Need help on SGS parameters


wangfang - Posted on 28 March 2011

Hi everyone, I have questions on Sequential Guassion Simulation parameters which confuse me. For SGS, the input parameters include nugget, contribution, ranges (max,med,min) and angles. I want to know how to connect the ranges to the three correlation length (lamda_x, lamda_y, lamda_z). Whether the range_max is three times of the Lamda_x, the range_med is three times of the Lamda_y, and the range_min is three times of Lamda_z. Am I right? Is the contribution is usually one for the unconditional data? The mean and variance are zero and one. If I want to get the stochastic field with mean of 10 and variance of 0.1, I should convert the output data and calculate them from standard normal distribution to normal distribution. Am I right? Thanks. I appreciate it very much! Fang
The definition for range for the exponential and Gaussian variograms are the traditional one from the geostatistical literature (see Goovarts or Chiles and Delfiner). In these case the range is defined as the "distance at which the (variogram) model value is at 95% of the sill" (Goovaerts, p.89)

So the exponential variogram the equation we use is:
g(h) = 1 - exp(-3h/a)
where a is the range.

For sgsim we usually assume that you want to simulate a field with zero mean and unit variance. In that case the sum of the contribution from the variograms models should be one. If you want a field with variance V then the sum of the contribution should be V. You will have to add a constant for a non-zero mean. This is ineficient to simulate Gaussian process but sgsim is usually (and I mean pretty much always) used in conjunction with the normal score transform that change the data distribution into a N(0,1) back and forth.

Hope that helps.

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