Fractal analysis of experimentally generated pyroclasts: A tool for volcanic hazard assessment

Rapid decompression experiments on natural volcanic rocks mimick explosive eruptions. Fragment size distributions (FSD) of such experimentally generated pyroclasts are investigated using fractal geometry. The fractal dimension of fragmentation, D, of FSD is measured for samples from Unzen (Japan) and Popocatépetl (Mexico) volcanoes.Results show that: (i) FSD are fractal and can be quantified by measuring D values; (ii) D increases linearly with potential energy for fragmentation (PEF) and, thus, with increasing applied pressure; (iii) the rate of increase of D with PEF depends on open porosity: the higher the open porosity, the lower the increase of D with PEF; (iv) at comparable open porosity, samples display a similar behavior for any rock composition.The method proposed here has the potential to become a standard routine to estimate eruptive energy of past and recent eruptions using values of D and open porosity, providing an important step towards volcanic hazard assessment.     

Self-diffusion studies of pore fluids in unconsolidated sediments by PFG NMR

The self-diffusion of water and hexadecane in medium and coarse sands from glacial sand deposits in central Germany were investigated by pulsed field gradient nuclear magnetic resonance (PFG NMR). Due to the restriction of the diffusion path at the pore/grain interface, the measured apparent self-diffusion coefficients (D(Δ)) in the pore space depend on the observation time (Δ) in the PFG NMR experiment. Although the bulk self-diffusion coefficients of water and hexadecane differ by about one order of magnitude, the apparent self-diffusion coefficients in the pore space obey the same characteristic time-behaviour, which depends only on geometrical properties of the pore system. Using the “short-time diffusion” model, surface-to-volume (S/V) ratios and inherent self-diffusion coefficients (D₀) of the pore fluids were extracted from these diffusion measurements. The S/V ratios obtained are independent of the pore fluid used and agree with known geometrical properties of the sand grains. Moreover, the D₀ values are consistent with the corresponding bulk self-diffusion coefficients measured separately. In contrast to these results of PFG NMR, simultaneous investigations of longitudinal (T₁) nuclear magnetic relaxation reveal that the relaxation time of the pore fluid is a less suitable parameter for a quantitative estimation of geometrical properties of the pore/grain interface in these unconsolidated sediments since it depends on chemical properties of the fluid/grain interface.     

The fractal geometry of flow paths in natural fractures in rock and the approach to percolation

The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold.     

Normal moveout for long offset in isotropic media using the Padé approximation

The normal moveout correction is important to long-offset observations, especially deep layers. For isotropic media, the conventional two-term approximation of the normal moveout function assumes a small offset-to-depth ratio and thus fails at large offset-to-depth ratios. We approximate the long-offset moveout using the Padé approximation. This method is superior to typical methods and flattens the seismic gathers over a wide range of offsets in multilayered media. For a four-layer model, traditional methods show traveltime errors of about 5 ms for offset-to-depth ratio of 2 and greater than 10 ms for offset-to-depth ratio of 3; in contrast, the maximum traveltime error for the [3, 3]-order Padé approximation is no more than 5 ms at offset-to-depth ratio of 3. For the Cooper Basin model, the maximum offset-to-depth ratio for the [3, 3]-order Padé approximation is typically double of those in typical methods. The [7, 7]-order Padé approximation performs better than the [3, 3]-order Padé approximation.     

