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Geostatistical
Geostatistics is a branch of statistics focusing on spatial or spatiotemporal datasets. Developed originally to predict probability distributions of ore grades for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, soil science, and agriculture (esp. in precision farming). Geostatistics is applied in varied branches of geography, particularly those involving the spread of diseases (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistical algorithms are incorporated in many places, including geographic information systems (GIS). Background Geostatistics is intimately related to interpolation methods but extends far beyond simple interpolation problems. Geostatistical techniques rely on statistical models based on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometallurgy
Geometallurgy relates to the practice of combining geological understanding with metallurgical test work and / or real time processing plant data (for extractive metallurgy), to create a geological based three-dimensional predictive model of mineral processing response. It is used in the hard rock mining industry for risk management and mitigation during mineral processing plant design. It is also used for production mine planning to optimize the ore feed to the processing plant. There are four important components or steps to developing a geometallurgical program,: *the geologically informed selection of a number of ore samples *laboratory-scale test work to determine the ore's response to mineral processing unit operations *the distribution of these parameters throughout the orebody using an accepted geostatistical technique *the application of a mining sequence plan and mineral processing models to generate a prediction of the process plant behavior Sample selection The samp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variogram
In spatial statistics the theoretical variogram, denoted 2\gamma(\mathbf_1,\mathbf_2), is a function describing the degree of spatial dependence of a spatial random field or stochastic process Z(\mathbf). The semivariogram \gamma(\mathbf_1,\mathbf_2) is half the variogram. For example, in gold mining, a variogram will give a measure of how much two samples taken from the mining area will vary in gold percentage depending on the distance between those samples. Samples taken far apart will vary more than samples taken close to each other. Definition The semivariogram \gamma(h) was first defined by Matheron (1963) as half the average squared difference between a function and a translated copy of the function separated at distance h. Formally :\gamma(h)=\frac\iiint_V \left (M+h) - f(M) \right2dM, where M is a point in the geometric field V, and f(M) is the value at that point. The triple integral is over 3 dimensions. h is the separation distance (e.g., in meters or km) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soil Science
Soil science is the study of soil as a natural resource on the surface of the Earth including soil formation, soil classification, classification and Soil survey, mapping; Soil physics, physical, Soil chemistry, chemical, Soil biology, biological, and fertility properties of soils; and these properties in relation to the use and Soil management, management of soils.Jackson, J. A. (1997). Glossary of Geology (4. ed.). Alexandria, Virginia: American Geological Institute. p 604. The main branches of soil science are ''pedology'' ― the study of formation, chemistry, morphology, and classification of soil ― and ''edaphology'' ― the study of how soils interact with living things, especially plants. Sometimes terms which refer to those branches are used as if synonymous with soil science. The diversity of names associated with this discipline is related to the various associations concerned. Indeed, engineers, agronomy, agronomists, chemists, geologists, physical geography, phys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space. It is closely related to the concepts of open set and Interior (topology), interior. Intuitively speaking, a neighbourhood of a point is a Set (mathematics), set of points containing that point where one can move some amount in any direction away from that point without leaving the set. Definitions Neighbourhood of a point If X is a topological space and p is a point in X, then a neighbourhood of p is a subset V of X that includes an open set U containing p, p \in U \subseteq V \subseteq X. This is equivalent to the point p \in X belonging to the Interior (topology)#Interior point, topological interior of V in X. The neighbourhood V need not be an open subset of X. When V is open (resp. closed, compact, etc.) in X, it is called an (resp. closed neighbourhood, compact neighbourhood, etc.). Some authors require neighbourhoods to be open, so i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution Support (measure theory), supported on the real numbers, discrete or "mixed" as well as Continuous variable, continuous, is uniquely identified by a right-continuous Monotonic function, monotone increasing function (a càdlàg function) F \colon \mathbb R \rightarrow [0,1] satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from negative infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potentiometric Surface
