The Frequency Dependence of Harmonic Fluid Flow Through Networks of Cracks and Pores

—The "dynamic" permeability k(ω) of heterogeneous networks of cracks, tubes and spheres, was determined by numerically simulating the harmonic flow of an interstitial fluid for a wide range of frequencies. For comparison with previous works, this procedure was applied to the 100 network realizations used in Bernabé (1995). In most cases, the calculated frequency dependence of the real and imaginary parts of k(ω) was consistent with the JKD model (Johnson et al., 1987), showing a transition from "viscous", macroscopic flow at low frequencies to "inertial" flow at high frequencies. The viscous skin depth δ _c at the transition was found to be proportional to the critical capillary radius r _c from a capillary invasion (Katz and Thompson, 1986). A simple explanation is that these two length scales arise from the same percolation problem. On the other hand, δ _c was not well correlated with the JKD parameter Λ. The conclusion is that Λ and δ _c (or r _c ?) are two independent parameters, derived from two unrelated approaches (i.e., weighted averaging and percolation theory). Finally, an attempt was made to relax the initial assumptions of a rigid solid matrix and an incompressible fluid. It was observed that the effect of the fluid compressibility could occasionally be very large, especially when networks with large amounts of storage pore space were considered.     

Permeability and pore-connectivity variation of pumices from a single pyroclastic flow eruption: Implications for partial fragmentation

The relationship between permeability and vesicularity in volcanic rocks has been used to infer the degassing behavior of hydrous magma. Recent data on natural samples from various eruptions show a wide variation, fitting a power–law relationship of the percolation models with low (< 30%) critical vesicularity (Ф_C). In this study, we present data on permeability and pore-connectivity of juvenile rhyolitic pumice clasts in a pyroclastic flow around Onikobe volcano, NE Japan, and investigate their relationship with vesicularity developed in a single eruption event. The permeability of the pumices having a relatively low abundance of microlites and microphenocrysts shows a trend increasing by 4 orders of magnitude (from 10^− 13.8 to 10^− 10.1 m²) in a high and narrow vesicularity range (from 72 to 80%). This trend intersects at a high angle with the fit to the permeability–vesicularity data in the previous studies that has a low Ф_C, and is located on the extension of the trend for the products of isotropic decompression experiments. The two-dimensional (2D) connectivities of pores for the pumices were also measured from thin sections. From the point of view of percolation theory, connectivity provides information about the probability of percolation. They showed a steep increase from ca. 0 to 0.7 in an almost similar vesicularity range, as compared to their permeabilities. We attribute the increase in 2D connectivity to the increasing amount of ruptured bubble walls, which might have provided less-tortuous paths through larger apertures for gas flow. This, in turn, would cause an effective increase in the permeability. Aggregates of bubble-wall-shaped glass shards were found in the pumices, and their amount and degree of welding are higher in the pumices that have a higher abundance of microlites and microphenocrysts. These pumices have relatively high permeability and 2D connectivity at low vesicularity, which is accounted for by the existence of large irregularly shaped pores. These textural characteristics suggest that a series of partial fragmentation processes, including local rupturing of bubble walls and subsequent foam-collapse with permeable gas flow, might have occurred before the ultimate bulk fragmentation, thus resulting in the increase in permeability. We suggest that the 2D connectivity of pores is a useful parameter to quantify the degree of fragmentation of bubble walls and has the potential for use to assess their permeability.     

Permeability Evolution and Rock Brittle Failure

This paper reports an experimental study of the evolution of permeability during rock brittle failure and a theoretical analysis of rock critical stress level. It is assumed that the rock is a strain-softening medium whose strength can be described by Weibull’s distribution. Based on the two-dimensional renormalization group theory, it is found that the stress level λ_c (the ratio of the stress at the critical point to the peak stress) depends mainly on the homogeneity index or shape parameter m in the Weibull’s distribution for the rock. Experimental results show that the evolution of permeability is closely related to rock deformation stages: the permeability has a rapid increase with the growth of cracks and their surface areas (i.e., onset of fracture coalescence point), and reaches the maximum at rock failure. Both the experimental and analytical results show that this point of rapid increase in permeability on the permeability-pressure curve corresponds to the critical point on the stress-strain curve; for rock compression, the stress at this point is approximately 80% of the peak strength. Thus, monitoring the evolution of permeability may provide a new means of identifying the critical point of rock brittle fracture.     

