Upward continuation of the deflections of the vertical by spherical integral formulas

Zusammenfassung In dieser Arbeit werden sph?rische Integralformeln für die Fortsetzung auf der Kugel gegebener Lotabweichungskomponenten ξ, η in den Au?enraum gegeben.

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Groundwater behaviour in Tenerife,volcanic island (Canary Islands,Spain)

Tenerife is the largest of the seven Canary Islands, encompassing an area of 2,058 km². It is situated in the Atlantic Ocean between 16–17°W longitude and 28–29°N latitude. The topography of the island is characterized by generally steep slopes. The Teide Volcano has an elevation of 3,718 m. Precipitation is caused mainly by invasions of maritime polar air. Maximum mean precipitation recorded for 25-year period (1940–1965) is 1,000 mm.The fractured volcanic aquifer of the Old Basaltic Series is the main supplier of groundwater in Tenerife. Smaller quantities of groundwater are supplied by the Cañadas Series and minor amounts by alluvial sediments. Groundwater compartments develop in areas of dikes and contacts between permeable and impermeable zones. These compartments are irregular in volume, shape, and structure. The groundwater system forms a tortuous chain of compartments. Water circulates from one groundwater compartment to another through secondary fractures and other permeable elements which branch and intersect. Fractures which extend to the surface play an important role in recharge.The hydrologic system at Tenerife is characterized by three zones: the upper vadose, the lower vadose, and the saturated zone. In both the upper and lower vadose zones the dominant direction of flow is vertical, while in the saturated zone flow is generally oblique toward the sea.     

Bayesian Modeling and Inference for Geometrically Anisotropic Spatial Data

A geometrically anisotropic spatial process can be viewed as being a linear transformation of an isotropic spatial process. Customary semivariogram estimation techniques often involve ad hoc selection of the linear transformation to reduce the region to isotropy and then fitting a valid parametric semivariogram to the data under the transformed coordinates. We propose a Bayesian methodology which simultaneously estimates the linear transformation and the other semivariogram parameters. In addition, the Bayesian paradigm allows full inference for any characteristic of the geometrically anisotropic model rather than merely providing a point estimate. Our work is motivated by a dataset of scallop catches in the Atlantic Ocean in 1990 and also in 1993. The 1990 data provide useful prior information about the nature of the anisotropy of the process. Exploratory data analysis (EDA) techniques such as directional empirical semivariograms and the rose diagram are widely used by practitioners. We recommend a suitable contour plot to detect departures from isotropy. We then present a fully Bayesian analysis of the 1993 scallop data, demonstrating the range of inferential possibilities.