A potentiometric surface is the imaginary plane where a given reservoir of fluid will "equalize out to" if allowed to flow. A potentiometric surface is based on hydraulic principles. For example, two connected storage tanks with one full and one empty will gradually fill/drain to the same level. This is because of atmospheric pressure and gravity. This idea is heavily used in city water supplies - a tall water tower containing the water supply has a great enough potentiometric surface to provide flowing water at a decent pressure to the houses it supplies. For groundwater "potentiometric surface" is a synonym of "piezometric surface" which is an imaginary surface that defines the level to which water in a confined aquifer would rise were it completely pierced with wells. If the potentiometric surface lies above the ground surface, a flowing artesian well results. Contour maps and profiles of the potentiometric surface can be prepared from the well data. See also * Hydraulic head ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nearest-neighbor Interpolation
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around (neighboring) that point. The nearest neighbor algorithm selects the value of the nearest point and does not consider the values of neighboring points at all, yielding a piecewise-constant interpolant. The algorithm is very simple to implement and is commonly used (usually along with mipmapping) in real-time 3D rendering to select color values for a textured surface. Connection to Voronoi diagram For a given set of points in space, a Voronoi diagram is a decomposition of space into cells, one for each given point, so that anywhere in space, the closest given point is inside the cell. This is equivalent to nearest neighbor interpolation, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilinear Interpolation
In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., ''x'' and ''y'') using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in another direction. Although each step is linear in the sampled values and in the position, the interpolation as a whole is not linear but rather quadratic in the sample location. Bilinear interpolation is one of the basic resampling techniques in computer vision and image processing, where it is also called bilinear filtering or bilinear texture mapping. Computation Suppose that we want to find the value of the unknown function ''f'' at the point (''x'', ''y''). It is assumed that we know the value of ''f'' at the four points ''Q''11 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Distance Weighting
Inverse distance weighting (IDW) is a type of Deterministic algorithm, deterministic method for multivariate interpolation with a known homogeneously scattered set of points. The assigned values to unknown points are calculated with a Weighted mean, weighted average of the values available at the known points. This method can also be used to create spatial weights matrices in spatial autocorrelation analyses (e.g. Moran's I, Moran's ''I''). The name given to this type of method was motivated by the Weighted mean, weighted average applied, since it resorts to the inverse of the distance to each known point ("amount of proximity") when assigning weights. Definition of the problem The expected result is a discrete assignment of the unknown function u in a study region: :u(x): x \to \mathbb, \quad x \in \mathbf \sub \mathbb^n, where \mathbf is the study region. The set of N known data points can be described as a list of tuples: :[(x_1, u_1), (x_2, u_2), ..., (x_N, u_N)]. The f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function (mathematics), function in which * the Domain of a function, domain is the set of possible Outcome (probability), outcomes in a sample space (e.g. the set \ which are the possible upper sides of a flipped coin heads H or tails T as the result from tossing a coin); and * the Range of a function, range is a measurable space (e.g. corresponding to the domain above, the range might be the set \ if say heads H mapped to -1 and T mapped to 1). Typically, the range of a random variable is a subset of the Real number, real numbers. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geographic Information Systems
A geographic information system (GIS) consists of integrated computer hardware and software that store, manage, analyze, edit, output, and visualize geographic data. Much of this often happens within a spatial database; however, this is not essential to meet the definition of a GIS. In a broader sense, one may consider such a system also to include human users and support staff, procedures and workflows, the body of knowledge of relevant concepts and methods, and institutional organizations. The uncounted plural, ''geographic information systems'', also abbreviated GIS, is the most common term for the industry and profession concerned with these systems. The academic discipline that studies these systems and their underlying geographic principles, may also be abbreviated as GIS, but the unambiguous GIScience is more common. GIScience is often considered a subdiscipline of geography within the branch of technical geography. Geographic information systems are utilized in mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Network
A spatial network (sometimes also geometric graph) is a graph in which the vertices or edges are ''spatial elements'' associated with geometric objects, i.e., the nodes are located in a space equipped with a certain metric.M. Barthelemy, "Morphogenesis of Spatial Networks", Springer (2018). The simplest mathematical realization of spatial network is a lattice or a random geometric graph (see figure in the right), where nodes are distributed uniformly at random over a two-dimensional plane; a pair of nodes are connected if the Euclidean distance is smaller than a given neighborhood radius. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks and biological neural networks are all examples where the underlying space is relevant and where the graph's topology alone does not contain all the information. Characterizing and understanding the structure, resilience and the evolution of spatial networks is crucial for ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