Pore structure of selected Chinese coals with heating and pressurization treatments

Pore structure of Chinese coals with heating and pressurization treatments was studied using small angle X-ray scattering(SAXS),N2adsorption/desorption isotherms and scanning electron microscope(SEM).SAXS was performed for some samples after heat treatment at seven elevated temperatures from 25 to 250°C at 0 MPa and for other samples with hydrostatic pressure treatment at 0,5,10,15 and 20 MPa at the room temperature.The results show that N2adsorption isotherm together with SAXS could be a comprehensive method to evaluate the pore shape and the pore size distribution:the pore shapes are generally spherical for low rank coal and they are mainly ellipsoidal for high rank coal.All these measurements were then interpreted using the fractal theory to reveal relationship between surface fractals and coal rank,and the evolution of surface fractals under heating and pressurization treatments.The results show that surface fractal dimension(Ds)changes with different treating temperature and pressure and maximum vitrinite reflectance(Ro,m).Especially in the bituminous stage,Ds shows an increasing trend with Ro,m under varied temperatures.Moreover,Ds shows an increasing trend with increasing temperature before 200°C,and a decreasing trend after 200°C.Furthermore,the results show that Ds has a more complex relationship with Ro,m under varied treating temperature than that under varied treating pressure.     

Magnetic interface forward and inversion method based on Padé approximation

The magnetic interface forward and inversion method is realized using the Taylor series expansion to linearize the Fourier transform of the exponential function. With a large expansion step and unbounded neighborhood, the Taylor series is not convergent, and therefore, this paper presents the magnetic interface forward and inversion method based on Padé approximation instead of the Taylor series expansion. Compared with the Taylor series, Padé’s expansion’s convergence is more stable and its approximation more accurate. Model tests show the validity of the magnetic forward modeling and inversion of Padé approximation proposed in the paper, and when this inversion method is applied to the measured data of the Matagami area in Canada, a stable and reasonable distribution of underground interface is obtained.     

Statistical characteristics of flow as indicators of channeling in heterogeneous porous and fractured media

We introduce two new channeling indicators D_ic and D_cc based on the Lagrangian distribution of flow rates. On the basis of the participation ratio, these indicators characterize the extremes of both the flow-tube width distribution and the flow rate variation along flow lines. The participation ratio is an indicator biased toward the larger values of a distribution and is equal to the normalized ratio of the square of the first-order moment to the second-order moment. Compared with other existing indicators, they advantageously provide additional information on the flow channel geometry, are consistently applicable to both porous and fractured media, and are generally less variable for media generated using the same parameters than other indicators. Based on their computation for a broad range of porous and fracture permeability fields, we show that they consistently characterize two different geometric properties of channels. D_ic gives a characteristic scale of low-flow zones in porous media and a characteristic distance between effectively flowing structures in fractured cases. D_cc gives a characteristic scale of the extension of high-flow zones in porous media and a characteristic channel length in fractured media. D_ic is mostly determined by channel density and permeability variability. D_cc is, however, more affected by the nature of the correlation structure like the presence of permeability channels or fractures in porous media and the length distribution in fracture networks.     

Influence of pore size and geometry on peat unsaturated hydraulic conductivity computed from 3D computed tomography image analysis

In organic soils, hydraulic conductivity is related to the degree of decomposition and soil compression, which reduce the effective pore diameter and consequently restrict water flow. This study investigates how the size distribution and geometry of air‐filled pores control the unsaturated hydraulic conductivity of peat soils using high‐resolution (45 µm) three‐dimensional (3D) X‐ray computed tomography (CT) and digital image processing of four peat sub‐samples from varying depths under a constant soil water pressure head. Pore structure and configuration in peat were found to be irregular, with volume and cross‐sectional area showing fractal behaviour that suggests pores having smaller values of the fractal dimension in deeper, more decomposed peat, have higher tortuosity and lower connectivity, which influences hydraulic conductivity. The image analysis showed that the large reduction of unsaturated hydraulic conductivity with depth is essentially controlled by air‐filled pore hydraulic radius, tortuosity, air‐filled pore density and the fractal dimension due to degree of decomposition and compression of the organic matter. The comparisons between unsaturated hydraulic conductivity computed from the air‐filled pore size and geometric distribution showed satisfactory agreement with direct measurements using the permeameter method. This understanding is important in characterizing peat properties and its heterogeneity for monitoring the progress of complex flow processes at the field scale in peatlands. Copyright © 2010 John Wiley & Sons, Ltd.     

