Spatial Autocorrelation Function Research Articles

A Clustering Approach for Atmospheric Phase Error Correction in Ground-Based SAR Using Spatial Autocorrelation.

When using ground-based synthetic aperture radar (GB-SAR) for monitoring open-pit mines, dynamic atmospheric conditions can interfere with the propagation speed of electromagnetic waves, resulting in atmospheric phase errors. These errors are particularly complex in rapidly changing weather conditions or steep terrain, significantly impacting monitoring accuracy. In such scenarios, traditional regression model-based atmospheric phase correction (APC) methods often become unsuitable. To address this issue, this paper proposes a clustering method based on the spatial autocorrelation function. First, the interferogram is uniformly divided into multiple blocks, and the phase consistency of each block is evaluated using the spatial autocorrelation function. Then, a region growing algorithm is employed to classify each block according to its phase pattern, followed by merging adjacent blocks based on statistical data. To verify the feasibility of the proposed method, both the traditional regression model-based method and the proposed method were applied to deformation monitoring of an open-pit mine in Northwest China. The experimental results show that for complex atmospheric phase scenarios, the proposed method significantly outperformed traditional methods, demonstrating its superiority.

Derivation of correlation dimension from spatial autocorrelation functions.

Spatial complexity is always associated with spatial autocorrelation. Spatial autocorrelation coefficients including Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation process is based on self-organized evolution, complex structure, and the distributions without characteristic scale, the eigenvalue will be ineffective. In this case, a scaling exponent such as fractal dimension can be used to compensate for the shortcoming of characteristic length parameters such as Moran's index. This paper is devoted to finding an intrinsic relationship between Moran's index and fractal dimension by means of spatial correlation modeling. Using relative step function as spatial contiguity function, we can convert spatial autocorrelation coefficients into spatial autocorrelation functions. By decomposition of spatial autocorrelation functions, we can derive the relation between spatial correlation dimension and spatial autocorrelation functions. As results, a series of useful mathematical models are constructed, including the functional relation between Moran's index and fractal parameters. Correlation dimension proved to be a scaling exponent in the spatial correlation equation based on Moran's index. As for empirical analysis, the scaling exponent of spatial autocorrelation of Chinese cities is Dc = 1.3623±0.0358, which is equal to the spatial correlation dimension of the same urban system, D2. The goodness of fit is about R2 = 0.9965. This fractal parameter value suggests weak spatial autocorrelation of Chinese cities. A conclusion can be drawn that we can utilize spatial correlation dimension to make deep spatial autocorrelation analysis, and employ spatial autocorrelation functions to make complex spatial autocorrelation analysis. This study reveals the inherent association of fractal patterns with spatial autocorrelation processes. The work may inspire new ideas for spatial modeling and exploration of complex systems such as cities.

Using spatial ordinal patterns for non-parametric testing of spatial dependence

We analyze data occurring in a regular two-dimensional grid for spatial dependence based on spatial ordinal patterns (SOPs). After having derived the asymptotic distribution of the SOP frequencies under the null hypothesis of spatial independence, we use the concept of the type of SOPs to define the statistics to test for spatial dependence. The proposed tests are not only implemented for real-valued random variables, but a solution for discrete-valued spatial processes in the plane is provided as well. The performances of the spatial-dependence tests are comprehensively analyzed by simulations, considering various data-generating processes. The results show that SOP-based dependence tests have good size properties and constitute an important and valuable complement to the spatial autocorrelation function. To be more specific, SOP-based tests can detect spatial dependence in non-linear processes, and they are robust with respect to outliers and zero inflation. To illustrate their application in practice, two real-world data examples from agricultural sciences are analyzed.

Direction‐of‐arrival estimation via coarray‐domain RELAX algorithm with source number estimation

AbstractA modified RELAX algorithm based on iterative coarray‐domain beamforming for fast source direction‐of‐arrival (DOA) estimation with fully augmentable sparse arrays is proposed. The authors exploit the deterministic centralised nature of the noise in the coarray domain and the Hermitian symmetry of the spatial autocorrelation function to efficiently incorporate source number estimation within the iterative framework. In doing so, the proposed algorithm allows low‐complexity, fast DOA estimation of more sources than sensors, without resorting to computationally expensive implementations of source number estimation using information theoretic criteria. Three variants of the proposed algorithm are presented, each differing in terms of the specific method employed for source number estimation. Extensive simulations are performed with a minimum redundancy array to compare and contrast the performance of the three variants in terms of their accuracy in estimating the number of sources in the field‐of‐view of the array. The results demonstrate that the modified RELAX algorithm can provide accurate estimates of the number and directions of sources, especially when the number of uncorrelated sources is equal to or higher than the number of sensors.

