Constrained voxel inversion using the cartesian cut cell method

Abstract

Cartesian voxel inversion of geophysical data has proven to be a useful aid to mineral exploration, particularly over the last two decades. Using Cartesian voxel models is appealing because of the simplicity of the representation: computationally it is straight forward to implement a Cartesian representation, to visualise it, and to perform mathematical operations on it. However Cartesian representations have the shortcoming of forcing a regular Cartesian representation on the earth which they are trying to represent and as such introduce modeling errors into forward modeling and inversion processes. This is particularly apparent when the Cartesian voxel representation is used to simulate topography where continuous topography must be represented in a step-stair, or piecewise constant fashion, dependent on the size of the voxels in the model. Likewise geologic features such as faults, or abrupt changes in lithology or mineralization from drilling results, must all be superimposed onto a piecewise constant voxel representation. Two emerging model representations used to overcome these modeling errors are the octree mesh and the unstructured mesh, both of which significantly increase computational and visualization complexity. In this work we present a third alternative, the Cartesian Cut Cell method, as a way to rather simply extend the regular Cartesian representation to accurately include continuous geologic features in the model. We apply this method to significantly improve the representation of topography and also demonstrate how it can be applied to allow natural implementation of abrupt lithology changes deduced from drill results. Not only does the Cartesian Cut Cell method allow us to more accurately represent geology, but it also imposes only a minor computational complexity into existing simple Cartesian voxel representations. We demonstrate the method on constrained inversion of synthetic and field data.