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A group of minerals having the general chemical formula XYSi2O6, in which the Y site contains iron (Fe) or magnesium (Mg) and the X site contains Fe, Mg, manganese (Mn), or a small amount of calcium (Ca; up to about 3%). They are characterized by…

Mineral phases containing only oxide or hydroxide anions in their structures. By volume, oxide and hydroxide minerals comprise only a small fraction of the Earth's crust. However, their geochemical and petrologic importance cannot be overstated.…

A geographic designation that includes thousands of mainly small coral and volcanic islands scattered across the Pacific Ocean from Palau in the west to Easter Island in the east (see illustration). Island archipelagos off the coast of the Asian…

The Pacific Ocean has an area of 6.3 × 107 mi2 (1.65 × 108 km2) and a mean depth of 14,049 ft (4282 m). It covers 32% of the Earth's surface and 46% of the surface of all oceans and seas, and its area is greater than that of all land areas combined.…

The study of the history of the ocean with regard to circulation, chemistry, biology, and patterns of sedimentation. The source of information is largely the biogenous deep-ocean sediments, so the field may be considered a branch of sedimentology…

The study of ancient climates. Climate is the long-term expression of weather; in the modern world, climate is most noticeably expressed in vegetation, soil types, and characteristics of the land surface. To study ancient climates,…

The geography of the ancient past. Paleogeographers study the changing positions of the continents and the ancient extent of land, mountains, and shallow-sea and deep-ocean basins. The Earth's geography changes because its surface is in constant…

The study of the direction and intensity of the Earth's magnetic field through geologic time. Paleomagnetism is an important tool in measuring the past movements of the Earth's tectonic plates. By studying ancient magnetic field directions recorded…

The study of geological evidence for past earthquakes. This is a scientific discipline that has contributed greatly to modern understanding of the nature of earthquakes. The patterns of earthquakes, in both space and time, evolve over centuries and…

A soil of the past, that is, a fossil soil. Paleosols are most easily recognized when they are buried by sediments. They also include surface profiles that are thought to have formed under very different conditions from those now prevailing, such…

A ratio comparison of two quantities expressed by using 100 equal parts, or hundredths; symbolized %. There are three major uses of percent: part of a whole, rate, and comparison of any two quantities. Part of a whole The basic idea of percent is…

A minor accessory mineral, formula CaTiO3, that occurs in basic rocks. Perovskite has given its name to a large family of materials, synthetic and natural, that crystallize in similar structures. The crystal structure is ideally cubic, with a…

Any of the oriented intergrowths of potassium- and sodium-rich feldspars, (K,Na)AlSi3O8, whose proportions are determined in part by the initial composition of the alkali feldspar from which they exsolved and whose physical properties are thus…

A modification in the mathematical structure of a problem changing the problem from one that can be solved exactly, the unperturbed problem, to one, the perturbed problem, for which it is usually possible to obtain only an approximate solution. The…

A rare pegmatitic mineral with composition LiAlSi4O10. Its economic significance is markedly disproportionate to the number of its occurrences. It is the only basic raw material suitable for production of a group of materials known as crystallized…

The systematic study of the fabrics of rocks, generally involving statistical study of the orientations and distributions of large numbers of fabric elements. The term fabric denotes collectively all the structural or spatial characteristics of a…

The description of rocks with goals of classification and interpretation of origin. Most schemes for the classification of rocks are based on the size of grains and the proportions of various minerals. Interpretations of origin rely on field…

The practice of utilizing geological principles and applying geological concepts to the discovery and recovery of petroleum. Related fields in petroleum discovery include geochemistry and geophysics. The related areas in petroleum recovery are…

The study of rocks, their occurrence, composition, and origin. Petrography is concerned primarily with the detailed description and classification of rocks, whereas petrology deals primarily with rock formation, or petrogenesis. Experimental…

A relatively large crystal embedded in a finer-grained or glassy igneous rock. The presence of phenocrysts gives the rock a porphyritic texture (see illustration). Phenocrysts are represented most commonly by feldspar, quartz, biotite, hornblende,…

