Minimal model for the onset of slip pulses in frictional rupture

The question ”what arrests an earthquake rupture?” sits at the heart of any potential prediction of earthquake magnitude. Here, we use a one‐dimensional, thin‐elastic‐strip, minimal model, to illuminate the basic physical parameters that may control the arrest of large ruptures. The generic formulation of the model allows for wrapping various earthquake arrest scenarios into the variations of two dimensionless variables (initial dimensionless stress parameter on the fault) and (dimensionless fracture energy), valid for both in‐plane and antiplane shear loading. Our continuum model is equivalent to the standard Burridge‐Knopoff model, with an added characteristic length scale, H, that corresponds to either the thickness of the damage zone for strike‐slip faults or to the thickness of the downward moving plate for subduction settings. We simulate the propagation and arrest of frictional ruptures and derive closed‐form expressions to predict rupture arrest under different conditions. Our generic model illuminates the different energy budget that mediates crack‐ and pulse‐like rupture propagation and arrest. It provides additional predictions such as generic stable pulse‐like rupture solutions, stress drop independence of the rupture size, the existence of back‐propagating fronts, and predicts that asymmetric slip profiles arise under certain pre‐stress conditions. These diverse features occur also in natural earthquakes, and the fact that they can all be predicted by a single minimal framework is encouraging and pave the way for future developments of this model.

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“…Here, Equation 1 is solved numerically using a finite difference scheme with uniform grid size

{\Delta }\bar{x}

and Euler‐Cromer (Cromer, 1981) time‐integration scheme with time step

{\Delta }\bar{t}

, as described in Thøgersen et al. (2021). At each grid point i and time step, the interface can be either stuck

\left({\dot{\bar{u}}}_{i}=0\right)

or slipping

\left({\dot{\bar{u}}}_{i}\ne 0\right)

.…”

Section: Numerical Simulations Of Frictional Rupture Arrestmentioning

confidence: 99%

How Do Earthquakes Stop? Insights From a Minimal Model of Frictional Rupture

et al. 2023

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“…1. Thøgersen et al (2021) discusses in details the properties of slip pulses in our one-dimensional model.…”

Section: The Crucial Role Of Boundary Conditions On the Rupture Stylementioning

confidence: 99%

“…Here, Eq. ( 1) is solved numerically using a finite difference scheme with uniform grid size ∆x and Euler-Cromer time-integration scheme with time step ∆ t, as described in Thøgersen et al (2021). At each grid point i and time step, the interface can be either stuck ( ui = 0) or slipping ( ui = 0).…”

Section: The Arrest Of Frictional Rupture In the One-dimensional Modelmentioning

confidence: 99%

“…Here, we explore the dynamics governing the propagation and arrest of frictional rupture by using a one-dimensional elastodynamic model that contains only two parameters in its dimensionless form (Thøgersen et al, 2021). A similar approach reproduces some observations made on slow, subshear, and supershear earthquakes, such as the scaling between duration and moment (Thøgersen, Sveinsson, et al, 2019).…”

Section: Introductionmentioning

confidence: 98%

“…The present study investigates rupture arrest using a minimal frictional rupture model that we developed in a previous study (Thøgersen et al, 2021). In this approach, the elastodynamic equations are reduced to a one-dimensional expression by assuming a block of finite height H in frictional contact along the plane y = 0, as presented in Figs.…”

Section: Introductionmentioning

confidence: 99%

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How do earthquakes stop? Insights from a minimal model of frictional rupture

Barras

Thøgersen

Aharonov

et al. 2022

Preprint

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The question "what arrests an earthquake rupture?" sits at the heart of any potential prediction of earthquake magnitude. Here, we use a one-dimensional, thin-elastic-strip, minimal model, to illuminate the basic physical parameters that control the arrest of large ruptures. The generic formulation of the model allows for wrapping various earthquake arrest scenarios into the variations of two dimensionless variables $\bar \tau k$ (initial pre-stress on the fault) and $\bar d c$ (fracture energy), valid for both in-plane and antiplane shear loading. Our continuum model is equivalent to the standard Burridge-Knopoff model, with an added characteristic length scale, $H$, that corresponds to either the thickness of the damage zone for strike-slip faults or to the thickness of the downward moving plate for subduction settings. We simulate the propagation and arrest of frictional ruptures and derive closed-form expressions to predict rupture arrest under different conditions. Our generic model illuminates the different energy budget that mediates crack-and pulse-like rupture propagation and arrest. It provides additional predictions such as generic stable pulse-like rupture solutions, stress drop independence of the rupture size, the existence of back-propagating fronts, and predicts that asymmetric slip profiles arise under certain pre-stress conditions. These diverse features occur also in natural earthquakes, and the fact that they can all be predicted by a single minimal framework is encouraging and pave the way for future developments of this model.

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Antiplane spectral boundary integral equation method for an interface between a layer and a half-plane

Gupta

Ranjith

2023

Journal of the Mechanics and Physics of Solids

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Minimal model for the onset of slip pulses in frictional rupture

Cited by 9 publications

References 56 publications

How Do Earthquakes Stop? Insights From a Minimal Model of Frictional Rupture

How Do Earthquakes Stop? Insights From a Minimal Model of Frictional Rupture

How do earthquakes stop? Insights from a minimal model of frictional rupture

Antiplane spectral boundary integral equation method for an interface between a layer and a half-plane

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