Orientation Tensor
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Orientation Tensor
In geology, especially in the study of glacial till, eigenvectors and eigenvalues are used as a method by which a mass of information of a clast fabric's constituents' orientation and dip can be summarized in a 3-D space by six numbers. In the field, a geologist may collect such data for hundreds or thousands of clast Clastic rocks are composed of fragments, or clasts, of pre-existing minerals and rock. A clast is a fragment of geological detritus,Essentials of Geology, 3rd Ed, Stephen Marshak, p. G-3 chunks, and smaller grains of rock broken off other rocks ...s in a soil sample, which can only be compared graphically such as in a Tri-Plot (Sneed and Folk) diagram, or as a stereographic projection. The output for the orientation tensor is in the three orthogonal (perpendicular) axes of space. Eigenvectors output from programs such as Stereo32 are in the order E1 > E2 > E3, with E1 being the primary orientation of clast orientation/dip, E2 being the secondary and E3 being the ...
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Geology
Geology () is a branch of natural science concerned with Earth and other astronomical objects, the features or rocks of which it is composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth sciences, including hydrology, and so is treated as one major aspect of integrated Earth system science and planetary science. Geology describes the structure of the Earth on and beneath its surface, and the processes that have shaped that structure. It also provides tools to determine the relative and absolute ages of rocks found in a given location, and also to describe the histories of those rocks. By combining these tools, geologists are able to chronicle the geological history of the Earth as a whole, and also to demonstrate the age of the Earth. Geology provides the primary evidence for plate tectonics, the evolutionary history of life, and the Earth's past climates. Geologists broadly study the properties and processes of E ...
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Glacial Till
image:Geschiebemergel.JPG, Closeup of glacial till. Note that the larger grains (pebbles and gravel) in the till are completely surrounded by the matrix of finer material (silt and sand), and this characteristic, known as ''matrix support'', is diagnostic of till. image:Glacial till exposed in roadcut-750px.jpg, Glacial till with tufts of grass Till or glacial till is unsorted glacier, glacial sediment. Till is derived from the erosion and entrainment of material by the moving ice of a glacier. It is deposited some distance down-ice to form terminal, lateral, medial and ground moraines. Till is classified into primary deposits, laid down directly by glaciers, and secondary deposits, reworked by fluvial transport and other processes. Description Till is a form of '' glacial drift'', which is rock material transported by a glacier and deposited directly from the ice or from running water emerging from the ice. It is distinguished from other forms of drift in that it is depos ...
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Eigenvector
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ...
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Eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root ass ...
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Fabric (geology)
In geology, a rock's fabric describes the spatial and geometric configuration of all the elements that make it up. In sedimentary rocks, the fabric developed depends on the depositional environment and can provide information on current directions at the time of deposition. In structural geology, fabrics may provide information on both the orientation and magnitude of the strains that have affected a particular piece of deformed rock. Types of fabric * Primary fabric — a fabric created during the original formation of the rock, e.g. a preferred orientation of clast long axes in a conglomerate, parallel to the flow direction, deposited by a fast waning current. * Shape fabric — a fabric that is defined by the preferred orientation of inequant elements within the rock, such as platy- or needle-like mineral grains. It may also be formed by the deformation of originally equant elements such as mineral grains. * Crystallographic preferred orientation — in plastically deforme ...
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Clast
Clastic rocks are composed of fragments, or clasts, of pre-existing minerals and rock. A clast is a fragment of geological detritus,Essentials of Geology, 3rd Ed, Stephen Marshak, p. G-3 chunks, and smaller grains of rock broken off other rocks by physical weathering.Essentials of Geology, 3rd Ed, Stephen Marshak, p. G-5 Geologists use the term clastic to refer to sedimentary rocks and particles in sediment transport, whether in suspension or as bed load, and in sediment deposits. Sedimentary clastic rocks Clastic sedimentary rocks are rocks composed predominantly of broken pieces or ''clasts'' of older weathered and eroded rocks. Clastic sediments or sedimentary rocks are classified based on grain size, clast and cementing material (matrix) composition, and texture. The classification factors are often useful in determining a sample's environment of deposition. An example of clastic environment would be a river system in which the full range of grains being transported by th ...
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Soil Sample
Soil test may refer to one or more of a wide variety of soil analysis conducted for one of several possible reasons. Possibly the most widely conducted soil tests are those done to estimate the plant-available concentrations of plant nutrients, in order to determine fertilizer recommendations in agriculture. Other soil tests may be done for engineering (geotechnical), geochemical or ecological investigations. Plant nutrition In agriculture, a soil test commonly refers to the analysis of a soil sample to determine nutrient content, composition, and other characteristics such as the acidity or pH level. A soil test can determine fertility, or the expected growth potential of the soil which indicates nutrient deficiencies, potential toxicities from excessive fertility and inhibitions from the presence of non-essential trace minerals. The test is used to mimic the function of roots to assimilate minerals. The expected rate of growth is modeled by the Law of the Maximum. Labs, su ...
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Earth Surface Processes And Landforms
''Earth Surface Processes and Landforms'' is a peer-reviewed scientific journal published by John Wiley & Sons on behalf of the British Society for Geomorphology. It covers geomorphology and more in general all aspects of Earth sciences dealing with the Earth surface. The journal was established in 1976 as ''Earth Surface Processes'', obtaining its current name in 1981. The journal primarily publishes original research papers. It also publishes ''Earth Surface Exchanges'' which include commentaries on issues of particular geomorphological interest, discussions of published papers, shorter journal articles suitable for rapid publication, and commissioned reviews on key aspects of geomorphological science. Foci include the physical geography of rivers, valleys, glaciers, mountains, hills, slopes, coasts, deserts, and estuary environments, along with research into Holocene, Pleistocene, or Quaternary science. The editor-in-chief is Stuart Lane (University of Lausanne). Abstracting and ...
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Stereographic Projection
In mathematics, a stereographic projection is a perspective projection of the sphere, through a specific point on the sphere (the ''pole'' or ''center of projection''), onto a plane (geometry), plane (the ''projection plane'') perpendicular to the diameter through the point. It is a smooth function, smooth, bijection, bijective function (mathematics), function from the entire sphere except the center of projection to the entire plane. It maps circle of a sphere, circles on the sphere to generalised circle, circles or lines on the plane, and is conformal map, conformal, meaning that it preserves angles at which curves meet and thus Local property, locally approximately preserves similarity (geometry), shapes. It is neither isometry, isometric (distance preserving) nor Equiareal map, equiareal (area preserving). The stereographic projection gives a way to representation (mathematics), represent a sphere by a plane. The metric tensor, metric induced metric, induced by the inverse s ...
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