June 2017: progress Review and Chapter Outline

Today I'll present:

• overview of my research 
• structure and some content of my first four chapters
• Talk a bit about areas and questions where each of us can collaborate

Overview

Chapter 1:

problem/  :

To model the dynamics of large areas of the earth, we treat rocks as  continua - great for most of the (visco-elastic) planet, but less-so for faults, which are discontinuous. The approximation, called psuedo-plasticity, gives rise to non-linear dynamics. It can also give rise to instabilities, intractability, and significant sensitivity in relation to outcomes of interest - fault angle, internal pressure etc. Another problem is that fault thickness is tied to mesh resolution. So this chapter in a nutshell is about how do we balance stability and accuracy.  I use a two different codes, two plasticity models and an exact (analytic) solution to perform these tests.  

 

Chapter 1:

  approach /:

Underworld and Fenics are used to study:

• Non-linear stability, under different methods, Picard and Newton
• the role of compressibility in pressure-sensitive rheological models
• discontinuous analytic solutions for isotropic anisotropic models
• Implementation of a model for long term lithospheric evolution from emergent isotropic shear band to anisotropic fault networks

 

In the basic pure shear experiment, we solve the instantaneous visco-plastic problem.    

Instability increases as the characteristic (viscous) stress scale increases AS WELL AS the pressure sensitivity.

 

shear band emergence

analytic model of Barr and Houseman (1996)

pre-existing fault

effective viscosity along fault

Chapter 2:

problem /  :

The subduction zone interface is a fault that allows one tectonic plate to slide beneath another. Interface strength controls a number of observables in the subduction system: the depth limit of seismicity, the stress state of the upper and lower plate, heat flow in the mantle wedge (arc location). yet we don't know that much about changes in interface strength and width with depth.

This chapter starts with a technical question: given resolution limitations, can we make a more consistent model of the subduction interface)?

Second, did this teach us anything we didn't already know about the rheology, systematics and tradeoffs in the subduction system?

 

 

Chapter 2:

problem /  :

Our understanding of the dynamics of the subduction interface has improved greatly in past decades. However, some fundamental questions remain such as:

• how fault strength varies with depth
• what determines brittle-ductile transition and decoupling depth;
• how feedbacks tend to stabilise the long-term weakness of subduction zones;
• How different (numerical) models of the subduction interface influence stress and thermal patterns in the sz vacinity

 

 

Chapter 2:

approach /  :

• Determine the extent to which a classic brittle-ductile strength profile can allow for stable subduction, and consistency with observables.
• Assess the viability and consistency of different influences on BDT  depth
  • down dip fluid-pressure changes
  • subduction channel width variation
• Consider the role of history dependence / anisotropy in allowing for rheological symmetry in upper-lower plates

 

 

Chapter 2:

results /  

A survey of literature, reveals subduction zones are a tightly bound system of constraints, with the subduction interface rheology playing a key trade off role between these. Constraints include:

• depth to brittle-ductile transition
• decoupling depth and heat flow (may be constant?)
• critical temperature range in the wedge (velocity correlation)
• fore arc stress is neutral in many SZs
• outer rise stress is not dependent on state of megathrust cycle

Chapter 2:

results /  

 

begin with a simple approach.  The subduction interface rheology only differs from background mantle in having a different friction coefficient,  and maximum viscosity

models without thermal diffusion show that BDT depths of 40 - 50 km fall out naturally with DP friction coefficients, of 0.04, (close to values independently estimated). However, with diffusion, models require a much lower friction coefficient, or they go stagnant. This suggests that one of the assumptions I made is wrong.

fc = 0.02                           fc = 0.04

fc = 0.005                           

Chapter 3:

problem /  :

Slabs are the downwelling parts of the mantle convection system - the subducted oceanic lithosphere.  Images of slabs reveal they can be strongly deformed at a depth range of 400 - 1000 km. A number of mechanisms have been proposed for slab weakening at depth, with many being "non-inconsistent" with slab morphology. The two main questions in the chapter are:

• whether, and under what parameter ranges these models are consistent with observed slab stress state, or geoid / dynamic topography constraints,
• whether any one of these mechanisms is favoured.  

 

Chapter 3:

approach /  :

Recent modelling studies have used a variety of methods to provide slab weakening at depth.  We can generalise these approaches with the following schema:

 

 

global

local

stress

viscosity

all models

Alisic, 2010

Garel, 2014

Peterson, 2017

Temp / depth -localised stress limits are used to mimic non-Byerlee 'low-temp' plasticity, perhaps Peierls creep. Temp-localise viscosity limits might mimic the grain size effect in Karato, 2001

 

 

Chapter 3:

local viscosity reduction

global viscosity reduction

global stress truncation

Chapter 3:

The thinking here is that the end-members give rise to very different styles of deep deformation, and stress patterns:

a cold slab in the deep transition zone is characterized by a weak, fine-grained spinel region surrounded by narrow but strong regions (Karato et al. 2001)

We suggest that the slab is essentially heterogeneous and isolated deep earthquakes may lie within some isolated cold, strong and high-stress blocks (Yang et al. 2017)

 

Chapter 3:

Where do deep earthquakes originate, in the cold slab-core, or in the high-strain-rate regions (or both)?

Can quantitative comparison with global seismicity help to resolve this question?

• is a "stochastic" approach viable? point-by-point / binned?

Chapter 3:

Evolution of slabs with different upper / lower plate ages  

 

Chapter 3:

Evolution of slabs with different upper / lower plate ages. We see a competition between upper and lower plate control  

 

Chapter 3:

Chapter 4:

problem /:

Outer-rise normal faulting patterns show little or no correlation with observed oceanic plate ages, convergence rates and slab pull magnitudes,  while the role of plate coupling at the subduction interface is disputed.  But intriguingly, the presence and depth of deeper compressional-related seismicity does seem to have a strong correlation with slab pull. The intermediate seismic zone also reveals seismicity that is dependent on both unbending and in-plane stress. Double seismic zones may be the result of unbending stress, or a manifestation of metamorphic reactions. Depths and relationships should differ in each case.

 

 

Chapter 4:

  approach /:

The previous chapters hopefully provide insights into, among other things, the magnitude of slab pull, the nature of the subduction interface. We also have the ability to model existing faults, through the anisotropic rheology. In this chapter I combine these advances, as well as the additional influence of elasticity, to look at the patterns of stress in the outer rise (bending) and intermediate (unbending) regions of the subduction zone.