Skip to Main Content

This chapter explores the critical role that kinematics plays in the construction and analysis of geological cross sections. The structures on any admissible cross section must arise from relative displacements that are consistent with reasonable deformation kinematics. Sections that violate this constraint are physically impossible. The deformation kinematics can be derived from a displacement field, but the scale at which the displacement field is analyzed affects our perceptions of the movement of rocks in the cross section. Microscopic displacement fields associated with grain-scale deformation may be derived by the standard techniques of finite strain analysis, while macroscopic displacement fields may be derived from the geometry of map-scale cross sections in those regions that have undergone uniform area strain.

Physical compatibility requires that the two scales be linked. In regions of uniform area strain, the displacement fields at the two levels may be linked through elementary vector analysis. Finite strain data indicate that the central Appalachians suffered uniform area strain. Elementary vector analysis of a blind autochthonous roof duplex in the central Appalachians shows that: (1) the faulted stiff layer and its overlying roof layer have separate displacement fields; and (2) restoration of structure sections across regions of uniform area strain requires that sections be constructed approximately parallel to the finite strain trajectory of maximum shortening.

Another way to link the microscopic and macroscopic deformation kinematics is the use of “loose lines” in the deformed and undeformed states. Loose lines drawn on geological cross sections predict the shear strains at any point within a thrust sheet. These shear strains, derived solely from the geometry of structures in the cross section, are independent data that can be compared to measured strains, providing an additional constraint for a cross section. Loose line analysis can also offer insight to the sequence of faulting in a cross section and the geometry of subsurface structures.

Macroscopic kinematic analysis, using vector analysis and loose lines, shows that the “excess section” technique for predicting depth to detachment and finding the initial section length contains implicit assumptions about the kinematics of deformation. Use of this technique without examining the boundary conditions may lead to inadmissible or incorrect cross sections. The problem is perhaps most acute in blind thrust terranes where use of the excess section technique has led to significant underestimates in the amount of shortening in these terranes.

Kinematic analysis suggests that “kinematic admissibility” is an additional criterion that can constrain geological cross sections. Since lines drawn on a section have kinematic significance, it is possible to test a section for kinematic admissibility by attempting to pass from its undeformed state, produced by “balancing” the section, to the deformed state by the process of “forward modeling.” This test is applied to several examples from the literature, and it is demonstrated that the proposed solutions can be rejected because they fail to meet the test of kinematic admissibility.

You do not currently have access to this chapter.

Figures & Tables




Citing Books via

Close Modal
This Feature Is Available To Subscribers Only

Sign In or Create an Account

Close Modal
Close Modal