Relations Between Igneous and Metamorphic Rock Fracture Patterns and Groundwater Yield from the Variography of Water–Well Yields—Pinardville Quadrangle,New Hampshire

Exploratory variography was used to examine the spatial continuity of water–well yields in the Pinardville 7 Minute Quadrangle in southern New Hampshire and to link the variography to the characteristics of the fractured igneous and metamorphic rocks within the aquifer system. In addition to the analyses of variograms computed by using data from 939 wells, analyses were performed on subsets of the data that were stratified according to the level of yield and to five rock types. The stratification according to yield was defined by using the industry standard of a high-yield well that produces 40 gallons per minute or more. The stratification of the low-yield wells by rock type was defined by using the classification on the bedrock map for the State of New Hampshire. Although the variability is high in the low-yield wells, as indicated by the large nugget value, overall continuity ranges to 6000 feet in the fracture zones in which these wells have been drilled. This continuity is dominant in the northwesterly direction, as indicated by the directional variography. This result is consistent with the general trend in the larger tectonic configuration of the region. A lack of spatial correlation for 81 high-yield wells is consistent with the geologic interpretation that these wells occur in locally determined configurations of sheeting and steeply dipping fractures. Yield data in only three of the five rock types were sufficient for variography. Within these three, the dominant direction of the correlation structure ranged from northwesterly for the Massabesic Gneiss Complex to northeasterly for the Rangeley Formation to northerly for the Spaulding Granite, where the signature of the continuity in the low-yield wells is predominately attributed to the fracture system.     

Geomorphic characterization of seafloor using Digital Elevation Model derivatives – a case study around Bombay High,Western Indian offshore

The present study demonstrates the use of gridded bathymetry in the form of a Digital Elevation Model (DEM) in a geographic information system (GIS) in geomorphic characterization of the seafloor in the Western Indian offshore around Bombay High region and presents the salient findings. The variography of bathymetry and its derivatives and their spatial correlation provides a technique to measure the presence of seafloor features and provides an insight into the processes involved. The current study utilizes tools available within a GIS for processing of a DEM and its derivatives involving spatial techniques like spatial correlation and variography studies for geomorphic characterization. A broad regional analysis for the study area comprising the near shore coast to the deep waters is discussed, followed up by a detailed study limiting to the coastal region around Bombay High.     

Using geology to control geostatistics in the Hellyer deposit

The Hellyer orebody, a polymetallic massive sulfide deposit, was discovered in western Tasmania by Aberfoyle in 1983. Delineation diamond drilling was carried out in 1984 on a nominal 50-m square grid pattern to outline the resource. Resource estimation methods were influenced by the requirement to develop a regular block model for conceptual mine planning studies. Detailed geological interpretation indicates that the interpolation technique must take into account several important features to retain geological credibility. The deposit has sharp limits defined by visual geological contacts with virtually barren enclosing rocks. Lateral terminations are rapid with no interfingering internal waste. The dip and strike are variable and a major fault with a measurable displacement cuts acutely through the center of the deposit. Ore grades are reasonably correlateable within specific layers from hole to hole indicating a significant across-dip anisotropy. A hanging wall enriched zone is well-defined throughout the deposit. To overcome the variable geometry problems, a stratigraphic coordinate system was defined arbitrarily to replace the normal z coordinate. This allowed variography in stratigraphic layers. Blocks to be estimated were constrained by hand-drawn and subsequently digitized hanging wall and footwall contours. Each block was ascribed a stratigraphic coordinate by calculating its spatial position in relation to nearby stratigraphic unit boundaries within the massive sulfide body. Estimates were generated for each element by ordinary linear kriging. Despite the relatively sparse data in a large massive deposit, the customized technique developed for Hellyer has provided a reliable model of spatial grade distribution by combining conventional geostatistical methods with careful geological observation and interpretation. Some geometry problems remain which are the subject of ongoing studies.This paper was presented at MGUS 87 Conference, Redwood City, California, 14 April 1987.     

