A STATISTICAL FRAMEWORK FOR DETERMINING REMOTELY-SENSED GEOLOGICAL SURFACE ORIENTATIONS AND THEIR ERROR DISTRIBUTIONS

Stereo photogrammetry using unmanned aerial vehicles (UAVs) supports the creation of high-resolution 3D models that can resolve geological features. The planar traces of bedded strata, faults, and dikes are of particular interest for structural geology, and the orientations of these features (e.g. strike and dip of bedding) are key structural data. The orientation of planar features on a 3D outcrop model can be readily estimated using regression statistics. However, to date, no standard quality metric for feature orientations has been developed. Because measurements are subject to uncertainty from multiple sources—inherited from input data, viewing geometry, and the regression itself—pairing orientations with meaningful error bars is crucial to structural geological interpretation from 3D models.

To address this problem, we have created a general statistical framework for representing uncertain orientations in Cartesian and spherical coordinates, supported by graphical techniques to visualize measurement uniqueness and quality (Quinn & Ehlmann, submitted to Earth and Space Science). We use principal-component analysis (PCA) regression, which models orientation independent of viewing geometry and input data structure. The PCA-based regression framework is particularly suited to ad-hoc UAV photogrammetry, in which errors are relative to multiple viewpoints of a moving aircraft. This new statistical tool has been verified with terrestrial UAV data and applied to planetary datasets from Mars and is publicly available as the attitude Python package (https://github.com/davenquinn/attitude).

We validate the technique using near-nadir satellite imagery and aerial elevation models of the San Rafael Swell, Utah. Orientation measurements derived from close-range, oblique-looking UAV imagery in the Naukluft Mountains, Namibia also replicate field-gathered orientations, with errors of only a few degrees mostly oriented with dip.

Relative to standard regression statistics that do not incorporate errors, this novel statistical and visualization approach increases the accuracy and comparability of structural measurements gathered by UAV, LIDAR, and other remote-sensing techniques. This toolset should be considered for use by the UAV community in orientation-measurement workflows.