Modeling and visualizing errors to geological surface orientations collected by UAV photogrammetry

Stereo photogrammetry using uncrewed aerial vehicles (UAVs) supports the creation of high-resolution 3D models that can resolve geological features. The traces of bedded strata, faults, and dikes are of particular geological interest because their orientations can be diagnostic of depositional processes and structural deformation. Standard regression statistics can estimate the orientation of planar features from a 3D terrain model but do not provide well-constrained error models for the orientations. Remotely-sensed orientation measurements are subject to multiple sources of uncertainty, including the input data, viewing geometry, and the regression itself. Correct representation of these spherical errors is crucial to geological interpretation from 3D models.

To address this problem, we have constructed ageneral statistical framework to represent orientation uncertainty in Cartesian and spherical coordinates (Quinn & Ehlmann, Earth and Space Science, 2019). We also provide graphical tools to quantify and visualize orientation uniqueness and quality in terms of bedding strike and dpi. Key to our method is principal-component analysis regression, which models orientation independent of viewing geometry and input data structure. This framework is particularly suited to ad-hoc UAV photogrammetry in which errors are relative to multiple viewpoints of a moving aircraft. Several applications of this technique to close-range, oblique-looking UAV imagery demonstrate its use in reconstructing high-quality orientation measurements. First, the method replicates field-gathered orientations in the Naukluft Mountains, Namibia, with errors of only a few degrees mostly oriented with dip. An example application to UAV imagery from Van Horn, Texas demonstrates a simple and flexible implementation of the workflow in the Jupyter Notebook analytical environment. This novel statistical and visualization approach increases the accuracy and comparability of structural measurements gathered by UAV techniques; it should be considered for use by the community. This new statistical approach has been validated with terrestrial UAV data, applied in orbital remote sensing of Mars, and is publicly available as the attitude Python package (https://github.com/davenquinn/Attitude).