Simulating non-homogeneous non-Gaussian corrosion fields on pipelines based on inline inspection data

This study presents a methodology to simulate non-homogeneous non-Gaussian corrosion fields on the external surface of buried steel pipelines by using inline inspection (ILI) data. It is assumed that the non-homogeneous non-Gaussian corrosion field consists of multiple homogeneous non-Gaussian anomalies that can be characterized by the marginal distribution and spatial autocorrelation function of the corresponding corrosion depths. Based on corrosion data collected from in-service pipelines, empirical relationships are developed to estimate parameters of the marginal distribution and autocorrelation function from the ILI information. To generate a synthetic corrosion field, one first generates realizations of corrosion anomalies and then merge the generated anomalies into a single non-homogeneous field by applying a spatial modulating function to each anomaly. The proposed methodology will improve the accuracy of the fitness-for-service assessment of corroded pipelines in practice as the burst capacity of the corroded pipeline can be more accurately evaluated by using the synthetic corrosion field than using the idealized corrosion field obtained from the ILI data.

Intensity correlations in perturbed optical vortices: diagnosis of the topological charge

We propose and experimentally verify a novel scheme for diagnosing the order of a perturbed optical vortex using its 2D spatial autocorrelation function. The order of a vortex was found to be equal to the number of dark rings or zero points present in the correlation function. We have provided a compact analytical expression for the correlation function in the form of Laguerre polynomials. Further, we have utilized the divergence of the first zero point of Laguerre polynomials upon propagation to obtain information about higher-order vortex beams and compared it with our experimental results. It has been shown that the accuracy of the obtained information can further be enhanced by increasing the collection area of scattered vortex beams. These results find applications in free-space optical and satellite communication as the proposed technique is alignment free, and information can be obtained even with a small portion of the scattered beam.

Characterization of the Blast Furnace Burden Surface: Experimental Measurement and Roughness Statistics

This paper is the first of a series of papers on the roughness characteristics of the burden surface in the blast furnace. The measurement method of the burden surface roughness texture is described, and the overall roughness characteristics of the burden surface are studied from a statistical point of view. This study focuses on two typical granularized burden materials, coke and sintered ore, which present four kinds of burden particles under two individual particle sizes. Simulated cold-state burden belts proportional to the practical burden radial sectors were stacked in a pilot plant. An RGBD camera was used to measure the simulated burden belt surfaces to obtain the surface texture details. Four corresponding digital elevation models of the burden belts were obtained through data processing. The root mean squared height, skewness, kurtosis, and spatial autocorrelation function are selected as statistical indexes. The obtained digital elevation models were counted. The results show that all four kinds of burden surfaces are Isotropic-Rough-Surface. In addition, the height distributions of the rough burden surface are close to the Gaussian distribution. Also, the spatial autocorrelation functions of the coke and large-sized sintered ore burden surfaces are close to the Gaussian function form. And lastly, the spatial autocorrelation function of the small sintered ore burden surface is close to the exponential function form.

Electrostatic effect due to patch potentials between closely spaced surfaces

The spatial variation and temporal variation in surface potential are important error sources in various precision experiments and deserved to be considered carefully. In the former case, the theoretical analysis shows that this effect depends on the surface potentials through their spatial autocorrelation functions. By making some modification to the quasilocal correlation model, we obtain a rigorous formula for the patch force, where the magnitude is proportional to $\frac{1}{{a}^{2}}{(\frac{a}{w})}^{\ensuremath{\beta}(a/w)+2}$ with $a$ the distance between two parallel plates, $w$ the mean patch size, and $\ensuremath{\beta}$ the scaling coefficient from $\ensuremath{-}2$ to $\ensuremath{-}4$. A torsion balance experiment is then conducted, and we obtain a 0.4 mm effective patch size and 20 mV potential variance. In the latter case, we apply an adatom diffusion model to describe this mechanism and predicts a ${f}^{\ensuremath{-}3/4}$ frequency dependence above 0.01 mHz. This prediction meets well with a typical experimental results. Finally, we apply these models to analyze the patch effect for two typical experiments. Our analysis will help to investigate the properties of surface potentials.

Ozone exposure and health risks of different age structures in major urban agglomerations in People's Republic of China from 2013 to 2018.

