Abstract Bedrock fractures influence the rates of surface processes that drive landscape evolution and are in turn influenced by landforms that perturb ambient tectonic and gravitational stress fields. In this modeling study, we examine how three‐dimensional topography and tectonic stress regimes influence elastic stress fields and bedrock fracture patterns beneath Earth's surface. We illustrate general effects of landform orientation and of tectonic stress magnitude and anisotropy using boundary element models of stresses beneath synthetic elongated ridges with different aspect ratios. We then examine the more detailed effects of landform shape using natural landscapes in Colorado and South Carolina. We show that the stress field is most sensitive to topographic perturbations if the most compressive horizontal tectonic stress is oriented perpendicular to the long axis of elongated landforms such as ridges and valleys and that topographic stress perturbations are most pronounced beneath landforms with higher mean curvatures, such as channel junctions and ridge crests. The shape of a predicted fracture‐rich zone in the subsurface depends mainly on the orientation of landforms relative to the most compressive horizontal tectonic stress direction and a dimensionless ratio that expresses the relative magnitudes of topographic stresses associated with horizontal tectonic compression and topographic relief. Variations in this dimensionless ratio can also change the predicted orientations of potential opening‐mode fracture planes. We use these model results to illustrate how topographic perturbations of three‐dimensional tectonic and gravitational stresses could influence landscape evolution by altering the rates and spatial heterogeneity of surface processes and groundwater flow.
Abstract Sediment transport by wind or water near the threshold of grain motion is dominated by rare transport events. This intermittency makes it difficult to calibrate sediment transport laws, or to define an unambiguous threshold for grain entrainment, both of which are crucial for predicting sediment transport rates. We present a model that captures this intermittency and shows that the noisy statistics of sediment transport contain useful information about the sediment entrainment threshold and the variations in driving fluid stress. Using a combination of laboratory experiments and analytical results, we measure the threshold for grain entrainment in a novel way and introduce a new property, the “shear stress variability”, which predicts conditions under which transport will be intermittent. Our work suggests strategies for improving measurements and predictions of sediment flux and hints that the sediment transport law may change close to the threshold of motion.
Abstract River valleys have been observed on Titan at all latitudes by the Cassini‐Huygens mission. Just like water on Earth, liquid methane carves into the substrate to form a complex network of rivers, particularly stunning in the images acquired near the equator by the Huygens probe. To better understand the processes at work that form these landscapes, one needs an accurate digital terrain model (DTM) of this region. The first and to date the only existing DTM of the Huygens landing site was produced by the U.S. Geological Survey (USGS) from high‐resolution images acquired by the DISR (Descent Imager/Spectral Radiometer) cameras on board the Huygens probe and using the SOCET SET photogrammetric software. However, this DTM displays inconsistencies, primarily due to nonoptimal viewing geometries and to the poor quality of the original data, unsuitable for photogrammetric reconstruction. We investigate a new approach, benefiting from a recent reprocessing of the DISR images correcting both the radiometric and geometric distortions. For the DTM reconstruction, we use MicMac, a photogrammetry software based on automatic open‐source shape‐from‐motion algorithms. To overcome challenges such as data quality and image complexity (unusual geometric configuration), we developed a specific pipeline that we detailed and documented in this article. In particular, we take advantage of geomorphic considerations to assess ambiguity on the internal calibration and the global orientation of the stereo model. Besides the novelty in this approach, the resulting DTM obtained offers the best spatial sampling of Titan's surface available and a significant improvement over the previous results.
We revisit the classic problem of the secular rotational stability of planets in response to loading using the fluid limit of viscoelastic Love number theory. Gold (1955) and Goldreich and Toomre (1969) considered the stability of a hydrostatic planet subject to an uncompensated surface mass load and concluded that a mass of any size would drive true polar wander (TPW) that ultimately reorients the load to the equator. Willemann (1984) treated the more self‐consistent problem where the presence of a lithosphere leads to both imperfect load compensation and a remnant rotational bulge. Willemann considered axisymmetric loads and concluded that the equilibrium pole location was governed by a balance, independent of elastic lithospheric thickness, between the load‐induced TPW and stabilization by the remnant bulge. Our new analysis demonstrates that the equilibrium pole position is a function of the lithospheric strength, with a convergence to Willemann's results evident at high values of elastic thickness (>400 km for an application to Mars), and significantly larger predicted TPW for planets with thin lithospheres. Furthermore, we demonstrate that nonaxisymmetric surface mass loads and internal (convective) heterogeneity, even when these are small relative to axisymmetric contributions, can profoundly influence the rotational stability. Indeed, we derive the relatively permissive conditions under which nonaxisymmetric forcing initiates an inertial interchange TPW event (i.e., a 90° pole shift). Finally, Willemann's analysis is often cited to argue for a small (<18°) TPW of Mars driven by the development of a Tharsis‐sized load. We show that even in the absence of the destabilizing effects of load asymmetry, the equations governing rotational stability permit higher excursions of the Martian rotation vector than has previously been appreciated.
