# Scaling seismic fault thickness from the laboratory to the field

Thomas P. Ferrand, Stefan Nielsen, Loïc Labrousse, Alexandre Schubnel

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Thomas P. Ferrand, Stefan Nielsen, Loïc Labrousse, Alexandre Schubnel. Scaling seismic fault thickness from the laboratory to the field. EGU General Assembly 2021 (online), Apr 2021, Online, France. 10.5194/egusphere-egu21-12188 . hal-03554522

HAL Id: hal-03554522

https://hal.science/hal-03554522

Submitted on 3 Feb 2022

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Scaling seismic fault thickness from the laboratory to the field

Thomas P. Ferrand<fnref n="1" />, Stefan Nielsen<fnref n="2" />, Loïc Labrousse<fnref n="3" />, and Alexandre Schubnel<fnref n="4" />

Pseudotachylytes originate from the solidification of frictional melt, which transiently forms and lubricates the fault plane during an earthquake. Here we observe how the pseudotachylyte thickness *a* scales with the relative displacement *D* both at the laboratory and field scales, for measured slip varying from microns to meters, over six orders of magnitude. Considering all the data jointly, a bend appears in the scaling relationship when slip and thickness reach ≈1 mm and 100 µm, respectively, i.e. *M*<sub>w</sub> > 1. This bend can be attributed to the melt thickness reaching a steady-state value due to melting dynamics under shear heating, as is suggested by the solution of a Stefan problem with a migrating boundary. Each increment of fault is heating up due to fast shearing near the rupture tip and starting cooling by thermal diffusion upon rupture. The building and sustainability of a connected melt layer depends on this energy balance. For plurimillimetric thicknesses (*a* > 1 mm), melt thickness growth reflects in first approximation the rate of shear heating which appears to decay in *D*<sup>-1/2</sup> to *D*<sup>-1</sup>, likely due to melt lubrication controlled by melt + solid suspension viscosity and mobility. The pseudotachylyte thickness scales with moment *M*<sub>0</sub> and magnitude *M*<sub>w</sub>; therefore, thickness alone may be used to estimate magnitude on fossil faults in the field in the absence of displacement markers within a reasonable error margin.

<footnote n="1">¹Institut des Sciences de la Terre d'Orléans, Université d'Orléans / CNRS UMR-7327, Orléans, France.</footnote>

<footnote n="2">²Department of Earth Sciences, Durham University, Durham DH1 5ED, United Kingdom.</footnote>

<footnote n="3">³Institut des Sciences de la Terre de Paris, Sorbonne Université, Campus Pierre et Marie Curie / CNRS UMR-7193, Paris, France.</footnote>

<footnote n="4">⁴Laboratoire de Géologie de l'Ecole Normale Supérieure, PSL Research University / CNRS UMR-8538, Paris, France.</footnote>