High concentration of surface ozone (O3) will cause health risks to people. In order to analyze the spatiotemporal characteristics of O3 and assess O3 exposure and health risks for different age groups in China, we applied multiple methods including standard deviation ellipse, spatial autocorrelation, and exposure-response functions. Results show that O3 concentrations increased in 64.5% of areas in China from 2013 to 2018. The central plain urban agglomeration (CPU), Beijing-Tianjin-Hebei (BTH), and Yangtze River Delta (YRD) witnessed the greatest incremental rates of O3 by 16.7%, 14.3%, and 13.1%. Spatially, the trend of O3 shows a significant positive autocorrelation, and high trend values primarily in central and east China. The proportion of the total population exposed to high O3 (above 160μg/m3) increased annually. Compared to 2013, the proportion of the young, adult, and old populations exposed to high O3 increased to different extents in 2018 by 26.8%, 29.6%, and 27.2%, respectively. The extent of population exposure risk areas in China expanded in size, particularly in north and east China. The total premature respiratory mortalities attributable to long-term O3 exposure in six urban agglomerations were about 177,000 in 2018 which has increased by 16.4% compared to that in 2013. Among different age groups, old people are more vulnerable to O3 pollution, so we need to strengthen their relevant health protection of them.

МНОГОЛЕТНЯЯ ИЗМЕНЧИВОСТЬ БИОМАССЫ ОКЕАНИЧЕСКОГО ЗООПЛАНКТОНА

Numerous scientific publications are dedicated to the analysis of long-term variability of zooplankton biomass in oceanic and neritic zones of the World Ocean. The number of these publications keeps growing with the availability of new data. Relevance of this research can be attributed to the crucial role of zooplankton biomass in the spatio-temporal and trophic structure of aquatic ecosystems. Inter-annual fluctuations of zooplankton biomass affect the catch volumes of small pelagic fish. This research is aimed at identification of statistically valid long-term trends of the World Ocean zooplankton biomass, which involves the analysis of the data from databases and published articles describing such variability. Regional and international databases (namely COPEPOD, HOT, JGOFS, ODATE and others), which are available in the form of CDs, archived materials, and online, have been used. For the time series of the biomass across 21 areas of the World Ocean (Pacific, Indian, Atlantic Oceans and internal seas), the regression analysis has been conducted, which made it possible to estimate the parameters of linear monotonic trends. Based on bivariate spatial autocorrelation functions, the areas within which the trends are statistically homogeneous have been identified. A comparative study of long-term variability of zooplankton biomass, phytoplankton biomass, primary production, and the total live biomass of the pelagic World Ocean is presented. It is shown that the spatial distribution of positive, negative and neutral trends of zooplankton biomass on the World Ocean scale is heterogeneous. The negative monotonic trends of zooplankton biomass are found to be prevailing (in 1980–2010s); the regression parameters describing them are presented.

Stochastic Buckling of Geometrically Imperfect Beams on Elastic Foundation

Abstract Geometrical imperfections are ubiquitous in load-bearing structures, including beams, columns, and shells. Fabrication processes of structural members most often create geometrical imperfections of random size and shape, which lead to non-deterministic load-carrying capacity. This study investigates the statistics of the buckling load of a beam with a random initial imperfection profile that rests on a nonlinear elastic foundation. The geometrical imperfection is represented by a zero-mean Gaussian random field, generated using the Karhunen–Loève expansion. The spatial distribution of the random imperfection is characterized by the probability distribution of the local imperfection magnitude and a spatial autocorrelation function. A finite-difference scheme is used to solve the governing equilibrium equation for a given initial imperfection profile, from which the buckling load is determined. Through a set of Monte Carlo simulations, the mean and variance of the buckling load are determined. The simulations reveal the influence of different length scales on the statistics of the buckling load, including the beam length and the autocorrelation length of the geometrical imperfection. The size effects predicted with the simplified model have implications for reliability-based structural design.

Combination of survival movement strategies in cyclic game systems during an epidemic

Disease outbreaks affect many ecosystems threatening species that also fight against other natural enemies. We investigate a cyclic game system with 5 species, whose organisms outcompete according to the rules of a generalised spatial rock–paper–scissors game, during an epidemic. We study the effects of behavioural movement strategies that allow individuals of one out of the species to move towards areas with a low density of disease vectors and a high concentration of enemies of their enemies. We perform a series of stochastic simulations to discover the impact of self-preservation strategies in pattern formation, calculating the species’ spatial autocorrelation functions. Considering organisms with different physical and cognitive abilities, we compute the benefits of each movement tactic to reduce selection and infection risks. Our findings show that the maximum profit in terms of territorial dominance in the cyclic game is achieved if both survival movement strategies are combined, with individuals prioritising social distancing. In the case of an epidemic causing symptomatic illness, the drop in infection risk when organisms identify and avoid disease vectors does not render a rise in the species population because many refuges are disregarded, limiting the benefits of safeguarding against natural enemies. Our results may be helpful to the understanding of the behavioural strategies in ecosystems where organisms adapt to face living conditions changes.

