Horizontal Spatial Correlation Research Articles

Horizontal Spatial Correlation of the Ionospheric Day‐To‐Day Variations at Low Latitudes Based on GOLD Nmax Data

AbstractPeak electron density data derived from GOLD measurements during 2018–2022 are used to analyze the magnitudes and correlations of ionospheric diurnal variability at low latitudes. The correlation distance describes the correlations between spatial locations and is defined in this paper as the angular separation at which the correlation coefficient decreases from 1 to 0.7. Variations in correlation distance with local time, season, magnetic latitude, solar activity, and geomagnetic activity are discussed in this study. The average value of the zonal correlation distance is approximately 8.55° and 3.56° for the meridional direction at low geomagnetic latitudes (magnetic latitudes <30°). The statistical results indicate that both zonal and meridional correlation distances vary little with local time premidnight, while they show pronounced seasonal and latitudinal variations. Both zonal and meridional correlation distances increase with increasing solar activity and decrease with enhancing geomagnetic activity. The EIA strength and gradient mainly modulate the distributions of correlation distances related to magnetic latitude, season, and solar flux level. An empirical model is constructed to describe the temporal and spatial variations in the correlation distance at low latitudes. The study of correlation distances would contribute to a better understanding of ionospheric variability and improvements in data assimilation.

Crustal Structure Beneath Mexico City From Joint Inversion of Receiver Functions and Dispersion Curves

AbstractOver the years, it has been clear to seismologists that the crustal structure beneath Mexico City is highly complex. This fact may influence the seismic waves' behavior when traveling through it. Consequently, many studies have been done to understand this crustal structure. This article presents a high‐resolution S‐wave velocity model obtained from joint inversion of radial receiver functions and group‐velocity dispersion curves beneath Mexico City (VMRFDC). This model includes azimuthal variations observed with receiver functions, which may be interpreted as crustal discontinuities. Receiver functions were retrieved from velocity and acceleration records, and dispersion curves were collected from a previous tomographic study. We performed a geostatistical analysis that revealed a horizontal spatial correlation of the crustal structure for up to 7.5 km. This distance was obtained from the S‐wave velocity omnidirectional semivariogram range per depth. Using ordinary kriging, we utilized this spatial correlation to estimate S‐wave velocities per depth and introduced two novel techniques: a resolution test for kriging and a geostatistical‐dependent smoothing technique. Finally, we compare our results with previous works, making our model consistent with geological and geophysical features reported in the literature.

Probabilistic analysis of water-sealed performance in underground oil storage considering spatial variability of hydraulic conductivity

For underground water-sealed oil storage, the spatial variability of the surrounding rock has a significant impact on the water-sealed effect of a water curtain system. This study presents a methodology for the probabilistic analysis of water curtain performance in underground oil storage, considering the spatial variability of hydraulic conductivity of the surrounding rock based on field data. Anisotropic random fields representing the spatial variability of hydraulic conductivity were established through spatial statistical analysis of field data and introduced into the finite element model of underground oil storage for water-sealed reliability analysis. The water-sealed performance of different water curtain system schemes was studied using Monte Carlo simulation (MCS). The results showed that the difference between the horizontal spatial correlation and the vertical spatial correlation of the surrounding rock has a significant impact on the water-sealed effect of the water curtain system. An excessively large pressure of water curtain boreholes provided a small contribution to improving water curtain performance. The distance between the water curtain holes and the caverns had the less significant affecting the water-sealed reliability of the storage cavern. Finally, the optimal design of the water curtain system is discussed. This study provides valuable insights and a theoretical basis for the optimisation of water curtain system design parameters for underground water-sealed oil storage.

Constrained Full Waveform Inversion for Borehole Multicomponent Seismic Data

Full-waveform inversion for borehole seismic data is an ill-posed problem and constraining the problem is crucial. Constraints can be imposed on the data and model space through covariance matrices. Usually, they are set to a diagonal matrix. For the data space, signal polarization information can be used to evaluate the data uncertainties. The inversion forces the synthetic data to fit the polarization of observed data. A synthetic inversion for a 2D-2C data estimating a 1D elastic model shows a clear improvement, especially at the level of the receivers. For the model space, horizontal and vertical spatial correlations using a Laplace distribution can be used to fill the model space covariance matrix. This approach reduces the degree of freedom of the inverse problem, which can be quantitatively evaluated. Strong horizontal spatial correlation distances favor a tabular geological model whenever it does not contradict the data. The relaxation of the spatial correlation distances from large to small during the iterative inversion process allows the recovery of geological objects of the same size, which regularizes the inverse problem. Synthetic constrained and unconstrained inversions for 2D-2C crosswell data show the clear improvement of the inversion results when constraints are used.

