Grid Tools: Primary Estimates

Primary estimates are performed to determine the Z values at grids nodes that are close to the input data locations. Primary estimates are performed when using any of the available gridding algorithms.

Minimum Curvature

Minimum curvature is the fastest algorithm for point sets of 500 or less, and provides an excellent, quick solution for point sets of less than 1000. This algorithm uses a close relative of the bi-harmonic equation solution to compute a set of equations that directly calculate a function that passes through each input point. For point sets of less than 1000 points, one set of equations is determined for the whole map, and output values are computed at all grid nodes, making secondary estimates unnecessary.

The minimum curvature algorithm uses a radial search method similar to that used in Radial Search, except that it uses all neighbors to find a solution and more nodes are assigned a value. This gives a better estimate at the primary nodes and at some secondary nodes that are nearby. Little or no averaging occurs before grid assignment because of the high-order surface in use.

Radial Search

The Radial Search method works best on large data sets that have grid masks or faults. A minimum of spatial averaging is employed on the points, and only points closer than 0.1 times the grid increment are averaged together. The resulting points are organized into search bins.

Each point is taken as a search origin and a collection of neighbors is formed by taking the two nearest points in each octant. A least-squares fit of a plane that passes through the origin point is determined and used to assign any adjacent grid nodes that are within one grid interval from the origin. This process repeats until all input points have been used as an origin. Depending upon the point distribution, averaging may occur during this process since the same grid nodes can be assigned values multiple times.

Once the primary estimates are complete, secondary estimates are performed.

Radial Search, Clustered

This method is similar to Radial Search, but it is specifically designed to minimize the effects of data that are noisy or positioned very close together. This method employs some averaging of the point data to avoid excessive gradient extrapolation. If other methods produce many anomalies adjacent to clusters of points, you should use this method.

More averaging is applied using Radial Search, Clustered than with the regular Radial Search. All points that are within 0.5 times a grid increment are averaged before gridding.

Another difference between Clustered and regular Radial Search occurs after neighbors are collected. Instead of attempting to force a plane through the center point, all points within a grid interval are ignored except the center point, and a least-squares fit to a plane is performed. So, the node values assigned are a projection of the background gradient rather than any local gradient implied by close neighbors. More averaging is usually applied at the grid nodes leading to a more desirable result.

Once the primary estimates are complete, secondary estimates are performed.

Weighted Resampling

Weighted Resampling is ideal for generating grids from 3D seismic horizon input data. In a seismic horizon, the number of input points usually far exceeds the resolution of any grid you may wish to compute for modeling or contouring. Initial estimates are performed very quickly using this method, and if input coverage is complete, secondary estimates are not needed.

This method weights the data for each grid node near an input point by combining the input points with weights that are inversely proportional to the distance from the node. Only points that are within one grid node are used to compute a given node. So, each input point contributes to the values of about five nodes, making this method very effective with sparse data sets. With sparse data, all points become the location of flat spots, usually a local minimum or maximum.