Geologic modellingGeologic modelling, geological modelling or geomodelling is the applied science of creating computerized representations of portions of the Earth's crust based on geophysical and geological observations made on and below the Earth surface. A geomodel is the numerical equivalent of a three-dimensional geological map complemented by a description of physical quantities in the domain of interest. Geomodelling is related to the concept of Shared Earth Model; which is a multidisciplinary, interoperable and updatable knowledge base about the subsurface.
Random variableA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.
GeologyGeology () is a branch of natural science concerned with the Earth and other astronomical objects, the 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. It is integrated with 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.
Random walkIn mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler.
Numerical modeling (geology)In geology, numerical modeling is a widely applied technique to tackle complex geological problems by computational simulation of geological scenarios. Numerical modeling uses mathematical models to describe the physical conditions of geological scenarios using numbers and equations. Nevertheless, some of their equations are difficult to solve directly, such as partial differential equations. With numerical models, geologists can use methods, such as finite difference methods, to approximate the solutions of these equations.
Random fieldIn physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as ). That is, it is a function that takes on a random value at each point (or some other domain). It is also sometimes thought of as a synonym for a stochastic process with some restriction on its index set. That is, by modern definitions, a random field is a generalization of a stochastic process where the underlying parameter need no longer be real or integer valued "time" but can instead take values that are multidimensional vectors or points on some manifold.
KrigingIn statistics, originally in geostatistics, kriging or Kriging, (pronounced /ˌˈkɹiːɡɪŋ/) also known as Gaussian process regression, is a method of interpolation based on Gaussian process governed by prior covariances. Under suitable assumptions of the prior, kriging gives the best linear unbiased prediction (BLUP) at unsampled locations. Interpolating methods based on other criteria such as smoothness (e.g., smoothing spline) may not yield the BLUP. The method is widely used in the domain of spatial analysis and computer experiments.
Geologic mapA geologic map or geological map is a special-purpose map made to show various geological features. Rock units or geologic strata are shown by color or symbols. Bedding planes and structural features such as faults, folds, are shown with strike and dip or trend and plunge symbols which give three-dimensional orientations features. Stratigraphic contour lines may be used to illustrate the surface of a selected stratum illustrating the subsurface topographic trends of the strata.
Statistical modelA statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
Random matrixIn probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables. Many important properties of physical systems can be represented mathematically as matrix problems. For example, the thermal conductivity of a lattice can be computed from the dynamical matrix of the particle-particle interactions within the lattice. In nuclear physics, random matrices were introduced by Eugene Wigner to model the nuclei of heavy atoms.
Geophysical surveyGeophysical survey is the systematic collection of geophysical data for spatial studies. Detection and analysis of the geophysical signals forms the core of Geophysical signal processing. The magnetic and gravitational fields emanating from the Earth's interior hold essential information concerning seismic activities and the internal structure. Hence, detection and analysis of the electric and Magnetic fields is very crucial.
Stratigraphic unitA stratigraphic unit is a volume of rock of identifiable origin and relative age range that is defined by the distinctive and dominant, easily mapped and recognizable petrographic, lithologic or paleontologic features (facies) that characterize it. Units must be mappable and distinct from one another, but the contact need not be particularly distinct. For instance, a unit may be defined by terms such as "when the sandstone component exceeds 75%". Sequences of sedimentary and volcanic rocks are subdivided on the basis of their shared or associated lithology.
GeophysicsGeophysics (ˌdʒiːoʊˈfɪzɪks) is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. Geophysicists, who usually study geophysics, physics, or one of the earth sciences at the graduate level, complete investigations across a wide range of scientific disciplines.
Geological engineeringGeological engineering is a discipline of engineering concerned with the application of geological science and engineering principles to fields, such as civil engineering, mining, environmental engineering, and forestry, among others. The work of geological engineers often directs or supports the work of other engineering disciplines such as assessing the suitability of locations for civil engineering, environmental engineering, mining operations, and oil and gas projects by conducting geological, geoenvironmental, geophysical, and geotechnical studies.
VariogramIn spatial statistics the theoretical variogram, denoted , is a function describing the degree of spatial dependence of a spatial random field or stochastic process . The semivariogram is half the variogram. In the case of a concrete example from the field of 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.
Stochastic processIn probability theory and related fields, a stochastic (stəˈkæstɪk) or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule.
Geologic time scaleThe geologic time scale or geological time scale (GTS) is a representation of time based on the rock record of Earth. It is a system of chronological dating that uses chronostratigraphy (the process of relating strata to time) and geochronology (scientific branch of geology that aims to determine the age of rocks). It is used primarily by Earth scientists (including geologists, paleontologists, geophysicists, geochemists, and paleoclimatologists) to describe the timing and relationships of events in geologic history.
Gaussian processIn probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g.
Markov random fieldIn the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it satisfies Markov properties. The concept originates from the Sherrington–Kirkpatrick model. A Markov network or MRF is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic.
Sequence stratigraphySequence stratigraphy is a branch of geology, specifically a branch of stratigraphy, that attempts to discern and understand historic geology through time by subdividing and linking sedimentary deposits into unconformity bounded units on a variety of scales. The essence of the method is mapping of strata based on identification of surfaces which are assumed to represent time lines (e.g. subaerial unconformities, maximum flooding surfaces), thereby placing stratigraphy in chronostratigraphic framework allowing understanding of the evolution of the earth's surface in a particular region through time.
