Bedforms and cross-bedding can be simulated mathematically using sine curves. SiSimulated structures, like real structures, fall into four categories: invariable two-dimensional bedforms and cross-bedding, variable two-dimensional bedforms and cross-bedding, invariable three-dimensional bedforms and cross-bedding, and variable three-dimensional bedforms and cross-bedding. The structures in each category can be distinguished in three-dimensional outcrops and in polar plots of cross-beds and bounding surfaces, but the structures often are indistinguishable in two-dimensional exposures.
Variability of bedforms can result from two processes: flow fluctuations that cause systematic changes to entire populations of bedforms, and migration of superimposed or intersecting bedforms in flows that may be steady. Cross-bedding produced by these two processes can often be distinguished by the relations between the dip directions of cross-beds and bounding surfaces within the cross-stratified beds. Structures produced by bedforms that change morphology or path of climb in response to flow fluctuations have cross-beds and bounding surfaces with the same strike. Structures produced by superimposed bedforms have cross-beds and bounding surfaces with differing strikes, because the crestlines of the superimposed bedforms are unlikely to parallel the crestlines of the main bedforms exactly.
Cyclic cross-bedding produced by cyclic flow fluctuations is useful for determining flow velocities. Cyclic cross-bedding produced by superimposed bedforms is useful for determining flow directions; structures deposited by bedforms that were oriented obliquely to the sediment transport direction can be recognized by along-crest migration of superimposed bedforms.