Fractal characterization and frequency properties of near-fault ground motions

This study explores the irregularity and complexity of strong earthquake ground motions from the perspective of fractal geometry, and constructs a relation with the frequency content of the ground motions. The box-counting fractal dimensions and five representative period parameters of near-fault ground motions from the Chi-Chi and Northridge earthquakes are calculated and compared. Numerical results indicate that the acceleration and velocity time histories of ground motions present the statistical fractal property, and the dominant pulses of near-fault ground motions have a significant influence on their box dimensions and periods. Further, the average box dimension of near-fault impulsive ground motions is smaller, and their irregular degree of wave forms is lower. Moreover, the box dimensions of ground motions reflect their frequency properties to a large extent, and can be regarded as an alternative indicator to represent their frequency content. Finally, the box dimension D of the acceleration histories shows a considerably negative correlation with the mean period T. Meanwhile, the box dimension of the velocity histories Dye is negatively correlated with the characteristic period T and improved characteristic period Tgi.     

Gas exsolution and flow during supersaturated water injection in porous media: II. Column experiments and continuum modeling

Degassing and in situ development of a mobile gas phase takes place when an aqueous phase equilibrated with a gas at a pressure higher than the subsurface pressure is injected in water-saturated porous media. This process, which has been termed supersaturated water injection (SWI), is a novel and hitherto unexplored means of introducing a gas phase in the subsurface. We give herein a first macroscopic account of the SWI process on the basis of continuum scale simulations and column experiments with CO₂ as the dissolved gas. A published empirical mass transfer correlation [Nambi IM, Powers SE. Mass transfer correlations for nonaqueous phase liquid dissolution from regions with high initial saturations. Water Resour Res 2003;39(2):1030. doi:10.1029/2001WR000667] is found to adequately describe non-equilibrium transfer of CO₂ between the aqueous and gas phases. Remarkably, the dynamics of gas-water two-phase flow, observed in a series of SWI experiments in homogeneous columns packed with silica sand or glass beads, are accurately predicted by traditional two-phase flow theory and the corresponding gas relative permeability is determined. A key consequence of this finding, namely that the displacement of the aqueous phase by gas is compact at the macroscopic scale, is consistent with pore scale simulations of repeated mobilization, fragmentation and coalescence of large gas clusters (i.e., large ganglion dynamics) driven entirely by mass transfer. The significance of this finding for the efficient delivery of a gas phase below the water table is discussed in connection to the alternative process of in situ air sparging, and potential advantages of SWI are highlighted.     

Possible causes of the variation in fractal dimension of the perimeter during the tropical cyclone Dan motion

We calculated the fractal dimensions Db of the perimeter of tropical cyclone(TC)Dan based on the satellite GMS-5 infrared sensor images from 1800 UTC,1 October 1999 to 1200 UTC,9 October 1999.The fractal dimensions Db were used to characterize objectively the temporal change of TC complex structure.Our results show that the change of fractal dimension during TC Dan motion can be divided into three stages.The statistically significant difference does not exist either between Dm1 and DL or between Dm3 and DL,but it exists between Dm2 and DL,where Dmi denotes the mean value of Db in i-th stage(i=1,2 and3);DL denotes Lovejoy’s fractal dimension calculated based on satellite and radar data within the size range(1–1.2×106 km2),which is used as a"normal value"of the fractal dimension of the cumulus cloud perimeter for the global tropical region.TC Dan turns to the north from the west abruptly at the end of the second stage.The emergence of the second stage with high fractal dimensions may be viewed as a possible premonition for the track turning.Our results also show that there are two kinds of processes resulting in the translation from the first stage to the second stage.One is the interaction of TC circulation and an adjacent small scale convective cloud cluster,causing to the complexity increase of a local segment of the perimeter.The other includes the fragmentation of a strong convective area within the TC inner region,the self-organization of the small strong convective cloud clusters,the emergence,development,and merger of the small scale non-convective holes,and the formation of a gap of the perimeter,causing to the complexity increase of the whole TC perimeter.     

