DSSIM-HR: A FORTRAN 90 program for direct sequential simulation with histogram reproduction

Abstract

Sequential simulation is a frequently used geostatistical simulation technique. The most widely used version of this technique is sequential Gaussian simulation, where the data are transformed to follow a Gaussian distribution and the entire multivariate distribution is then assumed to be Gaussian. This critical assumption greatly simplifies the simulation process since every conditional distribution is Gaussian with parameters given by kriging. Direct sequential simulation does not require any Gaussian assumption and simulates directly the data space; however, a longstanding problem of direct simulation is that the histogram of the variable is not reproduced even though the mean, variance, and variogram are reproduced. This lack of histogram reproduction is due to the unknown shape of the conditional distributions, which are used for drawing the simulated values. We derive a simple and theoretically valid approach by establishing the shapes of the sequentially constructed conditional distributions. These shapes ensure histogram reproduction. The approach has been coded in FORTRAN 90 and called DSSIM-HR, where the extension HR refers to the feature of “Histogram Reproduction”.