## B01 - Fault networks and scaling properties of deformation accumulation

**Head(s):** Prof. Dr. Onno Oncken (GFZ Potsdam), Dr. Matthias Rosenau (GFZ Potsdam), Prof. Dr. Ralf Kornhuber (FU Berlin), Prof. Dr. Alexander Mielke (WIAS)

**Project member(s):** Joscha Podlesny, Michael Rudolf

**Participating institution(s):** FU Berlin, GFZ Potsdam, WIAS

### Project Summary

During the first funding period, B01 established a stimulating interplay of analysis, numerical analysis, simulation, and experiments. Main directions of research involved the analysis of rateindependent models for solids, numerical and experimental investigations of subduction zones and single faults, respectively, statistical data analysis of analogue earthquake sequences (in cooperation with the CRC’s Mercator Fellow Illia Horenko), and first steps towards fractal and numerical homogenisation of multiscale fault networks.

In the second funding period, we plan to extend our numerical simulations to single faults in viscoelastic materials and, in parallel, concentrate on the investigation of multiscale fault networks. In particular, we will develop analogue experiments that involve networks of nonplanar, dipping faults with frictional heterogeneities in a layered crust under spatiotemporally variable loading conditions such as relaxation or triggering. On the mathematical side, we will concentrate on numerical methods for viscoelastic multiscale fault networks in 2D and 3D with viscous foundation. As in the first funding period, numerical analysis will be strongly connected to analytical foundations, addressing, e.g., homogenisation and closure of multiscale interface problems. As a joint effort of analysis, simulation, experiments, and data-driven modelling (Mercator Fellow) our goal is to investigate the multiscale structure of fault networks in order to provide a phyical understanding, e.g., of recently detected slow slip events and silent earthquakes apparently filling the gap in scales between short- and longterm geodynamic deformation processes.

### Project publications

Kornhuber, R. and Youett, E.
(2018)
*Adaptive Multilevel Monte Carlo Methods for Stochastic Variational Inequalities.*
SIAM Journal on Numerical Analysis, 56
(4).
pp. 1987-2007.
ISSN 0036-1429

Kornhuber, R. and Peterseim, D. and Yserentant, H.
(2018)
*An analysis of a class of variational multiscale methods based on subspace decomposition.*
Mathematics of Computation, 87
(314).
pp. 2765-2774.
ISSN 1088-6842 (online)

Heida, M. and Kornhuber, R. and Podlesny, J.
(2017)
*Fractal homogenization of multiscale interface problems.*
SFB 1114 Preprint in arXiv
.
pp. 1-17.
(Submitted)

Ritter, M. and Rosenau, M. and Oncken, O.
(2017)
*Growing Faults in the Lab: Insights into the Scale Dependence of the Fault Zone Evolution Process.*
Tectonics, 36
.
pp. 1-32.

Rosenau, M. and Horenko, I. and Corbi, F. and Rudolf, M. and Kornhuber, R. and Oncken, O.
(2017)
*Synchronization of great subduction megathrust earthquakes: Insights from scale model analysis.*
SFB 1114 Preprint in EarthArXiv
.
pp. 1-35.
(Unpublished)

Rudolf, M. and Rosenau, M. and Oncken, O.
(2017)
*Interseismic deformation transients and precursory phenomena: Insights from stick-slip experiments with a granular fault zone.*
SFB 1114 Preprint in EarthArXiv:10.17605/OSF.IO/6MWRX
.
pp. 1-26.
(Unpublished)

Ritter, M. and Santimano, T.N. and Rosenau, M. and Leever, K. and Oncken, O.
(2017)
*Sandbox rheometry: Coevolution of stress and strain in riedel- and critical wedge-experiments.*
Tectonophysics, 722
.
pp. 400-409.

Corbi, F. and Funiciello, F. and Brizzi, S. and Lallemand, S. and Rosenau, M.
(2017)
*Control of asperities size and spacing on seismic behavior of subduction megathrusts.*
Geophysical Research Letters, 44
(16).
pp. 8227-8235.

Kornhuber, R. and Podlesny, J. and Yserentant, H.
(2017)
*Direct and Iterative Methods for Numerical Homogenization.*
In:
Domain Decomposition Methods in Science and Engineering.
Lecture Notes in Computational Science and Engineering, XXIII
(116).
SpringerLink, pp. 217-225.
ISBN 978-3-319-52389-7

Pipping, E.
(2017)
*Existence of long-time solutions to dynamic problems of viscoelasticity with rate-and-state friction.*
SFB 1114 Preprint
.
(Submitted)

Mielke, A. and Roubícek, T.
(2016)
*Rate-Independent elastoplasticity at finite strain and its numerical approximation.*
Mathematical Models and Methods in Applied Sciences, 26
(12).
pp. 2203-2236.
ISSN 1793-6314

Rudolf, M. and Boutelier, D. and Rosenau, M. and Schreurs, G. and Oncken, O.
(2016)
*Rheological benchmark of silicone oils used for analog modeling of short- and long-term lithospheric deformation.*
Tectonophysics, 684
.
pp. 12-22.

Pipping, E. and Kornhuber, R. and Rosenau, M. and Oncken, O.
(2016)
*On the efficient and reliable numerical solution of rate-and-state friction problems.*
Geophysical Journal International, 204
(3).
pp. 1858-1866.
ISSN Online: 1365-246X Print: 0956-540X

Horenko, I. and Gerber, S.
(2015)
*Improving clustering by imposing network information.*
Science Advances, 1
(7).
ISSN 2375-2548