What is the appropriate sample size for strike and dip measurements? An evaluation from compass, smartphone and LiDAR measurements

Geological planar surfaces are irregular and therefore, an important question is: what is the appropriate sample size for measuring their orientations? We explore this question by measuring the orientation of two metre-sized surfaces, a shallow foliation in an overhang and a more irregular steep joint plane, in Cambro–Ordovician mica schists of the Svarthola cave, Rogaland, SW Norway. We use three methods: a geological compass; smartphones with digital compass clinometer applications, i.e., Stereonet Mobile (iPhone) and Fieldmove Clino (iPhone and Android); and LiDAR scans of increasing resolution. While geological compass measurements are generally robust, they provide inaccurate measurements in the challenging foliation overhang. Stereonet Mobile measurements are more accurate, while Fieldmove Clino is reliable in the iPhone but not in the Android device. Mean surface orientations reach a consistent result after 100–150 smartphone measurements. However, neither the compass nor the smartphone measurements can clearly define the joint-surface orientation. Triangulated surfaces from the LiDAR scans deliver precise but inconsistent results, especially at the highest resolution in the joint plane. Kriging of the surfaces significantly improves the representativeness of the computed orientations to reflect a more realistic model. A best-fit to plane routine using points within a radius, r, delivers the most representative results. At r ~0.5 m, the estimated orientations stabilise, and all scans deliver similar results. This is the appropriate sample size for measuring the studied planes. Similar strategies should be taken into consideration when measuring planes in outcrop (sighting as opposed to direct measurement) or from 3D geological models.