Multidimensional Topology Transforms

Abstract

Most currently constructed 3D geological models are to a first order the result of transformations of data with different dimensionality into 3D: • 0D (e.g. outcrop data, at the regional scale), • 1D (e.g. drill hole data, at the mine scale), • 2D data (e.g. satellite data, at the regional scale) or • 3D data (e.g. seismic data, when high resolution 3D geophysical data are available, such as in basins), • 4D models (3D evolutions with time). The datasets used to project between dimensions vary according to the scenario, however they generally consist of a mixture of 0D observations and local temporal or spatial relationships (their topology). Modern software systems are able to use a sub-set of these relationships (fault-stratigraphy relationships for example) to build 3D geological models, however the relationships are not typically used as an independent constraint on how much of the 3D model is constrained by observations, and how much is generated by the end user (or the algorithms they use). This study explores the relationships between topological observations in 1, 2 and 3D in order to better understand how these may be used in the future as inputs to a revised 3D modelling workflow. We have investigated both synthetic cases, where we have full control, and natural examples, which permit alternate hypotheses. This approach has potential relevance to mine-scale and regional 3D models where the 3D topologies are poorly defined by the existing data, but 1D and 2D constraints are available.