Effect Of Spatial Correlation Research Articles

Role of quantum coherence in shaping the line shape of an exciton interacting with a spatially and temporally correlated bath.

Kubo's fluctuation theory of line shape forms the backbone of our understanding of optical and vibrational line shapes, through such concepts as static heterogeneity and motional narrowing. However, the theory does not properly address the effects of quantum coherences on optical line shape, especially in extended systems where a large number of eigenstates are present. In this work, we study the line shape of an exciton in a one-dimensional lattice consisting of regularly placed and equally separated optical two level systems. We consider both linear array and cyclic ring systems of different sizes. Detailed analytical calculations of line shape have been carried out by using Kubo's stochastic Liouville equation (SLE). We make use of the observation that in the site representation, the Hamiltonian of our system with constant off-diagonal coupling J is a tridiagonal Toeplitz matrix (TDTM) whose eigenvalues and eigenfunctions are known analytically. This identification is particularly useful for long chains where the eigenvalues of TDTM help understanding crossover between static and fast modulation limits. We summarize the new results as follows. (i) In the slow modulation limit when the bath correlation time is large, the effects of spatial correlation are not negligible. Here the line shape is broadened and the number of peaks increases beyond the ones obtained from TDTM (constant off-diagonal coupling element J and no fluctuation). (ii) However, in the fast modulation limit when the bath correlation time is small, the spatial correlation is less important. In this limit, the line shape shows motional narrowing with peaks at the values predicted by TDTM (constant J and no fluctuation). (iii) Importantly, we find that the line shape can capture that quantum coherence affects in the two limits differently. (iv) In addition to linear chains of two level systems, we also consider a cyclic tetramer. The cyclic polymers can be designed for experimental verification. (v) We also build a connection between line shape and population transfer dynamics. In the fast modulation limit, both the line shape and the population relaxation, for both correlated and uncorrelated bath, show similar behavior. However, in slow modulation limit, they show profoundly different behavior. (vi) This study explains the unique role of the rate of fluctuation (inverse of the bath correlation time) in the sustenance and propagation of coherence. We also examine the effects of off-diagonal fluctuation in spectral line shape. Finally, we use Tanimura-Kubo formalism to derive a set of coupled equations to include temperature effects (partly neglected in the SLE employed here) and effects of vibrational mode in energy transfer dynamics.

The effect of road network patterns on pedestrian safety: A zone-based Bayesian spatial modeling approach

Pedestrian safety is increasingly recognized as a major public health concern. Extensive safety studies have been conducted to examine the influence of multiple variables on the occurrence of pedestrian-vehicle crashes. However, the explicit relationship between pedestrian safety and road network characteristics remains unknown. This study particularly focused on the role of different road network patterns on the occurrence of crashes involving pedestrians. A global integration index via space syntax was introduced to quantify the topological structures of road networks. The Bayesian Poisson-lognormal (PLN) models with conditional autoregressive (CAR) prior were then developed via three different proximity structures: contiguity, geometry-centroid distance, and road network connectivity. The models were also compared with the PLN counterpart without spatial correlation effects. The analysis was based on a comprehensive crash dataset from 131 selected traffic analysis zones in Hong Kong.The results indicated that higher global integration was associated with more pedestrian-vehicle crashes; the irregular pattern network was proved to be safest in terms of pedestrian crash occurrences, whereas the grid pattern was the least safe; the CAR model with a neighborhood structure based on road network connectivity was found to outperform in model goodness-of-fit, implying the importance of accurately accounting for spatial correlation when modeling spatially aggregated crash data.

Spatio-temporal evolution of urban innovation structure based on zip code geodatabase: An empirical study from Shanghai and Beijing

