Dixon resultant’s solution of systems of geodetic polynomial equations

The Dixon resultant is proposed as an alternative to Gröbner basis or multipolynomial resultant approaches for solving systems of polynomial equations inherent in geodesy. Its smallness in size, high density (ratio on the number of nonzero elements to the number of all elements), speed, and robustness (insensitive to combinatorial sequence and monomial order, e.g., Gröbner basis) makes it extremely attractive compared to its competitors. Using 3D-intersection and conformal C ₇ datum transformation problems, we compare its performance to those of the Sturmfels’s resultant and Gröbner basis. For the 3D-intersection problem, Sturmfels’s resultant needed 0.578 s to solve a 6  ×  6 resultant matrix whose density was 0.639, the Dixon resultant on the other hand took 0.266 s to solve a 4  ×  4 resultant matrix whose density was 0.870. For the conformal C ₇ datum transformation problem, the Dixon resultant took 2.25 s to compute a quartic polynomial in scale parameter whereas the computaton of the Gröbner basis fails. Using relative coordinates to compute the quartic polynomial in scale parameter, the Gröbner basis needed 0.484 s, while the Dixon resultant took 0.016 s. This highlights the robustness of the Dixon resultant (i.e., the capability to use both absolute and relative coordinates with any order of variables) as opposed to Gröbner basis, which only worked well with relative coordinates, and was sensitive to the combinatorial sequence and order of variables. Geodetic users uncomfortable with lengthy expressions of Gröbner basis or multipolynomial resultants, and who aspire to optimize on the attractive features of Dixon resultant, may find it useful.     

Spatial correlation of earthquake ground motion: non-parametric estimation

A non-parametric method, called multidimensional correlation mapping (MCM), is used to describe the local spatial correlation of different components of earthquake ground acceleration. The method estimates spatial correlation without presuming homogeneity or isotropy of the phase-aligned local ground motion fields. For selected events recorded by the SMART1 accelerograph array, we obtain contour plots of equal correlation of ground acceleration, with respect to the center of the array. Displacement time-histories are also computed from the accelerograms and the spatial correlation of the displacements is estimated for comparison with that of the accelerations.     

Three-dimensional deformation analysis: Global vector spherical harmonic and local finite element representation

Deformation elements which have global support, such as tidal induced displacements, are represented in terms of vector spherical harmonics. In contrast, local strain and local rotation are represented in terms of irregularly shaped three-dimensional finite elements. These geodetic finite elements reflect the structure of a geodetic network which is arbitrarily shaped. Various continuity classes are discussed. Numerical examples are presented.     

A Younger Dryas Ash Bed in western Norway,and its possible correlations with tephra in cores from the Norwegian Sea and the North Atlantic

A bed of volcanic ash up to 23 cm thick is found in lacustrine and marine sediments in western Norway. It is formally mamed the Vedde Ash Bed, and its age is approximately 10,600 yr B.P., i.e., mid-Younger Dryas. The bed consits of pure glass having a bimodal basaltic and rhyolitic somposition. The geochemistry of the glass shards suggests an Icelandic source. By means of stratigraphic position and geochemistry, the ash is correlated with ash zones found in cores from the continental shelf, the Norwegian Sea, and the North Atlatic.     

Coccolithen-Diagenese in Malm-Kalken (Solnhofen/Frankenalb,Oberalm/Salzburg)

Zusammenfassung Rasterelektronenmikroskopische Untersuchungen der Solnhofener Plattenkalke (Lagunensediment) und der Oberalmer Kalke (bathyale Sedimente) zeigen weitgehend ähnliche diagenetische Veränderungen der Coccolithen-Morphologie. Die Vielfalt der während der Sedimentation, am Meersboden und im Sediment möglichen Lösungs- und Abscheidungsvorgänge (siehe Abb. 1) erscheinen in den beiden, aus unterschiedlichen paläogeographischen Bereichen stammenden Malm-Kalken homogenisiert.

