Defining the interpolation method

This method uses the inverse distance-weighted algorithm to interpolate the data.

• Power - The power parameter controls how strongly the weight depends on the distance from each data point. Any value greater than zero is allowed. Values between 0.5 and 10 are recommended. The default value of 2 produces a smooth interpolation and is appropriate for most applications. Smaller values for the power parameter generate more equal weights and interpolations approximating a constant value with spikes at each data point. Larger values for the power parameter generate larger weights for nearby data points and interpolations approximating a nearest neighbor interpolation.

For Advanced Settings, see below.

This method uses the Kriging algorithm to interpolate the data.

• Type - select 'Ordinary', 'Ordinary (legacy)' or 'Simple':
  • Ordinary - The search ellipsoid is used to find the data points to be used in the calculation. The mean is not a-priori known but based on the data points found in the search ellipsoid. Good approach when there are many hard data and there is some evidence of non-stationarity. The industry standard Kriging library is used. For the size of the search ellipsoid, see Search factor below.
  • Ordinary (legacy) - By definition, the search ellipsoid spans the entire set of input data points. Because of this, the number of calculations is reduced and usually faster. This type of Ordinary Kriging does not make use of the industry standard Kriging library. When you choose this option (as opposed to non-legacy Ordinary Kriging), the 'Advanced Settings' button becomes active and the 'Search Factor' is grayed-out. For 'Advanced Settings' see below.
  • Simple - The search ellipsoid is used to find the data points to be used in the calculation. The global mean is known and is held constant over the area of interpolation. Simple Kriging is the best approach when there is no or little evidence of significant non-stationarity and few hard data. The industry standard Kriging library is used. For the size of the search ellipsoid, see Search factor below.
• Variogram Type - Choose a variogram type to control how the variogram model is auto-fitted to the data:
  • Exponential
  • Gaussian
  • Spherical
  • Exponential Power - Only available when 'Ordinary (legacy)' is selected under 'Type'. Set the value in the Power entry field, which sets the lateral extension of the kriging.
A default value of 0.0001 is used for the nugget effect of the variogram model.
• Major range - Specify the distance at which the values become independent (the variogram reaches its plateau). The distance is measured in the direction with the greatest spatial continuity.
• Minor range - Specify the distance at which the values become independent (the variogram reaches its plateau). The distance is measured in the direction with the least spatial continuity and is orthogonal to the major direction.
When your data does not have anisotropy, enter the same value for both the Major range and Minor range.
• Azimuth (GN) - Enter the azimuth (angle with Northing direction) of the axis corresponding with the major range.
• Search factor - (Not available when 'Ordinary (legacy)' is selected under 'Type') The variogram model ranges are multiplied with the search factor to obtain the size of the search ellipsoid, i.e. Search ellipsoid = Search factor x Variogram model range. The search factor is applied to both ranges of the variogram model so that the shape of the search ellipsoid reflects the spatial anisotropy.

In the following example, the search ellipsoid is calculated with three different search factors applied to the same variogram model (with a major range of 5000 m and a minor range of 3000 m):

• Search factor = 1: Search ellipsoid = 5000 m, 3000 m.
• Search factor = 2: Search ellipsoid = 10000 m, 6000 m.
• Search factor = 3: Search ellipsoid = 15000 m, 9000 m.

This interpolation method uses linear least squares regression to find a plane at each node point of the surface that fits a set of neighboring data points. The plane is then evaluated at the node point to produce an interpolated value. This method is a smoothing interpolator. That is, it produces a smoothed result that does not reproduce the data points exactly.

• Maximum neighbors  This setting controls the number of neighbor points to use for each least squares fit. Larger values will produce a smoother result. Checking the option off, or setting the maximum larger than the total number of data, will produce a single plane fit to the entire data set.

This method is the simplest interpolation method that just assigns the value of the nearest data point to each node point of the surface. The nearest neighbor is applied using vertical projection. That is, the nearest neighbor is found by comparing horizontal distances.

Use this method to create a property with smooth contours, extrapolation and trends. The method creates a grid around your input data and assigns values from the data points to the nodes of the grid (snapping) in order to build the output property. The grid starts with a coarse resolution and it is refined iteratively in order to reach the resolution of the output 2D grid that you specified on the Create Property Definition form. For more information on this interpolation method, see the section Recursive Refinement.

