Geostatistical Modeling of Evolving Landscapes by Means of Image Quilting

Abstract:

Realistic geological representation of subsurface heterogeneity remains an important outstanding challenge. While many geostatistical methods exist for representing sedimentary systems, such as multiple-point geostatistics, rule-based methods or Boolean methods, the question of what the prior uncertainty on parameters (or training images) of such algorithms are, remains outstanding. In this initial work, we investigate the use of flume experiments to constrain better such prior uncertainty and to start understanding what information should be provided to geostatistical algorithms. In particular, we study the use of image quilting as a novel multiple-point method for generating fast geostatistical realizations once a training image is provided. Image quilting is a method emanating from computer graphics where patterns are extracted from training images and then stochastically quilted along a raster path to create stochastic variation of the stated training image. In this initial study, we use a flume experiment and extract 10 training images as representative for the variability of the evolving landscape over a period of 136 minutes. The training images consists of wet/dry regions obtained from overhead shots taken over the flume experiment. To investigate whether such image quilting reproduces the same variability of the evolving landscape in terms of wet/dry regions, we generate multiple realizations with all 10 training images and compare that variability with the variability seen in the entire flume experiment. By proper tuning of the quilting parameters we find generally reasonable agreement with the flume experiment.