A phyllosilicate (sheet silicate) mineral with an ideal composition of KMg3(AlSi3)O10(OH)2. Phlogopite belongs to the mica mineral group.Structure Phlogopite is a trioctahedral mica, where all three possible octahedral cation sites are occupied by…

A light-colored, aphanitic (not visibly crystalline) rock of volcanic origin, composed largely of alkali feldspar, feldspathoids (nepheline, leucite, sodalite), and smaller amounts of dark-colored (mafic) minerals (biotite, soda amphibole, and soda…

Any naturally occurring inorganic salts of phosphoric acid, H3[PO4]. All known phosphate minerals are orthophosphates since their anionic group is the insular tetrahedral unit [PO4]3−. Mineral salts of arsenic acid, H3[AsO4], have a similar crystal…

A type of metamorphic rock formed during low-grade metamorphism of clay-rich sediments called pelites. Phyllites are very fine grained rocks with a grain size barely visible in a hand specimen. They have a well-developed planar element called…

The study of the Earth's surface features and associated processes. Physical geography aims to explain the geographic patterns of climate, vegetation, soils, hydrology, and landforms, and the physical environments that result from their…

The term picrite has been used with several different meanings. It is generally considered to include certain medium- to fine-grained ultramafic igneous rocks composed chiefly of olivine with smaller amounts of pyroxene, hornblende, and plagioclase…

The name given to the monoclinic pyroxenes of the general formula (Mg,Fe)SiO3 with some augite in solid solution. Pigeonite bears the same relation to the orthorhombic pyroxenes as augite does to the diopside-hedenbergite series. Pigeonite is the…

A natural glass with dull or pitchy luster and generally brown, green, or gray color. It is extremely rich in microscopic, embryonic crystal growths (crystallites) which may cause its dull appearance. The water content of pitchstone is high and…

The relatively smooth sections of the continental surfaces, occupied largely by gentle rather than steep slopes and exhibiting only small local differences in elevation. Because of their smoothness, plains lands, if other conditions are favorable,…

The locus of points in the euclidean plane that satisfy some geometric or algebraic definition. Not all sets of points deserve to be called a curve, but the distinction is somewhat arbitrary. For most of this article, a curve is considered to be…

The branch of mathematics that deals with geometric figures, that is, collections of points that all lie in the same plane (coplanar). Although the words “point” and “plane” are undefined concepts, for elementary applications the intuitive meanings…

Any elevated area of relatively smooth land. Usually the term is used more specifically to denote an upland of subdued relief that on at least one side drops off abruptly to adjacent lower lands. In most instances the upland is cut by deep but…

A nearly level, generally dry surface in the lowest part of a desert basin with internal drainage. When its surface is covered by a shallow sheet of water, it is a playa lake. Playas and playa lakes are also called dry lakes, alkali flats, mud…

Spherical or elliptical regions up to 40 micrometers in diameter in which there is a change in color from the surrounding mineral when viewed with a petrographic microscope. Pleochroic halos are found around small inclusions of radioactive…

A solid rock body that formed by cooling and crystallization of molten rock (magma) within the Earth. Most plutons, or plutonic bodies, are regarded as the product of crystallization of magma intruded into surrounding “country rocks” within the…

The alteration of rocks or crystallization of minerals by gases or supercritical fluids (generically termed magmatic fluids) derived from solidifying magma. At surface conditions, magmatic fluids sampled from active volcanoes contain steam with…

The science of weather and climate in the high latitudes of the Earth. In the polar regions the Sun never rises far above the horizon and remains below it continuously for part of the year, so that snow and ice can persist for long periods even at…

A geometric figure consisting of an ordered set of three or more (but a finite number of) points called vertices, each vertex connected by line segments called sides or edges to two other vertices. These two sides are said to be adjacent, and so are…

A solid whose boundary consists of a finite number of polygonal faces, that is, planar regions that are bounded by polygons. The sides of the faces are edges of the polyhedron; the vertices of the faces also are vertices of the polyhedron.Plane…

A collection of equations in several unknowns, expressed in terms of addition, subtraction, and multiplication. System (1)1is a system of polynomial equations in the three unknowns (or variables) x, y, and z. Typically, the objective is to solve…