The Kozeny‐Carman Equation with a Percolation Threshold

A procedure has been developed for calculating permeability (k) from the Kozeny‐Carman equation, a procedure that links ideas from percolation theory with the ideas of Koltermann and Gorelick (1995) and Esselburn et al. (2011) . The approach focuses on the proportion of coarser pores that are occupied by finer sediments relative to a percolation threshold proportion (ω_c). If the proportion occupied is below ω_c, then the unoccupied coarser pores percolate. Otherwise they do not percolate. Following the ideas of Koltermann and Gorelick (1995) , the effective grain‐size term in the Kozeny‐Carman equation is calculated using the geometric mean if the unoccupied coarse pores percolate, and using the harmonic mean if otherwise. Following ideas of Esselburn et al. (2011) , this approach is implemented by evaluating the potential for grains in each size category to occupy pores among sediment of each larger‐size category. Application of these ideas to physical sediment models for sands and gravels, which have known k, indicates that a threshold does indeed exist. Results also suggest that the Kozeny‐Carman equation is robust and gives representative values for k, even though ω_c is not precisely known.     

Continuum percolation theory for pressure–saturation characteristics of fractal soils: extension to non-equilibrium

Systematic experimental deviations from theoretical predictions derived for water retention characteristics of fractal porous media have previously been interpreted in terms of continuum percolation theory (at low moisture contents, below the critical volume fraction of water, α_c capillary flow ceases). In other work, continuum percolation theory was applied to find the hydraulic conductivity as a function of saturation for saturations high enough to guarantee percolation of capillary flow. Now these two problems are further linked, using percolation theory to estimate non-equilibrium water retention at matric potential values such that the equilibrium water content is too low for percolation of capillary flow paths. In particular, a procedure for developing a time-dependent moisture content is developed for experimental time scales long enough that film flow can provide an alternate mechanism for equilibrating when continuous capillary flow is not possible. The time scales are defined in terms of moisture-dependent length scales and film flow and capillary flow hydraulic conductivities. Imbibition is treated in the extreme case of no film-flow contribution to equilibration. In another application at higher matric potentials, recursive relations are derived for the water content of porous media during drying when external pressures are changed at rates too rapid for equilibrium to be attained by capillary flow.     

Multiphase Modeling of Geologic Carbon Sequestration in Saline Aquifers

Geologic carbon sequestration (GCS) is being considered as a climate change mitigation option in many future energy scenarios. Mathematical modeling is routinely used to predict subsurface CO₂ and resident brine migration for the design of injection operations, to demonstrate the permanence of CO₂ storage, and to show that other subsurface resources will not be degraded. Many processes impact the migration of CO₂ and brine, including multiphase flow dynamics, geochemistry, and geomechanics, along with the spatial distribution of parameters such as porosity and permeability. In this article, we review a set of multiphase modeling approaches with different levels of conceptual complexity that have been used to model GCS. Model complexity ranges from coupled multiprocess models to simplified vertical equilibrium (VE) models and macroscopic invasion percolation models. The goal of this article is to give a framework of conceptual model complexity, and to show the types of modeling approaches that have been used to address specific GCS questions. Application of the modeling approaches is shown using five ongoing or proposed CO₂ injection sites. For the selected sites, the majority of GCS models follow a simplified multiphase approach, especially for questions related to injection and local‐scale heterogeneity. Coupled multiprocess models are only applied in one case where geomechanics have a strong impact on the flow. Owing to their computational efficiency, VE models tend to be applied at large scales. A macroscopic invasion percolation approach was used to predict the CO₂ migration at one site to examine details of CO₂ migration under the caprock.     

