Fast and Accurate Approximation to Kriging Using Common Data Neighborhoods

Unknown values of a random field can be predicted from observed data using kriging. As data sets grow in size, the computation times become large. To facilitate kriging with large data sets, an approximation where the kriging is performed in sub-segments with common data neighborhoods has been developed. It is shown how the accuracy of the approximation can be controlled by increasing the common data neighborhood. For four different variograms, it is shown how large the data neighborhoods must be to get an accuracy below a chosen threshold, and how much faster these calculations are compared to the kriging where all data are used. Provided that variogram ranges are small compared to the domain of interest, kriging with common data neighborhoods provides excellent speed-ups (2–40) while maintaining high numerical accuracy. Results are presented both for data neighborhoods where the neighborhoods are the same for all sub-segments, and data neighborhoods where the neighborhoods are adapted to fit the data densities around the sub-segments. Kriging in sub-segments with common data neighborhoods is well suited for parallelization and the speed-up is almost linear in the number of threads. A comparison is made to the widely used moving neighborhood approach. It is demonstrated that the accuracy of the moving neighborhood approach can be poor and that computational speed can be slow compared to kriging with common data neighborhoods.     

RbSr isotope systematics at amphibolite facies conditions,Uppsala Region,Eastern Sweden

On the basis of U-Pb, Rb-Sr and K-Ar isotope analyses of Proterozoic rocks and minerals, a chronology has been established for the tectonic, intrusive and metamorphic evolution of the Svecokarelian orogeny 1750–1950 Ma ago in the Uppsala Region, Eastern Sweden. It is suggested that when synkinematic granitoids intruded the orogenic belt, at a stage of general subsidence and at medium metamorphic conditions (600°C and 3.5–4 kbar), the U-Pb isotope system in zircons closed earlier than the Rb-Sr whole-rock system. The zircon age (1886 Ma) reflects the intrusion and crystallization of the rock melt and the Rb-Sr whole-rock age (1830 Ma) the time when the temperature had decreased below the threshold for ⁸⁷Sr migration. The Rb-Sr whole rock age (1898 Ma) determined for metaandesites and metadacites reflects a recrystallization related to the intrusion of the granitoids. On the contrary, the more silicic metarhyodacitic volcanic rocks have a Rb-Sr whole rock age (1830 Ma) reflecting the cessation of the synkinematic metamorphism. The difference in the way the Rb-Sr isotope system responds in subsilicic or silicic metavolcanics is probably dependent on the amount of radiogenic ⁸⁷Sr and on the fixation of ⁸⁷Sr in Ca-rich minerals. Subsequent, late-kinematic, low amphibolite facies metamorphism has not altered the Rb-Sr ages of the granitoids and the recrystallized metavolcanics.     

Spectroscopic active IVFe3+–VIFe3+ clusters in spinel–magnesioferrite solid solution crystals: a potential monitor for ordering in oxide spinels

Optical absorption spectra (OAS) of synthetic single crystals of the solid solution spinel sensu stricto (s.s.)–magnesioferrite, Mg(Fe³⁺Al_1???y)₂O₄ (0?y?≤ 0.3), have been measured between 12 500 and 28 500?cm^?1. Chemical composition and Fe³⁺ site distribution have been measured by electron microprobe and Mössbauer spectroscopy, respectively. Ferric iron is ordered to the tetrahedral site for samples with small magnesioferrite component, and this ordering is shown to increase with magnesioferrite component. The optical absorption spectra show a strong increase in band intensities with Fe³⁺→Al substitution. Prominent and relatively sharp absorption bands are observed at 25 300 and 21 300?cm^?1, while less intense bands occur at 22 350, 18 900, 17 900 and 15 100?cm^?1. On the basis of band energies, band intensities and the compositional effect on band intensity, as well as structural considerations, we assign the observed bands to electronic transitions in ^IVFe³⁺–^VIFe³⁺clusters. A linear relationship (R ²= 0.99) between the α_net value of the absorption band at 21 300?cm^?1 and [^IVFe³⁺]?·?[^VIFe³⁺] concentration product has been defined: α_net=2.2?+?15.8 [^IVFe³⁺]?·?[^VIFe³⁺]. Some of the samples have been heat-treated between 700 and 1000?°C to investigate the relation between Fe³⁺ ordering and absorption spectra. Increase of cation disorder with temperature is observed, which corresponds to a 4% reduction in the number of active clusters. Due to the high spatial resolution (??～?10?μm), the OAS technique may be used as a microprobe for determination of Fe³⁺ concentration or site partitioning. Potential applications of the technique include analysis of small crystals and of samples showing zonation with respect to total Fe³⁺ and/or ordering.     

