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Flattening




The flattening, '''ellipticity''', or '''oblateness''' of an Oblate Spheroid is the "squashing" of the spheroid's Pole , down towards its Equator .


FIRST AND SECOND FLATTENING

The first, primary flattening, ''f'', is the Versine of the spheroid's Angular Eccentricity ("o\! arepsilon\,\!"), equaling the relative difference between its equatorial radius, a\,\!, and its polar radius, b\,\!:
:::f=\operatorname{ver}(o\! arepsilon)=2\sin\left( rac{o\! arepsilon}{2} ight)^2=1-\cos(o\! arepsilon)= rac{a-b}{a};\,\!

  • The flattening of the 6378.137 - 6356.752 km) and would not be realized visually from space, ''since the difference represents only 0.335 %''.

  • The flattening of ;

  • Conversely, that of the barely 1:900.


The amount of flattening depends on



There is also a second flattening, ''f' '' (sometimes denoted as "''n''"), that is the half-angle tangent2 of o\! arepsilon\,\!:

:::f'= an\left( rac{o\! arepsilon}{2} ight)^2= rac{1-\cos(o\! arepsilon)}{1+\cos(o\! arepsilon)}= rac{a-b}{a+b};\,\!


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