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According to Stereoscan Electron Microscope Studies of the Upper Jurassic (Tithonian) Solnhofen limestone (Southern Franconia) and of the Oberalm limestone (Northern Calcareous Alps) similar diagenetic criteria can be recognized in the alterations of the coccolith morphology. In contrast to the various solution- and precipitation patterns formed during the sedimentation of the ultraplancton, on the sea-floor or in the sediment (see fig. 1) no differentiation can be made with regard to the submicroscopic criteria caused by diagenetic processes in different environments (Solnhofen: subtidal lagoon with alternating hypersaline conditions with growth of blue-green-algal mats and normal marine water conditions with the sedimentation of ultraplancton. — Oberalm: bathyal basin with strongly burrowed soft bottoms and common sedimentation of ultraplancton).

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Résumé Les études par S.E.M. des calcaires en minces bancs de Solenhofen (sédiment lagunaire) et des calcaires d'Oberalm (sédiment bathyal) montrent des transformations diagénétiques sensiblement les mÊmes dans la morphologie des coccolithes. La multiplicité des processus de dissolution et de précipitation pouvant intervenir au cours de la sédimentation sur le fond de la mer et dans le sédiment, apparaissent comme s'homogénéisant dans ces deux calcaires du Mahn provenant de domaines paléogéographiques différents.

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Field characterization of vertical bromide transport in a fractured glacial till

A study of the fracture distribution, hydraulic properties, groundwater levels and the transport of bromide was conducted to characterize vertical transport in the oxidized and reduced zones of a fractured glacial till. Detailed vertical profiles of groundwater levels and solute concentrations were obtained over a 4.5-year period. Vertical migration occurred at several time scales, as a low concentration front was rapidly transported at rates of 100–500 m/year ahead of a slower moving main plume, which advanced at rates of 0.2–0.8 m/year. Concentrations in the leading edge of the plume displayed a high degree of spatial variability over short vertical distances through day 1,000. Late in the test, the influence of matrix diffusion became apparent as concentration patterns developed from being irregular to more uniform distributions. Calculations show that the mass within the low concentration plume front accounts for less than 1% of the total solute mass. Simulation of the breakthrough curves using a simple one-dimensional advection-dispersion model of transport in porous media indicates that vertical transport is dominated by advection. Furthermore, the results indicate that vertical transport of solutes in oxidized and reduced zones of the till can be adequately simulated using an equivalent porous media.     

Diatom assemblage response to Iroquoian and Euro-Canadian eutrophication of Crawford Lake,Ontario, Canada

Diatom and geochemical data from Crawford Lake, Ontario, have been used to document limnological responses to periods of cultural disturbance resulting from native Iroquoian occupation of the watershed (1268–1486 AD) and Euro-Canadian agriculture and deforestation (1867 AD–present). Here, we further develop the high-resolution nature of the Crawford Lake sediment record to examine the physical, chemical and biological aspects of limnological response to human disturbances in the lake catchment area with exceptional detail. We report detailed diatom abundance and flux data for individual taxa from Crawford Lake, and further describe the relationship between assemblage composition and environmental conditions using canonical correspondence analysis (CCA). Diatom assemblage data are used to calculate diatom inferred-total phosphorus (DI-TP) concentrations for the past ∼1,000 years. We also examine the diatom community response during and after periods of disturbance by Iroquoian and Euro-Canadian populations, and compare this response to existing geochemical proxies of lake production and new elemental geochemical indicators of catchment area erosion. In particular, we explore the differing limnological response to the two distinct periods of cultural eutrophication and examine the limnological processes that occurred during the period of␣low (or no) human activity (1487–1866 AD), when geochemical indicators of lake production recovered to pre-disturbance conditions, but diatom assemblages notably did not. Our results illustrate the highly susceptible nature of diatom communities to periods of anthropogenic disturbance, and emphasize that ecological indicators (such as diatom assemblages) should be included with other proxies (such as nutrient concentrations and physical characteristics) when assessing disturbance and recovery in lake systems.