Dynamics of a spherical viscoelastic shell: Implications to a criterion for fragmentation/expansion of bubbly magma

This paper investigates dynamics of a spherical bubble surrounded by a viscoelastic fluid. The purpose of the study is to understand the parameters which control expansion and fragmentation of bubbly magma by decompression. In particular, we focus on which occurs first, fragmentation or expansion. Supposing that rupture of the bubble wall occurs in a critical stress condition, we calculate the change of the bubble radius and tensile stress at the bubble wall for various decompression rates. Conditions in which tensile stress is stored in the shell are represented in terms of dimensionless parameters. The results are interpreted as follows: when magma viscosity is larger than a critical value, and the decompression time is shorter than viscous expansion time, tensile stress is stored before expansion; when magma viscosity is smaller than the critical value, tensile stress is not stored, no matter how rapid the decompression. Although it is a generally accepted theory that fragmentation is effected by stress conditions and decompression time, exactly how decompression time (t₁) effects the fragmentation is not yet fully understood. This study demonstrates that the stress condition is controlled by the length of the decompression time not relative to the viscoelastic relaxation time (t₁ / τ), but relative to the viscous expansion time (t₁ / τ^l_rlx). As suggested by recent experimental studies, the decompression time relative to viscoelastic relaxation time (t₁ / τ) is also significant to the fragmentation process itself. It indicates that the decompression time effects the fragmentation not through the stress condition. However more work must be completed to fully understand the particular relationship between the decompression time and relaxation time in terms of its influence on fragmentation.     

Geobarometry of ultramafic xenoliths from Loihi Seamount,Hawaii, on the basis of CO2 inclusions in olivine

Abundant fluid inclusions in olivine of dunite xenoliths (～1–3 cm) in basalt dredged from the young Loihi Seamount, 30 km southeast of Hawaii, are evidence for three coexisting immiscible fluid phases—silicate melt (now glass), sulfide melt (now solid), and dense supercritical CO₂ (now liquid + gas)—during growth and later fracturing of some of these olivine crystals. Some olivine xenocrysts, probably from disaggregation of xenoliths, contain similar inclusions.Most of the inclusions (2–10 μm) are on secondary planes, trapped during healing of fractures after the original crystal growth. Some such planes end abruptly within single crystals and are termed pseudosecondary, because they formed during the growth of the host olivine crystals. The “vapor” bubble in a few large (20–60 μm), isolated, and hence primary, silicate melt inclusions is too large to be the result of simple differential shrinkage. Under correct viewing conditions, these bubbles are seen to consist of CO₂ liquid and gas, with an aggregate ? = ～ 0.5–0.75 g cm^?3, and represent trapped globules of dense supercritical CO₂ (i.e., incipient “vesiculation” at depth). Some spinel crystals enclosed within olivine have attached CO₂ blebs. Spherical sulfide blebs having widely variable volume ratios to CO₂ and silicate glass are found in both primary and pseudosecondary inclusions, demonstrating that an immiscible sulfide melt was also present.Assuming olivine growth at ～ 1200°C and hydrostatic pressure from a liquid lava column, extrapolation of CO₂P-V-T data indicates that the primary inclusions were trapped at ～ 220–470 MPa (2200–4700 bars), or ～ 8–17 km depth in basalt magma of ? = 2.7 g cm^?3. Because the temperature cannot change much during the rise to eruption, the range of CO₂ densities reveals the change in pressure from that during original olivine growth to later deformation and rise to eruption on the sea floor. The presence of numerous decrepitated inclusions indicates that the inclusion sample studied is biased by the loss of higher-density inclusions and suggests that some part of these olivine xenoliths formed at greater depths.     