Efficient flow and transport simulations in reconstructed 3D pore geometries

Upscaling pore-scale processes into macroscopic quantities such as hydrodynamic dispersion is still not a straightforward matter for porous media with complex pore space geometries. Recently it has become possible to obtain very realistic 3D geometries for the pore system of real rocks using either numerical reconstruction or micro-CT measurements. In this work, we present a finite element–finite volume simulation method for modeling single-phase fluid flow and solute transport in experimentally obtained 3D pore geometries. Algebraic multigrid techniques and parallelization allow us to solve the Stokes and advection–diffusion equations on large meshes with several millions of elements. We apply this method in a proof-of-concept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity to simulate pore-scale solute transport and diffusion. From this, we are able to calculate the a priori emergent macroscopic hydrodynamic dispersion coefficient of the porous medium for a given molecular diffusion D_m of the solute species. By performing this calculation at a range of flow rates, we can correctly predict all of the observed flow regimes from diffusion dominated to convection dominated.     

A dual percolation model for predicting the connectivity of fractured porous media

This paper presents a dual-percolation model coupling the percolation theory and the fracture percolation theory to study the conductivity of the fractured porous media. The Monte-Carlo method is used in the numerical simulation. First an appropriate computing scale by considering the calculation precision and elapsed time together is validated. Then, two parameters, A ₀ and D are presented in this model to determine the conductivity of the media. Generally the media can be blocked by itself in the condition of D > 2. However, the increase of pore connection and the randomness of fracture direction may release the selfblockage, increase the conductivity and make the dual porous media dissipated. A few long fractures can play a great role in the connection of media.     

Process inference from topographic fractal characteristics in the tectonically active Northwest Himalaya,India

Topography evolves under the coupled effect of exogenic and endogenic governing factors, and their scale-(in)variant dynamics. This results in a self-affine topography across a finite range, with a characteristic fractal dimension. Fractal analysis has been used to classify geological terrains having distinct litho-tectonic settings. However, process-based understanding of the fractal behaviour of a natural landscape is still limited. The current study aims to substantiate and expand upon the present knowledge of topographic response to the complex actions of the governing factors using fractal characteristics. We examined the association between the litho-tectonic, climatic settings and the fractal characteristics of the topography in the tectonically active Northwest Himalaya. Our analysis was carried out in three separate sectors having diverse litho-tectonic settings. We used the roughness–length method to calculate the fractal parameters (fractal dimension, D; ordinate intercept, q). The Higher and the Lesser Himalaya were found to be characterized by low D and high q, while the tectonically active Sub Himalaya was found to have moderate D and low q. The southernmost foreland alluvial plains were characterized by high D and low q. Clusters of the fractal parameters were found to be consistent in spatial pattern across the three sectors. Our results showed that the geological–geomorphological settings and the associated processes (e.g. uplift, erosion and diffusion) can be well inferred using the fractal characteristics of the topography. Further, our results implied first-order control of lithology in sustaining and shaping the topographic geometry (both its amplitude and texture) in the tectonically active Northwest Himalaya. The spatial distribution of the fractal parameters also suggested the secondary control of tectonic uplift and, to a much lesser extent, mean annual rainfall on the topographic geometry. These results collectively point to the role of complex actions of the governing factors in the landscape evolution process. © 2020 John Wiley & Sons, Ltd.     

