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+---
+templateKey: model
+slug: yang-2023-eqcycles
+title: Numerical Modeling of Earthquake Cycles Based On Navier-Stokes Equations With Viscoelastic-Plasticity Rheology
+date: '2024-08-16T07:38:53.000Z'
+featuredpost:
+for_codes:
+  - 370401
+status:
+  - completed
+doi: ''
+url: https://mate.science//models/yang-2023-eqcycles
+creditText: ''
+software:
+  name: Underworld
+  doi: https://doi.org/10.5281/zenodo.3975252
+  url_source: ''
+licence:
+  licence_url: https://creativecommons.org/licenses/by/4.0/legalcode
+  licence_image: ../../../img/licence/by.png
+  description: Creative Commons Attribution 4.0 International
+  licence_file: license.txt
+submitter:
+  name: Haibin
+  family_name: Yang
+  ORCID: https://orcid.org/0000-0002-8628-3704
+creators:
+  - name: Haibin
+    family_name: Yang
+    ORCID: 0000-0002-8628-3704
+  - name: Louis-Noel
+    family_name: Moresi
+    ORCID: 0000-0003-3685-174X
+  - name: Huihui
+    family_name: Weng
+    ORCID: 0000-0002-2936-2342
+  - name: Julian
+    family_name: Giordani
+    ORCID: 0000-0003-4515-9296
+associated_publication:
+  title: Numerical Modeling of Earthquake Cycles Based On Navier‐Stokes Equations With Viscoelastic‐Plasticity Rheology
+  url: http://dx.doi.org/10.1029/2023gc010872
+  doi: 10.1029/2023gc010872
+  publisher: American Geophysical Union (AGU)
+  journal: Geochemistry, Geophysics, Geosystems
+  date: 2023-9
+  authors:
+    - name: Haibin
+      family_name: Yang
+    - name: Louis
+      family_name: Moresi
+    - name: Huihui
+      family_name: Weng
+    - name: Julian
+      family_name: Giordani
+compute_info:
+  name: ''
+  organisation: ''
+  url: ''
+  doi: ''
+research_tags:
+  - Earthquake Cycles
+  - Navier-Stokes
+  - Viscoelastic-Plasticity
+  - Cratonic Earthquakes
+compute_tags:
+  - Python
+  - Finite element
+  - Particle-in-cell
+funder:
+  - name: National Natural Science Foundation of China
+    doi: https://ror.org/01h0zpd94
+  - name: National Computational Infrastructure
+    doi: https://ror.org/04yx6dh41
+funding:
+  - name: National Natural Science Foundation of China
+    doi: https://ror.org/01h0zpd94
+    number_id: '#42030306'
+abstract: "Visco-elastic-plastic modeling approaches for long-term tectonic deformation assume that\r\nco-seismic fault displacement can be integrated over 1000s–10,000s years (tens of earthquake cycles) with the\r\nappropriate failure law, and that short-timescale fluctuations in the stress field due to individual earthquakes\r\nhave no effect on long-term behavior. Models of the earthquake rupture process generally assume that the\r\ntectonic (long-range) stress field or kinematic boundary conditions are steady over the course of multiple\r\nearthquake cycles. This study is aimed to fill the gap between long-term and short-term deformations by\r\nmodeling earthquake cycles with the rate-and-state frictional (RSF) relationship in Navier-Stokes equations.\r\nWe reproduce benchmarks at the earthquake timescale to demonstrate the effectiveness of our approach. We\r\nthen discuss how these high-resolution models degrade if the time-step cannot capture the rupture process\r\naccurately and, from this, infer when it is important to consider coupling of the two timescales and the level of\r\naccuracy required. To build upon these benchmarks, we undertake a generic study of a thrust fault in the crust\r\nwith a prescribed geometry. It is found that lower crustal rheology affects the periodic time of characteristic\r\nearthquake cycles and the inter-seismic, free-surface deformation rate. In particular, the relaxation of the\r\nsurface of a cratonic region (with a relatively strong lower crust) has a characteristic double-peaked uplift\r\nprofile that persists for thousands of years after a major slip event. This pattern might be diagnostic of active\r\nfaults in cratonic regions."