In today’s world, the innovation of science and technology has become the key support for improving comprehensive national strength and changing the mode of social production and lifestyle. The country that possesses world-class scientific and technological innovation cities maximizes the attraction of global innovation factors and wins a strategic initiative in international competition. Based on the urban zip code geodatabase, an evaluation system of urban innovation with the perspective of innovation outputs, and the spatial evolutionary mode, concerning the structure of innovation space of Shanghai and Beijing from 1991 to 2014, was developed. The results of the research indicated that the zip code geodatabase provided a new perspective for studying the evolving spatial structure of urban innovation. The resulting evaluation of the spatial structure of urban innovation using the urban zip code geodatabase established by connecting random edge points, was relatively effective. The study illustrates the value of this methodology. During the study period, the spatial structure of innovation of Shanghai and Beijing demonstrated many common features: with the increase in urban space units participating in innovation year by year, the overall gap of regional innovation outputs has narrowed, and the trend towards spatial agglomeration has strengthened. The evolving spatial structure of innovation of Shanghai and Beijing demonstrated differences between the common features during the 25 years as well: in the trend towards the suburbanization of innovation resources, the spatial structure of innovation of Shanghai evolved from a single-core to a multi-core structure. A radiation effect related to traffic arteries as spatial diffusion corridors was prominent. Accordingly, a spatial correlation effect of its innovation outputs also indicated a hollowness in the city center; the spatial structure of innovation of Beijing had a single-core oriented structure all the way. Together with the tendency for innovation resources to be agglomerated in the city center, the spatial correlation effect of innovation outputs reflected the characteristics of the evolutionary feature where “rural area encircles cities”. The innovation spatial structure of Shanghai and Beijing have intrinsic consistency with the spatial structure of their respective regions (Yangtze River Delta urban agglomeration and Beijing-Tianjin-Hebei metropolitan region), which suggested that the principle of proportional and disproportional distribution of a city-scale pattern of technological and innovational activities is closely related to its regional innovation pattern.

Transport and localization in a topological phononic lattice with correlated disorder

Recently proposed classical analogs of topological insulators in phononic lattices have the advantage of much more accessible experimental realization as compared to conventional materials. Drawn to their potential practical structural applications, we investigate how disorder, which is generically non-negligible in macroscopic realization, can attenuate the topologically protected edge (TPE) modes that constitute robust transmitting channels at zero disorder. We simulate the transmission of phonon modes in a quasi-one-dimensional classical lattice waveguide with mass disorder, and show that the TPE mode transmission remains highly robust ($\Xi\sim1$) in the presence of uncorrelated disorder, but diminishes when disorder is spatially correlated. This reduction in transmittance is attributed to the Anderson localization of states within the mass disorder domains. By contrast, non-TPE channels exhibit qualitatively different behavior, with spatial correlation in the mass disorder leading to significant transmittance reduction (enhancement) at low (high) frequencies. Our results demonstrate how topologically protected edge modes drastically modify the effect of spatial correlation on mode localization.

Functional principal component analysis of spatially correlated data

This paper focuses on the analysis of spatially correlated functional data. We propose a parametric model for spatial correlation and the between-curve correlation is modeled by correlating functional principal component scores of the functional data. Additionally, in the sparse observation framework, we propose a novel approach of spatial principal analysis by conditional expectation to explicitly estimate spatial correlations and reconstruct individual curves. Assuming spatial stationarity, empirical spatial correlations are calculated as the ratio of eigenvalues of the smoothed covariance surface Cov(X_i(s),X_i(t)) and cross-covariance surface Cov(X_i(s), X_j(t)) at locations indexed by i and j. Then a anisotropy Matérn spatial correlation model is fitted to empirical correlations. Finally, principal component scores are estimated to reconstruct the sparsely observed curves. This framework can naturally accommodate arbitrary covariance structures, but there is an enormous reduction in computation if one can assume the separability of temporal and spatial components. We demonstrate the consistency of our estimates and propose hypothesis tests to examine the separability as well as the isotropy effect of spatial correlation. Using simulation studies, we show that these methods have some clear advantages over existing methods of curve reconstruction and estimation of model parameters.

A design method of fairing acoustic noise mitigation for Korean space launcher

In this presentation, fairing acoustic protection system (APS) for Korean space launcher is introduced. The design of APS for payload fairing of KSLV-II is summarized. The current APS consists of acoustic blankets for midfrequency range absorption and acoustic resonators for low frequency noise absorption. Detailed design procedures of APS, which include external acoustic loading prediction based on the modified NASA SP-8072 monograph and fairing system vibro-acoustic analysis, are presented. An acoustic test of a cylindrical composite structure with APS is also presented. The effect of spatial correlation of external acoustic excitation on the vibro-acoustic response of fairing structure and its interior volume is discussed. The concept of future APS by using the micro-perforated panel absorber combined with Helmholtz resonators is also introduced. Effects of high pressure environment on the acoustic absorption of micro-perforated panel is discussed.

