numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media a numerical procedure for the determination of equivalent grid block permeability tensors for heterogeneous porous media is presented the method entails solution of the fine scale pressure equation subject to periodic boundary conditions to yield upon appropriate averaging of the fine scale velocity field the coarse scale or equivalent grid block permeability when the region over which this coarse scale permeability is computed constitutes a representative elementary volume rev the resulting equivalent permeability may be interpreted as the effective permeability of the region solution of the pressure equation on the fine scale is accomplished through the application of an accurate triangle based finite element numerical procedure which allows for the modeling of geometrically complex features the specification of periodic boundary conditions is shown to yield symmetric positive definite equivalent permeability tensors in all cases the method is verified through application to a periodic model problem and is then applied to the scale up of areal and cross sections with fractally generated permeability fields the applicability and limitations of the method for these more general heterogeneity fields are discussed

oscillations of first order neutral delay differential equations abstract consider the neutral delay differential equation d dt y t py t qy t 0 t t 0 where q and are positive constants while p 1 0 for the case p 1 0 see ladas and sficas oscillations of neutral delay differential equations to appear the following results are then proved theorem 1 assume p and q 1 p 1 e then every solution of eq oscillates theorems 3 assume p 0 then every nonoscillatory solution y t of eq tends to zero as t theorem 4 assume p 0 then a necessary condition for all solutions of eq to oscillate is that theorem 5 assume p 0 and q 1 p 1 e then every solution of eq oscillates extensions of these results to equations with variable coefficients are also obtained

nonlinear joint inversion of tomographic data using swarm intelligence geophysical techniques offer the potential to tomographically image physical parameter variations in the ground in two or three dimensions due to the limited number and accuracy of the recorded data geophysical model generation by inversion suffers ambiguity linking the model generation process of disparate data by jointly inverting two or more data sets allows for improved model reconstruction fully nonlinear inversion using optimization techniques searching the solution space of the inverse problem globally enables quantitative assessment of the ambiguity inherent to the model reconstruction we used two different multiobjective particle swarm optimization approaches to jointly invert synthetic crosshole tomographic data sets comprising radar and p wave traveltimes respectively beginning with a nonlinear joint inversion founded on the principle of pareto optimality and game theoretic concepts we obtained a set of pareto optimal solutions comprising commonly structured radar and p wave velocity models for low computational costs however the efficiency of the approach goes along with some risk of achieving a final model ensemble not adequately illustrating the ambiguity inherent to the model reconstruction process taking advantage of the results of the first approach we inverted the database using a different nonlinear joint inversion approach reducing the multiobjective optimization problem to a single objective one computational costs were significantly higher but the final models were obtained mutually independently allowing for objective appraisal of model parameter determination despite the high computational effort the approach was found to be an efficient nonlinear joint inversion formulation compared to what could be extracted from individual nonlinear inversions of both data sets

three dimensional stochastic analysis of macrodispersion in aquifers the dispersive mixing resulting from complex flow in three dimensionally heterogeneous porous media is analyzed using stochastic continuum theory stochastic solutions of the perturbed steady flow and solute transport equations are used to construct the macroscopic dispersive flux and evaluate the resulting macrodispersivity tensor in terms of a three dimensional statistically anisotropic input covariance describing the hydraulic conductivity with a statistically isotropic input covariance the longitudinal macrodispersivity is convectively controlled but the transverse macrodispersivity is proportional to the local dispersivity and is several orders of magnitude smaller than the longitudinal term with an arbitrarily oriented anisotropic conductivity covariance all components of the macrodispersivity tensor are convectively controlled and the ratio of transverse to longitudinal dispersivity is of the order of 10 1 in this case the off diagonal components of the dispersivity tensor are significant being numerically larger than the diagonal transverse terms and the transverse dispersion process can be highly anisotropic dispersivities predicted by the stochastic theory are shown to be consistent with controlled field experiments and monte carlo simulations the theory which treats the asymptotic condition of large displacement indicates that a classical gradient transport fickian relationship is valid for large scale displacements

upscaling of permeability of anisotropic heterogeneous formations 1 the general framework in numerical simulations of flow through heterogeneous formations the domain is partitioned into numerical elements the solution requires assigning physical properties to each numerical block the process of transferring information from the scale of actual heterogeneity to that of the numerical elements is known as upscaling we consider steady one phase flow and the only property of interest is the permeability which is regarded as a random space function and the same is true for the upscaled conductivity in this paper we establish the necessary and sufficient conditions to be satisfied by upscaling the necessary conditions are expressed with the aid of the global response of the formation e g the total flux caused by a constant pressure head drop applied on the boundaries the requirement is that the expected value and the variance of the total flux are the same in the actual and upscaled domains these are supplemented by local conditions which stipulate that space averages of flow variables over the numerical blocks in the upscaled domain tend to those in the actual formation when the elements size tends to 0 the result of this analysis is that the upscaled permeability must be such as to ensure the equality in a statistical sense between the space averaged dissipation in the two media by assuming an unbounded domain average uniform flow and stationarity simplified relationships between the moments of the dissipation in the upscaled and actual media are derived it is shown that the effective permeability of the two media is the same the approach is illustrated for stratified formations for which exact composition rules are possible even in this simple case the upscaled permeability is a tensor characterized at second order by two mean components and three covariance functions

stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers 2 impervious boundary the spatial variability of the head h in a two dimensional flow in the vicinity of an impervious boundary is investigated this study is a continuation of a previous one rubin and dagan 1988 which dealt with the influence of a given head boundary by representing h and the log transmissivity y as space random function and by solving the flow equation first order closed form analytical expressions for the head variogram and the head log transmissivity y covariance are developed these expressions offer the means to evaluate the influence of the boundary on the joint y h random field the assumption of unbounded domain is examined and it is found to be a good approximation at distances larger than three log transmissivity integral scales from the boundary by using conditional probabilities a simple method to estimate the statistical moments close to the boundary is presented it requires the knowledge of the moments of y and h in the unbounded domain only the method is compared with the exact analytical solution showing favorable results

new oscillation criteria for first order nonlinear neutral delay differential equations some new oscillation criteria of first order nonlinear neutral delay differential equations with variable coefficients are given our results extend and improve some of the well known previously results in the literature some examples are considered to illustrate our main results

stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers 1 constant head boundary the spatial variability of log transmissivity y and head h in aquifers assumes a major role in determining the solutions of the direct flow problem as well as of the inverse problem investigation of the joint y h variability has been cast in the past in numerical and analytic frames analytic solutions for the y h statistical moments in two dimensions assumed the flow to occur in an unbounded domain in this study exact analytical expressions for the y h moments are derived which account for the presence of a given head boundary in a half plane this result is achieved by a first order approximation and for an exponential y covariance the result offers the opportunity to examine the effects of boundaries on the semivariogram of h and on the y h cross covariance the assumption of unbounded domain is examined and shown to be accurate at distances larger than two y integral scales from the boundary by using conditional probabilities a general and simple method to estimate the moments close to the boundary is presented it requires the knowledge of the moments of y and h in the unbounded domain only the method is compared with the exact analytic solution showing excellent results

nonlocal properties of nonuniform averaged flows in heterogeneous media the properties of nonuniform average potential flows in media of stationary random conductivity are studied the mathematical model of average flow is derived as a system of governing equations to be satisfied by mean velocity and mean head the averaged darcy s law determines the effective conductivity as an integral operator of the convolution type relating the mean velocity to the mean head gradient in a nonlocal way in fourier domain the mean velocity is proportional to the mean head gradient the coefficient of proportionality is referred to as the effective conductivity tensor and is derived by perturbation methods in terms of functionals of the conductivity spatial moments it is shown that the effective conductivity cannot be defined uniquely for potential flows however this nonuniqueness does not affect the spatial distribution of the mean head and velocity analytical expressions of the effective conductivity tensor are derived for two and three dimensional flows and for exponential and gaussian correlations of isotropic conductivity the fundamental solution of the governing equations in effective media mean green function is calculated for the same cases two new asymptotic models of the averaged darcy s law are developed to be applicable to large and small scales of heterogeneity several asymptotic expansions of tue two dimensional and three dimensional mean green functions are derived for exponential and gaussian correlations

a dynamic programming approach to first arrival traveltime computation in media with arbitrarily distributed velocities curved ray tomographic traveltime inversion reverse time migration and various other seismic modeling applications require the calculation of traveltime and raypath information throughout a two or three dimensional medium when arbitrary velocity distributions and curved rays are involved traditional ray shooting or bending procedures can be time consuming and error prone a two dimensional dynamic programming traveltime computation technique based upon fermat s principle uses simple calculus techniques and a systematic mapping scheme to determine first arrival times on a uniform grid given an arbitrary discrete velocity distribution it accurately handles large contrast discontinuous velocity distributions including those that generate caustics first arrival seismic energy can travel either as transmitted waves diffracted waves or headwaves and this technique models all types the traveltime computations begin with starting values computed near the source location then the mapping systemat

a higher order approximation to effective conductivity in media of anisotropic random structure properties of the effective conductivity tensor keff are studied by deriving the second order terms in its expansion in the variance 2 of normally distributed log conductivity it is shown that for media of anisotropic structure the components of the effective conductivity tensor are expressed by a functional of the log conductivity covariance that is it depends on the shape of the correlation function and not only on anisotropy ratios variance 2 and space dimensions however the trace of keff is independent of the log conductivity autocovariance and for a given mean conductivity depends only on 2 the dependence of the effective conductivity on the correlation structure is illustrated for gaussian and exponential autocovariances of log conductivity and for two and three dimensional flows

