## Rupture Dynamics at the Interface Between a Thin Compliant Layer and Stiffer Underlying Half-Space

Lauren S. Abrahams, Kali L. Allison, & Eric M. DunhamSubmitted August 14, 2018, SCEC Contribution #8546, 2018 SCEC Annual Meeting Poster #202

In this study we examined the sliding dynamics of a frictional interface between elastic solids. Sliding dynamics is well understood for two identical or dissimilar half-spaces (e.g., Rice et al, 2001; Aldam et al., 2017). Sliding between a thin layer over a half-space has also been studied, but to a lesser extent (Ranjith, 2009; Aldam et al., 2016; Lipovsky & Dunham, 2017). The thin layer over half space problem arises in many contexts, ranging from shallowing dipping subduction zones to ice streams (in particular, the Whillans Ice Plain (WIP), which advances via twice-daily Mw 7 slow slip events). Our objective is to quantify sliding stability and rupture styles for this geometry with rate-and-state friction. Specifically, we study the influence of layer thickness (H) on conditions for steady sliding vs. slow slip cycles vs. fast slip cycles, using both linear stability analysis and earthquake cycle simulations on a 2D anti-plane shear sliding of a thin compliant layer over a stiffer half-space.

Steady sliding with velocity-weakening rate-and-state friction is linearly unstable above a critical wavelength (Lc). For thin layers, such as the WIP, Lc is proportional to the square-root of H. But, as H is increased, Lc becomes independent of H and approaches to the well-known solution for sliding between two half-spaces.

The stability analysis provides insight into more complex situations, such as the nonlinear earthquake cycle dynamics of a nominally velocity-strengthening interface containing a velocity-weakening patch of width W. For small W, the patch slides steadily with the rest of the interface, and for large W the patch fails in fast earthquakes. Between these two limits, the patch exhibits slow slip events. We use our cycle simulations to map sliding style as a function of H and W, finding a trend that is consistent with the stability analysis. Overall this study demonstrates how the decreasing elastic stiffness associated with small layer thickness reduces the critical wavelength for instability, with important implications for rupture dynamics in thin layer geometries.

**Key Words**

rupture dynamics, critical wavelength, earthquake cycle

**Citation**

Abrahams, L. S., Allison, K. L., & Dunham, E. M. (2018, 08). Rupture Dynamics at the Interface Between a Thin Compliant Layer and Stiffer Underlying Half-Space. Poster Presentation at 2018 SCEC Annual Meeting.

**Related Projects & Working Groups**

Fault and Rupture Mechanics (FARM)