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Variational Autoencoder Geostatistical Approach (VEGA) with Subsurface Applications.
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Assessing the effectiveness of ground truth data to capture landscape variability from an agricultural region using Gaussian simulation and geostatistical techniques
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A Geostatistical Framework for Quantifying the Imprint of Mesoscale Atmospheric Transport on Satellite Trace Gas Retrievals
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Geostatistical evaluation of satellite radar altimetry for high-resolution mapping of Lambert Glacier, Antarctica
The potential of satellite radar altimetry for high-resolution mapping of Antarctic ice streams is evaluated, using retracked and slope-corrected data from the Lambert Glacier and Amery Ice Shelf area, East Antarctica, acquired by Geosat during the Exact Repeat Mission (ERM), 1986-89. The map area includes lower Lambert Glacier north of 72.18 deg S, the southern Amery Ice Shelf, and the grounded inland ice sheet on both sides. The Geosat ERM altimetry is found to provide substantially more complete coverage than the 1978 Seasat altimetry, due to improved tracking. Variogram methods are used to estimate the noise levels in the data as a function of position throughout the map area. The spatial structure in the data is quantified by constructing experimental variograms using altimetry from the area of the grounding zone of Lambert Glacier, which is the area chiefly of interest in this topographically complex region. Kriging is employed to invert the along-track height measurements onto a fine-scale 3 km grid. The unsmoothed along-track Geosat ERM altimetry yields spatially continuous maps showing the main topographic features of lower Lambert Glacier, upper Amery Ice Shelf and the adjacent inland ice sheet. The probable position of the grounding line of Lambert Glacier is identified from a break in slope at the grounded ice/floating ice transition. The approximate standard error of the kriged map is inferred from the data noise levels.
Image analysis by geostatistical and neural-network methods applications in glaciology
The applicability of neural network techniques, in the classification of ice surfaces and crevasse patterns, was analyzed. The observations of the Bering Glacier (Alaska) obtained from a surface survey and from the global positioning system (GPS) were used. A geographical information system was applied to test the usefulness of standard approaches. The information in the image needed to be reduced prior to the classification. The reduction was performed with a fast variogram algorithm sampling in three oblique directions. The resultant vectors provided the input for the neural network.
Application of Geostatistical Simulation to Enhance Satellite Image Products
With the deployment of Earth Observing System (EOS) satellites that provide daily, global imagery, there is increasing interest in defining the limitations of the data and derived products due to its coarse spatial resolution. Much of the detail, i.e. small fragments and notches in boundaries, is lost with coarse resolution imagery such as the EOS MODerate-Resolution Imaging Spectroradiometer (MODIS) data. Higher spatial resolution data such as the EOS Advanced Spaceborn Thermal Emission and Reflection Radiometer (ASTER), Landsat and airborne sensor imagery provide more detailed information but are less frequently available. There are, however, both theoretical and analytical evidence that burn scars and other fragmented types of land covers form self-similar or self-affine patterns, that is, patterns that look similar when viewed at widely differing spatial scales. Therefore small features of the patterns should be predictable, at least in a statistical sense, with knowledge about the large features. Recent developments in fractal modeling for characterizing the spatial distribution of undiscovered petroleum deposits are thus applicable to generating simulations of finer resolution satellite image products. We will present example EOS products, analysis to investigate self-similarity, and simulation results.