Experimental investigation of the elastic modulus of a fractal system—A model of fractured rocks

The elastic properties of a physical model representing a damaged rock matrix were studied using a square lattice deformed under tensile stress. The elastic modulusM of such a system varies in agreement with percolation theory as|x–x _c | ^f , wherex is the damage parameter andx _c the threshold value of the damage parameter,f3.6. Atxx _c the scale dependence ofM can be expressed asML ^–f/v , whereL is the size of the sample andv the correlation exponent in percolation theory.The experimental results are of interest in assessing elastic properties in earthquake focal zones and fault zones in general.     

Spatial and Temporal Variation of LURR and its Implication for the Tendency of Earthquake Occurrence in Southern California

— Based on the theory of LURR and its recent development, spatial and temporal variation of Y/Y _c (value of LURR/critical value of LURR) in the Southern California region during the period from 1980 through March, 2001 was studied. According to the previous study on the fault system and stress field in Southern California, we zoned the Southern California region into 11 parts in each of which the stress field is almost uniform. With the time window of one year, time moving step of three months, space window of a circle region with a radius of 100 km and space moving step of 0.25 degree in latitude and longitude direction, the evolution of Y/Y _c were snapshot. The scanning results show that obvious Y/Y _c anomalies occurred before 5/6 of strong earthquakes considered with a magnitude of 6.5 or greater. The critical regions of Y/Y _c are near the epicenters of the strong earthquakes and the Y/Y _c anomalies occur months to years prior to the earthquakes. The tendency of earthquake occurrence in the California region is briefly discussed on the basis of the examination of Y/Y _c .     

Dimensional analysis of two-phase flow including a rate-dependent capillary pressure–saturation relationship

The macroscopic modelling of two-phase flow processes in subsurface hydrosystems or industrial applications on the Darcy scale usually requires a constitutive relationship between capillary pressure and saturation, the P_c(S_w) relationship. Traditionally, it is assumed that a unique relation between P_c and S_w exists independently of the flow conditions as long as hysteretic effects can be neglected. Recently, this assumption has been questioned and alternative formulations have been suggested. For example, the extended P_c(S_w) relationship by Hassanizadeh and Gray [Hassanizadeh SM, Gray WG. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Resources 1990;13(4):169–86] proposes that the difference between the phase pressures to the equilibrium capillary pressure is a linear function of the rate of change of saturation, thereby introducing a constant of proportionality, the coefficient τ. It is desirable to identify cases where the extended relationship needs to be considered. Consequently, a dimensional analysis is performed on the basis of the two-phase balance equations. In addition to the well-known capillary and gravitational number, the dimensional analysis yields a new dimensionless number. The dynamic number Dy quantifies the ratio of dynamic capillary to viscous forces. Relating the dynamic to the capillary as well as the gravitational number gives the new numbers DyC and DyG, respectively. For given sets of fluid and porous medium parameters, the dimensionless numbers Dy and DyC are interpreted as functions of the characteristic length and flow velocity. The simulation of an imbibition process provides insight into the interpretation of the characteristic length scale. The most promising choice for this length scale seems to be the front width. We conclude that consideration of the extended P_c(S_w) relationship may be important for porous media with high permeability, small entry pressure and high coefficient τ when systems with a small characteristic length (e.g. steep front) and small characteristic time scale are under investigation.     