Horizontal spatial correlation of reverberation for rough sea-bottom interface

Correlation sonar, which estimates the velocity of vessel utilizing the principle of waveform invariance, can achieve the sampling of the horizontal spatial correlation of sea-bottom reverberation. The horizontal spatial correlation can be expressed as a correlation function and is affected by sea-bottom characteristics. The expression of the correlation function of the sea-bottom reverberation is derived, which is written as the convolution of the autocorrelation function of transmitted signal, the cross-correlation function of the backscattered impulse response from a plane interface, and the autocorrelation function of the probability density function of the sea-bottom roughness. The isotropic interface roughness of the sea-bottom leads to a circular planform of the correlation function whose width varies with roughness. The anisotropic interface roughness of the sea-bottom leads to an elliptical planform of the correlation function whose major axis is in the direction of weaker roughness. Simulation of submarine reverberation and correlation function verifies this conclusion. The model for the spatially covariant field is used to estimate the backscattering cross section which varies with azimuth angle under the condition of anisotropic seafloor roughness. It should be noted that the horizontal spatial correlation of reverberation is also related to sonar parameters and other sea-bottom characteristics.

Horizontal spatial correlation of the ionospheric TEC derived from GPS global ionospheric maps

The spatial correlations of ionospheric day-to-day variability are investigated by statistical analysis on TEC production that provided by the Jet Propulsion Laboratory (JPL). First, we use the monthly-averaged TEC over the world to calculate the deviation of the TEC and then the spatial correlation coefficient matrix of the deviation is also derived. According to the definition of correlation distance in statistics, the spatial characteristic scale is retrieved in the Zonal and meridian directions, and their variation of solar activity levels, geomagnetic field configuration conditions and seasonal conditions are investigated in details. Our study indicates strong correlations between geomagnetic conjugate points, which are large at low-latitudes than at mid-latitudes. Furthermore, in the equatorial anomaly region, due to the process of forming double crest structure, the electron distribution at low-latitudes will be affected by the upwelling of the plasma, thus the anomaly of correlation scale is notable. The correlation scale, which usually increases in LT 6:00, peaks at LT 12:00 and LT 14:00 and then decreases. It is overall larger in the daytime and smaller in the nighttime. These spatial correlations are important for understanding the physical mechanisms that cause ionospheric weather variability. For the potential application in development of ionospheric data assimilation model, the spatial correlations are fitted by elliptic Gaussian formula scale. In general, the correlation scale is regressed better in the Zonal direction than in the Meridional direction, better in low-latitude than in middle-latitude, and better in spring and autumn than in winter and summer. These results can help us to accurately construct the background field error covariance matrix in ionospheric data assimilation.

Probabilistic assessment of total and differential settlements due to spatial soil variability

Design of shallow foundations is often guided by serviceability requirements. In particular, the amount of differential settlements becomes usually decisive in selecting the type of foundation – shallow or deep foundation. In practice, differential settlements are estimated by multiplying the average total settlement by an empirical factor accounting for inherent spatial variability of soils. For shallow foundations on clays and sands, ratios of differential to total settlements have been suggested varying roughly from 40 to 100%, respectively. Important factors of influence such as the spacing of footings, variability of the foundation soil, as well as variance reduction because of averaging are not taken into account. A general analytical approach to assess the total and differential settlements of strip footings is developed. The compressibility of the soil is modeled as a spatial random field. The probabilistic approach explicitly considers the inherent soil variability, the zone of influence of settlement to account for variance reduction, and the spacing of adjacent footings because of horizontal spatial correlation. The method presented is compared to the approach advocated in Eurocode EC7. The findings indicate the widely used design criteria used to judge differential settlements to be overly conservative, in particular for sandy subsoil. Examples are presented to illustrate the method.

Landscape distribution and ecology of Plio-Pleistocene avifaunal communities from Lowermost Bed II, Olduvai Gorge, Tanzania

Plio-Pleistocene avifaunal communities are used to reconstruct Lowermost Bed II landscapes at the early hominin site of Olduvai Gorge, Tanzania. These deposits are laterally extensive, have strong chronostratigraphic control, and were excavated using a landscape archaeological approach. Such factors allow for horizontal spatial-correlation of avian communities across the paleolandscape over a geologically short time frame (approximately 65,000 years). Lowermost Bed II avifaunal communities point to an extensive freshwater wetland system across the extent of paleo-Lake Olduvai's eastern margin.

