CoreandServices.book - Ocean - Schlumberger

Geometry
a rectangular area on the earth's surface that is divided into a number of rectangular cells
or bins. The cells are referred to with integral (i, j) coordinates with (0, 0) being one
(arbitrarily chosen) corner. Both I and J must be greater than or equal to 0. Each cell has
an (X, Y) projection coordinate. This world coordinates is by definition the center of the
cell. Bulk data, such as seismic or grids, will contain a sample for each cell.
In addition to the (X, Y) projection coordinates, each cell has a pair of (P, S) annotation
values. These run parallel to the edges of the lattice. So if moving from cell (I, J) to (I+N,
J) or (I, J+N) for any N, only one of the P (primary) or S (secondary) index values will
change. In the context of seismic data, the primary annotation is Inline and the secondary
is Crossline.
The most intuitive way of specifying a lattice is to give the world position (easting,
northing) and the annotation (primary, secondary) of each of the four corner points and
the number of cells in each direction. This will completely specify the lattice. A consistency
check will be done on creation to verify that the corners actually form a rectangle.
The first specified point is designated as the origin for indexing, so (I, J) == (0, 0) will
refer to the first corner. And the second corner is by definition in the "I" direction. Using
the symmetrical approach with four corners emphasizes the fact that the choice of origin is
somewhat arbitrary. In many cases, two lattices will be considered equal if the four
corners are equal, even if they do not occur in the same order and even if I and J are
reversed. To simplify the lattice, the primary annotation numbers are required to run along
the I axis. The real-world direction that is the primary (a.k.a. inline) axis is often important
to the end user. This means that the application is not free to order the I and J axes as it
wants.
A lattice may also be specified by a single origin point, a rotation angle, I and J spacing,
and I and J size. A third alternative is to use a set of unit vectors. Give the coordinates and
annotation of cell (0, 0) (the origin), cell (1, 0), and cell (0, 1).
A lattice must have at least one cell, which means that size must be 1 or more in both
dimensions. A lattice is considered to be a degenerate lattice if the size is exactly 1 in
either dimension. If a degenerate lattice is specified using the four corners method, then
some of the other properties such as rotation and spacing will be undefined. One might
argue that spacing is meaningless for a lattice with just a single cell. The coordinates of all
its four corners will be the same, but the issue needs to be kept in mind. You cannot
extrapolate positions and annotation outside a degenerate lattice if the original
specification and/or the internal storage use only the corners.
Annotation must always be provided when defining a lattice. Some applications depend on
it. It is possible to set AnnotationValid = false to indicate that the annotation was
only added to fulfill this requirement. Applications are encouraged not to display such
annotation if they can avoid it. Also, the Equals method will ignore such dummy
annotation.
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Ocean Services 4-167