Cross-bedding analysis is an indispensable technique for interpreting sedimentary deposits. Cross-bedding is an important indicator of depositional environments, paleoflow velocities, and paleocurrent directions. Although most studies of cross-bedding have been directed toward determining ancient flow conditions or toward basic research to enable such applied studies, a second reason to study cross-bedding is equally important. Cross-bedding provides information about how modern bedforms behave—how they migrate, how they change in morphology, and how they interact with other bedforms. This kind of information is particularly valuable for bedforms whose behavior cannot be observed, either because they migrate or change shape too slowly, or because they are active in environments where repeated observations cannot be made. For example, the tendency of longitudinal dunes to migrate laterally was recognized from studies of eolian cross-bedding before modern dunes were known to exhibit such behavior (Rubin and Hunter, 1985). Subsequently, sedimentologists began investigating why bedforms behave in such a manner.
Regardless of whether the goal is to interpret ancient sedimentary deposits or to learn how modern bedforms behave, interpretation of cross-bedding is a two-step process. The first step—reconstructing the morphology and behavior of bedforms from cross-bedding—is primarily a problem of solid geometry. This geometry problem is the basis of this publication. The second step—determining flow conditions from bedform morphology and behavior—is mainly a problem of fluid dynamics. Previous studies of the origin of cross-bedding have not always distinguished these two steps but have nevertheless greatly advanced our understanding of the origin of cross-bedding. The conceptual breakthrough regarding the geometric origin of cross-bedding was Sorby's (1859) realization that cross-laminated beds originate by the climbing of ripples. Subsequent studies have addressed both the geometric and fluid-dynamics aspects of the problem using a variety of approaches, including field observations of bedforms and their internal structures, observations of stratification in rocks, flume experiments, theoretical analyses, and numerical modeling.