Effects of grain-size distribution and shape on sediment bed stability,near-bed flow and bed microstructure

Different studies investigating the stability of mixed sediment have found that the fine fraction can either stabilize or mobilize the bed. This study aims to find where the transition between these two modes occurs for sandy sediment and to identify the underlying (grain-scale) processes. Flume experiments with bimodal sediment were used to investigate near-bed processes of a non-cohesive sediment bed, and in particular how the grain shape and the ratio of different grain sizes influence bed mobility. Medium sand (D_50,c ≈ 400 μm) was mixed with 40 % fine material of different diameters (D_50,f = 53; 111; 193 μm) and subjected to increasing flow velocities (U = 1.3–22.2 cm s^-1). The bed mobility (i.e. the change of the bed level over time), turbidity and near-bed hydrodynamics were analysed. Selected results were compared with similar previous experiments with spherical glass beads. The findings indicate that, due to the complex grain shapes of natural sediment, a sand bed is more stable than a bed composed of glass beads. The grain-size ratio RD = D_c /D_f between the coarse and fine grain diameters controls whether the mixed bed is stabilized or mobilized by the presence of fines, with the transition between the modes occurring at RD = 4–5.5. Mixed beds with a very low RD < 2 behave like a unimodal bed. The results suggest that RD and grain shape influence bed roughness, near-bed flow, bed microstructure and the flow into and through the upper bed layers, which subsequently governs bed mobility. The interplay between all these processes can explain the transition between the stabilizing effect (high RD, small pore space) and the mobilizing effect (low RD, large pore space) of a fine fraction in a grain-size mixture. © 2018 John Wiley & Sons, Ltd.     

Elastic moduli of dry rocks containing spheroidal pores based on differential effective medium theory

Differential effective medium (DEM) theory is applied to determine the elastic properties of dry rock with spheroidal pores. These pores are assumed to be randomly oriented. The ordinary differential equations for bulk and shear moduli are coupled and it is more difficult to obtain accurate analytical formulae about the moduli of dry porous rock. In this paper, we derive analytical solutions of the bulk and shear moduli for dry rock from the differential equations by applying an analytical approximation for dry-rock modulus ratio, in order to decouple these equations. Then, the validity of this analytical approximation is tested by integrating the full DEM equation numerically. The analytical formulae give good estimates of the numerical results over the whole porosity range. These analytical formulae can be further simplified under the assumption of small porosity. The simplified formulae for spherical pores (i.e., the pore aspect ratio is equal to 1) are the same as Mackenzie's equations. The analytical formulae are relatively easy to analyze the relationship between the elastic moduli and porosity or pore shapes, and can be used to invert some rock parameters such as porosity or pore aspect ratio. The predictions of the analytical formula for the sandstone experimental data show that the analytical formulae can accurately predict the variations of elastic moduli with porosity for dry sandstones. The effective elastic moduli of these sandstones can be reasonably well characterized by spheroidal pores, whose pore aspect ratio was determined by minimizing the error between theoretical predictions and experimental measurements. For sandstones the pore aspect ratio increases as porosity increases if the porosity is less than 0.15, whereas the pore aspect ratio remains relatively stable (about 0.14) if the porosity is more than 0.15.     

Temporal variations of seismicity parameters in the Central Alborz,Iran

Temporal changes of b-value, fractal (correlation) dimensions of epicenters (D _e ) and occurrence time of earthquakes (D _t ) and relations between these parameters were calculated to investigate precursory changes before 28 May 2004, Baladeh-Kojour earthquake (M _w = 6.3) of Central Alborz, Iran. 2086 events with M _N ≥ 1.7 were selected for our analyses. A wide range of variation was seen in these parameters: b-value ～ 0.6–1.11, D _e ～ 0.97–1.64, and D _t ～ 0.13–0.93. The results showed decreases in all fractal parameters several months before the main shock. This decrease, which might have arisen due to clusters of events occurred between 2002–2003, was followed by a systematic increase, corresponding to the increased level of low-magnitude seismicity. It seems that changes in fractal parameters may be precursors of Baladeh-Kojour earthquake which was caused by seismic activation and quiescence. Furthermore, a positive correlation between b-value and D _e was detected before the main shock (D _e = 0.87 + 0.7b) and during aftershock sequences (D _e = 2b ± 0.09), which was further on changed to a negative one (D _e = 2.56–1.32b).     

