Reconciling Data at Seismic and Well Log Scales in 3-D Earth Modelling
Authors: Doyen P.M. , Psaila D.E. , den Boer L.D. , Jans D. 
Published: December 2007

Abstract
Three-dimensional seismic data, with their dense lateral coverage, provide a valuable source of information for constraining earth models. One drawback is the inherent lower vertical resolution of seismic measurements compared to well logs. This means that the use of seismic attributes is often limited to the areal mapping of zone average reservoir properties. A novel stochastic simulation method is introduced to constrain 3-D earth models with seismic attribute maps. The method accounts explicitly for the difference in vertical scale between seismic and wireline log measurements. Each vertical column of cells in a simulated 3-D model may be constrained to reproduce approximately a seismic-derived average value. The sequential simulation procedure is based on a Bayesian updating of point kriging estimates with a seismic average likelihood function and does not require solving block kriging systems. Three-dimensional porosity simulations are generated for a chalk reservoir layer of the Ekofisk Field, Norwegian North Sea. Vertical average constraints are imposed using a seismic impedance map representative of the gross average porosity across the reservoir interval.

Introduction
In the last several years, considerable attention has been given to the problem of integrating seismic attribute information in subsurface mapping applications. One complication arises because the vertical resolution of seismic data is much lower than that of well logs. Seismic attributes are therefore typically correlated with petrophysical data averaged vertically across reservoir zones which may be several tens of feet thick, depending on seismic resolution. The seismic attributes are then used to guide the areal interpolation of the well-derived zone average data. Areal reservoir models are useful in many applications such as optimum well siting and volumetric calculations. However, when performing dynamic flow simulation, three-dimensional models with grid-block thicknesses much finer than vertical seismic resolution are usually required to adequately describe the heterogeneities controlling flow. Several authors have recently proposed techniques for constraining 3-D reservoir models with 2-D seismic attribute maps. Gorell and Burns et al. proposed an empirical technique where each vertical column of cells in a 3-D porosity model is linearly re-scaled to reproduce a seismic-derived average porosity map. The technique has the advantage of being straightforward to implement but the re-scaled 3-D model will not tie at deviated wells. Furthermore, the re-scaling process may distort the data histogram. Deutsch et al. introduced an heuristic procedure based on simulated annealing. They built an objective function which includes a term measuring the degree of misfit between vertical average data and average values computed from the 3-D model. Simulated annealing is used to perturb the 3-D model until the degree of misfit is reduced to a value below a user-specified tolerance. One advantage of this method is that it is possible to account for the precision of the seismic average information.