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Ellipticity redirects here. For the mathematical topic of ellipticity, see elliptic operator
Elliptic operator

In mathematics, an elliptic operator is one of the major types of differential operator. It can be defined on spaces of complex-valued functions, or some more general function-like objects....
.


The flattening, ellipticity, or oblateness of an oblate spheroid is the "squashing" of the spheroid's pole
Geographical pole

A geographical pole , is either of two points on the surface of a spinning planet or other spinning body, at 90 degrees from its equator, at one of the two points where the Axis of rotation around which the body spins meets the surface of the body....
, towards its equator
Equator

The equator is the intersection of the Earth's surface with the Plane perpendicular to the Earth's rotation and containing the Earth's center of mass....
.

first, primary flattening, f, is the versine
Versine

The versed sine, also called the versine and, in Latin, the sinus versus or the sagitta , is a trigonometric function versin .Although the versine function appeared in some of the earliest trigonometric tables and was once widespread , it is now little-used....
 of the spheroid's angular eccentricity
Angular eccentricity

In the study of ellipses and related geometry, various parameters in the distortion of a circle into an ellipse are identified and employed: Aspect ratio, flattening and Eccentricity ....
 (""), equalling the relative difference between its equatorial radius, , and its polar radius, :



The amount of flattening depends on


and in detail on


There is also a second flattening, f' (sometimes denoted as "n"), that is the squared half-angle tangent of :

lattening without picking is an efficient full-volume automatic dense-picking method for flattening seismic data.






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Encyclopedia


Ellipticity redirects here. For the mathematical topic of ellipticity, see elliptic operator
Elliptic operator

In mathematics, an elliptic operator is one of the major types of differential operator. It can be defined on spaces of complex-valued functions, or some more general function-like objects....
.


The flattening, ellipticity, or oblateness of an oblate spheroid is the "squashing" of the spheroid's pole
Geographical pole

A geographical pole , is either of two points on the surface of a spinning planet or other spinning body, at 90 degrees from its equator, at one of the two points where the Axis of rotation around which the body spins meets the surface of the body....
, towards its equator
Equator

The equator is the intersection of the Earth's surface with the Plane perpendicular to the Earth's rotation and containing the Earth's center of mass....
.

First and second flattening

The first, primary flattening, f, is the versine
Versine

The versed sine, also called the versine and, in Latin, the sinus versus or the sagitta , is a trigonometric function versin .Although the versine function appeared in some of the earliest trigonometric tables and was once widespread , it is now little-used....
 of the spheroid's angular eccentricity
Angular eccentricity

In the study of ellipses and related geometry, various parameters in the distortion of a circle into an ellipse are identified and employed: Aspect ratio, flattening and Eccentricity ....
 (""), equalling the relative difference between its equatorial radius, , and its polar radius, :

  • The flattening of the Earth
    Earth

    Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...
     in WGS-84
    World Geodetic System

    The World Geodetic System is a standard for use in cartography, geodesy, and navigation. It comprises a standard Cartesian coordinates for the Earth, a standard spheroid reference surface for raw altitude data, and a gravitation equipotential surface that defines the "nominal sea level"....
     is 1:298.257223563 (which corresponds to a radius difference of 21.385 km of the Earth radius
    Earth radius

    Because the Earth is not perfectly Sphere, no single value serves as its natural radius. Instead, being nearly spherical, a range of values from #Polar radius:  b to #Equatorial radius:  a spans all proposed radii according to need, and several different ways of modeling the Earth as a sphere all yield a convenient...
     6378.137 - 6356.752 km) and would not be realized visually from space, since the difference represents only 0.335 %.
  • The flattening of Jupiter
    Jupiter

    Jupiter is the fifth planet from the Sun and the Solar system by size planet within the Solar System. It is two and a half times as massive as all of the other planets in our Solar System combined....
     (1:16) and Saturn (nearly 1:10), in contrast, can be seen even in a small telescope
    Telescope

    A telescope is an instrument designed for the observation of remote objects by the collection of electromagnetic radiation. The first known practically functioning telescopes were invented in the Netherlands at the beginning of the 17th century....
    ;
  • Conversely, that of the Sun
    Sun

    The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....
     is less than 1:1000 and that of the Moon
    Moon

    The Moon is Earth's only natural satellite and the List of natural satellites by diameter satellite in the Solar System. The average centre-to-centre distance from the Earth to the Moon is km, about thirty times the diameter of the Earth....
     barely 1:900.


The amount of flattening depends on
  • the relation between gravity and centrifugal force
    Centrifugal force

    In classical mechanics, centrifugal force is an outward force associated with rotation. Centrifugal force is one of several so-called pseudo-forces , so named because, unlike Fundamental interaction, they do not originate in interactions with other bodies situated in the environment of the particle upon which they act....
    ;


and in detail on
  • size and density
    Density

    The density of a material is defined as its mass per unit volume. The symbol of density is ....
     of the celestial body (see Figure of the Earth
    Figure of the Earth

    The expression figure of the Earth has various meanings in geodesy according to the way it is used and the precision with which the Earth's size and shape is to be defined....
    , last chapter);
  • the rotation
    Rotation

    A rotation is a movement of an object in a circular motion. A two-dimensional object rotates around a center of rotation. A Three-dimensional space object rotates around a line called an axis....
     of the planet or star;
  • and the elasticity
    Elasticity (physics)

    In physics, elasticity is the physical property of a material when it deforms under stress , but returns to its original shape when the stress is removed....
     of the body.


There is also a second flattening, f' (sometimes denoted as "n"), that is the squared half-angle tangent of :

Flattening without picking

Flattening without picking is an efficient full-volume automatic dense-picking method for flattening seismic data. First, local dips (step-outs) are calculated over the entire seismic volume. The dips are then resolved into time shifts (or depth shifts) relative to reference trace using a non-linear Gauss-Newton iterative approach that exploits Discrete Cosine Transforms (DCT's) to minimize computation time. At each point in the image two dips are estimated; one dip in the x direction and one dip in the y direction. Because each point in the image has two dips, each horizon is estimated from an over-determined system of dips in a least-squares sense.

See also


  • Angular eccentricity
    Angular eccentricity

    In the study of ellipses and related geometry, various parameters in the distortion of a circle into an ellipse are identified and employed: Aspect ratio, flattening and Eccentricity ....
  • Astronomy
    Astronomy

    Astronomy is the science of Astronomical object and Phenomenon that originate outside the Earth's atmosphere . It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the physical cosmology....
  • Earth rotation
    Earth rotation

    Earth's rotation is the rotation of the solid Earth around its own axis. The Earth rotates towards the east. As viewed from the North Star Polaris, the Earth turns counter-clockwise....
  • Gravitational field
    Gravitational field

    A gravitational field is a scientific model used within physics to explain how gravitation exists in the universe. In its original concept, gravity was a force between point masses....