numerical simulations of silverpit crater collapse: a comparison of tekton and sales 2 gareth...

Numerical Simulations of Silverpit Crater Collapse:

A Comparison ofTEKTON and SALES 2

Gareth Collins, Zibi Turtle, and

Jay Melosh

LPL, Univ. of Arizona

Silverpit(Stewart and Allen, 2002)

(Allen and Stewart, 2003)

Objectives

• Understand Silverpit• Ring formation

• Compare 2 modeling techniques to assess:• Consistency• Limitations• Degree to which they are complementary

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

€

vf = K

v d

Finite-element Method: Rheology• Elastic

• Newtonian

• Power-law

• Plastic• < c: power-law; ≥ c: Newtonian

• Exponential

€

ε =σE

€

˙ ε = Aσ n exp −H

RT

⎛ ⎝ ⎜

⎞ ⎠ ⎟

€

˙ ε = A' exp −H

RT1 −

σ

σ p

⎛

⎝ ⎜

⎞

⎠ ⎟

2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

˙ ε =σ

η

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:

€

vx =

v f i∑

mΔt2

Lagrangian Hydrocode: Rheology

• Elastic

• Newtonian fluid flow

• Plastic• < Y: elastic; ≥ Y: Newtonian• Yield strength Y may be a function of pressure,

pressure vibrations, damage and internal energy.

€

ε =σE

€

˙ ε =σ

η

TEKTON (Finite-Element)

• Lagrangian

• Complex rheology

• Limited strength

• Faults

• No inertia

• Lagrangian

• Limited rheology

• Complex strength

• No faulting

• Inertia

SALES-2 (Hydrocode)

TEKTON Silverpit Mesh

TEKTON Silverpit Mesh

TEKTON Silverpit Mesh

TEKTON Silverpit Mesh

TEKTON Silverpit Mesh

TEKTON Silverpit Mesh

TEKTON Silverpit Mesh

SALES-2 Silverpit Mesh

SALES-2 Silverpit Mesh

SALES-2 Silverpit Mesh

SALES-2 Silverpit Mesh

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