A Geostatistical Data Fusion Technique for Merging Remote Sensing and Ground-Based Observations of Aerosol Optical Thickness
Particles in the atmosphere reflect incoming sunlight, tending to cool the Earth below. Some particles, such as soot, also absorb sunlight, which tens to warm the ambient atmosphere. Aerosol optical depth (AOD) is a measure of the amount of particulate matter in the atmosphere, and is a key input to computer models that simulate and predict Earth's changing climate. The global AOD products from the Multi-angle Imaging SpectroRadiometer (MISR) and the MODerate resolution Imaging Spectroradiometer (MODIS), both of which fly on the NASA Earth Observing System's Terra satellite, provide complementary views of the particles in the atmosphere. Whereas MODIS offers global coverage about four times as frequent as MISR, the multi-angle data makes it possible to separate the surface and atmospheric contributions to the observed top-of-atmosphere radiances, and also to more effectively discriminate particle type. Surface-based AERONET sun photometers retrieve AOD with smaller uncertainties than the satellite instruments, but only at a few fixed locations. So there are clear reasons to combine these data sets in a way that takes advantage of their respective strengths. This paper represents an effort at combining MISR, MODIS and AERONET AOD products over the continental US, using a common spatial statistical technique called kriging. The technique uses the correlation between the satellite data and the "ground-truth" sun photometer observations to assign uncertainty to the satellite data on a region-by-region basis. The larger fraction of the sun photometer variance that is duplicated by the satellite data, the higher the confidence assigned to the satellite data in that region. In the Western and Central US, MISR AOD correlation with AERONET are significantly higher than those with MODIS, likely due to bright surfaces in these regions, which pose greater challenges for the single-view MODIS retrievals. In the east, MODIS correlations are higher, due to more frequent sampling of the varying AOD. These results demonstrate how the MISR and MODIS aerosol products are complementary. The underlying technique also provides one method for combining these products in such a way that takes advantage of the strengths of each, in the places and times when they are maximal, and in addition, yields an estimate of the associated uncertainties in space and time.
Comprehensive Observations and Geostatistics of Slope Streaks within the Olympus Mons Aureole
Slope streaks (SS) are enigmatic linear features characterized by relatively low-albedo features that appear and fade on high-albedo slopes on Mars. Despite numerous hypotheses proposed to explain their formation, the primary mechanism behind SS remains elusive. Here, we examine 702 SS features using 32 multitemporal Context Imager (CTX) images and mesoscale modeling data obtained from a site (centered at 31.230°N, 216.281°E) in the Olympus Mons Aureole region. Our investigation revealed several key findings that shed light on the dynamics of SS formation and fading. We discovered a significant preference for SS formation on south-facing (equator-facing) slopes compared to north-facing slopes, with SS being over seven times more likely to occur on the former. Furthermore, SS formation was found to be seasonal with significantly enhanced by a factor of ∼6 near the equinoxes (from solar longitude Ls 337°-42° and 136°-227°) compared to other times of the year. Our analysis also revealed a correlation between the rates of SS formation and fading, with scree slopes exhibited the fastest-fading SS also experiencing the highest rates of newly-formed SS. Additionally, we measured the median starting and stopping slopes of SS to be 23.4° and 14.9°, respectively, significantly below the angle of repose of sand. These low slopes suggest the necessity for an energetic trigger mechanism to initiate SS formation. Infrared spectroscopy revealed that the principal distinction between the material inside and outside of a SS lies in the reduced abundance of dust within the streak. Notably, this site demonstrates the highest rates of SS formation (a 29.6% increase in new SS per Mars year) and fading (a 12% fading of SS per Mars year) ever quantified. These elevated rates may be attributed to the site's topography, which facilitates calm surficial nighttime winds throughout the year, leading to widespread dust deposition. Daytime downhill winds near the ridgelines of S-facing slopes may then trigger movement of newly deposited dust aggregates or alternatively, a Knudsen pump phenomenon could serve as a potential trigger for SS. We propose that SS is inhibited during the northern summer solstice season due to the relatively clear aphelion atmosphere, which limits dust deposition. Similarly, the lack of triggering activity during the winter solstice is likely due to more moderate daytime winds. Overall, our findings are consistent with the wind-triggered dry avalanche hypothesis as a plausible explanation for SS formation.
Geostatistical Analysis of Mesoscale Spatial Variability and Error in SeaWiFS and MODIS/Aqua Global Ocean Color Data
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Comprehensive observations and geostatistics of slope streaks within the Olympus Mons aureole
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Geostatistical Inversion in Geologic CO2 Sequestration Using a Variational Autoencoder
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Overcoming Data Scarcity in Carbon Storage Assessment: Estimating Petrophysical Properties in Legacy Wells Integrating Sample Logs and Geostatistical Approaches
Geological CO2 sequestration feasibility studies in mature basins frequently face challenges associated with legacy well data, which often lack the comprehensive logging suites required for accurate reservoir characterization. This study evaluates the storage potential of Ordovician– Devonian formations in a filed in the Delaware Basin portion of the Permian Basin, using a dataset of 47 wells.
