Structural geology is the study of the three-dimensional distribution of rock units with respect to their deformational histories. The primary goal of structural geology is to use measurements of present-day rock geometries to uncover information about the history of deformation (strain) in the rocks, and ultimately, to understand the stress field that resulted in the observed strain and geometries. This understanding of the dynamics of the stress field can be linked to important events in the geologic past; a common goal is to understand the structural evolution of a particular area with respect to regionally widespread patterns of rock deformation due to plate tectonics.
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three real numbers: the radial distancer along the radial line connecting the point to the fixed point of origin; the polar angleθ between the radial line and a given polar axis; and the azimuthal angleφ as the angle of rotation of the radial line around the polar axis. (See graphic re the "physics convention".) Once the radius is fixed, the three coordinates (r, θ, φ), known as a 3-tuple, provide a coordinate system on a sphere, typically called the spherical polar coordinates. The plane passing through the origin and perpendicular to the polar axis (where the polar angle is a right angle) is called the reference plane (sometimes fundamental plane).
An azimuth is the horizontal angle from a cardinal direction, most commonly north, in a local or observer-centric spherical coordinate system.
Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.
In Euclidean geometry, a plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space . A prototypical example is one of a room's walls, infinitely extended and assumed infinitesimal thin. While a pair of real numbers suffices to describe points on a plane, the relationship with out-of-plane points requires special consideration for their embedding in the ambient space .
Indirect fire is aiming and firing a projectile without relying on a direct line of sight between the gun and its target, as in the case of direct fire. Aiming is performed by calculating azimuth and inclination, and may include correcting aim by observing the fall of shot and calculating new angles.
A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane containing the purple section). The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.
In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object. The angle value can be specified in various angular units, such as degrees, mils, or grad. More specifically:
A theodolite is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but it is also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching.
A 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.
An inclinometer or clinometer is an instrument used for measuring angles of slope, elevation, or depression of an object with respect to gravity's direction. It is also known as a tilt indicator, tilt sensor, tilt meter, slope alert, slope gauge, gradient meter, gradiometer, level gauge, level meter, declinometer, and pitch & roll indicator. Clinometers measure both inclines and declines using three different units of measure: degrees, percentage points, and topos. The astrolabe is an example of an inclinometer that was used for celestial navigation and location of astronomical objects from ancient times to the Renaissance.
Foliation in geology refers to repetitive layering in metamorphic rocks. Each layer can be as thin as a sheet of paper, or over a meter in thickness. The word comes from the Latin folium, meaning "leaf", and refers to the sheet-like planar structure. It is caused by shearing forces, or differential pressure. The layers form parallel to the direction of the shear, or perpendicular to the direction of higher pressure. Nonfoliated metamorphic rocks are typically formed in the absence of significant differential pressure or shear. Foliation is common in rocks affected by the regional metamorphic compression typical of areas of mountain belt formation.
A Brunton compass, properly known as the Brunton Pocket Transit, is a precision compass made by Brunton, Inc. of Riverton, Wyoming. The instrument was patented in 1894 by Canadian-born geologist David W. Brunton. Unlike most modern compasses, the Brunton Pocket Transit utilizes magnetic induction damping rather than fluid to damp needle oscillation. Although Brunton, Inc. makes many other types of magnetic compasses, the Brunton Pocket Transit is a specialized instrument used widely by those needing to make accurate navigational and slope-angle measurements in the field. Users are primarily geologists, but archaeologists, environmental engineers, mining engineers and surveyors also make use of the Brunton's capabilities. The United States Army has adopted the Pocket Transit as the M2 Compass for use by crew-served artillery.
Lineations in structural geology are linear structural features within rocks. There are several types of lineations, intersection lineations, crenulation lineations, mineral lineations and stretching lineations being the most common. Lineation field measurements are recorded as map lines with a plunge angle and azimuth.
A cave survey is a map of all or part of a cave system, which may be produced to meet differing standards of accuracy depending on the cave conditions and equipment available underground. Cave surveying and cartography, i.e. the creation of an accurate, detailed map, is one of the most common technical activities undertaken within a cave and is a fundamental part of speleology. Surveys can be used to compare caves to each other by length, depth and volume, may reveal clues on speleogenesis, provide a spatial reference for other areas of scientific study and assist visitors with route-finding.
Magnetic dip, dip angle, or magnetic inclination is the angle made with the horizontal by Earth's magnetic field lines. This angle varies at different points on Earth's surface. Positive values of inclination indicate that the magnetic field of Earth is pointing downward, into Earth, at the point of measurement, and negative values indicate that it is pointing upward. The dip angle is in principle the angle made by the needle of a vertically held compass, though in practice ordinary compass needles may be weighted against dip or may be unable to move freely in the correct plane. The value can be measured more reliably with a special instrument typically known as a dip circle.
In structural geology, rake is formally defined as "the angle between a line [or a feature] and the strike line of the plane in which it is found", measured on the plane. The three-dimensional orientation of a line can be described with just a plunge and trend. The rake is a useful description of a line because often features (lines) follow along a planar surface. In these cases the rake can be used to describe the line's orientation in three dimensions relative to that planar surface. One might also expect to see this used when the particular line is hard to measure directly. The rake always sweeps down from the horizontal plane.
The Rayleigh sky model describes the observed polarization pattern of the daytime sky. Within the atmosphere, Rayleigh scattering of light by air molecules, water, dust, and aerosols causes the sky's light to have a defined polarization pattern. The same elastic scattering processes cause the sky to be blue. The polarization is characterized at each wavelength by its degree of polarization, and orientation.
There are a number of different specialized magnetic compasses used by geologists to measure orientation of geological structures, as they map in the field, to analyze and document the geometry of bedding planes, joints, and/or metamorphic foliations and lineations. In this aspect the most common device used to date is the analogue compass.
In forestry, a tree crown measurement is one of the tree measurements taken at the crown of a tree, which consists of the mass of foliage and branches growing outward from the trunk of the tree. The average crown spread is the average horizontal width of the crown, taken from dripline to dripline as one moves around the crown. The dripline is the outer boundary to the area located directly under the outer circumference of the tree branches. When the tree canopy gets wet, any excess water is shed to the ground along this dripline. Some listings will also list the maximum crown spread which represents the greatest width from dripline to dripline across the crown. Other crown measurements that are commonly taken include limb length, crown volume, and foliage density. Canopy mapping surveys the position and size of all of the limbs down to a certain size in the crown of the tree and is commonly used when measuring the overall wood volume of a tree.
