# petrel algorhithms

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Internal Algorithms for PETREL

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Appendix 2 - AlgorithmsThis appendix contains descriptions and examples of different algorithms used in Petrel. The algorithms that are described are those used in the Make Surface, Make Horizon and Petrophysical Modeling processes. Averaging Methods Interpolation Algorithms Make Horizon Algorithms Velocity Modeling Algorithms Wavelets

Vertical averaging (Algorithms) (Petrophysical modeling)New!Under vertical averaging the user can specify whether or not the petrophysical modeling should follow structural layers or the horizontal plane. The vertical influence to interpolate vertically can be set by distance or by number of cells. The vertical influence can also be weighted.Parent topic:Interpolation AlgorithmsVertical Average - moving average, exp 2, averaging follows layer

An example of a property model created with the Moving average algorithm with the exponent set to 2 together with the vertical averaging set to follow layer.Vertical Average - moving average, exp 2, horizontal averaging

An example of a property model created with the Moving average algorithm with the exponent set to 2 together with the vertical averaging set to horizontal.Vertical Average - moving average, exp 2, directional trend 45deg, weight 10

An example of a property created with the Moving average algorithm with the exponent set to 2, together with a directional trend of 45oand the weight set to 10.Vertical Average - moving average, exp 2, directional trend 45deg, weight 3

An example of a property created with the Moving average algorithm with the exponent set to 2, together with a directional trend of 45oand the weight set to 3.

Kriging interpolation (Algorithms) (Make surface and Petrophysical modeling)Krigingis an Estimation Technique / Mapping Method based on fundamental statistical properties of the data, the Mean and the Variance. It does assumptions of the data set, such as stationary in regards to the rules for behavior of the properties which are analized, studied or modeled with geostatistical tools. This technique can be defined based on the interaction between the variogram parameters and the local neighborhood data.The algorithm uses a variogram to express the spatial variability of the input data. The user can define type of function for the variogram (Exponential, Spherical and Gaussian), range, sill and nugget. See Background Information on Variograms for more information on variograms. The algorithm using an Exponential and Spherical variogram will not generate values larger or smaller than the min/max values of the input data. In some extreme cases the algorithm using a Gaussian variogram with a clustered input data can produce values higher than the max or lower than the min.Nugget(unit)=Nugget/Sill, where Nugget(unit) equals the nugget relative to the unit sill; and the nugget and the sill are the figures from the estimated variogram. In other words, the Sill is internally always set to 1 and the Nugget is a fraction of the Sill.TheKriginginterpolationalgorithm use the same method as Kriging by Gslib algorithm but work internally. Differences include: Kriging interpolation works in XYZ rather than IJK (Simbox, see Visualize a property as a regular box (simbox view)) for Kriging and Kriging by Gslib. Kriging interpolation only considers data within the variogram range (can lead to strange effects in areas with no data when trends have not been removed correctly). Kriging interpolation and Krging are much faster because transfer to external algorithms is not required. Kriging and Kriging by Gslib give the user control of advanced settings (Expert tab). Kriging and Kriging by Gslib offer Collocated Co-kriging (Co-kriging tab).In the figures below is shown the Kriging interpolation panel for Petrophysical modeling.

Further information related to these algorithms can be found in theGSLIB manual: GSLIB Geostatistical Software Library and User's Guide, 2ndEdition, 1998 by Clayton V. Deutsch, Andre G. Journel or on theGSLIB websitehttp://www.gslib.com (Support/Training section).Additionally, collocated co-kriging is now available as an option in Make/edit surface. This option appears in the Distribution tab when the method is set to kriging and kriging with Gslib.Parent topic:Interpolation Algorithms

