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 av-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 res-ervoir interval.