Changes

Weighting methods assign weights to values at control points based on their distance from the grid node being estimated. There are various strategies for devising weighting schemes. The most commonly encountered scheme used for geological data is inverse distance weighting. For this scheme, values at control points are weighted by the inverse of the distance from the node. Variations of this scheme allow the control point values to be weighted by the inverse of distance raised to a selected power. Positive powers cause the influence of more distant points to make a smaller contribution to the value estimated at the grid node. Selection of the power to which the distance is to be raised depends upon the surface “roughness” and a feeling for the relationship between control points and surface shape. Several of these weighting schemes are reviewed by Clarke<ref name=pt08r4 /> and Davis.<ref name=pt08r6 />

Weighting methods assign weights to values at control points based on their distance from the grid node being estimated. There are various strategies for devising weighting schemes. The most commonly encountered scheme used for geological data is inverse distance weighting. For this scheme, values at control points are weighted by the inverse of the distance from the node. Variations of this scheme allow the control point values to be weighted by the inverse of distance raised to a selected power. Positive powers cause the influence of more distant points to make a smaller contribution to the value estimated at the grid node. Selection of the power to which the distance is to be raised depends upon the surface “roughness” and a feeling for the relationship between control points and surface shape. Several of these weighting schemes are reviewed by Clarke<ref name=pt08r4 /> and Davis.<ref name=pt08r6 />

Trend projection methods are an adaptation of a [[Correlation and regression analysis|linear regression]] technique called ''trend surface analysis''. This method has been devised because geological subsurface sampling rarely provides observations at the highest or lowest points on a surface, and it is sometimes desirable to allow the interpolation procedure to exceed the measured maximum and minimum. Trend projection methods use one of the search criteria previously described to select points that are taken in groups of three and fitted exactly to a plane using a least squares or bicubic spline methods. The grid node estimate is obtained by averaging projections of these planes. This method can be quite effective for smooth surfaces where regional dip orientation remains relatively constant over a large area of the map. This method can produce a surface that is more highly textured than the actual surface in highly deformed areas where the dip direction changes rapidly over small distances. Sampson<ref name=pt08r19>Sampson, R. J., 1978, Surface II graphics system (revision 1): Lawrence, KS, Kansas Geological Survey, Series on Spatial Analysis, n. 1, 240 p.</ref> reviews this method in detail.

Trend projection methods are an adaptation of a [[Correlation and regression analysis|linear regression]] technique called ''trend surface analysis''. This method has been devised because geological subsurface sampling rarely provides observations at the highest or lowest points on a surface, and it is sometimes desirable to allow the interpolation procedure to exceed the measured maximum and minimum. Trend projection methods use one of the search criteria previously described to select points that are taken in groups of three and fitted exactly to a plane using a least squares or bicubic spline methods. The grid node estimate is obtained by averaging projections of these planes. This method can be quite effective for smooth surfaces where regional [[dip]] orientation remains relatively constant over a large area of the map. This method can produce a surface that is more highly textured than the actual surface in highly deformed areas where the dip direction changes rapidly over small distances. Sampson<ref name=pt08r19>Sampson, R. J., 1978, Surface II graphics system (revision 1): Lawrence, KS, Kansas Geological Survey, Series on Spatial Analysis, n. 1, 240 p.</ref> reviews this method in detail.

[[:file:introduction-to-contouring-geological-data-with-a-computer_fig7.png|Figure 7]] is the same portion of the surface shown in [[:file:introduction-to-contouring-geological-data-with-a-computer_fig4.png|Figure 4]]. The map in [[:file:introduction-to-contouring-geological-data-with-a-computer_fig7.png|Figure 7]] was produced by a gridding method with nearest neighbor search. Contours for this map are smooth, and their shape closely approximates those of the original fourth-order polynomial surface from which control points were obtained. However, contours are not in the same geographic positions as in the original surface, and some control points are not strictly honored.

[[:file:introduction-to-contouring-geological-data-with-a-computer_fig7.png|Figure 7]] is the same portion of the surface shown in [[:file:introduction-to-contouring-geological-data-with-a-computer_fig4.png|Figure 4]]. The map in [[:file:introduction-to-contouring-geological-data-with-a-computer_fig7.png|Figure 7]] was produced by a gridding method with nearest neighbor search. Contours for this map are smooth, and their shape closely approximates those of the original fourth-order polynomial surface from which control points were obtained. However, contours are not in the same geographic positions as in the original surface, and some control points are not strictly honored.