Space–Time Network Coding With Antenna Selection

In this paper, we investigate the space–time network coding (STNC) with antenna selection (AS) in the cooperative multiple-input–multiple-output (MIMO) network, where $U$ users communicate with a common destination $D$ with the aid of $R$ decode-and-forward (DF) relays. In this network, the best transmit/receive antenna pair with the highest signal-to-noise (SNR) ratio is selected to perform the signal transmission and reception over the user–destination and relay–destination links. To quantify the performance degradation of STNC with AS due to time delay between instants of channel state information (CSI) estimation and data transmission, we derive the symbol error rate (SER) and capacity expressions over flat Rayleigh fading channels. The asymptotic SER expression reveals that STNC with AS guarantees full diversity order of $(N_u \!+\! \sum_{r = 1}^R N_r)N_{D}$ , where $N_u$ , $N_r$ , and $N_{D}$ are the antenna numbers of user $u$ , relay $r$ , and the destination $D$ , respectively, when the AS is performed based on perfect CSI, and outdated CSI degrades the full diversity order to $R+\mbox{1}$ . We also examine the effect of spatial correlation on the performance of STNC with AS by obtaining new closed-form expression for the asymptotic SER, which indicates that STNC with AS achieves the full diversity order over flat correlated Rayleigh channels, regardless of the value of spatial correlation coefficient. Numerical and simulation results are provided to demonstrate the accuracy of our theoretical analysis and evaluate the performance of STNC with AS.

Fully Connected Continuous Conditional Random Field With Stochastic Cliques for Dark-Spot Detection In SAR Imagery

Dark-spot detection from synthetic aperture radar (SAR) imagery is a fundamental step in marine oil-spill detection and monitoring. However, achieving robust and accurate detection is difficult due to SAR sensor limitations and the complex marine environment. To address this problem, the large-scale spatial contextual information in SAR imagery has to be utilized to increase the class separability between the dark spot and the background. A stochastic fully connected continuous conditional random field (SFCCRF) approach to model SAR imagery and perform soft-label inference has been designed and built, leading to an efficient detection algorithm. Instead of treating all pixels in the imagery as being connected, SFCCRF determines the connectivity of two pixels in a stochastic manner based on their proximity in both feature space and image space. Since SFCCRF provides an efficient and effective way for modeling the large-scale spatial correlation effect, the resulting soft labels can resist the influence of speckle noise and highlight the difference between dark spot and the background. Dark-spot detection is achieved by binarizing the soft labels estimated by SFCCRF. The proposed algorithm is tested on both simulated and real SAR imageries. The results show that SFCCRF can delineate the dark spot with low commission and omission error rates.

Finite SNR diversity-multiplexing tradeoff with spatial correlation and mutual coupling effects for Rayleigh MIMO channels

In the literature, the finite signal-to-noise ratio (SNR) situation for the fundamental diversity-multiplexing tradeoff (DMT) of multiple-input–multiple-output systems (MIMO systems) has been attached great importance. However, only lower bounds or coarse approximations of the outage probability have been proposed to develop coarse bounds of the finite-SNR DMT in the literature, and their approximation errors are still non-negligible. In order to solve the aforementioned weaknesses, we first propose an accurate finite-SNR outage probability for Rayleigh MIMO fading channels and then use it to derive the corresponding finite-SNR DMT. The proposed finite-SNR DMT can be used as an accurate guideline at finite SNR for rate-adaptive MIMO applications. In addition, the impact of antenna mutual coupling (along with antenna spatial correlation) on the finite-SNR outage probability and consequently its impact on the finite-SNR DMT are analyzed. Our results reveal that the spatial correlation of antenna arrays cannot provide gains to the outage performance and the finite-SNR DMT. In contrast, when the antenna spacing of antenna arrays is appropriately specified, the mutual coupling of antenna arrays is in favor of the outage performance and the finite-SNR DMT. Finally, we present computer simulation results for illustration and comparison to confirm the validity of our research work.

