Geologists interested in analytical structural geology should be aware of the fundamental role of displacements in the analysis of deformation. In two dimensions, information on the x and y components of displacements of points from their undeformed state to their deformed state permits the two-dimensional determination of strains. The spatial derivations of the x and y displacements functions are related to the transformation constants of finite homogeneous strain and, in turn, to the state of strain.
The variation of strain at a point of the material with time can be evaluated if the values of the strain component there at infinitesimally different times are known. In turn, time derivatives of strain at a point of the material can be obtained.
The practical problem of strain analysis based on the movements of points is to construct various valid mathematical functions (for example, the displacements function) from limited data. This article shows that geologists can graphically construct these functions and in turn make analyses of strain.
The method applies to the analysis of recent, instrument-measured deformation of the Earth, to the analysis of deformed fossils, and is applicable in principle to existent large-scale geologic structures.