Ultrasonic thickness measurement: Difference between revisions

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[[Image:TwoCells.png|thumb|A trivial example of a Corner-point grid with only two cells.]]
In [[geometry]], a '''corner-point grid''' is a [[tessellation]] an [[Euclidean space|Euclidean]] 3D volume where the base cell has 6 [[Face (geometry)|faces]] ([[hexahedron]]).


A set of straight lines defined by their end points define the ''pillars'' of the corner-point grid. The pillars have a lexicographical ordering that determines neighbouring pillars. On each pillar, a constant number of nodes (corner-points) is defined. A corner-point cell is now the volume between 4 neighbouring pillars and two neighbouring points on each pillar.


Each cell can be identified by integer coordinates <math>(i,j,k)</math>, where the <math>k</math> coordinate runs along the pillars, and <math>i</math> and <math>j</math> span each layer. The cells are ordered naturally, where the index <math>i</math> runs the fastest and <math>k</math> the slowest.
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In the special case of all pillars being vertical, the top and bottom face of each corner-point cell are described by [[Bilinear interpolation|bilinear surfaces]] and the side faces are [[plane (geometry)|plane]]s.
 
Corner-point grids are supported by most [[reservoir simulation]] software, and has become an industry standard.
 
==Degeneracy==
 
A main feature of the format is the ability to define [[erosion]] surfaces in [[geological modelling]], effectively done by collapsing nodes along each pillar. This means that the corner-point cells degenerate and may have less than 6 faces.
 
For the corner-point grids non-neighboring connections are supported, meaning that grid cells that are not neighboring in ijk-space can be defined as neighboring. This feature allows for representation of faults with significant throw/displacement. Moreover, the neighboring grid cells do not need to have matching cell faces (just overlap).
 
[[Category:Tessellation]]
[[Category:Geometry]]
[[Category:Petroleum production]]
 
 
{{geometry-stub}}

Revision as of 00:31, 7 February 2014


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