[S-CG39] Science of slow earthquakes: Toward unified understandings of whole earthquake process

[SCG39-07] Systematic understanding of the slip-front-propagation velocity in terms of Linear Marginal Stability Hypothesis

*Takehito Suzuki¹ (1.Department of Physics and Mathematics, Aoyama Gakuin University)

Keywords:slip-front-propagation velocity, friction law, Linear Marginal Stability Hypothesis

Slip-front-propagation on an interface between two media has attracted interests of many researchers in scientific and industrial fields. In particular, the slip-front-propagation velocity has been obtained using some friction laws such as the slip-velocity-dependent law. Notably, to obtain the propagation velocity, Linear Marginal Stability Hypothesis (LMSH) has been widely employed. First, LMSH assumes the plane wave solution for the slip profile near the slip front, i.e., u~exp(i (k x-omega t)), where u is the slip and k and omega are the complex wave number and frequency, respectively. The imaginary parts of k and omega are written as k_i and omega_i, respectively, and the slip-front-propagation velocity is given by v=omega_i/k_i. We consider the friction law depending on both the slip and slip velocity, leading to two model parameters in the governing equation. We therefore assume that the terms C₁ u and C₂ \dot{u}, where C₁ and C₂ are the constants, emerge in the governing equation for u. We have obtained the cubic equation for omega_i using LMSH, and found that the numbers of the solutions for omega_i can be categorized into 12 regions on the C₁-C₂ phase space. Here, we aim to categorize the slip-front-propagation velocity on the C₁-C₂ phase space, and give some implications associated with slow earthquakes.

We should emphasize that the slip front has two forms: the intruding and extruding fronts (see details in Suzuki and Matsukawa, 2019). Actually, we have obtained the analytical solutions for omega_i, and they are called omegaⁱⁿ₁, omegaⁱⁿ₂, and omegaⁱⁿ₃ for the intruding front, and omega^ex₁, omega^ex₂, and omega^ex₃ for the extruding front. Using these values and the relationship between k_i and omega_i, we have also obtained the analytical forms of k_i, which are called kⁱⁿ₁, kⁱⁿ₂, and kⁱⁿ₃ for the intruding front, and k^ex₁, k^ex₂, and k^ex₃ for the extruding front. Therefore, we can write analytical forms for the intruding and extruding slip-front-propagation velocities, vⁱⁿ_j=omegaⁱⁿ_j/kⁱⁿ_j and v^ex_j=omega^ex_j/k^ex_j (j=1,2,3), respectively.

In terms of the solutions of vⁱⁿ_j and v^ex_j, the C₁-C₂ phase space is divided into 7 regions. They are the regions with (A) vⁱⁿ₁, (B) v^ex₁, (C) vⁱⁿ₁ and v^ex₂, (D) v^ex₁ and v^ex₃, (E) vⁱⁿ₁, v^ex₂, and vⁱⁿ₃, (F) vⁱⁿ₁, v^ex₂, and v^ex₃, and (G) no propagation velocity. In particular, we emphasize that there exists the region where vⁱⁿ_j or v^ex_j does not exist. This region cannot generate the steady slip-front-propagation, and may imply the generation of slow earthquakes from seismological viewpoint.