Bayesian Sequential Indicator Simulation of Channel Sands From 3-D Seismic Data in The Oseberg Field, Norwegian North Sea

Abstract

Abstract Subsurface models of lithology are often poorly constrained due to the lack of dense well control. Although limited in vertical resolution, high quality 3-D seismic data usually provide valuable information regarding the lateral variations of lithology. The Bayesian Sequential Indicator SIMulation (BSISIM) technique is a new stochastic method to generate seismically constrained models of lithology. Unlike cokriging-based simulation methods, BSISIM does not rely on a generalized linear regression model, which is inadequate when combining lithology indicator variables and continuous seismic attributes. Instead, BSISIM uses a Bayesian updating rule to construct a posterior probability distribution of lithoclasses at each location. The posterior distribution combines a local prior distribution obtained by indicator kriging with a function representing the seismic likelihood of the different lithofacies. The local posterior distributions are sampled sequentially at all points in space to generate realizations from the joint posterior distribution. The realizations define alternative, equiprobable lithologic models, representing a compromise between fidelity to the seismic data, as measured by the likelihood functions, and consistency with spatial continuity information, as expressed by the lithology indicator correlation functions. The simulation technique is applied to predict the lateral distribution of channel sands in the Ness Formation of the Oseberg Field. Channel sand maps are simulated using lithologic observations in fourteen wells, and seismic amplitude and channel orientation data extracted from a 3-D survey. Sand probability maps, generated by summarizing a large number of simulations, allow delineation of the probable lateral extent of the channel deposits. Comparison of seismically derived lithologic models to well-derived models demonstrates the improved definition of channel geometry achieved by integrating the geophysical information.