New M@TE! model:

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Section 1: Summary of your model

Model Submitter:

Haibin Yang (0000-0002-8628-3704)

Model Creator(s):

• Haibin Yang (0000-0002-8628-3704)
• Louis-Noel Moresi (0000-0003-3685-174X)
• Huihui Weng (0000-0002-2936-2342)
• Julian Giordani (0000-0003-4515-9296)

Model slug:

yang-2023-eqcycles

(this will be the name of the model repository when created)

Model name:

Numerical Modeling of Earthquake Cycles Based On Navier-Stokes Equations With Viscoelastic-Plasticity Rheology

License:

Creative Commons Attribution 4.0 International

Model Category:

• model published in study
• community benchmark
• forward model

Model Status:

• completed

Associated Publication title:

Numerical Modeling of Earthquake Cycles Based On Navier‐Stokes Equations With Viscoelastic‐Plasticity Rheology

Short description:

The numerical modeling method for long-term tectonic deformations averages out the co-seismic fault displacement into thousands to tens of thousands of years, and neglects near-fault damages of earthquakes; therefore, it may not be able to decipher fault activities in detail. Software simulating earthquake rupture dynamics may not have a good estimation of background stress due to longterm tectonic deformations. In this study, we develop a numerical framework that embeds earthquake rupture dynamics into a long-term tectonic deformation model by adding inertial terms and using highly adaptive time-stepping that can capture deformation at plate-motion rates as well as individual earthquakes. The inertia term, which is neglected in long-term large-scale modeling methods, is considered to simulate the dynamic rupture processes. The rate-and-state frictional relationship for co-seismic fault slip is implemented in viscoelastic-plastic earth. Benchmarks of viscous flow, viscoelastic wave propagation and earthquake cycle simulations are tested. Based on these benchmarks, we undertake a generic study of a thrust fault in crust. We find that lower crustal rheology affects the periodic time of characteristic large earthquake cycles and the inter-seismic free surface movement. Cratons with a relatively strong lower crust due to lower temperature remain two peaks in surface uplift profiles around the fault zone for thousands of years after one characteristic earthquake, which help identify active faults in cratons.

Abstract:

Visco-elastic-plastic modeling approaches for long-term tectonic deformation assume that co-seismic fault displacement can be integrated over 1000s–10,000s years (tens of earthquake cycles) with the appropriate failure law, and that short-timescale fluctuations in the stress field due to individual earthquakes have no effect on long-term behavior. Models of the earthquake rupture process generally assume that the tectonic (long-range) stress field or kinematic boundary conditions are steady over the course of multiple earthquake cycles. This study is aimed to fill the gap between long-term and short-term deformations by modeling earthquake cycles with the rate-and-state frictional (RSF) relationship in Navier-Stokes equations. We reproduce benchmarks at the earthquake timescale to demonstrate the effectiveness of our approach. We then discuss how these high-resolution models degrade if the time-step cannot capture the rupture process accurately and, from this, infer when it is important to consider coupling of the two timescales and the level of accuracy required. To build upon these benchmarks, we undertake a generic study of a thrust fault in the crust with a prescribed geometry. It is found that lower crustal rheology affects the periodic time of characteristic earthquake cycles and the inter-seismic, free-surface deformation rate. In particular, the relaxation of the surface of a cratonic region (with a relatively strong lower crust) has a characteristic double-peaked uplift profile that persists for thousands of years after a major slip event. This pattern might be diagnostic of active faults in cratonic regions.

Scientific Keywords:

• Earthquake Cycles
• Navier-Stokes
• Viscoelastic-Plasticity
• Cratonic Earthquakes

Funder(s):

• National Natural Science Foundation of China (https://ror.org/01h0zpd94)
• National Computational Infrastructure (https://ror.org/04yx6dh41)

Section 2: your model code, output data

No embargo on model contents requested

Include model code:

True

Include model output data:

True

Section 3: software framework and compute details

Software Framework DOI/URL:

Found software: Underworld

Name of primary software framework:

Underworld

Software framework authors:

• John Mansour (0000-0001-5865-1664)
• Julian Giordani (0000-0003-4515-9296)
• Louis Moresi (0000-0003-3685-174X)
• Romain Beucher (0000-0003-3891-5444)
• Owen Kaluza (0000-0001-6303-5671)
• Mirko Velic
• Rebecca Farrington (0000-0002-2594-6965)
• Steve Quenette (0000-0002-0368-7341)
• Adam Beall (0000-0002-7182-1864)

Software & algorithm keywords:

• Python
• Finite element
• Particle-in-cell

Section 4: web material (for mate.science)

Landing page image:

Filename: Fig5_Compare1100.jpg
Caption: Figure 5. Evolution of the stress at the reference point (0, 0, −10 km) (a), maximum slip rate along the entire fault zone (b) and the adaptive time step used in simulation (c) for the reference model.

Animation:

Filename:

Graphic abstract:

Filename:

Model setup figure:

Filename: Fig4_BP5ModelSetup.jpg
Caption: Figure 4. The benchmark model BP5 for 3D sequence of earthquakes and aseismic slip modeling. (a) A vertical planar fault is embedded in the middle of a homogenous, isotropic half-space with a free surface at z = 0. Fault behavior is controlled by the rate-and-state friction law. A periodic boundary condition is applied in y direction. (b) The velocity-weakening (VW) region (dark and light blue) is located within a transition zone (white), outside of which is the velocity-strengthening (VS) region (gray). In y and z directions, the frictional domain and VW region are (L2, L3) and (l, w), respectively. An initial nucleation zone (dark blue square with a width of w) is designed at the left end of the VW region.
Description: The BP5 benchmark is first simulated with a reference model size of 96 km (L1) × 100 km (L2) × 30 km (L3) by 128 × 64 × 64 quadrilateral bilinear elements. Results from the SEAS code comparison platform (https:// strike.scec.org/cvws/seas/) with the mesh resolution of 1000 m are selected for comparison in this study (Table 2). The stress at a depth of 10 km in the middle point along the fault strike (y = 0) and the maximum slip rate along the entire fault are tracked for comparison (Figure 5). 0.1 m/s is taken as a threshold of fault slip rate to mark the earthquake initiation.