Back in 2015 I wrote a blog post about modeling anisotropic rheology in the geodynamic finite element code, aspect. Since then, I've been working on applying those tools to anisotropic material properties in the lithosphere, resulting from aligned igneous intrusions. I recently wrote a new paper on the subject with Leif Karlstrom titled "Anisotropic viscosity and time-evolving lithospheric instabilities due to aligned igneous intrusions" (doi: 10.1093/gji/ggy466 preprint).
The idea is pretty simple. Magma travels through the brittle upper crust through cracks. For very large eruptions, like flood basalt events, these cracks can be many kilometers long, and tens of meters thick. They tend to preferentially align with one another, such that they open against the direction of least compressive regional tectonic stress. Therefore, it's not uncommon, in large eruptions, that the lithosphere becomes segmented by preferentially-aligned dikes and sills. In these cases, the intruded lithosphere acts like a deck of cards, with planes of weakness that allow unbroken blocks to slide against one another.
In this paper, we do two things—
First, we quantify the magnitude of anisotropy expected in magmatically active lithosphere, by considering a material with repeating layers of different viscosities. We show, as expected, that the apparent viscosity of such a material is highly sensitive to the weak layers, when stress is applied in a simple shear orientation relative to the weak planes, but is most sensitive to the stronger layers when stressed perpendicular to layering.
Second, we test the effect of such a material on the properties of Rayleigh-Taylor instabilities, approximating lithospheric foundering associated with flood basalt eruptions. Prior studies have shown that the orientation of anisotropic viscosity affects the stability of lithosphere, but have only looked at the beginning stage of lithospheric foundering in a linear stability framework. Here we quantify the growth of Rayleigh-Taylor instabilities throughout their time-evolution. We find that the most unstable orientation, and relative instability growth rates change through time, ultimately reversing the interpretation one would draw from time-independent linear stability analysis.
I'll leave it up to the reader to check out the details of our implementation in the full paper.