Factors controlling permeability–porosity relationships in magma

A model has been developed to investigate the sensitivity of magma permeability, k, to various parameters. Power-law relationships between k and porosity J are revealed, in agreement with previous experimental and theoretical studies. These relationships take the form % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBae % rbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyavP1wzZbIt % LDhis9wBH5garqqtubsr4rNCHbGeaGqiVCI8FfYJH8sipiYdHaVhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfeaY-biLkVcLq-JHqpepeea0-as % 0Fb9pgeaYRXxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaabau % aaaOqaaiqbdUgaRzaajaGaeyypa0Jaem4AaSMaei4la8IaemOCai3a % aWbaaSqabeaacqaIYaGmaaGccqGH9aqpcqWGHbqycqGGOaakcqaHgp % GzcqGHsislcqaHgpGzdaWgaaWcbaGaem4yamMaemOCaihabeaakiab % cMcaPmaaCaaaleqabaGaemOyaigaaaaa!4CE4! [^(k)] = k/r² = a(f- f_cr )^b\hat k = k/r^2 = a(\phi - \phi _{cr} )^b where r is the mean bubble radius, J_cr is the percolation threshold below which permeability is zero, and a and b are constants. It is discovered that % MathType!MTEF!2!1!+- % feaaeaart1ev0aaatCvAUfKttLearuavTnhis1MBaeXatLxBI9gBae % rbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyavP1wzZbIt % LDhis9wBH5garqqtubsr4rNCHbGeaGqiVCI8FfYJH8sipiYdHaVhbb % f9v8qqaqFr0xc9pk0xbba9q8WqFfeaY-biLkVcLq-JHqpepeea0-as % 0Fb9pgeaYRXxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaabau % aaaOqaaiqbdUgaRzaajaGaeyOeI0IaeqOXdygaaa!3CDB! [^(k)] - f\hat k - \phi relationships are independent of bubble size. The percolation threshold was found to lie at around 30% porosity. Polydisperse bubble-size distributions (BSDs) give permeabilities around an order of magnitude greater than monodisperse distributions at the same porosity. If bubbles are elongated in a preferred direction then permeability in this direction is increased, but, perpendicular to this direction, permeability is unaffected. In crystal-free melts the greatest control on permeability is the ease of bubble coalescence. In viscous magmas, or when the cooling time-scale is short, bubble coalescence is impeded and permeability is much reduced. This last effect can cause variations in permeability of several orders of magnitude.     

Upscaling hydraulic conductivity based on the topology of the sub-scale structure

The hydraulic conductivity of heterogeneous porous media depends on the distribution function and the geometry of local conductivities at the smaller scale. There are various approaches to estimate the effective conductivity K_eff at the larger scale based on information about the small scale heterogeneity. A critical geometric property in this ‘upscaling’ procedure is the spatial connectivity of the small-scale conductivities. We present an approach based on the Euler-number to quantify the topological properties of heterogeneous conductivity fields, and we derive two key parameters which are used to estimate K_eff. The required coefficients for the upscaling formula are obtained by regression based on numerical simulations of various heterogeneous fields. They are found to be generally valid for various different isotropic structures. The effective unsaturated conductivity function K_eff (ψ_m) could be predicted satisfactorily. We compare our approach with an alternative based on percolation theory and critical path analysis which yield the same type of topological parameters. An advantage of using the Euler-number in comparison to percolation theory is the fact that it can be obtained from local measurements without the need to analyze the entire structure. We found that for the heterogeneous field used in this study both methods are equivalent.     

Using velocimeter signal to noise ratio as a surrogate measure of suspended mud concentration

This study examines the relationship between suspended sediment concentration (SSC) and the signal to noise ratio (SNR) recorded by a 6 MHz Nortek Vector velocimeter in a laboratory water tank using four different synthetic and natural mud mixtures and different combinations of the user-set Vector parameters transmit power level and velocity range. For concentrations less than 1500 mg/l (1.5 g/l), a region of linearity between the logarithm of concentration and time-average SNR was found for all sediment types and transmitter power level settings. Within this concentration range, the experimental data was used to develop calibrated equations of the form, log(SSC)=c₁SNR+c₂; R² values for all calibrated equations were greater than 0.98, suggesting that properly calibrated relations can yield accurate time-averaged SSC measurements using Vector measured SNR. An analysis of the general calibration equation indicated that the predicted SSC values are sensitive to changes in the coefficient values for c₁ and c₂. Even small (10%) deviations in coefficient values resulted in 20%-65% changes in the predicted SSC. Variation in c₁ and c₂ values among all four mud mixtures were significant enough that the calibrated equations could not be used interchangeably. This was true even among three samples that had similar particle-size distributions. Translation of raw 32 Hz SNR data to 32 Hz SSC time series produced excessively large variation in the SSC time series. Several smoothing and filtering schemes were examined to reduce the magnitude of these fluctuations to more reasonable levels. Of the methods tested, a two-sided moving average functioned best at removing fine-scale variation while retaining larger-scale trends. A 96-point (3 Hz) averaging window brought 98.6% of the Vector estimated SSC time series values to within ±10% of the time-average physical samples. Impacts of turbulent kinetic energy and sampling volume size on instrument recorded SNR were also empirically examined.     

