Haromonic Curvature and Bedding Uncertainty Across Scales

Observations of geological structures are often made at different scales and often can cross multple orders of magnitude. This attribute of scale though is often not explicitly incorporated into the workflow of geological modeling and is usually treated as data preparation or sampling bias. The spectral properties of the discrete Laplacian operator, when applied to reconstructed surfaces from implicit modeling though offer a potential means of bridging this gap, when also combined with appropriate directional statistical anaysis. We present an example of how bedding orientation measurements from a 1:5000 scale surface map and drillhole bedding orientation picks from borehole televiewer images can be integrated using the manifold harmonics of the Laplacian operator and a mixture of von-Mises Fisher probability distributions. This provides automated insights for sampling for modeling and also possible kinematic and tectonics processes.