+description: "The numerical modeling method for long-term tectonic deformations\r\naverages out the co-seismic fault displacement into thousands to tens of thousands of years, and neglects\r\nnear-fault damages of earthquakes; therefore, it may not be able to decipher fault activities in detail. Software\r\nsimulating earthquake rupture dynamics may not have a good estimation of background stress due to longterm\r\ntectonic deformations. In this study, we develop a numerical framework that embeds earthquake rupture\r\ndynamics into a long-term tectonic deformation model by adding inertial terms and using highly adaptive\r\ntime-stepping that can capture deformation at plate-motion rates as well as individual earthquakes. The inertia\r\nterm, which is neglected in long-term large-scale modeling methods, is considered to simulate the dynamic\r\nrupture processes. The rate-and-state frictional relationship for co-seismic fault slip is implemented in\r\nviscoelastic-plastic earth. Benchmarks of viscous flow, viscoelastic wave propagation and earthquake cycle\r\nsimulations are tested. Based on these benchmarks, we undertake a generic study of a thrust fault in crust.\r\nWe find that lower crustal rheology affects the periodic time of characteristic large earthquake cycles and the\r\ninter-seismic free surface movement. Cratons with a relatively strong lower crust due to lower temperature\r\nremain two peaks in surface uplift profiles around the fault zone for thousands of years after one characteristic\r\nearthquake, which help identify active faults in cratons."
+images:
+  landing_image:
+    src: ./graphics/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)\nand the adaptive time step used in simulation (c) for the reference model."
+  graphic_abstract:
+    src: ''
+    caption: ''
+  model_setup:
+    src: ./graphics/Fig4_BP5ModelSetup.jpg
+    caption: "Figure 4. The benchmark model BP5 for 3D sequence of earthquakes and\naseismic slip modeling. (a) A vertical planar fault is embedded in the middle\nof a homogenous, isotropic half-space with a free surface at z = 0. Fault\nbehavior is controlled by the rate-and-state friction law. A periodic boundary\ncondition is applied in y direction. (b) The velocity-weakening (VW) region\n(dark and light blue) is located within a transition zone (white), outside of\nwhich is the velocity-strengthening (VS) region (gray). In y and z directions,\nthe frictional domain and VW region are (L2, L3) and (l, w), respectively. An\ninitial nucleation zone (dark blue square with a width of w) is designed at the\nleft end of the VW region."
+animation:
+  src: ./graphics/
+  caption: ''
+model_setup_info:
+  url: ''
+  summary: "The BP5 benchmark is first simulated with a reference model size of 96 km (L1) × 100 km (L2) × 30 km\r\n(L3) by 128 × 64 × 64 quadrilateral bilinear elements. Results from the SEAS code comparison platform (https://\r\nstrike.scec.org/cvws/seas/) with the mesh resolution of 1000 m are selected for comparison in this study (Table 2).\r\nThe stress at a depth of 10 km in the middle point along the fault strike (y = 0) and the maximum slip rate along\r\nthe entire fault are tracked for comparison (Figure 5). 0.1 m/s is taken as a threshold of fault slip rate to mark\r\nthe earthquake initiation."
+model_files:
+  url: ''
+  notes: ''
+  file_tree: ''
+  existing_identifier: ''
+  nci_file_path: https://thredds.nci.org.au/thredds/catalog/nm08/MATE/yang-2023-eqcycles/catalog.html
+  include: true
+dataset:
+  url: ''
+  notes: ''
+  existing_identifier: ''
+  nci_file_path: https://thredds.nci.org.au/thredds/catalog/nm08/MATE/yang-2023-eqcycles/catalog.html
+  include: true
+metadataFile: ro-crate-metadata.json
+---