The Dependence of Constitutive Properties on Temperature and Effective Normal Stress in Seismogenic Environments

— We have evaluated how the parameters prescribing the slip-dependent constitutive law are affected by temperature and effective normal stress, by conducting the triaxial fracture experiments on Tsukuba-granite samples in seismogenic environments, which correspond to a depth range to 15 km. The normalized critical slip displacement D _c almost remains constant below 300^oC (insensitive to both temperature and effective normal stress σ _n ^eff); D _c increases with increasing temperature above 300 °C, and the rate of D _c increase with temperature tends to be largest at higher σ _n ^eff. The breakdown stress drop Δτ _b for the granite at constant σ _n ^eff is roughly 80 MPa below 300 °C, and does not depend on σ _n ^eff. Above 300 °C, Δτ _b decreases gradually with increasing temperature, and the rate of Δτ _b reduction with temperature increases at higher σ _n ^eff. The peak shear strength τ _p increases nearly linearly with increasing σ _n ^eff below 300 °C. However, τ _p becomes lower above 300 °C, deviating from the linear relation extrapolated from below 300 °C. This is consistent with the onset of crystal plastic deformation mechanisms of Tsukuba granite.     

Predicting DNAPL entrapment and recovery: the influence of hydraulic property correlation

The influence of aquifer property correlation on multiphase fluid migration, entrapment and recovery was explored by incorporating correlated and uncorrelated porosity, permeability, and capillary pressure-saturation (P_c-Sat) parameter fields in a cross-sectional numerical multiphase flow model. Comparison of two-dimensional entrapped organic saturation distributions for a simulated tetrachloroethylene (PCE) spill in ensembles of aquifer realizations suggests that the degree of spatial correlation in P_c-Sat parameters exerts a controlling influence on dense nonaqueous phase liquid (DNAPL) spreading and redistribution in saturated aquifers. The predicted evolution of DNAPL source zones and resultant remediation efficiency under surfactant enhanced aquifer remediation (SEAR) also appear to be strongly influenced by the spatial correlation of aquifer parameters and multiphase flow constitutive relationships. Results for a limited number of realizations selected from each ensemble showed that removal of 60% to 99% of entrapped PCE could reduce dissolved contaminant concentration and mass flux by approximately two orders of magnitude under natural gradient conditions. Aqueous phase contaminant mass flux did not vary uniformly as a function of % DNAPL removed, however, and notable differences in behavior were observed for models incorporating correlated versus uncorrelated P_c-Sat and permeability fields. Although these results must be confirmed through analysis of additional realizations, it is likely that similar or larger differences between correlated and uncorrelated system behavior will be observed in aquifers with greater spatially variability than that of the nonuniform, homogeneous sand aquifer studied here. Funding for this research was provided by the United States Environmental Protection Agency, Great Lakes and Mid-Atlantic Center for Hazardous Substance Research under Grant No. R-825540, the Michigan Department of Environmental Quality under Contract No. Y80011, and the Strategic Environmental Research and Development Program under Project No. CU-1293. The content of this publication does not necessarily represent the views of these agencies and has not been subject to agency review.     

