The geometry of sedimentary strata records the dynamics of the surfaces that produced them. Cross strata are one of the most common features preserved in the stratigraphic record and are typically formed by migrating ripples, dunes, and bars. Cross-stratal geometry depends on the movement and shape of the bed forms. In this study, we provide theoretical relationships that map the statistics of surface kinematics and geometry of migrating bed forms into the 2-D geometrical structure of the preserved stratigraphy. The surface kinematics is characterized by the migration (translation of the waveforms) and deformation (change in shape of the waveforms) of the bed forms. We show that, for transverse, unidirectional bed forms, the local slope and curvature of the preserved stratigraphic boundaries depend on the competition between migration and deformation of the bed forms. Further, we show that deformation is the sole cause of curved cross-set boundaries and define a quantitative relationship between the curvature of the bounding surfaces of the preserved cross sets and the deformation rate of the bed forms. The theoretical results compare well with experimental data of subaqueous, transverse bed form evolution under equilibrium, steady state conditions with no net deposition.
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