Subpatch roughness in earthquake rupture investigations

Zielke, Olaf; Martin, P.

doi:10.1002/2015gl067084

Cited by 6 publications

(3 citation statements)

References 24 publications

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“…We show that the fractal geometry of faults can be maintained during wear caused by slip when asperity failure occurs over all length scales. With our results, the extensive literature covering the geomechanical implications of roughness (e.g., Dunham et al, ; Fang & Dunham, ; Harbord et al, ; Marone & Cox, ; Zielke & Mai, ; Zielke et al, ) implies a measurable difference between earthquakes occurring on major faults and earthquakes occurring, for example, off‐fault along immature fractures.…”

Section: Discussionsupporting

confidence: 68%

Smoothing of Fault Slip Surfaces by Scale‐Invariant Wear

2018

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Previous field observations suggest that fault slip surface roughness may decrease with slip. However, measurements have yet to confidently isolate the effect of slip from other possible controls, such as lithology or tectonic setting. We describe the evolution of slip surfaces in normal faults in SE Utah that cut well‐sorted, high‐porosity sandstones and accommodated regional extension at 1‐ to 4‐km depth. Tight controls on fault offset and uniform tectonic history allowed us to isolate the effect of slip during early stages of faulting (0‐ to 55‐m slip). Slip surfaces progress from rough joints and deformation bands toward smooth, continuous, and mirror‐like surfaces with increasing slip. We collected 123 scans of pristine slip surfaces, which measure surface geometry from micrometers to meters in length scale. Results indicate that slip surface roughness is systematically smoother than joint surfaces and deformation band edges. Over the best resolved length scales (0.1–10 mm), we observe roughness decreases with slip according to a power law with exponent −1 in the slip direction. Slip‐perpendicular profiles, though rougher, exhibit the same smoothing trend. The Hurst scaling exponent does not change with slip. These observations require wear to be multiscale. Boundary element method models suggest that mechanical wear of completely mated surfaces occurs by asperity failure and that the wear rate depends on the aspect ratio of asperities. These results indicate that at large slip, asperity failure at all length scales can cause slip surfaces to smooth while maintaining the fractal geometry characteristic of faults.

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Section: Discussionsupporting

confidence: 68%

Smoothing of Fault Slip Surfaces by Scale‐Invariant Wear

2018

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“…The adopted numerical setup requires a sufficiently fine spatial discretization of the rupture surface to represent its fractal characteristics [e.g., Power et al, 1988;Sagy et al, 2007;Candela et al, 2012;Brodsky et al, 2016;Zielke and Mai, 2016] with regards to slip D associated with stress drop Δτ, i.e., the fault's elastic response. We identify the corresponding model resolution (patch number N) by examining the average amount of induced stress along a rupture surface due to slip along that surface (also known as back slip model [e.g., Tullis et al, 2012]) for varying spatial discretization.…”

Section: Sampling the Fractal Fault Surfacementioning

confidence: 99%

Fault roughness and strength heterogeneity control earthquake size and stress drop

Zielke

Gális

Martin

2017

Geophysical Research Letters

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An earthquake's stress drop is related to the frictional breakdown during sliding and constitutes a fundamental quantity of the rupture process. High‐speed laboratory friction experiments that emulate the rupture process imply stress drop values that greatly exceed those commonly reported for natural earthquakes. We hypothesize that this stress drop discrepancy is due to fault‐surface roughness and strength heterogeneity: an earthquake's moment release and its recurrence probability depend not only on stress drop and rupture dimension but also on the geometric roughness of the ruptured fault and the location of failing strength asperities along it. Using large‐scale numerical simulations for earthquake ruptures under varying roughness and strength conditions, we verify our hypothesis, showing that smoother faults may generate larger earthquakes than rougher faults under identical tectonic loading conditions. We further discuss the potential impact of fault roughness on earthquake recurrence probability. This finding provides important information, also for seismic hazard analysis.

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“…The significance of effects originating from heterogeneity around and across the fault (including damage zones) and the fault geometric complexity has been recognized since the mid 1980s. These are still subject to active research; for a recent study, see [41]. Fault geometric complexities have been shown to strongly affect a fault's seismic behavior at the corresponding spatial scales, while affecting the dynamic rupture process.…”

Section: Formulation Of the Inverse Problem: A Uniqueness Resultsmentioning

confidence: 99%

Analysis of a Model of Elastic Dislocations in Geophysics

Aspri

Beretta

Mazzucato

et al. 2019

Arch Rational Mech Anal

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We analyze a mathematical model of elastic dislocations with applications to geophysics, where by an elastic dislocation we mean an open, oriented Lipschitz surface in the interior of an elastic solid, across which there is a discontinuity of the displacement. We model the Earth as an infinite, isotropic, inhomogeneous, elastic medium occupying a half space, and assume only Lipschitz continuity of the Lamé parameters. We study the well posedness of very weak solutions to the forward problem of determining the displacement by imposing traction-free boundary conditions at the surface, continuity of the traction and a given jump on the displacement across the fault. We employ suitable weighted Sobolev spaces for the analysis. We utilize the well posedness of the forward problem and unique-continuation arguments to establish uniqueness in the inverse problem of determining the dislocation surface and the displacement jump from measuring the displacement at the surface of the Earth. Uniqueness holds for tangential or normal jumps and under some geometric conditions on the surface.

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Subpatch roughness in earthquake rupture investigations

Cited by 6 publications

References 24 publications

Smoothing of Fault Slip Surfaces by Scale‐Invariant Wear

Smoothing of Fault Slip Surfaces by Scale‐Invariant Wear

Fault roughness and strength heterogeneity control earthquake size and stress drop

Analysis of a Model of Elastic Dislocations in Geophysics

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