Characterisation of heterogeneity and spatial autocorrelation in phase separating mixtures using Moran’s I

Thompson, Emma S.; Saveyn, Pieter; Declercq, Marc; Meert, Joris; Guida, Vincenzo; Eads, Charles D.; Robles, Eric S. J.; Britton, Melanie M.

doi:10.1016/j.jcis.2017.10.115

Cited by 44 publications

(37 citation statements)

References 35 publications

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“…To quantify the spatial localization of the incremental strain populations, we used the coefficient Moran's I (Moran, ) to characterize spatial clustering (e.g., Thompson et al, ; Zhang & Lin, ). When Moran's I is positive, populations are spatially correlated with each other so that members of the population with similar values are located nearby to each other.…”

Section: Methodsmentioning

confidence: 99%

Volumetric and Shear Strain Localization in Mt. Etna Basalt

McBeck

Cordonnier

Vinciguerra

et al. 2019

Geophysical Research Letters

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To examine the impact of preexisting weaknesses on fracture coalescence during volcanic edifice deformation, we triaxially compressed Mount Etna basalt while acquiring in situ dynamic X‐ray microtomograms and calculated the internal strain tensor fields using image correlation. Contraction localization preceded dilation and shear strain localization into the protofault zone. This onset of strain localization preceded macroscopic yielding and coincided with increases in the magnitude and volume of rock experiencing dilation, and spatial clustering of the strain populations. The exploitation of weaknesses by propagating fractures enabled the dominant shear strain to switch senses as propagating fractures lengthened along 30–60° from σ1. Scanning electron microscopy images reveal pore‐emanated fractures, and fractures linking pores. These experiments provide evidence of internal contraction preceding dilation and shear, consistent with inferences from field and laboratory observations. The transition from contraction to dilation may provide a precursory signal of volcanic flank eruption.

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Section: Methodsmentioning

confidence: 99%

Volumetric and Shear Strain Localization in Mt. Etna Basalt

McBeck

Cordonnier

Vinciguerra

et al. 2019

Geophysical Research Letters

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“…Cluster and outlier analysis, given a set of weighted features, statistically identifies significant hot spots and cold spots, which depict high and low value collection areas, respectively, using the Anselin Local Moran's I statistic. Some papers can be consulted for more information regarding the tools [50][51][52].…”

Section: Spatial Statisticsmentioning

confidence: 99%

Spatial Heterogeneity of the Carbon Emission Effect Resulting from Urban Expansion among Three Coastal Agglomerations in China

Wen

Chuai

Li³

et al. 2019

Sustainability

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Land-use change, particularly urban expansion, can greatly affect the carbon balance, both from the aspects of terrestrial ecosystems and anthropogenic carbon emissions. Coastal China is a typical region of rapid urban expansion, and obvious spatial heterogeneity exists from the north to south. However, the different urban change characteristics and the effect on carbon balance remain undetermined. By unifying the spatial-temporal resolution of carbon source and sink data, we effectively compared the carbon budgets of three coastal urban agglomerations in China. The results show that all of the three urban agglomerations have undergone an obvious urban expansion process, with the built-up area increasing from 1.03 × 104 km2 in 2000 to 3.06 × 104 km2 in 2013. For Beijing–Tianjin–Hebei (BTH), the built-up area gradually expanded. The built-up area in the Yangtze River Delta (YRD) gradually changed before 2007 but rapidly grew thereafter. The built-up expansion of the Pearl River Delta (PRD) passed through three growing stages and showed the largest mean patch size. Carbon emission spatial patterns in the three urban agglomerations are consistent with their economic development, from which the net ecosystem production (NEP) spatial patterns are very different. Compared to carbon emissions, NEP has a carbon sink effect and can absorb some carbon emissions, but the amounts were all much lower than the carbon emissions in the three urban agglomerations. The carbon sink effect in the Yangtze River Delta is the most obvious, with the Pearl River Delta following, and the lowest effect is in Beijing–Tianjin–Hebei. Finally, a scientific basis for policy-making is provided for viable CO2 emission mitigation policies.

