Main Parameters

Input Geostatistical Set

Select here your Input Geostatistical Set which contains geostatistical parameters required to achieve simulations: variogram model, anamorphosis (to apply the back transformation from the gaussian variable(s) to the raw variable(s)), stationarity option (to apply ordinary kriging, simple kriging, or to use drift(s)) and input variable(s) if you wish to compute conditional simulations. A Print button enables you to check the content of the Geostatistical Set defined (sent in the Application Messages).

The simulation theory requires the variable to follow a standard normal distribution. In this way, it is advised to apply a gaussian anamorphosis before performing variography (in the Exploratory Data Analysis). Simulations are performed in the gaussian space and final simulation results are provided in the original raw scale (by applying the Gaussian Back Transformation). It is always possible to consider data without anamorphosis if it already follows a standard normal distribution. In this case, a warning will be displayed.

Input File

Select the Input File option to compute Conditional Simulations. Information of data required for conditioning is displayed: Data Table, an optional Selection which you may modify, Conditioning Variable(s) and Stationarity Option.

Output File

Select the Output Data Table on which you want to store your the simulations and/or the associated results. It can be of any type. You may define a Selection on the output samples - useful when the data is heterogeneous and when several steps should be processed one after the other, using different models and/or neighborhoods.

Calculation Mode

Simulations can provide different types of results depending on the selected option:

  • Select Point Simulations if you wish to calculate simulations of the variable at the target point;
  • Select Block Simulations (Discretized) if you wish to calculate simulations of the average value of a variable over a surface/volume, called a block (generally a cell centered at the target grid node). This option may only be used if the Output Data Table is a Grid and is not compatible with the definition of drift(s) (associated to the Input Geostatistical Set). It is not compatible with the SPDE method.
  • Select Direct Block Simulations if you wish to simulate block values and optionally values related to one sample inside each block in the framework of the Discrete Gaussian Model. To perform Direct Block Simulations, you need to calculate the change of support coefficients and the block gaussian variogram related to the normal (0,1) gaussian block values, using the Support Correction tool with the Gaussian method chosen. It is not compatible with the Sequential Gaussian method.

With Block Simulations (Discretized), the blocks are in fact simulated as an average of discretized point simulations.The discretization of the blocks is defined in the Special Options either by entering a Discretization Steps Number or a Discretization Steps Size (regarding each direction U, V and W).

Simulation Method

Three simulation methods are here available. Each method has its own limitations:

  • the Turning Band Simulations (TBS): The method does not provide the possibility to take local anisotropies into account.
  • the Stochastic Partial Differential Equations (SPDE): The variogram model to be simulated is supposed to be constituted of a nugget plus a sum of Matérn (aka Bessel-K) and/or Exponential structures; if not, the model is automatically approximated with such structures.
  • The SPDE method works only with a unique neighborhood even if the number of conditioning data is large.

  • In the current implementation, it does not allow the non-stationary models (i.e. models involving drifts) or the following options:

    • Filtering model components,
    • Collocated cosimulations,
    • Take faults into account,
    • Conditioning the simulations using ordinary kriging (always simple kriging even if the model is not flagged as "Strict Stationarity".

  • the Sequential Gaussian Simulations (SGS): The current implementation does not allow Direct Block Simulations calculation mode and the following options:

    • Filtering model components,
    • Collocated cosimulations.

The three different methods should generate similar results. The quality and the speed heavily depend on the chosen parameters.

Note: There is no limitation on the method in the sense that this application may be used with raw variables (with a distribution not necessary gaussian). Nevertheless, it is strongly recommended that gaussian distributed variables are worked with.

Special Options

You may activate special options in order to perform particular types of simulations:

  • Collocated Cosimulations: This option is only available for the TBS method when a multivariate model has been fitted and specified in the Input Geostatistical Set. It is a particular case of cosimulations, using one or several auxiliary variables densely sampled. The auxiliary variables are supposed to be known everywhere, i.e. at the input file sample locations and at the output file sample locations. It requires the definition of collocated variables on an auxiliary grid file, in this case values of collocated variables will be estimated on the output grid by a bilinear interpolation, or directly on the output grid. These variables must match the variable(s) that are specified in the input data table.
  • Rescaled cokriging: This method is only available when a multivariate model with a strict stationarity has been fitted and has been specified in the Input Geostatistical Set. It aims at reducing the risk of negative estimates because of negative weights assigned by Ordinary Cokriging to the secondary variables.
  • Filtering Model Components: This option is available only for the TBS method. If the model is made of several nested basic structures, you may consider that the phenomenon is a combination of several components, at different scales - which could be filtered out during the simulation process. It is also possible to filter drift(s) contained in the Input Geostatistical Set. It requires defining the structure(s) of the variogram and/or the drift(s) to be filtered.
  • Use Local Anisotropies: This option is available only for the SPDE and SGS methods. It allows you to take into account locally varying parameters (model rotation, sill, range of the variogram model and/or rotation, radius of the neighborhood) to address non-stationarity and local anisotropies ensuring a better adequacy between the geostatistical model and the data. It requires a Grid data table on output. Variables corresponding to local parameters will be defined on the output grid or on an auxiliary grid.
  • Take faults into account: This option is available only for the TBS and SGS methods. It is not compatible with a unique neighborhood. This method enables taking into account geographical discontinuities during the conditioning step (i.e. in kriging interpolation). By consequence, it is only accessible if the Input File (Conditional) option has been checked. Basically, Faults are used as "screens" when searching for neighbors during estimation.
  • Use Simple Kriging: This option is available for TBS (for conditional simulations only) and SGS methods if the Input Geostatistical Set is associated to an Ordinary Kriging (stationarity option). This Use Simple Kriging option assumes strict stationarity hypotheses which must be compatible with the definition of the model. By default, simple kriging (with a mean equal to 0) is performed for SGS, but not TBS. Clear the option should you wish to run ordinary kriging.

Note: Be aware that when defining a mean different from 0, the program cannot ensure consistency. Indeed, the simulation algorithm assumes that calculations are performed in the gaussian space - mean null and variance equal to 1. If you choose not to work in this gaussian space, the entered mean must be consistent with your data as well as the variogram sill.

Advanced

  • Use Parcelling: This option is available only for the TBS method. It enables you to deal with a large amount of input samples or for per-layer simulations. The parcelling will split the grid into smaller sub-grids of a given size. The input data table will be split in the same way including overlapping areas. Simulations are performed on these sub-divisions and are finally copied on the original grid. This option is not available if the defined output data table is a points file.