Vertical Stacking Statistics of Multi-facies Object-Based Models

Equations describing facies proportions and amalgamation ratios are derived for randomly placed objects belonging to two or three foreground facies embedded in a background facies, as a function of the volume fractions and object thicknesses of independent facies models combined in a stratigraphically meaningful order. The equations are validated using one-dimensional continuum models. Evaluation of the equations reveals a simple relationship between an effective facies proportion and an effective amalgamation ratio, both measured as a function only of the facies in question and the background facies. This relationship provides a firm analytical basis for applying the compression algorithm to multi-facies object-based models. A set of two-dimensional cross-sectional models illustrates the approach, which allows models to be generated with realistic object stacking characteristics defined independently for each facies in a multi-facies object-based model.