GHG Emissions, Economic Growth and Urbanization: A Spatial Approach

To gain a greater understanding of the spatial spillover effect of greenhouse gas emissions and their influencing factors, this paper provides a spatial analysis of four gas pollutants (CO2 emissions, SO2 emissions, NOx emissions, and dust emissions). Focusing on China, the paper also explores whether the four gas pollutants are influenced by the emissions of neighboring regions and other possible sources. The paper uses a global spatial autocorrelation analysis, local spatial association analysis and spatial lag model for empirical work. The results suggest that CO2, SO2, and NOx emissions show significant positive results for both the spatial correlation and space cluster effect in provincial space distribution.CO2 and NOx emissions have a significant positive spillover effect, while the SO2 emissions’ spatial spillover effect is positive but not significant. Economic growth and urbanization are the key determinants of CO2, dust, and NOx emissions, while energy efficiency and industrialization do not appear to play a role. This raises questions about the method of examining the spatial relationship between gas pollution, economic growth and urbanization in the future.

Evaluation of rainfall spatial correlation effect on rainfall-runoff modeling uncertainty, considering 2-copula

Lack of accuracy of rainfall-runoff simulation (RRS) remains critical for some applications. Among various sources of uncertainty, precipitation plays a particular role. Rainfall rates as the main input data of RRS are of the first factors controlling the accuracy. In addition to the depth, spatial and temporal distributions of rainfall impact the flood discharge. Most of the previous studies on RRS uncertainty have ignored rainfall spatial distribution, where in large catchments, it is necessary to be modeled explicitly. Karoon III is one most important basin of the Iran because of the Karoon III dam in the outlet. In the present work, effect of spatial correlation of rainfall on HEC-HMS (SMA) continuous RRS uncertainty is evaluated using 2variate copula (2copula). Monte Carlo simulation (MCS) approach was used to consider the rainfall spatial dependence. To reduce the computational expense, sampling efficiency and convergence for MCS, Latin hypercube sampling (LHS) was used. Copula functions consider wide range of marginal probability distribution functions (PDFs), eliminating limits of regular join PDFs. For this aim, two scenarios were investigated. In the first scenario, sub-basin rainfall was considered independent, and in the second scenario, 2copula was adopted to model spatial correlation of rainfall. Dimensionless rainfall depths were calculated for each sub-basin, and the PDFs were determined. The generated random dimensionless rainfalls were reweighted and multiplied by watershed’s mean rainfall value. Stochastic Climate Library was used to generate continuous daily rainfalls. Sampling from dimensionless rainfalls using LHS algorithm, 100 runs of calibrated model-simulated 100 flows for each day following MCS, and 80 % certainty bound was calculated. Results showed that considering dependence decreased 18 % of the maximum uncertainty bound width, so the methodology could be recommended for decreasing predicted runoff error.

Structure Function Estimated From Histological Tissue Sections.

Ultrasonic scattering is determined by not only the properties of individual scatterers but also the correlation among scatterer positions. The role of scatterer spatial correlation is significant for dense medium, but has not been fully understood. The effect of scatterer spatial correlation may be modeled by the structure function as a frequency-dependent factor in the backscatter coefficient (BSC) expression. The structure function has been previously estimated from the BSC data. The aim of this study is to estimate the structure function from histology to test if the acoustically estimated structure function is indeed caused by the scatterer spatial distribution. Hematoxylin and eosin stained histological sections from dense cell pellet biophantoms were digitized. The scatterer positions were determined manually from the histological images. The structure function was calculated from the extracted scatterer positions. The structure function obtained from histology showed reasonable agreement in the shape but not in the amplitude, compared with the structure function previously estimated from the backscattered data. Fitting a polydisperse structure function model to the histologically estimated structure function yielded relatively accurate cell radius estimates ([Formula: see text]). Furthermore, two types of mouse tumors that have similar cell size and shape but distinct cell spatial distributions were studied, where the backscattered data were shown to be related to the cell spatial distribution through the structure function estimated from histology. In conclusion, the agreement between acoustically estimated and histologically estimated structure functions suggests that the acoustically estimated structure function is related to the scatterer spatial distribution.