Estimating the Parameters of the Spatial Autocorrelation of Rainfall Fields by Measurements From Commercial Microwave Links

The spatial structure of rain fields is important to the understanding of their effects on ground-level aspects, such as runoff generation, and is considered crucial information for the accurate reconstruction of these fields. It is commonly characterized by a simplified spatial autocorrelation function (ACF). The near-ground ACF, and—particularly—its decorrelation distance, is evaluated from point measurements (rain gauges and distrometers). However, the spatial representation of such measurements is limited and therefore rarely sufficient for reliable ACF estimation. The emerging use of commercial microwave links (CMLs) for near-ground rain retrieval, and their spatial abundance, suggests using them for ACF estimation. In this study, we propose a method for extracting spatial features of a rain field, and in particular its decorrelation distance, from CML measurements. When sampled by path integration, the rain measurements acquire a distortion as a result of the averaging of a once fluctuating signal, where extreme rain intensities are being smeared. When evaluating the AFC from CMLs’ measurements, this effect needs to be compensated for. We propose methods for retrieving the original parameters characterizing the AFC and validate them on semisynthetic simulated data, based on actual rain events. The error was found to be 5%.

Mathematical description of imaging processes in ultra-wideband active aperture synthesis systems using stochastic sounding signals

Mathematical models of the fields of stochastic ultra-wideband signals that are necessary for solving problems of aperture synthesis of images using active radar methods are presented. The expediency of using V-transformations in these problems has been substantiated, the effectiveness of which has already been proven for the mathematical description of ultra-wideband spatio-temporal fields in the methods of passive and active radar, as well as remote sensing, that are used to solve problems of radio astronomy, medicine, navigation. Using modern methods of mathematical analysis and the theory of ultra-wideband systems, the physical essence of radio images obtained with the help of algorithms for coherent and incoherent signal processing is investigated. According to these algorithms, it is proposed to divide images into coherent and incoherent. Coherent images include those in which its amplitude and phase are recorded separately. In the case of an incoherent image, only its amplitude (power or related characteristic) is recorded. To describe of the obtained radio image structure, new concepts of the spectral density of the complex spatial coherence function (SDCSCF) and the spectral density of the spatial autocorrelation function of the amplitude-phase distribution (SDFSAF APD) are introduced. Application-use of functions is expedient and fundamentally necessary for solving problems of aperture synthesis using stochastic ultra-wideband signals. A mathematical description of the structures obtained by aperture synthesis of radio images is given. Here, studies are conducted for the general case of using a continuous (idealized) aperture, and for using an antenna system with spatially separated receiving elements. Simulation of the heuristic synthesized algorithm for constructing incoherent radio images is conducted. The possibility of using antenna arrays and synthesized aperture synthesis algorithms for solving problems of image formation in a survey located directly under the aircraft (at sounding angles close to vertical) are substantiated.

Manipulating single-photon emitter radiative lifetime in transition-metal dichalcogenides through Förster resonance energy transfer to graphene

Structural defects can crucially impact the optical response of monolayer (ML) thick materials as they enable trapping sites for excitons. These trapped excitons appear in photoluminescence spectra as new emissions below the free bright exciton and it can be exploited for single photon emissions (SPE). In this work we outline criteria, within our frame work, by which single photon emission can be detected in two dimensional materials and we explore how these criteria can be fulfilled in atomically thin transition metal dichalcogenides (TMD). In particular, we model the effect of defects, in accordance with the most common experimental realisations, on the spatial autocorrelation function of the random disorder potential. Moreover, we provide a way to control the radiative lifetime of these emissions by a hybride heterostructrue of the ML TMD with a graphene sheet and a dielectric spacer that enables the Forster resonance energy transfer process. Our work predict that the corresponding SPE quenched radiative lifetime will be in the picosecond range, this time scale is in good agreement with the recently measured exciton lifetime in this heterostructures

The Power Spectrum and Structure Function of the Gamma-Ray Emission from the Large Magellanic Cloud