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“…Spatial autocorrelation is one aspect of spatial heterogeneity and can be measured by various indices, including Moran's I [34], Geary's C [35], and others [36]. The most widely used of these measures is Moran's I [37][38][39], which provides a simple means to assess the degree of spatial autocorrelations. The value of Moran's I ranges from −1 to 1.…”

Section: Spatial Autocorrelation Analysismentioning

confidence: 99%

“…When the spatial unit i is the neighbor of the spatial unit j, the value of W ij is 1. Otherwise, the value of W ij is zero [37]. The variables X i and X j are the values of X in the corresponding spatial units i and j, respectively; X is the average of the X value; n is the total number of spatial units; and i represents the i-th unit.…”

Section: Spatial Autocorrelation Analysismentioning

confidence: 99%

Spatial Factor Analysis for Aerosol Optical Depth in Metropolises in China with Regard to Spatial Heterogeneity

Shi

Zhang

2018

Atmosphere

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A substantial number of studies have analyzed how driving factors impact aerosols, but they have been little concerned with the spatial heterogeneity of aerosols and the factors that impact aerosols. The spatial distributions of the aerosol optical depth (AOD) retrieved by Moderate Resolution Imaging Spectrometer (MODIS) data at 550-nm and 3-km resolution for three highly developed metropolises, the Beijing-Tianjin-Hebei (BTH) region, the Yangtze River Delta (YRD), and the Pearl River Delta (PRD), in China during 2015 were analyzed. Different degrees of spatial heterogeneity of the AOD were found, which were indexed by Moran's I index giving values of 0.940, 0.715, and 0.680 in BTH, YRD, and PRD, respectively. For the spatial heterogeneity, geographically weighted regression (GWR) was employed to carry out a spatial factor analysis, where terrain, climate condition, urban development, and vegetation coverage were taken as the potential driving factors. The results of the GWR imply varying relationships between the AOD and the factors. The results were generally consistent with existing studies, but the results suggest the following: (1) Elevation increase would more likely lead to a strong negative impact on aerosols (with most of the coefficients ranging from −1.5~0 in the BTH, −1.5~0 in the YRD, and −1~0 in the PRD) in the places with greater elevations where the R-squared values are always larger than 0.5. However, the variation of elevations cannot explain the variation of aerosols in the places with relatively low elevations (with R-squared values approximately 0.1, ranging from 0 to 0.3, and approximately 0.1 in the BTH, YRD, and PRD), such as urban areas in the BTH and YRD. (2) The density of the built-up areas made a strong and positive impact on aerosols in the urban areas of the BTH (R-squared larger than 0.5), while the R-squared dropped to 0.1 in the places far away from the urban areas. (3) The vegetation coverage led to a stronger relief on the AOD in parts of the YRD and PRD (with coefficients less than −0.6 and ranging from −0.4~−0.6, respectively) where there is greater vegetation coverage, and led to a weaker relief on the AOD in the urban area of the PRD with a coefficient of approximately −0.2~−0.4.Atmosphere 2018, 9, 156 2 of 14 images [2,5] and their variations can now be fully studied [6]. Moreover, a factor analysis for aerosols has been widely carried out. The Ordinary Least Square (OLS) based regression is usually used to identify the relationships between aerosols and their impact factors [7][8][9].However, OLS assumes that the relationship between the dependent and independent variables is consistent and cannot handle the spatial data with heterogeneity, which makes it difficult to meet the assumptions and requirements of OLS [10]. Heterogeneity here includes two aspects: spatial autocorrelation and spatially non-stationarity. Spatial autocorrelation means that the value of a variable at a location depends on the value of the same variable at nearby locations [11,12]. Spatial non-stati...

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Characterisation of heterogeneity and spatial autocorrelation in phase separating mixtures using Moran’s I

Cited by 44 publications

References 35 publications

Volumetric and Shear Strain Localization in Mt. Etna Basalt

Volumetric and Shear Strain Localization in Mt. Etna Basalt

Spatial Heterogeneity of the Carbon Emission Effect Resulting from Urban Expansion among Three Coastal Agglomerations in China

Spatial Factor Analysis for Aerosol Optical Depth in Metropolises in China with Regard to Spatial Heterogeneity

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