Viscous folding of multilayer rocks under layer-parallel shortening: discrete layering vs. anisotropic models

Layer-parallel shortening of multilayer rocks results in the formation of folds. Using linear stability analysis, we obtain a growth rate curve. It allows us to determine the dominant wavelength during the initial stage of viscous folding. We derive an analytical expression for the growth rate curve of a single layer embedded in an anisotropic host, including confinement effects. The analytical results obtained for an anisotropic medium are compared to the growth rates obtained numerically for the corresponding cases of a finely laminated host. These cases split into two groups depending on whether a low- or high-viscosity layer borders perturbed interfaces of the central layer. However, in the limit of fine layering, their arithmetic mean tends to the results obtained for the anisotropic host. In search of an explanation, we calculate growth rates of the laminated host case analytically and show where the anisotropic approximation breaks down.

Next, we investigate an anisotropic rock medium under shortening along the anisotropy direction, with a locally perturbed axis of anisotropy orientation. It is a mean-field upscaled approximation to a multilayer system, which can tackle arbitrarily perturbed layer interfaces. In addition to the analytical approach, we use numerical simulations to study folding instability in such multilayer systems based on the direct (discretely layered medium) and upscaled (anisotropic medium) approaches. As a limiting case, we find the evolution of chevron fold amplitudes and study the convergence of the bilaminate dominant eigenmode to that obtained for the anisotropic medium.

Those results shed light on the limitations of the effective anisotropic models of layered rock systems, and provide a framework for more accurate mean-field approximations.

 

The work was supported by the National Science Centre, Poland, under research project “Numerical and field studies of anisotropic rocks under large strain: applying micro-POLAR mechanIcS in structural geology (POLARIS)”, no UMO-2020/39/I/ST10/00818.