• Multiplier for initial coarse resolution - The number that is multiplied by the resolution of the output 2D grid to produce the initial grid resolution. With the default value of 0, the method will automatically determine the most suitable multiplier value based on the desired final resolution and the distribution of your input data. Enter a number greater than the default in the entry field, or use the up and down arrows at the side of the field.
• Extrapolation method - Select an extrapolation method to ensure that the final property is fully populated with values (in cases of insufficient input data or input settings).
  • None - Select this option to not extrapolate.
  • Linear (default) - Extrapolate using a linear function.
  • Quadratic - Extrapolate using a quadratic polynomial technique.
• Extrapolation area (active only when an extrapolation method is selected) - Specify the extent of the extrapolation by selecting one of the two options from the drop-down list:
  • Outside convex hull - Extrapolate outside the convex hull around the input data.
  • As needed (default) - Extrapolate in areas where grid nodes have not received a value.
• Grid nodes affected by snapping - The number of grid nodes that will be affected by each input data point. By default, the value of each input data point will be assigned to the nearest 16 grid nodes. Enter a value less than the default value of 16 in the entry field, or use the up and down arrows at the side of the field.

SGS is a stochastic modeling method which is able to reproduce a desired target distribution. SGS employs Simple or Ordinary Kriging. The functionality does not auto-generate multiple realizations; you need to update the seed and re-run the algorithm for each new realization.

• Kriging Type - select 'Ordinary' or 'Simple':
  • Ordinary - The mean is unknown and only constant over the search ellipsoid. Good approach when there are many hard data and there is some evidence of non-stationarity. The industry standard Kriging library is used.
  • Simple - The global mean is known and is held constant over the area of interpolation. Simple Kriging is the best approach when there is no or little evidence of significant non-stationarity and few hard data. The industry standard Kriging library is used.
A default value of 0.0001 is used for the nugget effect of the variogram model.
• Mean (only when you selected 'Without data' on Assign Data form) - This value is the mean of the output data points generated with SGS.
• Dip (only when you selected 'Without data' on Assign Data form) - The value you enter applies a trend to the output data. The dip defines the amount of increase/decrease of the property value. Note that even a small dip can cause tremendous value differences when the area is large.
• Dip azimuth (GN) (only when you selected 'Without data' on Assign Data form) - This is the angle with Grid North. The dip azimuth defines the direction of increase/decrease of the property value.
• Variogram Type - Choose a variogram type to control how the variogram model is auto-fitted to the data:
  • Exponential
  • Gaussian
  • Spherical
• Major range - Specify the distance at which the values become independent (the variogram reaches its plateau). The distance is measured in the direction with the greatest spatial continuity.
• Minor range - Specify the distance at which the values become independent (the variogram reaches its plateau). The distance is measured in the direction with the least spatial continuity (by definition perpendicular to the major direction).
When your data does not have anisotropy, enter the same value for both the Major range and Minor range.
• Azimuth (GN) - Enter the azimuth (angle with Northing direction) of the axis corresponding with the major range.
• Search factor - (Not available when you are creating an artificial surface with SGS.) The variogram model ranges are multiplied with the search factor to obtain the size of the search ellipsoid, i.e. Search ellipsoid = Search factor x Variogram model range. The search factor is applied to both ranges of the variogram model so that the shape of the search ellipsoid reflects the spatial anisotropy.

Example: three different search factors are applied to the same variogram model with a major range of 5000m and a minor range of 3000m:

• Search factor = 1: Search ellipsoid = 5000m, 3000m.
• Search factor = 2: Search ellipsoid = 10000m, 6000m.
• Search factor = 3: Search ellipsoid = 15000m, 9000m.
• Seed - The number that starts the stochastic algorithm. When all parameter settings remain the same, a different seed number will produce a slightly different result. Only when all parameter settings are the same and the seed number is identical, you can reproduce the results.

With this method you can create a planar property. You can optionally apply a trend by entering a dip and dip direction. With increased distance from the origin the constant value will gradually increase/decrease, based on the dip and dip direction. Note that even a small dip can cause tremendous value differences if the area is large.

• Value at origin - Enter the value of the output property. In case you apply a trend by entering a dip and dip azimuth (next steps), the value you enter here is the value at the origin of the output representation; from there, values will increase/decrease based on the trend.
• Dip - The value you enter applies a trend to the output property. The dip defines the amount of increase/decrease of the property value.
• Dip azimuth (GN) - This is the angle with Grid North. The dip azimuth defines the direction of increase/decrease of the property value.