Differential Geometry of Fault Surfaces and Glacial Beds: Associated Deformation Patterns

We measure glacial sliding surfaces and the striations on them and argue that these surfaces at the base of hard-bedded mountain glaciers can be compared to geologic fault surfaces albeit the obvious rheological differences. The reorientation of glacial striations around topographic anomalies provides quantifiable information about the otherwise inaccessible conditions. We use a ground-based LiDAR to measure the first high-precision orientations of these streaks at a field locality near Tenaya Lake, CA. We find that they are resolvably deflected around topographic highs. For example, bumps of about 0.3 m deflect the striations by up to 10°. Deviations from planar geometries can be quantified using the principles of differential geometry. These methods calculate the principal normal curvatures at each point on the surface and admit classification of one of eight basic shapes. Two of these shapes (synform and antiform) exhibit a zero principal normal curvature in one direction, one (plane) has no nonzero curvature, and another (perfect saddle) requires equal but opposite principal curvatures. None of these shapes are found in raw field data, so a curvature threshold and/or spectral filtering are applied to remove curvatures not distinguishable from zero. Common sliding surface shapes that can be described by this classification are domes, basins, antiformal, synformal, and perfect saddles. These non- developable shapes induce strains in the adjacent rock and ice masses as relative particle motions on either side of the fault or sliding surface are expected to be non-zero. These strains are not induced by surfaces with at most one non-zero principal normal curvature if the sliding direction is perpendicular to the direction of non-zero principal normal curvature. The additional strains may lead to nonparallel striations and off-fault deformation. Our goal is to relate the magnitudes of the two principle curvatures to changes in sliding direction. We show how the geometric shapes of the glacial sliding surfaces compare and contrast with fault surface shapes and how these shapes relate to glacial striations and slickenlines preserved on faults. Our field examples reveal the significance of geometric complexities to the mechanics of faulting and glacial sliding, and elucidate the interplay of surface geometry and slip behavior.