A relatively large crystal formed in a metamorphic rock. The presence of abundant porphyroblasts gives the rock a porphyroblastic texture. Minerals found commonly as porphyroblasts include biotite, garnet, chloritoid, staurolite, kyanite,…

An igneous rock characterized by porphyritic texture, in which large crystals (phenocrysts) are enclosed in a matrix of very fine-grained to aphanitic (not visibly crystalline) material.Porphyries are generally distinguished from other porphyritic…

The Pleistocene or Glacial Epoch is less remarkable for radical evolutionary changes in plant life than for repeated shifts of position because of climatic changes and the resulting ice movements. The influence of these changes is known to have…

In a formal deductive system, a proposition accepted without proof, from which other propositions are deduced by the conventional methods of formal logic. There is a certain arbitrariness as to which propositions are to be treated as postulates,…

The materials found in nature that are used frequently as gemstones, including amber, beryl (emerald and aquamarine), chrysoberyl (cat's-eye and alexandrite), coral, corundum (ruby and sapphire), diamond, feldspar (moonstone and amazonite), garnet…

The fallout of waterdrops or frozen particles from the atmosphere. Liquid types are rain and drizzle; frozen types are snow, hail, small hail, ice pellets (also called ice grains or, in the United States, sleet), snow pellets (graupel, soft hail),…

Instruments used to measure the amount of rain or snow that falls on a level surface. Such measurements are made with instruments known as precipitation gages. A precipitation gage can be as simple as an open container on the ground to collect rain,…

A mineral, Ca2(Al,Fe3 +)(OH)2[Si3AlO10], with Al in parentheses in octahedral and Al in brackets in tetrahedral coordination by oxygens. The [Si3AlO10] tetrahedral sheet reflects its perfect platy cleavage. Owing to difficulty in securing suitable…

A polyhedron of which two faces are congruent polygons in parallel planes, and the other faces are parallelograms (see illustration). The bases B are the congruent polygons; the lateral faces are the parallelograms; the lateral edges are the edges…

The chance likelihood of a specified event or circumstance, usually expressed as the ratio of the number of times that event occurs to the large number of trials that take place to observe its occurrence or failure to occur. Although probability…

To the physicist the concept of probability is like an iceberg. The part of it which the physicist uses and which is, therefore, in full view for him or her is but a small fraction of what is hidden in other and larger disciplines. The philosophy…

The results of a series of independent trials, random variables, or errors often occur in fairly regular and predictable patterns. These patterns can be expressed mathematically, and the most important are called the binomial, normal, and Poisson…

Ordered, countable sets of numbers, x1, x2, x3,…, not necessarily all different. In general such sets are called sequences, whereas the term progression is usually confined to the special types: the arithmetic, in which the difference xk − xk−1…

A geometry that investigates those properties of figures that are unchanged (invariant) when the figures are projected from a point to a line or plane. Although isolated theorems appeared earlier, the first systematic treatment of the subject was…

A mineral having composition Ag3AsS3 and crystallizing in the hexagonal system. It occurs in prismatic crystals terminated by steep ditrigonal pyramids, but is more commonly massive or in disseminated grains. There is good rhombohedral cleavage.…

In sedimentary geology, all characteristics of the source area from which clastic sediments and sedimentary rocks are derived, including relief, weathering, and source rocks. Weathering processesThe goal of most provenance studies of sedimentary…

An instrument consisting of two thermometers which is used in the measurement of the moisture content of air or other gases. The bulb or sensing area of one of the thermometers either is covered by a thin piece of clean muslin cloth wetted…

A study of the physical and thermodynamic properties of the atmosphere. The properties of primary concern in air conditioning are (1) dry-bulb temperature, (2) wet-bulb temperature, (3) dew-point temperature, (4) absolute humidity, (5) percent…

A rock froth, formed by the extreme puffing up (vesiculation) of liquid lava by expanding gases liberated from solution in the lava prior to and during solidification. Some varieties will float in water for many weeks before becoming waterlogged.…

The basic building block of volcanic deposits formed by explosive eruptions. A pyroclast (or pyroclastic fragment) is any rock or mineral fragment—regardless of its size, shape, composition, origin, or mode of deposition—that is ejected during…