Horizontal spatial correlation of hydraulic and reactive transport parameters as related to hierarchical sedimentary architecture at the Borden research site

Key Points auto and cross correlation have a common correlation structure correlation structure is defined by hierarchical sedimentary architecture stratal lengths at different scales define correlation substructures

Field measurement and analysis of turbulence coherence for Typhoon Nuri at Macao Friendship Bridge

For the purpose of investigating the turbulent and spatial coherent characteristics of strong wind during typhoon landing period, two 3-dimensional ultrasonic anemometer stations were set up 30 m horizontally apart on the Macao Friendship Bridge to caputure the turbulent wind velocities of Typhoon Nuri. Based on the reliable and representative field measured data, the mean wind speed and direction, turbulence intensity, turbulence integral scale, turbulence power spectra, spatial correlation coefficient and coherence function were statistically evaluated. The field measurement analysis have presented the following results: 1) Two anemometer stations provided consistent results. The mean wind speed variation in time domain presented typical M-shape curves. The strong wind (10-minute mean wind speed higher than 8th grade in Beaufort wind scale) direction changed in a big range up to 122-degrees-angle, indicating the field measurements scoped over the typhoon landing period. 2) The ratio of the longitudinal, lateral and vertical turbulence intensities of the strong wind in the typhoon eye wall region was 1:0.96:0.36. Compared with the code defined ratio 1:0.88:0.5, the lateral component was larger and the vertical component was smaller. 3) The value of integral scale increased when the eye wall of Typhoon Nuri passed over the field measurement site. Before the center of Typhoon Nuri arrived, the integral scale of the strong typhoon wind was about twice compared with that for the non-typhoon wind. 4) The spatial correlation of the turbulent wind, coherence function curve and the decay factor had significant differences at different times during the typhoon process. In the eye wall of the typhoon, the horizontal spatial correlation was relatively strong and horizontally spatial correlation spectrum decayed slower with frequency increase. The minimum regressed coefficient C in coherence function model was 4.67, which is lower than the code defined low limit. The maximum decay factor was 27.75 which is larger than the code defined upper bound. The strong wind characteristic parameters of Typhoon Nuri mentioned above partly represented the turbulent and spatial coherent characteristic during strong typhoon wind period.

Characterization of Soil Water Content Variability and Soil Texture using GPR Groundwave Techniques

Accurate characterization of near-surface soil water content is vital for guiding agricultural management decisions and for reducing the potential negative environmental impacts of agriculture. Characterizing the near-surface soil water content can be difficult, as this parameter is often both spatially and temporally variable, and obtaining sufficient measurements to describe the heterogeneity can be prohibitively expensive. Understanding the spatial correlation of near-surface soil water content can help optimize data acquisition and improve understanding of the processes controlling soil water content at the field scale. In this study, ground penetrating radar (GPR) methods were used to characterize the spatial correlation of water content in a three acre field as a function of sampling depth, season, vegetation, and soil texture. GPR data were acquired with [Formula: see text] and [Formula: see text] antennas, and measurements of the GPR groundwave were used to estimate soil water content at four different times. Additional water content estimates were obtained using time domain reflectometry measurements, and soil texture measurements were also acquired. Variograms were calculated for each set of measurements, and comparison of these variograms showed that the horizontal spatial correlation was greater for deeper water content measurements than for shallower measurements. Precipitation and irrigation were both shown to increase the spatial variability of water content, while shallowly-rooted vegetation decreased the variability. Comparison of the variograms of water content and soil texture showed that soil texture generally had greater small-scale spatial correlation than water content, and that the variability of water content in deeper soil layers was more closely correlated to soil texture than were shallower water content measurements. Lastly, cross-variograms of soil texture and water content were calculated, and co-kriging of water content estimates and soil texture measurements showed that geophysically-derived estimates of soil water content could be used to improve spatial estimation of soil texture.

