Generation of random fields characterized by discrete regions of constant value

摘要

A new simulator is introduced which provides realizations of parameter fields characterized by randomly sized regions within which the parameter value is constant. This generator produces second-order stationary random fields with specified mean and correlation structure. The structure of the simulated field is significantly different than that which can be obtained by previously existing techniques. This new structure provides a valuable simulation tool for discretely varying fields such as required when modeling complex lithologies. One application of this method utilizing ovals in two dimensions and ellipsoids in three dimensions is demonstrated for grids in which a finite number of simulation points are to be generated. This technique is compared with a recently published turning-bands routine and is faster in terms of cpu time for large values of I/L, where I is the integral scale of the correlation structure and L is the length of the longest side of the simulation grid. For small values of I/L, the turning-bands routine is faster. Conditional simulation based on kriging has been studied for this method. The resulting random field varies continuously rather than discretely. A second method of conditioning, which produces discretely varying random fields, is suggested but not examined computationally.