# GMS:Interpolation

GMS contains a powerful suite of interpolation tools. GMS can interpolate to TINs, 2D meshes, 2D grids, 3D meshes, 3D grids, and UGrids. In addition to interpolating scalar values, GMS also supports interpolation of materials with T-PROGS. The T-PROGS software is used to perform transition probability geostatistics on borehole data.

## Interpolation Types

The following types of interpolation are available in GMS:

### Clough-Tocher

- Main page: GMS:Clough-Tocher

The Clough-Tocher interpolation technique is a finite element method because it has origins in the finite element method of numerical analysis. Before any points are interpolated, the points are first triangulated to form a network of triangles. A bivariate polynomial is defined over each triangle, creating a surface made up of a series of triangular Clough-Tocher surface patches.

### Gaussian Field Generator

- Main page: GMS:Gaussian Field Generator

A Gaussian Sequential Simulation (GSS) is used to generate a set of scalar datasets (Gaussian fields) using a Gaussian sequential simulation. This is somewhat similar to indicator kriging or T-PROGS in that it generates a set of equally probable results which exhibit heterogeneity and are conditioned to values at scatter points. However, the resulting arrays are floating point scalar datasets, rather than the integer arrays produced by T-PROGS and indicator kriging.

### Inverse Distance Weighted

- Main page: GMS:Inverse Distance Weighted

Inverse Distance Weighted (IDW) is one of the most commonly used techniques for interpolation of point data. Its methods are based on the assumption that the interpolating surface should be influenced most by the nearby points and less by the more distant points.

### Jackknifing

- Main page: GMS:Jackknifing

Jackknifing is a special type of interpolation useful in analyzing a scatter point set or an interpolation scheme. When Jackknifing, the active scatter point set is interpolated to itself using the currently-selected interpolation scheme. Each point in the set is processed one at a time. The point is temporarily removed and the selected interpolation scheme is used to interpolate to the location of the missing point using the remaining points. This generates a new dataset for the scatter point set. This new dataset can then be compared with the original dataset.

### Kriging

- Main page: GMS:Kriging

Kriging is based on the assumption that the parameter being interpolated can be treated as a regionalized variable. A regionalized variable is intermediate between a truly random variable and a completely deterministic variable because it varies in a continuous manner from one location to the next. Therefore points that are near each other have a certain degree of spatial correlation, but points that are widely separated are statistically independent.^{[1]} Kriging is a set of linear regression routines which minimize estimation variance from a predefined covariance model.

### Linear

- Main page: GMS:Linear

The Linear interpolation scheme uses data points that are first triangulated to form a network of triangles. The network of triangles only covers the convex hull of the point data, making extrapolation beyond the convex hull not possible.

### Natural Neighbor

- Main page: GMS:Natural Neighbor

Natural neighbor interpolation is based on the Thiessen polygon network of the point data. The Thiessen polygon network can be constructed from the Delaunay triangulation of a set of points. A Delaunay triangulation is a network of triangles that has been constructed so that the Delaunay criterion has been satisfied. As with IDW interpolation, the nodal functions can be either constants, gradient planes, or quadratics.

## How To Interpolate in GMS

Interpolation is performed using the 2D Scatter Points and the 3D Scatter Points. To interpolate values from a scatter set either right-click on a scatter set in the Project Explorer and select the **Interpolate to** command or select the command from the *Interpolation* menu. The commands in the *Interpolation* menu act on the "active" item in the Project Explorer.

UGrids can also be interpolated to other UGrids.

## Related Topics

## References

- ^ Davis, J.C.
*Statistics and Data Analysis in Geology*. John Wiley & Sons, New York, 1986.

GMS – Groundwater Modeling System | ||
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