What unsteady transpression models tell us about orogenic wedge kinematics of progressive arcs

Arc kinematics is mostly oblique, such that deformation at different parts of their orogenic wedges responds to specific combinations of rotational and non-rotational strains. To inquire about the influence of obliquity evolution in orogenesis, we propose a kinematic model that helps to understand bulk strain distribution along arcuate wedges, which is essential to interpret their structural patterns. Our model set-up considers one branch of a progressive arc, where curvature increases with arc evolution, in this case from an initial straight configuration. Displacement vectors are parallel along the arc and normal to the arc chord. This configuration imposes convergence with increasing obliquity towards the arc tips and along time at any point along the arc but its apex, where it is always orthogonal. We have applied the unsteady vorticity analytical model of Alonso-Henar et al. (2025) to reproduce bulk strain kinematics along an orogenic wedge developed in such a progressive arc. We consider the deformation zone boundary is defined by a vertical backstop, which results in monoclinic transpressional kinematics. We define ten sectors along the arc branch from the apex to the tip. Each sector is defined by its final obliquity, which ranges from α = 90º at the apex to α = 0º at the tip, with 10º variations. Sectional kinematic vorticity (Wk) increases accordingly from 0 to 1, and also along time. Maximum shortening normal to the backstop is 0.8 at the apex, and progressively decreases toward the tip, where it is 0.4. Arc evolution is divided into eight stages, each one defined by 0.1 increase of the frontal shortening.

Our model reproduces similar results (strain accumulation along time and along the arc) to those obtained through more classical steady models. However, some of our results are specific to unsteady vorticity evolution, thus inherent to progressive arcs. For instance, there is not a unique relationship between some strain parameters (e.g., the orientation of the maximum horizontal stretching axis) and the obliquity of one arc segment, because the path followed by the orogenic wedge to attain such obliquity is also relevant. Unexpectedly, our model also suggests that passive lines rotate faster than strain ellipsoids. Therefore, at any sector along the arc and any evolutionary stage, the angle that such lines make with the displacement vector is larger than the angle that the main structural traces make with the arc chord. This result poses questions on the interpretations of the so-called orocline test.

References:

Alonso-Henar, J., Fernández, C., Díaz-Azpiroz, M., Druguet, E. (2025) Unsteady transpression: How progressive variations in kinematic vorticity influence finite strain in shear zone evolution. Journal of Structural Geology 198, 105462.