Sky view factors in forest canopies calculated with IDRISI

Summary  The sky view factor (SVF) is used in forest, road and urban climatology to characterise radiative properties. We now propose a method suitable for forest canopies using the raster based and commercially available software IDRISI. It uses quadratic pixels in rows and columns in a scanned equiangular fish-eye image. A threshold value is chosen to divide the image into sky and non-sky areas. The resulting image is then multiplied with a sky view weight image, where the weights of the pixels depend on the angular distance from zenith. The sum of pixel products gives the SVF. Quality analysis of the method is also performed. The choice of threshold value gives some uncertainties due to leaves reflecting sunlight. This error will be reduced by observing details (branches etc.) in the image and by choosing an overcast day for capturing the image. The precision range for SVF calculations will be better than 0.1. Received November 22, 1999 Revised July 17, 2000     

Relationships between drainage area characteristics and lake water quality

The aim of this work is to quantify some of the complex relationships between drainage area characteristics (such as bedrocks and quaternary deposits) and lake water quality (pH, alkalinity, conductivity, and hardness). Seventysix drainage lakes, mainly oligotrophic, are described with respect to drainage area characteristics, morphometry, and water chemistry. The DAZ (drainage area zonation) method has been used to describe the drainage areas. The method utilizes a weighting system to reduce the impact of land types with increasing distance from the lake. The most significant parameter governing the water chemistry parameters seems to be the percentage of open land (cultivated land and/or meadows) in the drainage areas. High percentage leads to high pH, alkalinity, conductivity, and hardness. The correlations concerning alkalinity and pH are improved using the DAZ method. No significant relationships between bedrock geology of the drainage areas and lake water chemistry have been recorded.     

Amplitudes of explosion-generated seismic waves

Summary Records of underwater explosions in Iceland in 1959 and 1960, mainly performed for crustal studies, have been investigated with regard to amplitudes. The amplitudes ofP2 in the 1959 explosions and of the first arrivingP waves in the 1960 explosions were found to be proportional to the first power of the charge weight, whereas amplitudes ofP1 andS1 in the 1959 explosions were proportional to the 3/4-power of the charge up to 200 kg, but increased much slower for larger charges. The influence of water depth of shot point on the charge weights, required to obtain a certain amplitude, has been determined and it was found that the logarithm of the charge weight has a linear relation to water depth down to about 8 meters. The amplitudes of first arrivingP waves decrease as the inverse 2.2-power of the distance up to about 30 km. For greater distances an exponential decrease of the form (const./) exp (–) is valid. ForP2 waves with a frequency of 10 cps we found =0.027±0.003 km^–1 for a profile across central Iceland and =0.009±0.004 km^–1 for a profile in the western part of Iceland.