Abstract The Fermi-LAT observational data of the diffuse γ ray emission from the Large Magellanic Cloud (LMC) were examined to test for the existence of underlying long-range correlations. A statistical test applied to the data indicated that the probability that data are random is extremely small. Thus we proceeded and have used the counts-number data to compute 2D spatial autocorrelation, power spectrum, and structure function. The most important result of the present study is a clear indication for large-scale spatial underlying correlations. This is evident in all the functions mentioned above. The 2D power spectrum has a logarithmic slope of −3 on large spatial scales and a logarithmic slope of −4 on small spatial scales. The structure function has logarithmic slopes equaling 1 and 2 for the large and small scales, respectively. The logarithmic slopes of the structure function and the power spectrum are consistent. A plausible interpretation of these results is the existence of a large-scale supersonic compressible turbulence with a 3D logarithmic slope of −4 extending over scales comparable to the size of the LMC. Both the power spectrum and structure function exhibit steeper logarithmic slopes for smaller spatial scales. This is interpreted as an indication that the turbulent region has an effective depth of about 1.5 kpc.

Characteristics of the speckle field under sharper focusing conditions.

In inertial confinement fusion (ICF) systems, a continuous phase plate is often used to generate a speckle pattern in order to reduce the growth of parametric instabilities. An analytic model based on the vector diffraction theory is proposed in order to analyze the characteristics of the speckle field generated under sharper focusing conditions. The statistical and spatial autocorrelation function of the speckle field are deduced and calculated. Results show that more accurate results can be achieved by vector theory than by scalar theory. Furthermore, since light-field components in different directions are involved in the vector diffraction integral, more comprehensive information on statistical characteristics of the speckle field can be discovered. Additionally, the impact of the speckle field on three waves plasma parametric instabilities are discussed. Results show that speckle field generated under sharp focusing conditions can efficiently increase the phase mismatch among the three waves and then limit the growth of the instability.

An analytical process of spatial autocorrelation functions based on Moran's index.

A number of spatial statistic measurements such as Moran's I and Geary's C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time lag replaced by spatial weights so that the autocorrelation functions degenerated to autocorrelation coefficients. This paper develops 2-dimensional spatial autocorrelation functions based on the Moran index using the relative staircase function as a weight function to yield a spatial weight matrix with a displacement parameter. The displacement bears analogy with the time lag in time series analysis. Based on the spatial displacement parameter, two types of spatial autocorrelation functions are constructed for 2-dimensional spatial analysis. Then the partial spatial autocorrelation functions are derived by using the Yule-Walker recursive equation. The spatial autocorrelation functions are generalized to the autocorrelation functions based on Geary's coefficient and Getis' index. As an example, the new analytical framework was applied to the spatial autocorrelation modeling of Chinese cities. A conclusion can be reached that it is an effective method to build an autocorrelation function based on the relative step function. The spatial autocorrelation functions can be employed to reveal deep geographical information and perform spatial dynamic analysis, and lay the foundation for the scaling analysis of spatial correlation.

Spatial analysis of Toxocara spp. eggs in soil as a potential for serious human infection

Toxocara spp. cause one of the most widespread soil-transmitted helminthic infections worldwide. In both developed and developing countries, soil contamination with Toxocara eggs is considered as a major threat to public health. A total of 515 soil samples from 89 sampling sites were collected from different locations of public health such as Wastelands and Streets, public parks, and marginal areas. The soil samples were examined for Toxocara eggs using a centrifugal-floatation technique utilizing a saturated sodium nitrate solution. centralization of positive soil samples in the province was studied by Spatial Statistics Techniques such as Average Nearest Neighbors and Spatial Autocorrelation and Kernel Density Function Toxocara spp. eggs were found in 94 (18.25 %) out of 515 samples collected from the studied areas. According to the results obtained, marginal areas are often contaminated with eggs of Toxocara. Consequently, preventive measures including health education should be implemented to reduce the potential risk of this parasitic infection.

Image degradation due to different in-flight aero-optical environments

High speed time-resolved wavefront and imaging measurements were taken synchronously in-flight through both boundary layer and shear layer environments around the Airborne Aero-Optical Laboratory for Beam Control. Instantaneous modulation transfer functions and point spread functions (PSFs), which characterize image degradation, were generated using wavefront data. Instantaneous power-in-bucket ratios were extracted from both the image data and computed from the wavefront data, and the ratios were found to correlate well with each other. The lower power-in-bucket values and related increased blurring that occurred predominantly in the streamwise direction were associated with large-scale, large-amplitude wavefront spatial variations due to large organized vortical structures present in the shear layer. The boundary layer did not create any significant image blurring due to the low level of aero-optical distortions. Finally, spatial autocorrelation functions were extracted from the wavefront data using the stitching method and were used to compute time-averaged PSFs for different aperture diameters.