Kriging (Algorithms) (Make surface and Petrophysical modeling)The newKrigingalgorithm that was introduced in Petrel 2008.1 was further improved in Petrel 2009.1. The new algorithm differs from the standard GSLIB kriging in the way that it searches for neighbours and in certain aspects of housekeeping regarding which matrices need to be inverted. The improvement gains are due to parallelization and some additional numerical efficiency. While it is difficult to give general figures as there are some machine dependencies, on a 4 processer machine, the typical improvement is about a factor of 2.5. Addition of a fast Collocated co-kriging algorithm and some additional options to extend user control over the style of Kriging.TheKrigingalgorithm differences include: Kriging works in XYZ and IJK coordinates. Kriging interpolation works in XYZ rather than IJK for Kriging by Gslib (see Visualize a property as a regular box (simbox view)). Kriging and Kriging interpolation are much faster because transfer to external algorithms is not required. Kriging and Kriging by Gslib offer Collocated Co-kriging. Kriging and Kriging by Gslib give the user control of advanced settings.This algorithm uses a variogram to express the spatial variability of the input data. The user can define type of function for the variogram (Exponential, Spherical and Gaussian), range, sill and nugget. See Background Information on Variogramsfor more information on variograms. The algorithm using an Exponential and Spherical variogram will not generate values larger or smaller than the min/max values of the input data. In some extreme cases the algorithm using a Gaussian variogram with a clustered input data can produce values higher than the max or lower than the min.Nugget(unit)=Nugget/Sill, where Nugget(unit) equals the nugget relative to the unit sill; and the nugget and the sill are the figures from the estimated variogram. In other words, the Sill is internally always set to 1 and the Nugget is a fraction of the Sill.Parent topic:Interpolation AlgorithmsTheKrigingalgorithm works principally like the existing Kriging by Gslib algorithm but has two main differences. At first the search algorithm works on the basis of the k-d tree (k-dimensional) to look for the n nearest points. The space will be subdivided into subspaces to organize the data structure and optimize the data search (Figure 1). It will work faster than the known Super Block or Spiral search used in Kriging by Gslib or Stochastic Simulation.

Figure 1 - Example for a kd tree, after 3 splits (red, green, blue) 8 subspaces for optimized data search exist (image from Wikipedia).The second significant difference is the way how the Kriging matrix is set up and solved. The system divides up the set of points to be kriged into equivalence classes of points which have the same sets of neighbours. Then the inversion of the matrix will be done once for each equivalence class instead of for each point. Depending on how many neighbours are used, this can give minor or major (factor of 10 or more) speed ups.TheKrigingalgorithm inPetrel 2009has alsofast Collocated co-krigingalgorithm (see Co-kriging tab (Petrophysical modeling - Kriging and Kriging by Gslib))and some additional options to extend user control over the style of Kriging in theExpert tab(advanced settings) (see Expert tab (Petrophysical modeling - Kriging and Kriging by Gslib)). Users who are not familiar with the Gslib algorithms should not edit these special settings.Further information related to these algorithms can be found in theGSLIB manual: GSLIB Geostatistical Software Library and User's Guide, 2ndEdition, 1998 by Clayton V. Deutsch, Andre G. Journel or on theGSLIB websitehttp://www.gslib.com(Support/Training section).

Kriging by Gslib (Algorithms) (Make surface and Petrophysical modeling)TheKriging by Gslibalgorithm uses the same method as Kriging algorithms but using external files and the Gslib executable. Differences include: Kriging interpolation works in XYZ rather than IJK (Simbox, see Visualize a property as a regular box (simbox view)) for Kriging by Gslib and Kriging. Kriging interpolation only considers data within the variogram range (can lead to strange effects in areas with no data when trends have not been removed correctly). Kriging interpolation and Kriging are much faster because transfer to external algorithms is not required. Kriging by Gslib and Kriging give the user control of advanced settings (see Expert tab (Petrophysical modeling - Kriging and Kriging by Gslib)). Kriging by Gslib and Kriging offer Collocated co-kriging. The Collocated co-kriging for Kriging is faster than for Kriging by Gslib, see Co-kriging tab (Petrophysical modeling - Kriging and Kriging by Gslib)for detailed information.In theExpert tab(advanced settings) in which some special settings can be defined by the user, are the same options as for the Sequential Gaussian Simulation method and the settings are internal parameters used by the Gslib algorithm. Users who are not familiar with the Gslib algorithms should not edit these special settings.Further information related to these algorithms can be found in theGSLIB manual: GSLIB Geostatistical Software Library and User's Guide, 2ndEdition, 1998 by Clayton V. Deutsch, Andre G. Journel or on theGSLIB websitehttp://www.gslib.com(Support/Training section).Additionally, collocated co-kriging is now available as an option in Make/edit surface. This option appears in the Distribution tab when the method is set to kriging and kriging with Gslib.Parent topic:Interpolation Algorithms

Cos expansion (Algorithms) (Make Sur