A PCA-Based Framework for Determining Remotely Sensed Geological Surface Orientations and Their Statistical Quality

The orientations of planar rock layers are fundamental to our understanding of structural geology and stratigraphy. Remote sensing platforms including satellites, unmanned aerial vehicles, and Light Detection and Ranging scanners are increasingly used to build three-dimensional models of structural features on Earth and other planets. Remotely gathered orientation measurements are straightforward to calculate but subject to uncertainty inherited from input data, differences in viewing geometry, and the plane-fitting process, complicating geological interpretation. Here, we improve upon the present state of the art by developing a generalized means for computing and reporting errors in strike-dip measurements from remotely sensed data. We outline a general framework for representing the error space of uncertain orientations in Cartesian and spherical coordinates and develop a principal component analysis (PCA) regression method, which captures statistical errors independent of viewing geometry and input data structure. We also introduce graphical techniques to visualize the uniqueness and quality of orientation measurements and a process to increase statistical power by jointly fitting bedding planes under the assumption of parallel stratigraphy. These new techniques are validated by comparison of field-gathered orientation measurements with those derived from minimally processed satellite imagery of the San Rafael Swell, Utah, and unmanned aerial vehicle imagery from the Naukluft Mountains, Namibia. We provide software packages supporting planar fitting and visualization of error distributions. This method increases the precision and comparability of structural measurements gathered using a new generation of remote sensing techniques.