Rocks formed by the accumulation of fragmental volcanic materials (also called pyroclasts) ejected during explosive eruptions. Pyroclasts can vary widely in origin, fragment size and shape, composition, texture, structure (such as their arrangement…

A mineral having composition MnO2. Pyrolusite is the most important ore of manganese. It crystallizes in the tetragonal system but well-developed crystals (polianite) are rare. It is usually in radiating fibers or reniform coatings. The hardness is…

A mineral series in the apatite group, or in the larger grouping of phosphate, arsenate, and vanadate-type minerals. In this series lead (Pb) substitutes for calcium (Ca) of the apatite formula Ca5(PO4)3(F,OH,Cl), and little fluorine (F) or…

A hydrated aluminum silicate with composition Al2Si4O10(OH)2. The mineral is commonly white, grayish, greenish, or brownish, with a pearly to waxy appearance and greasy feel. It occurs as compact masses, as radiating aggregates (see illustration),…

A large, geologically significant group of dark, rock-forming silicate minerals. Pyroxene is found in abundance in a wide variety of igneous and metamorphic rocks. Because of their structural complexity and their diversity of chemical composition…

A heavy, dark-colored, phaneritic (visibly crystalline) igneous rock composed largely of pyroxene with smaller amounts of olivine or hornblende. Pyroxenite composed largely of orthopyroxene occurs with anorthosite and peridotite in large, banded…

A group of silicate minerals whose physical properties resemble those of pyroxenes. In contrast with the two-tetrahedra periodicity of pyroxene single silicate chains, the pyroxenoid crystal structures contain single chains of (SiO4)4- silicate…

This theorem states that in any right triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides: r2 = x2 + y2. More than 100 different proofs have been given for this extremely important theorem of euclidean…

A surface defined analytically by an equation of the second degree in three variables. If these variables are x, y, z, such an equation has the form of Eq. (1). 1Every plane section of such a surface is a conic. To simplify the notation, the…

The most common oxide on the Earth's surface, constituting 12% of the crust by volume. Quartz is a crystalline form of silicon dioxide (SiO2). When cooling magmas solidify into igneous rocks and when preexisting rocks metamorphose into new mineral…

A metamorphic rock consisting largely or entirely of quartz. Most quartzites are formed by metamorphism of sandstone; but some have developed by metasomatic introduction of quartz, SiO2, often accompanied by other chemical elements, for example,…

An associative, noncommutative algebra based on four linearly independent units or basal elements. Quaternions were originated in Dublin, Ireland, on October 16, 1843, by W. R. Hamilton (1805–1865), who is famous because of his canonical functions…

The mathematical theory of the formation and behavior of queues or waiting lines. The name is also applied loosely to the mathematical study of a wide variety of problems connected with traffic congestion and storage systems. Uneven flow through a…

A radian is the angle subtended at the center of a circle by an arc of the circle equal in length to its radius. It is proved in geometry that equal central angles of two circles subtend arcs proportional to their radii; and the converse is true.…

Minerals that contain uranium (U) or thorium (Th) as an essential component of their chemical composition. Examples are uraninite (UO2) or thorite (ThSiO4). There are radioactive minerals in which uranium and thorium substitute for ions of similar…

A branch of environmental geochemistry and isotope geology concerned with the occurrence of radioactive nuclides in sediment, water, air, biological tissues, and rocks. The nuclides have relatively short half-lives ranging from a few days to about…

An area of diminished precipitation on the lee side of mountains. There are marked rain shadows, for example, east of the coastal ranges of Washington, Oregon, and California, and over a larger region, much of it arid, east of the Cascade Range and…

Naturally occurring solids, formed by geological processes, that contain the rare-earth elements—the lanthanides (atomic numbers 57–71) and yttrium (atomic number 39)—as essential constituents. In a rare-earth mineral, at least one crystallographic…

A variable whose range is a subset of the real numbers. By extension the term is also used to refer to the theory of functions of one or more real variables. This theory has to do with properties of broad classes of functions, such as continuity,…

A function that maps natural numbers to natural numbers and is special in that it must be calculable by using a precisely specified algorithm. The mathematical definitions of partial recursive functions and recursive functions were developed to give…

