structures and macroscopic rock properties which is crucial for the interpretation of seismic velocity data.

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“…However, for most rocks, this assumption is not valid. The proposed model (PARIS equation, Pape et al, 1987) for a constant-phase-angle (CPA) to calculate K (in m s −1 ) is…”

Section: Methodsmentioning

confidence: 99%

“…The hydrogeophysical research of the IP method has shown that SIP data can be correlated with physical properties of the pore space in non-metallic soils and rocks, such as the specific surface area (S por ) and K (e.g., Pape et al, 1987;Börner et al, 1996;and Weller et al, 2010a). There is a growing interest in the use of SIP for a wide range of environmental applications, in particular those focused on hydrogeological investigations.…”

Section: Introductionmentioning

confidence: 99%

Spectral induced polarization measurements for predicting the hydraulic conductivity in sandy aquifers

Attwa

Günther

2013

Hydrol. Earth Syst. Sci.

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Abstract. Field and laboratory spectral induced polarization (SIP) measurements are integrated to characterize the hydrogeological conditions at the Schillerslage test site in Germany. The phase images are capable of monitoring thin peat layers within the sandy aquifers. However, the field results show limitations of decreasing resolution with depth. In comparison with the field inversion results, the SIP laboratory measurements show a certain shift in SIP response due to different compaction and sorting of the samples. The SIP data are analyzed to derive an empirical relationship for predicting the hydraulic conductivity (K). In particular, two significant but weak correlations between individual real resistivities (ρ ) and relaxation times (τ ), based on a Debye decomposition (DD) model, with measured K are found for the upper groundwater aquifer. The maximum relaxation time (τ max ) and logarithmically weighted average relaxation time (τ lw ) show a better relation with K values than the median value τ 50 . A combined power law relation between individual ρ and τ with K is developed with an expression of A · (ρ ) B · (τ lw ) C , where A, B and C are determined using a least-squares fit between the measured and predicted K. The suggested approach with the calculated coefficients of the first aquifer is applied for the second. Results show good correlation with the measured K indicating that the derived relationship is superior to single phase angle models as Börner or Slater models.

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Theory of self‐similar network structures in sedimentary and igneous rocks and their investigation with microscopical and physical methods

Cited by 79 publications

References 19 publications

Measuring fractal dimension and complexity — an alternative approach with an application

Measuring fractal dimension and complexity — an alternative approach with an application

A fractal model for physical properties of porous rock: Theoretical formulations and application to elastic properties

Spectral induced polarization measurements for predicting the hydraulic conductivity in sandy aquifers

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