Multiscale structure in sedimentary basins

Hierarchies of superimposed structures are found in maps of geological horizons in sedimentary basins. Mapping based on three‐dimensional (3D) seismic data includes structures that range in scale from tens of metres to hundreds of kilometres. Extraction of structures from these maps without a priori knowledge of scale and shape is analogous to pattern recognition problems that have been widely researched in disciplines outside of Geoscience. A number of these lessons are integrated and applied within a geological context here. We describe a method for generating multiscale representations from two‐dimensional sections and 3D surfaces, and illustrate how superimposed geological structures can be topologically analysed. Multiscale analysis is done in two stages – generation of scale‐space as a geometrical attribute, followed by identification of significant scale‐space objects. Results indicate that Gaussian filtering is a more robust method than conventional moving average filtering for deriving multiscale geological structure. We introduce the concept of natural scales for identifying the most significant scales in a geological cross section. In three dimensions, scale‐dependent structures are identified via an analogous process as discrete topological entities within a four‐dimensional scale‐space cube. Motivation for this work is to take advantage of the completeness of seismic data coverage to see ‘beyond the outcrop’ and yield multiscale geological structure. Applications include identifying artefacts, scale‐specific features and large‐scale structural domains, facilitating multiscale structural attribute mapping for reservoir characterisation, and a novel approach to fold structure classification.