Spartan Random Fields and Applications in Spatial Interpolation and Conditional Simulation

Geostatistics plays an important role in the estimation and simulation of reservoir parameters, and in forecasting reservoir production. This presentation focuses on Spartan spatial random fields (SSRFs), which provide a new framework for geostatistical applications. The idea motivating SSRF development is that spatial correlations can be represented by local interactions. A brief overview of SSRF mathematical properties will be given. SSRF variogram models, which in the isotropic case contain 3-4 parameters and thus offer more flexibility than standard models, will be presented. It will be argued that empirical variogram estimation is not necessary to infer SSRF parameters. SSRF spatial interpolation of scattered data will be discussed. It will be shown that approximate but closed-form, efficiently calculable expressions become possible. Hence, numerical solution of kriging linear systems is avoided, leading to improved numerical complexity. Connections will be drawn between to Markov random fields, statistical physics, minimum curvature estimation, and local random fields. An SSRF application to 2D conditional simulation will be presented. Finally, directions for the future development of SSRFs will be discussed, including extensions to non-Gaussian data distributions, using discretized random field models with “spin” interactions.