traveltime inversion for 2 d anomaly structures this work presents a traveltime inversion method that uses parametric functions to represent 2 d anomaly structures these functions are described by a small set of unknown parameters which in turn are obtained after solving a highly nonlinear optimization problem via simulated annealing sa the procedure favors neither smooth nor high contrasting anomalies and keeps the number of unknowns very small so as to make the problem tractable using sa yet the strategy allows one to accommodate a large class of velocity models results indicate that this new approach typically yields better images than a standard linearized inversion based on a cell parameterization scheme

on the oscillation of solutions and existence of positive solutions of neutral difference equations abstract we obtain sufficient conditions for the oscillation of all solutions and existence of positive solutions of the neutral difference equation x n cx n m p n x n k 0 n 0 1 2 where c and p n are real numbers m and k are integers and p n m and k are nonnegative

on first order neutral differential equations of euler form with unbounded delays abstract in this paper we investigate the first order neutral differential equation of euler form with variable unbounded delay d d t x t cx t 1 t i 1 n p i x i t 0 t t 0 0 where 0 c 1 0 1 0 i 1 and p i 0 are constants i 1 2 n some necessary and sufficient as well as explicit sufficient conditions for the oscillation of all solutions are established several relevant results in the literature are improved

oscillation and nonoscillation in first order neutral differential equations abstract verifiable sufficient conditions are obtained respectively for the oscillation and nonoscillation of the neutral differential equation x t cx t px t 0

existence of bounded nonoscillatory solutions of first order nonlinear neutral delay differential equations the aim of this paper is to study the following first order nonlinear neutral delay differential equation ddt x t c t x email protected h t f x email protected 1 x email protected 2 x email protected k g t t t 0 where c h email protected c t 0 r t 0 s email protected r for email protected j k 1 k and email protected c r k r by using the schauder and krasnoselskii fixed point theorems we establish the existence of uncountably many bounded nonoscillatory solutions for the above equation to dwell upon the importance and advantages of our results seven nontrivial examples are included

reservoir characterization and inversion uncertainty via a family of particle swarm optimizers history matching provides to reservoir engineers an improved spatial distribution of physical properties to be used in forecasting the reservoir response for field management the ill posed character of the history matching problem yields nonuniqueness and numerical instabilities that increase with the reservoir complexity these features might cause local optimization methods to provide unpredictable results not being able to discriminate among the multiple models that fit the observed data production history also the high dimensionality of the inverse problem impedes estimation of uncertainties using classical markov chain monte carlo methods we attenuated the ill conditioned character of this history matching inverse problem by reducing the model complexity using a spatial principal component basis and by combining as observables flow production measurements and time lapse seismic crosswell tomographic images additionally the inverse problem was solved in a stochastic framework for this purpose

oscillation of first order neutral functional differential equations abstract some new sufficient conditions are obtained for oscillation of a kind of neutral differential equations these conditions improve some recent results

prediction of steady state flow in nonuniform geologic media by conditional moments exact nonlocal formalism effective conductivities and weak approximation we consider the effect of measuring randomly varying local hydraulic conductivities k x on one s ability to predict steady state flow within a bounded domain driven by random source and boundary functions more precisely we consider the prediction of local hydraulic head h x and darcy flux q x by means of their unbiased ensemble moments h x and q x conditioned on measurements of k x these predictors satisfy a deterministic flow equation in which q x x h x r x where x is a relatively smooth unbiased estimate of k x and r x is a residual flux we derive a compact integral expression for r x which is rigorously valid for a broad class of k x fields including fractals it demonstrates that q x is nonlocal and non darcian so that an effective hydraulic conductivity does not generally exist we show analytically that under uniform mean flow the effective conductivity may be a scalar a symmetric or a nonsymmetric tensor or a set of directional scalars which do not form a tensor we demonstrate numerically that in two dimensional mean radial flow it may increase from the harmonic mean of k x near interior and boundary sources to the geometric mean far from such sources for cases where r x can neither be expressed nor approximated by a local expression we propose a weak integral approximation closure which appears to work well in media with pronounced heterogeneity and improves as the quantity and quality of k x measurements increase the nonlocal deterministic flow equation can be solved numerically by standard methods our theory shows clearly how the scale of grid discretization should relate to the scale quantity and quality of available data after providing explicit approximations for the second moments of head and flux prediction errors we conclude by discussing practical methods to compute x from noisy measurements of k x and to calculate required second moments of the associated estimation errors when k x is lognormal