Homogeneous steady deformation: A review of computational techniques

Homogeneous steady models are frequently used in the structural geology community to describe rock deformation. We review the literature on these models in a streamlined, coordinate-free framework based on matrix exponentials and logarithms. These mathematical tools allow us to compute progressive and simultaneous deformations easily. As an application, we develop transpression with triclinic symmetry in two ways. The tools let us integrate field data related to position and velocity in computing best-fit models with many degrees of freedom. As an application, we reanalyze a published study to demonstrate the extent to which kinematic vorticity is sensitive to modeling assumptions. The tools also open the door to an increased role for the mathematics of Lie groups (spaces of deformations) in structural geology. We suggest two topics for further study: numerical methods for non-steady deformations, and statistics of deformation tensors.

► Matrix exponentials/logarithms let us easily compute homogeneous steady deformations.
► They also clarify relationships among deformation concepts.
► In one application, we build triclinic transpression models.
► In another, we integrate velocity and position data to find best-fit models.
► The exponential/logarithm framework suggests that Lie groups will useful in future work.