A body of water that separates northeastern Africa from the Arabian Peninsula. The Red Sea forms part of the African Rift System, which also includes the Gulf of Aden and a complex series of continental rifts in East Africa extending as far south as…

Clastic sediments and sedimentary rocks that are pigmented by red ferric oxide which coats grains, fills pores as cement, or is dispersed as a muddy matrix. These conspicuously colored rocks commonly constitute thick sequences of nonmarine, paralic…

The mantle or blanket of unconsolidated or loose rock material that overlies the intact bedrock and nearly everywhere forms the land surface. The regolith may be residual (weathered in place), or it may have been transported to its present site. The…

The n-dimensional analogs of the regular polygons (n = 2) and platonic solids (n = 3). They are conveniently denoted by their Schläfli symbols {p, q, …}; for instance, the pentagon, hexagon, octagon, tetrahedron, octahedron are denoted by {5}, {6},…

In science, remote sensing refers to the process of observing the Earth and other terrestrial planets and moons from above. It is used in many practical applications and day-to-day operations, including mapping, weather forecasting, and as an aid…

The mineral form of manganese carbonate. Calcium, iron, magnesium, and zinc have all been reported to replace some of the manganese. The equilibrium replacement of manganese by calcium has been determined and found to increase with the temperature…

A mineral inosilicate with composition MnSiO3. Rhodonite crystallizes in the triclinic system in crystals that are commonly tabular parallel to the base (see illustration). More often it is in cleavable to compact masses or in embedded grains.…

A rhumb line, or loxodrome, is a line on the Earth of constant compass bearing. A navigator following a rhumb line between two points on the Earth would cross each meridian at the same angle, with the compass needle never wavering. The resulting…

A very light-colored, aphanitic (not visibly crystalline), volcanic rock that is rich in silica and broadly equivalent to granite in composition. Migration of rhyolitic magma through the Earth's crust, which causes much of the Earth's explosive and…

A generalization of the complex plane that was originally conceived to make sense of mathematical expressions such as z or log z. These expressions cannot be made single-valued and analytic in the punctured plane C\{0} (that is, the complex plane…

The geometry of Riemannian manifolds. Riemannian geometry was initiated by B. Riemann in 1854, following the pioneering work of C. F. Gauss on surface theory in 1827. Riemann introduced a coordinate space in which the infinitesimal distance between…

One of the geomorphological expressions between two tectonic plates that are opening relative to each other or sliding past each other. The term originally was used to describe the central graben structures of such classic continental rift zones as…

The mathematical term ring is used to designate a type of algebraic system with two compositions satisfying most but not all the properties of addition and multiplication in the system of integers, 0, ±1, ±2, …. In precise terms a ring is a set R…

A natural, freshwater surface stream that has considerable volume compared with its smaller tributaries. The tributaries are known as brooks, creeks, branches, or forks. Rivers are usually the main stems and larger tributaries of the drainage…

Tides that occur in rivers with an open connection to a tidal estuary or ocean. These tides are highly modified from coastal ocean tides as they propagate landward into shallow water, often through a brackish estuary and then into a freshwater…

A relatively common aggregate of mineral grains. Some rocks consist essentially of but one mineral species (monomineralic, such as quartzite, composed of quartz); others consist of two or more minerals (polymineralic, such as granite, composed of…

Finding the age of rocks based on the presence of naturally occurring long-lived radioactive isotopes of several elements in certain minerals and rocks. Measurements of rock ages have enabled geologists to reconstruct the geologic history of the…

A secondary, planar structure of deformed rocks. A cleavage is penetrative and systematic, as opposed to fractures and shear zones which may occur alone or in widely spaced sets. It is generally better developed in fine grained rocks than in coarse…

The permanent and induced magnetism of rocks and minerals on scales ranging from the atomic to the global, including applications to magnetic field anomalies and paleomagnetism. Natural compasses, concentrations of magnetite (Fe3O4) called…

The scientific discipline that deals with understanding how rocks deform and fail due to natural and human-induced forces at scales ranging from micrometers to kilometers. Rock mechanics is also the engineering discipline for designing and…