Phase annealing for the conditional simulation of spatial random fields

Simulated annealing (SA) is a popular geostatistical simulation method as it provides great flexibility. In this paper possible problems of conditioning its realizations are discussed. A statistical test to recognize whether the observations are well embedded in their simulated neighborhood or not is developed. A new simulated annealing method, phase annealing (PA), is presented which makes it possible to avoid poor embedding of observations. PA is based on the Fourier representation of the spatial field. Instead of the individual pixel values, phases corresponding to different Fourier components are modified (i.e. shifted) in order to match prescribed statistics. The method treats neighborhoods together and thus avoids singularities at observation locations. It is faster than SA and can be used for the simulation of high resolution fields. Examples demonstrate the applicability of the method.