The capability to gather precise and abundant geodetic data on the movement of points on the earth's surface has called attention to the use of displaced points to understand present-day deformation (Burchfiel, 2004). The analysis of displacements clearly leads to insight into the spatial and temporal variation of strain on the earth's surface today. The analysis, however, of displacements in understanding the deformation of existent geologic structures, specifically stratified rocks, appears limited. This said, although many geologists have restored cross-sections and, in so doing, have implicitly presented information useful to construct parts of complete displacements fields needed to appreciate strains associated with evolution of a structure.

A complete statement of the displacement fields that have yielded even a simple 2-D structure of stratified formations is challenging because there are many possible solutions. Nevertheless, all should honor certain fundamentals. One that all acknowledge is that a present day structure, composed of strata, be derived from more or less flat layers with thickness of limited range. Other requirements are that strain markers be honored; the density of the deformed strata remain within certain limits; and that movements of adjacent parts of the structure be compatible.

The example used to illustrate these fundamentals is taken from a fold with strain markers from the Appalachians. Two possible displacements fields were conceived: one in which the original strata moved in a single, simple step from original horizontality to its present shape; a second, one in which the strata first formed an open, slightly strained syncline and then were further tightly compressed, as suggested by strain markers, to form the structure seen today.

A greater focus on displacements analysis, as illustrated in this presentation, leads to rigorous (although not unique) explanations for development of a structure. It also leads to exact meanings for embedded strain markers and to a greater awareness of the need for a definition of continua in studying structural geology and relating structural geology to applied mechanics.