Magnetic hysteresis as a function of low temperature for deep-sea basalts containing large titanomagnetite grains-inference of domain state and controls on coercivity

Hysteresis loops to 1200 oersteds (9.55×10⁴ A m^?1) are measured between 295 K and 105 K for two deep-sea basalts (DSDP, Leg 34 and 37) containing large (～200 μm) unexsolved titanomagnetite grains. The Curie points, electron microprobe analyses and saturation magnetizations of the magnetic grains are the same as for unoxidized synthetic titanomagnetite (xFe₂TiO₄·(l ? x)Fe₃O₄) with x=0.6.As temperature is lowered from 295 to 190 K, coercive force H_c slowly rises from ～40 Oe to ～95 Oe approximately in proportion to the rise in the magnetostriction constant λ. Presumably, H_c is controlled by λ through internal stresses impeding domain wall motion. As expected of multidomain grains, the ratio of saturation remanence to saturation magnetization (in 1200 oersted cycles) j_R/j_S rises approximately in proportion to H_c, with a constant of proportionality consistent with titanomagnetite (x=0.6).As temperature is lowered from 190 to 120 K, H_c rises rapidly to ～400 Oe as a roughly linear function of the magnetocrystalline anisotropy constant K₁. Perhaps H_c is now controlled by K₁ through non-magnetic inclusions impeding domain wall motion.As temperature is lowered from 120 to 105 K, H_c rises even more rapidly to ～600 Oe. The control over H_c seems to have changed again, though most of the titanomagnetite is in grains large enough to still contain a few domains. The ratio j_R/j_S reaches 0.7 by 105 K and appears to be saturating towards the theoretical limit of 0.83.     

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.     

Attenuation characteristics of coda waves and estimation ofQc values in eastern China

For short-period near-earthquake records in eastern China, from the empirical attenuation formula of coda ground motion amplitudeA with timeτ: lgA=G?2. 235 lgτ, using the single scattering theory modified with epicentral distance, we obtain the curve family of corrected coda amplitudeA _c(r,t), andω/2Q _c values for each time interval of coda. From this,Q _c(f,h) values, which correspond to each observational average frequency and sampling depth, are calculated. The results substantially agree with those observationalQ _c values in Yunnan, Beijing and central Asia.     

Modelling investigation of water partitioning at a semiarid ponderosa pine hillslope

The effects of vegetation root distribution on near‐surface water partitioning can be two‐fold. On the one hand, the roots facilitate deep percolation by root‐induced macropore flow; on the other hand, they reduce the potential for deep percolation by root‐water‐uptake processes. Whether the roots impede or facilitate deep percolation depends on various conditions, including climate, soil, and vegetation characteristics. This paper examines the effects of root distribution on deep percolation into the underlying permeable bedrock for a given soil profile and climate condition using HYDRUS modelling. The simulations were based on previously field experiments on a semiarid ponderosa pine (Pinus ponderosa) hillslope. An equivalent single continuum model for simulating root macropore flow on hillslopes is presented, with root macropore hydraulic parameterization estimated based on observed root distribution. The sensitivity analysis results indicate that the root macropore effect dominates saturated soil water flow in low conductivity soils (K_matrix below 10^?7 m/s), while it is insignificant in soils with a K_matrix larger than 10^?5 m/s, consistent with observations in this and other studies. At the ponderosa pine site, the model with simple root‐macropore parameterization reasonably well reproduces soil moisture distribution and some major runoff events. The results indicate that the clay‐rich soil layer without root‐induced macropores acts as an impeding layer for potential groundwater recharge. This impeding layer results in a bedrock percolation of less than 1% of the annual precipitation. Without this impeding layer, percolation into the underlying permeable bedrock could be as much as 20% of the annual precipitation. This suggests that at a surface with low‐permeability soil overlying permeable bedrock, the root penetration depth in the soil is critical condition for whether or not significant percolation occurs. Copyright © 2010 John Wiley & Sons, Ltd.