Validation of the relation between structural patterns in fractured bedrock and structural information interpreted from 2D-Variogram maps of water-well yields in Loudoun county,Virginia

Field geology was used to validate the hypothesis that the variography of the initial yields of water wells drilled into fractured crystalline bedrock reveals the geologic structure of the bedrock. Patterns in two-dimensional (2D)-variogram maps were predicted for four areas using geology gained from field mapping. Variograms were calculated for the areas and compared with the predictions. The predictions made by the field geologist (Scott Southworth) corresponded well with the variograms. This implies that variography may suggest the underlying geologic structure in areas that have many water wells but little rock outcrop.     

The Channel Tunnel: Geostatistical prediction of the geological conditions and its validation by the reality

Geometric modeling of the geological layers in the Channel Tunnel area employed local variography and kriging for computing meaningful predictions and confidence intervals. The results were used to design the alignment of the tunnel, and tunneling was completed on March 28, 1991, 1 month ahead of the initial schedule. Data from 85 borehole pairs drilled during tunneling enable the geostatistical prediction to be compared with the reality, which is seldom possible. They fully validate the geostatistical approach.     

A comprehensive framework for exploratory spatial data analysis: Moran location and variance scatterplots

Abstract

A significant Geographic Information Science (GIS) issue is closely related to spatial autocorrelation, a burning question in the phase of information extraction from the statistical analysis of georeferenced data. At present, spatial autocorrelation presents two types of measures: continuous and discrete. Is it possible to use Moran's I and the Moran scatterplot with continuous data? Is it possible to use the same methodology with discrete data? A particular and cumbersome problem is the choice of the spatial-neighborhood matrix (W) for points data. This paper addresses these issues by introducing the concept of covariogram contiguity, where each weight is based on the variogram model for that particular dataset: (1) the variogram, whose range equals the distance with the highest Moran I value, defines the weights for points separated by less than the estimated range and (2) weights equal zero for points widely separated from the variogram range considered. After the W matrix is computed, the Moran location scatterplot is created in an iterative process. In accordance with various lag distances, Moran's I is presented as a good search factor for the optimal neighborhood area. Uncertainty/transition regions are also emphasized. At the same time, a new Exploratory Spatial Data Analysis (ESDA) tool is developed, the Moran variance scatterplot, since the conventional Moran scatterplot is not sensitive to neighbor variance. This computer-mapping framework allows the study of spatial patterns, outliers, changeover areas, and trends in an ESDA process. All these tools were implemented in a free web e-Learning program for quantitative geographers called SAKWeb© (or, in the near future, myGeooffice.org).     

Variography of submarine morphology: Problems of deregularization, and cartographical implications

During the German Antarctic Expedition VI (leg 3, December 1987 to March 1988), bathymetric surveys were made in the Weddell Sea by the SEABEAM sonar system. For the first time geostatistical methods were applied in the SEABEAM-postprocessing. The investigations of variography that were necessary prior to the cartographical-geomorphological evaluation shed new light on classical geostatistical concerns. SEABEAM data provide a good example of a mean square, differentiable regionalized variable, where data are sampled over a two-dimensional support due to the technique of the sonar device. By deregularizations of the sample variograms, spatial continuity can be shown to be a property of seafloor depth as well as a point variable. The results are discussed in a sedimentological context. As an application of the regional variogram analyses, large-scale kriged bathymetric maps are presented.     

Geostatistical analysis in weathering studies: case study for Stanton Moor building sandstone

Geostatistical techniques for spatial prediction and spatial simulation have been used in an innovative application to the study of weathering of natural building stone. The study investigates the differences in the spatial variation of permeability characteristics between fine‐ and coarse‐grained Stanton Moor building sandstone. Non‐destructive permeability measurements, using an unsteady‐state Portable Probe Permeameter, were made on three adjacent faces of two cubic blocks representative of fine‐ to medium‐grained and medium‐ to coarse‐grained Stanton Moor Sandstone. The findings provide greater understanding in the investigation of the durability characteristics of the Stanton Moor Sandstone and show that the spatial distribution and variability of permeability is more important in predicting the overall strength and weathering properties than mean permeability and absolute minimum and maximum values. The results suggest that both primary textural characteristics (such as grain size) and extent of cementation appear to be important factors in determining the overall durability properties of Stanton Moor Sandstone as a building stone. Geostatistical analysis has been shown to be an important tool in the characterization of spatial variation for the investigation of weathering of building stones. Copyright © 2006 John Wiley & Sons, Ltd.