Spatio-temporal change detection from multidimensional arrays: Detecting deforestation from MODIS time series

Growing availability of long-term satellite imagery enables change modeling with advanced spatio-temporal statistical methods. Multidimensional arrays naturally match the structure of spatio-temporal satellite data and can provide a clean modeling process for complex spatio-temporal analysis over large datasets. Our study case illustrates the detection of breakpoints in MODIS imagery time series for land cover change in the Brazilian Amazon using the BFAST (Breaks For Additive Season and Trend) change detection framework. BFAST includes an Empirical Fluctuation Process (EFP) to alarm the change and a change point time locating process. We extend the EFP to account for the spatial autocorrelation between spatial neighbors and assess the effects of spatial correlation when applying BFAST on satellite image time series. In addition, we evaluate how sensitive EFP is to the assumption that its time series residuals are temporally uncorrelated, by modeling it as an autoregressive process. We use arrays as a unified data structure for the modeling process, R to execute the analysis, and an array database management system to scale computation. Our results point to BFAST as a robust approach against mild temporal and spatial correlation, to the use of arrays to ease the modeling process of spatio-temporal change, and towards communicable and scalable analysis.

Spatial scan statistics for detection of multiple clusters with arbitrary shapes.

In applying scan statistics for public health research, it would be valuable to develop a detection method for multiple clusters that accommodates spatial correlation and covariate effects in an integrated model. In this article, we connect the concepts of the likelihood ratio (LR) scan statistic and the quasi-likelihood (QL) scan statistic to provide a series of detection procedures sufficiently flexible to apply to clusters of arbitrary shape. First, we use an independent scan model for detection of clusters and then a variogram tool to examine the existence of spatial correlation and regional variation based on residuals of the independent scan model. When the estimate of regional variation is significantly different from zero, a mixed QL estimating equation is developed to estimate coefficients of geographic clusters and covariates. We use the Benjamini-Hochberg procedure (1995) to find a threshold for p-values to address the multiple testing problem. A quasi-deviance criterion is used to regroup the estimated clusters to find geographic clusters with arbitrary shapes. We conduct simulations to compare the performance of the proposed method with other scan statistics. For illustration, the method is applied to enterovirus data from Taiwan.

Industrial Carbon Emissions of China’s Regions: A Spatial Econometric Analysis

This paper proposes an extended Stochastic Impacts by Regression on Population, Affluence, and Technology (STIRPAT) model to investigate the factors driving industrial carbon emissions in China. In the first stage, a spatial Durbin model is applied to investigate the determinants of regional industrial carbon emissions. In the second stage, a geographically and temporally weighted regression is applied to investigate temporal and spatial variations in the impacts of these driving factors on the scale and intensity of regional industrial carbon emissions. The empirical results suggest that the provinces with low carbon emissions act as exemplars for those with high carbon emissions and that driving factors impact carbon emission both directly and indirectly. All of the factors were investigated, except energy intensity, energy price, and openness, significantly impact carbon emissions. Overall, the results suggest that spatial correlation, heterogeneity, and spillover effects should be taken into account when formulating policies aiming at reducing industrial carbon emissions. The paper concludes with relevant policy recommendations taking full account of the regional industrial carbon emissions, heterogeneity and spillover.

Intrinsic Representation of Hyperspectral Imagery for Unsupervised Feature Extraction

Unsupervised feature extraction from hyperspectral images (HSIs) relies on efficient data representation. However, classical data representation techniques, e.g., principal component analysis and independent component analysis, do not reflect the intrinsic characteristics of HSI, and as such, they are less efficient for producing discriminative features. To address this issue, we have developed an intrinsic representation (IR) approach to support HSI classification. Based on the linear spectral mixture model, the IR approach explains the underlying physical factors that are responsible for generating HSI. Moreover, it addresses other important characteristics of HSI, i.e., the noise variance heterogeneity effect in the spectral domain and the spatial correlation effect in image domain. The IR model is solved iteratively by alternating the estimation of IR coefficients given IR bases and the update of IR bases given the coefficients. The resulting IR coefficients are discriminative, compact, and noise resistant, thereby constituting powerful features for improved HSI classification. The experiments on both simulated and real HSI demonstrate that the features extracted by the IR model are more capable of boosting the classification performance than the other referenced techniques.