Coupled Assimilation of Geostationary Satellite Sounder Data into a Mesoscale Model Using the Bratseth Analysis Approach

Abstract A satellite–model coupled procedure for assimilating geostationary satellite sounder data was adapted to a mesoscale analysis and forecast system jointly developed by the Naval Research Laboratory and the Air Force Research Laboratory. The coupled procedure involves the use of the model output fields as the first guess for the thermodynamic retrievals. Atmospheric thermodynamic profiles and ground temperatures were retrieved from observed radiances of the VISSR Atmospheric Sounder (VAS) on board the Geostationary Operational Environmental Satellite. The successive corrections objective analysis scheme in the mesoscale analysis and forecast system was modified to consider the horizontal spatial correlation of the satellite data. The procedure was tested using a wintertime case from the 1986 Genesis of Atlantic Lows Experiment project. The retrievals generated by the coupled method were modestly improved relative to independent stand-alone retrievals. Coupled analyses and forecasts of temperature a...

Integrated Geostatistics For Modeling Fluid Contacts and Shales in Prudhoe Bay

Summary Geostatistics techniques are being used increasingly to model reservoir heterogeneity at a wide range of scales. A variety of techniques is now available with differing underlying assumptions, complexity, and applications. This paper introduces a novel method of geostatistics to model dynamic gas-oil contacts and shales in the Prudhoe Bay reservoir. The method integrates reservoir description and surveillance data within the same geostatistical framework. Surveillance logs and shale data are transformed to indicator variables. These variables are used to evaluate vertical and horizontal spatial correlation and cross-correlation of gas and shale at different times and to develop variogram models. Conditional simulation techniques are used to generate multiple three-dimensional (3D) descriptions of gas and shales that provide a measure of uncertainty. These techniques capture the complex 3D distribution of gas-oil contacts through time. We compare results of the geostatistical method with conventional techniques as well as with infill wells drilled after the study. Predicted gas-oil contacts and shale distributions are in close agreement with gas-oil contacts observed at infill wells.

The spatial correlation of rough seabed scattering of surface-generated ambient noise

This article considers the effect of rough seabed scattering on the spatial correlation of low-frequency ambient noise. Extending the study presented by Liu et al. [J. Acoust. Soc. Am. 93, 753–769 (1993)], it is shown here that seabed roughness may alter the horizontal spatial correlation of the noise field primarily through the excitation of an interface wave along the bottom. The horizontal coherence and directionality of the noise field are shown to be a function of the correlation length and angular dependence of the roughness. Since the interface wave component decays rapidly away from the bottom, the vertical noise field correlation is minimumly affected by the seabed roughness. An examination of the noise field under two different statistical descriptions of seabed roughness, the Goff–Jordan and Gaussian models, shows that detailed differences in the roughness spectral shape produce only minor changes in the noise spatial correlation at infrasonic frequencies.

Horizontal spatial correlation of bottom reverberation for normal incidence

The spatial correlation in the backscattered field for waves incident normally on a random boundary is derived using Kirchhoff–Helmholtz scattering theory in which the effects of both boundary heights and slopes are included. The acoustically rough case is considered and it is shown that the scattering process may be interpreted in terms of a deep, random phase screen; the influence of the boundary slopes is interpreted as diffraction at the screen. For a directive source, it is shown that the spatial correlation distance of the field is determined by the correlation of the source shading for a wide variety of boundary conditions; limited experimental data supports this result. For an omnidirectional source, the spatial correlation coefficient is 2J1(kg)/kg.

Analysis of the Spatial Structure of Properties of Selected Aquifers

Data from 31 regional aquifers are analyzed to identify the horizontal spatial correlation structure of transmissivity, hydraulic conductivity, and storage coefficient. Three parameters are estimated: the variance of small‐scale variability (or nugget) and the variance and integral scale (range) of an exponential covariance function. The assumption of normality of the aforementioned geohydrologic parameters and their logarithmic transformations is also examined. Results are obtained which indicate that the logarithms of these properties generally pass normality tests.

Spatial correlation of surface generated noise in a stratified ocean

A model is developed for the calculation of the spatial properties of the noise field produced in a stratified ocean by the action of wind at the surface. The random noise sources are represented by correlated monopoles distributed over an infinite plane located an arbitrary depth below the surface. Wave-theoretical methods are applied to derive expressions for the intensity and spatial correlation of the noise field. A normal-mode representation of the noise field is used to reduce these expressions to forms which allow physical interpretation and are suitable for numerical computation. Examples are given of intensity profiles and spatial correlation in the vertical for three generic sound-speed profiles. The results show that the sound-speed profile and the presence of the bottom can be important in determining the spatial properties of the noise field. An example is given of a calculation of the horizontal spatial correlation using the fast field program (FFP).