A hierarchical approach to stochastic simulation of correlated systems Free

A description is given of a new algorithm for simulating systems with known density correlations, a problem that has been intensively studied in the context of petroleum reservoirs. Given an assumed spatial correlation function (covariance) and known densities at an arbitrary set of constrained points, it generates members of an ensemble defined by Gaussian statistics, the covariance function, and the known constraints. In the case of a power‐law correlation function, this is a fractal distribution. Our algorithm is significantly more efficient than existing techniques for doing this—in the fractal case, the computer time requirement is proportional to N, rather than N³, where N is the number of grid points. In applications, where N can be 10⁴ or larger, this is a significant difference.