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:''Ellipticity redirects here. For the mathematical topic of ellipticity, see elliptic operator.''
The 'flattening', 'ellipticity', or 'oblateness' of an oblate spheroid is the "squashing" of the spheroid's pole, down towards its equator.
The first, primary flattening, ''f'', is the versine of the spheroid's 'angular eccentricity' (""), equaling the relative difference between its equatorial radius, , and its polar radius, :
:::
:
★ The flattening of the Earth is 1:298.25275 (which corresponds to a radius difference of 21.385 km of the Earth radius 6378.137 - 6356.752 km) and would not be realized visually from space, ''since the difference represents only 0.335 %''.
:
★ The flattening of Jupiter (1:16) and Saturn (nearly 1:10), in contrast, can be seen even in a small telescope;
:
★ Conversely, that of the Sun is less than 1:1000 and that of the Moon barely 1:900.
The amount of flattening depends on
:
★ the relation between gravity and centrifugal force;
and in detail on
:
★ size and density of the celestial body (see Figure of the Earth, last chapter);
:
★ the rotation of the planet or star;
:
★ and the elasticity of the body.
There is also a second flattening, ''f' '' (sometimes denoted as "''n''"), that is the half-angle tangent2 of :
:::
'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.
★ Angular eccentricity
★ Astronomy
★ Earth rotation
★ gravity field
The 'flattening', 'ellipticity', or 'oblateness' of an oblate spheroid is the "squashing" of the spheroid's pole, down towards its equator.
| Contents |
| First and second flattening |
| Flattening without picking |
| See also |
First and second flattening
The first, primary flattening, ''f'', is the versine of the spheroid's 'angular eccentricity' (""), equaling the relative difference between its equatorial radius, , and its polar radius, :
:::
:
★ The flattening of the Earth is 1:298.25275 (which corresponds to a radius difference of 21.385 km of the Earth radius 6378.137 - 6356.752 km) and would not be realized visually from space, ''since the difference represents only 0.335 %''.
:
★ The flattening of Jupiter (1:16) and Saturn (nearly 1:10), in contrast, can be seen even in a small telescope;
:
★ Conversely, that of the Sun is less than 1:1000 and that of the Moon barely 1:900.
The amount of flattening depends on
:
★ the relation between gravity and centrifugal force;
and in detail on
:
★ size and density of the celestial body (see Figure of the Earth, last chapter);
:
★ the rotation of the planet or star;
:
★ and the elasticity of the body.
There is also a second flattening, ''f' '' (sometimes denoted as "''n''"), that is the half-angle tangent2 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
★ Astronomy
★ Earth rotation
★ gravity field
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