---

Zusammenfassung In den Jahren 1959 und 1960 wurden auf Island Unterwasser-Explosionen ausgelöst, deren Hauptziel Untersuchung der Erdkruste waren. Die Aufzeichnungen der Explosionen werden hier in Hinsicht auf die Amplituden der Wellen untersucht. DieP2-Amplituden in den Explosionen von 1959 und die Amplituden der zuerst ankommendenP-Wellen in den Explosionen von 1960 waren proportional der ersten Potenz des Ladungsgewichtes, während diePl-undSl-Amplituden in den Explosionen von 1959 proportional der 3/4-Potenz des Ladungsgewichtes bis 200 kg waren. Für höhere Ladungsgewichte wuchsen die Amplituden langsamer an. Es wurde der Einfluss der Tiefe des Schusspunktes unterhalb des Wasserspiegels auf das für eine gewisse Amplitude benötigte Ladungsgewicht bestimmt. Es ergab sich dabei, dass der Logarithmus des Ladungsgewichtes in einer linearen Beziehung zur Tiefe, bis etwa 8 m, steht. Die Amplituden der zuerst ankommendenP-Wellen sind umgekehrt proportional der 2.2-Potenz der Entfernung, bis etwa 30 km. Für grössere Entfernungen ist die Abnahme der Amplituden exponential und kann durch (Konst./) exp (–) dargestellt werden. FürP2 mit einer Frequenz von 10 cps haben wir =0.027±0.003 km^–1 für ein Profil in Zentral-Island und =0.009 ± 0.004 km^–1 für ein Profil in West-Island gefunden.

     

Surface waves from earthquakes in Northern Atlantic-Arctic Ocean

Summary Earthquakes in the region of Jan Mayen exhibit two different appearances on records of near-by stations: classa with extremely well developed Love waves and less well developed Rayleigh waves, classb with poorly developed or missing Love waves but with clear Rayleigh waves. The difference between the two classes is ascribed to different focal depths. The Love waves of classa start simultaneously with theS wave and have initial periods over 40 sec; they have a small vertical component increasing along the wave train. They are unable to propagate beyond the continental margin for any considerable distance, probably due to a breakdown of the condition for constructive interference valid for their oceanic propagation.The oceanic dispersion curves both of Love and Rayleigh waves have been deduced using records at Kiruna, Uppsala, Bergen, Copenhagen, Scoresby Sund, Reykjavik, and Akureyri. The average thickness of the oceanic crust is around 15 km in the Norwegian Sea. For the Mid-Atlantic Ridge southwest of Reykjavik a crustal thickness of 10 km is obtained. The average thickness of unconsolidated sediments is around 2.4 km for the Norwegian Sea, and around 1.0 km in shallower regions of the ocean toward Iceland and Greenland.

---

Zusammenfassung Erdbeben in der Gegend von Jan Mayen zeigen zwei verschiedene Erscheinungen in den Aufzeichnungen naheliegender Stationen: Klassea mit ausserordentlich gut entwickelten Love-Wellen und weniger gut ausgebildeten Rayleigh-Wellen, Klasseb mit schwach entwickelten oder fehlenden Love-Wellen aber mit deutlichen Rayleigh-Wellen. Der Unterschied zwischen den beiden Klassen wird verschiedener Herdtiefe zugeschrieben. Die Love-Wellen der Klassea beginnen unmittelbar mit derS-Welle und haben Anfangsperioden über 40 sek; sie haben eine geringe vertikale Komponente, die im Laufe des Wellenzuges zunimmt. Sie können sich nicht über den Kontinentalrand beträchtlich weit fortpflanzen, was möglicherweise einem Aufhören der Voraussetzung für konstruktive Interferenz, die bei ihrer ozeanischen Ausbreitung vorhanden ist, zugeschrieben werden muss.Unter der Benutzung der Aufzeichnungen von Kiruna, Uppsala, Bergen, Kopenhagen, Scoresby Sund, Reykjavik und Akureyri wurden ozeanische Dispersionskurven sowohl für Love- als auch für Rayleigh-Wellen bestimmt. Die mittlere Mächtigkeit der ozeanischen Kruste beträgt ungefähr 15 km unter dem Europäischen Nordmeer. Für die Mittelatlantische Schwelle südwestlich von Reykjavik wurde eine Krustenmächtigkeit von 10 km erhalten. Die mittlere Mächtigkeit von unbefestigten Sedimenten ist ungefähr 2.4 km für das Europäische Nordmeer und ungefähr 1.0 km in Gegenden flacheren Meeres nach Island und Grönland hin.