Canopy Cover Predictions using Ground Observations and Remotely Sensed Data
Maps of vegetation status are needed at many scales, from the field level to monitor ecosystem condition to the global level to understand the carbon cycle. Status is quantified by such variables as leaf area index, biomass, and fraction of canopy cover. Current methods of predicting vegetation variables use remote sensing data to provide a spatially exhaustive data source. In a study in western Montana, several hundred ground observations made by the US Forest Service on tenth-acre conifer plots were used to develop aspatial regression and geostatistical prediction models. Normalized Difference Vegetation Index (NDVI) values from Landsat Thematic Mapper images were used as ancillary data. These models were then used to predict canopy cover at unsampled locations in a 97 square kilometer region on the boundary of the Flathead National Forest and the Bob Marshall Wilderness. Independent data from two dates six years apart were used for validation. Given the assumption that actual canopy cover remained relatively unchanged within this time period, partial validation can be achieved by measuring the correspondence of the two maps. This criterion results in ranking the aspatial regression maps as less accurate than the geostatistically generated maps. The geostatistical approach emphasizes ground measurements more heavily than does aspatid regression. Geostatistical simulations of canopy cover also provide a means of describing uncertainty about the patterns of canopy cover.
Mitigation of spatial nonstationarity with vision transformers
Spatial nonstationarity, the location variance of features’ statistical distributions, is ubiquitous in many natural settings. For example, in geological reservoirs rock matrix porosity varies vertically due to geomechanical compaction trends, in mineral deposits grades vary due to sedimentation and concentration processes, in hydrology rainfall varies due to the atmosphere and topography interactions, and in metallurgy crystalline structures vary due to differential cooling. Conventional geostatistical modeling workflows rely on the assumption of stationarity to be able to model spatial features for geostatistical inference. Nevertheless, this is often not a realistic assumption when dealing with nonstationary spatial data and this has motivated a variety of nonstationary spatial modeling workflows such as trend and residual decomposition, cosimulation with secondary features, and spatial segmentation and independent modeling over stationary subdomains. The advent of deep learning technologies has enabled new workflows for modeling spatial relationships. However, there is a paucity of demonstrated best practice and general guidance on mitigation of spatial nonstationarity with deep learning in the geospatial context. We demonstrate the impact of two common types of geostatistical spatial nonstationarity on deep learning model prediction performance and propose the mitigation of such impacts using self-attention (vision transformer) models. We demonstrate the utility of vision transformers for the mitigation of nonstationarity with relative errors as low as 10%, exceeding the performance of alternative deep learning methods such as convolutional neural networks. We establish best practice by demonstrating the ability of self-attention networks for modeling large-scale spatial relationships in the presence of commonly observed geospatial nonstationarity.
The influence of permeability anisotropy in the upper ocean crust on advective heat transport by a ridge-flank hydrothermal system
Here, in this study, we highlight the importance of permeability anisotropy on the hydrogeological regime of a ridge-flank hydrothermal system. Our study site, North Pond, is a marine sediment pond on ~8 Ma seafloor in the North Atlantic, and represents a low-temperature, end-member ridge-flank hydrothermal system. Previous simulations of North Pond elucidated long-standing hypotheses concerning hydrothermal fluid and heat transport in the upper volcanic crust but failed to fully explain observed patterns of seafloor heat flux in this area. Here we use variography, a geostatistical method, to quantify relations between seafloor heat-flux measurements, and coupled numerical simulations of fluid and heat flow to simulate the hydrogeologic regime. Directional variography shows that heat-flux observations are correlated along-strike of the regional crustal fabric. Three-dimensional simulations that include permeability anisotropy are able to replicate seafloor heat-flux patterns across North Pond. The simulations that result in the best match to thermal data incorporate permeability anisotropy in the horizontal plane. We find that the feedback between permeability anisotropy and the asymmetric geometry of North Pond combine to promote advective removal of heat and mass within the crustal aquifer. These findings suggest that permeability anisotropy in the oceanic crust may influence ridge-flank hydrothermal circulation more broadly.