Numerical Simulations of Silverpit Crater Collapse: A Comparison of TEKTON and SALES 2

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Numerical Simulations of Silverpit Crater
CollapseA Comparison ofTEKTON and SALES 2

• Gareth Collins, Zibi Turtle, and
• Jay Melosh
• LPL, Univ. of Arizona

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Silverpit

• 6 km diameter
• Central peak 250 m high 750 m diameter
• Surrounded by gt10 concentric deformation rings 2
  - 10 km in diameter
• Formed in Cretaceous chalk above Jurassic shales
• 60-65 Ma

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Silverpit(Stewart and Allen, 2002)
(Allen and Stewart, 2003)
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Objectives

• Understand Silverpit
• Ring formation
• Compare 2 modeling techniques to assess
• Consistency
• Limitations
• Degree to which they are complementary

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Finite-Element Method

• Model structure as an assemblage of elements
  bounded by nodes
• Specify
• Geometry
• Material properties and rheologies
• Boundary and initial conditions
• Construct system of equations
• Solve simultaneously for displacements at nodes
• Calculate stresses using constitutive equations

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Finite-element Method Rheology

• Newtonian
• Power-law
• Plastic
• t lt c power-law t c Newtonian
• Exponential
• T temperature R ideal gas constant h
  viscosity
• H activation enthalpy A, A, sp, n
  constants
• c cohesion

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Finite-element Method Rheology

• Elastic
• Newtonian
• Power-law
• Plastic
• t lt c power-law t c Newtonian
• Exponential

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Finite-element methodConstitutive equations

• E Youngs modulus n Poissons ratio h
  viscosity

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Finite-Element Method

• Advantages
• Realistic spatial scales and timescales
• Simulation of variety of rheologies and
  geometries
• Spatial and temporal variation in material
  properties
• Reproduce complex structures, including faults
• Possible to measure credibility of solution
• Disadvantage
• Langrangian method, so significant distortion of
  mesh can lead to numerical instabilities

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Lagrangian Hydrocode Method

• Model structure as a regular grid of cells
  bounded by nodes
• Specify
• Geometry
• Material properties
• Boundary and initial conditions
• Calculate all forces acting on each cell.
• Assuming forces constant for time step, compute
  node displacements

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Lagrangian Hydrocode Rheology

• Elastic
• Newtonian fluid flow
• Plastic
• t lt Y elastic t Y Newtonian
• Yield strength Y may be a function of pressure,
  pressure vibrations, damage and internal energy.

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Hydrocode Method

• Advantages
• Realistic spatial scales and timescales
• Simulation of variety of rheologies and
  geometries
• Spatial and temporal variation in material
  properties
• Includes inertia
• Disadvantage
• Langrangian method, so significant distortion of
  mesh can lead to numerical instabilities.
• No built-in accuracy measure.

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TEKTON (Finite-Element)
SALES-2 (Hydrocode)

• Lagrangian
• Complex rheology
• Limited strength
• Faults
• No inertia

• Lagrangian
• Limited rheology
• Complex strength
• No faulting
• Inertia

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TEKTON Silverpit Mesh

• Axisymmetric
• 7 km deep, 12 km wide
• Elements 100 m x 100 m
• Boundaries
• Center and outer free vertically fixed
  horizontally
• Bottom fixed vertically and horizontally

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TEKTON Silverpit Mesh
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TEKTON Silverpit Mesh

• Transient crater
• 3 km diameter
• Excavated in uniform mesh using the Z-model
• Simple case Two materials
• Low viscosity Newtonian, h 107 Pa s
• Acoustic fluidization
• Weak layer
• Power-law, A, Q, n for dolomite (Schmid et al.,
  1977)
• Constant density, Youngs modulus, Poissons ratio

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TEKTON Silverpit Mesh
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TEKTON Silverpit Mesh
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TEKTON Silverpit Mesh
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TEKTON Silverpit Mesh
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TEKTON Silverpit Mesh
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TEKTON Silverpit Mesh
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SALES-2 Silverpit Mesh

• Axisymmetric
• 4 km deep, 23.6 km wide
• Elements 50 m x 50 m
• Boundaries
• Center free vertically fixed horizontally
• Bottom fixed vertically free horizontally
• Outer fixed vertically and horizontally

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SALES-2 Silverpit Mesh
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SALES-2 Silverpit Mesh

• Transient crater
• 3 km diameter
• Excavated in uniform mesh using the Z-model
• Simple case Two materials
• Low viscosity Newtonian, h 107 Pa s
• Acoustic fluidization
• Weak layer
• Constant density, shear modulus, Poissons ratio

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SALES-2 Silverpit Mesh
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SALES-2 Silverpit Mesh
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SALES-2 Silverpit Mesh
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Results

• Central, near-surface, deformation differs
• Comparable uplift at depth, few hundred m
• Timescales for deformation differ
• Magnitudes and orientations of surface stresses
  outside of crater are consistent
• Stress orientations and consequently fault types
  are broadly consistent with Silverpit observations

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TEKTON Silverpit results
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TEKTON Silverpit results
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SALES-2 Silverpit Results
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SALES-2 Silverpit Results
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TEKTON Silverpit Results
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TEKTON Silverpit Results
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TEKTON Silverpit Results
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TEKTON Silverpit Results