INDUCED POLARIZATION,A METHOD TO STUDY WATER-COLLECTING PROPERTIES OF ROCKS*

During the last decade many hypotheses were suggested to explain the phenomenon of induced electrical polarization in ionic conductive media. The most reliable of these is Fredricksberg's. Fredricksberg (1962) supposed that the pore spaces of a rock is composed of successively narrow (active zones) and wide (inactive zones). He simulated these pore spaces by a synthetic material that has an extremely high resistance. The pore spaces were generally in tube forms which exhibited some constrictions. He saturated these tubes with an electrolyte of a given concentration. An electric current was passed through this model. He observed an induced polarization voltage after current interruption. He attributed the formation of this voltage to a concentration gradient which took place due to the presence of excess charges in the active zones. Fredricksberg introduced a parameter (9) which described the relation among the lengths and cross sectional areas of the wide zones, the number of ions within each zone after current interruption with the recorded polarizability. The aim of this work is to correlate Fredricksberg's parameter with a parameter determined for natural rocks and to show experimentally the validity of this hypothesis when applying for some varieties of sandstones and volcanic rocks. The new parameter will help to evaluate a relationship between the polarizability and the water-collecting properties of rocks. Herein, we used the tortuosity T of sandstone samples instead of the parameter φ which was used by Fredricksberg to represent the pore geometry within his model (tortuosity of the passes within the model). It was shown that both φ and T have the same relationship with the polarizability ν of the rock samples and if φ or T have very low or very high values the polarizability ν tends to its minimum value, i.e. the curve representing the relation between ν and T has a maximum point corresponding to an intermediate value of T. This result supports Fredricksberg's hypothesis and confirm his results on synthetic models. For volcanic rocks the formation factor F was used since it was difficult to determine the porosity of the samples and consequently to calculate the tortuosity T as for sandstone samples. Experimental results confirm those obtained from sandstone. The grain constituents of sandstone samples were represented on equilateral triangle and the magnitude of induced polarization ν of each sample was deduced and represented on this triangle. Equipolarizability values ν drawn on this triangle showed that TJ will increase as the silty fractions of the rock increase, where the center of this triangle (represents minimum porosity) has polarizability less than 0.25%. An attempt was made to determine the coefficient of anisotropy of volcanic rock samples using the induced polarization method. For this reason the polarizability was deduced by measuring the induced polarization voltage for two perpendicular directions in a fractured cubes of andesitic basalt samples the coefficient of anisotropy was found to be equal 1.18.     

Visualization experiments of biodegradation in porous media and calculation of the biodegradation rate

Biodegradation in porous media is studied with carefully controlled and well-characterized experiments in model porous media constructed of etched glass. Porous media of this type allow visual observation of the phenomena that take place at pore scale. An aqueous solution of five organic pollutants (toluene, phenol, o-cresol, naphthalene and 1,2,3-trimethylbenzene) was used as a model NAPL (representing creosote). The bacteria used were Pseudomonas fluorescens, which are indigenous (even predominant) in many contaminated soils. The maximum aqueous concentrations of the specific organic substances, below which biodegradation becomes possible, were determined as a function of temperature from toxicity experiments. Visualization experiments were made under various flow velocities and organic loadings to study the morphology and thickness of the biofilm as a function of the pore size and the distance from the entrance, and the efficiency of biodegradation. The efficiency of biodegradation decreased as the aqueous concentration of NAPL at the inlet increased and/or as the flow velocity increased. The thickness of biofilm decreased as the distance from the inlet increased and/or the pore diameter decreased. A quasi-steady-state theoretical model of biodegradation was used to calculate the values of the mesoscopic biochemical rates and to predict the profile of NAPL concentration in the porous medium and the thickness of biofilm in pores. The agreement between experimental data and model predictions is quite satisfactory.