Robust Scheduling and Resource Allocation in the Downlink of Spatially Correlated MIMO-OFDMA Wireless Systems With Imperfect CSIT

Multiple-input-multiple-output (MIMO) orthogonal frequency-division multiple access (OFDMA) has been selected as the core physical-layer access scheme for the downlink of state-of-the-art and next-generation wireless communications standards. In these systems, scheduling and resource allocation (SRA) algorithms, jointly assigning transmission data rates, bandwidth, and power, become crucial in optimizing resource utilization while providing support to multimedia applications with heterogeneous quality-of-service (QoS) requirements. To this end, the transmitter is assumed to have channel state information at the transmitter (CSIT) that will typically be imperfect. This paper introduces a unified analytical framework for robust channel- and queue-aware QoS-guaranteed cross-layer SRA algorithms for the downlink of MIMO-OFDMA networks with imperfect CSIT. The framework is based on the statistical characterization of the signal-to-noise ratio (SNR) under imperfect CSIT and is general enough to encompass spatial correlation effects in the Tx and Rx antenna arrays, different types of traffic, uniform and continuous power allocation, discrete and continuous rate allocation, and protocols with different amounts of channel and queue awareness. Simulation results using parameters drawn from the Third-Generation Partnership Project Long-Term Evolution (3GPP-LTE) standard demonstrate the validity and advantages of the proposed robust cross-layer unified approach.

Exponential decay of spatial correlation in driven diffusive system: A universal feature of macroscopic homogeneous state.

Driven diffusive systems have been a paradigm for modelling many physical, chemical, and biological transport processes. In the systems, spatial correlation plays an important role in the emergence of a variety of nonequilibrium phenomena and exhibits rich features such as pronounced oscillations. However, the lack of analytical results of spatial correlation precludes us from fully understanding the effect of spatial correlation on the dynamics of the system. Here we offer precise analytical predictions of the spatial correlation in a typical driven diffusive system, namely facilitated asymmetric exclusion process. We find theoretically that the correlation between two sites decays exponentially as their distance increases, which is in good agreement with numerical simulations. Furthermore, we find the exponential decay is a universal property of macroscopic homogeneous state in a broad class of 1D driven diffusive systems. Our findings deepen the understanding of many nonequilibrium phenomena resulting from spatial correlation in driven diffusive systems.

Analysis of Compensation Network in a Correlated-based Channel using Angle of Arrivals

We explore combined effect of spatial correlation and mutual coupling matrix, and its subsequent effects on performance of multiple input multiple output (MIMO) systems After the decoupling process. We will also look at a correlation based stochastic channel model with the linear antenna arrays as the signal source. For the purpose of understanding, it is assumed that fading is correlated at both transmitter and receiver sides, in spite of the fact that the decoupling network enhances isolation between Receiving antenna array. In this paper, we model the transmit the antenna array in CST Microwave Studio, as a uniform linear Array with monopoles as antenna elements. On the receiving side, the scattering parameters of the coupled and decoupled monopole Array are measured in an anechoic chamber. The theoretical analysis and simulation results show the joint dependency of the system capacity on an angle of arrival (AoA) and antenna element spacing, with enhanced system performance at reduced AoAs with Increased antenna element separation. Consequently, essential benefits of MIMO system performance can be achieved with an efficient decoupling network while boosting the signal sources by adding further antenna elements.

Experimental analysis of spatial correlation effects on capillary trapping of supercritical CO2 at the intermediate laboratory scale in heterogeneous porous media

AbstractSeveral numerical studies have demonstrated that the heterogeneous nature of typical sedimentary formations can favorably dampen the accumulation of mobile CO2 phase underneath the caprock. Core flooding experiments have also shown that contrasts in capillary entry pressure can lead to buildup of nonwetting fluid phase (NWP) at interfaces between facies. Explicit representation of geological heterogeneity at the intermediate (cm‐to‐m) scale is a powerful approach to identify the key mechanisms that control multiphase flow dynamics in porous media. The ability to carefully control flow regime and permeability contrast at a scale that is relevant to CO2 plume dynamics in saline formations offers valuable information to understand immiscible displacement processes and provides a benchmark for mathematical models. To provide insight into the impact of capillary heterogeneity on flow dynamics and trapping efficiency of supercritical CO2 under successive drainage and imbibition conditions, we present an experimental investigation conducted in a synthetic sand reservoir. By mimicking the interplay of governing forces at reservoir conditions via application of surrogate fluids, we performed three immiscible displacement experiments to observe the entrapment of NWP in heterogeneous porous media. Capillary trapping performance is evaluated for each scenario through spatial and temporal variations of NWP saturation; for this reason we adopted X‐ray attenuation to precisely measure phase saturation throughout the flow domain and apply spatial moment analysis. The sweeping performance of two different permeability fields with comparable variance but distinct spatial correlation was compared against a homogeneous base case with equivalent mean permeability by means of spatial moment analysis.