My general research interests are focused on learning about the
rheologic structure of the lithosphere and mantle. I use a variety of numerical and
analytical methods to predict how the Earth might deform given a particular
rheologic structure and then compare these predictions to observations. This page
describes some the projects that I, and my graduate students, are currently
working on.
Much of the research I do is focused on subduction zones and uses
3-D finite element models to study how observations at the surface
depend on variations in the strength of the rocks and modes of deformation
deep in the mantle. These numerical models are run on the Mantle Dynamics Beowulf
Cluster, AMALA.
Some Background on Subduction Dynamics
The thermal structure in subduction zones strongly influences where
melting occurs beneath island arcs and if subducting crust undergoes
melting in addition to dehydration. The thermal structure of the shallow mantle in
subduction zones depends on parameters such as the rate of subduction, age of the
subducting plate and the viscosity structure in the upper mantle and lithosphere.
However, since the viscosity is both temperature and strain-rate dependent (as well
as depending on the presence of water and/or melt), the thermal evolution and viscosity
structure of a subduction are dependent on each other.
Cartoon illustrating some of processes occuring in a subduction zone, which
influence the viscosity structure and slab dynamics.
Previously, I have investigated how variations in the viscosity structure
affect observations of topography, gravity and stress in instantaneous
models of subduction zones, and found that a localized region of low viscosity
within the mantle wedge was needed to match observations
(Completed Research). In these models, the thermal
structure is imposed independent of the viscosity for the present configuration of a particular
subduction zone. Similarly, several researchers have investigated the steady-state
thermal structure of subduction zones, using corner-flow type models of flow
within the mantle wedge driven by a plate subducting at a fixed dip and velocity.
Both of these approaches have their advantages and disadvantages.
Dynamic Interaction of the Samoan Plume and Tongan Slab
This is a new NSF-CSEDI collaborative project with Stan Hart, John Collins, Greg Hirth,
Mark Behn, Matt Jackson (all from WHOI), and Chris Kincaid (from Univ. of Rhode Island)
to model the recent (less than 10 million years) interaction between the Samoan plume
and the Tongan slab. Until recently these two features were separated by a large distance in
the mantle (more than 1000 km), but the Tongan subduction zone has been steadily rolling back
towards Samoan plume and they are now only a few hundred kilometers apart. This rare interaction
provides a special opportunity to use observations of their interaction to learn about
the length-scales of mantle flow, entrainment of geochemical signatures and the viscosity
structure of the upper mantle.
Figure illustrating the possible flow pattern around the northern edge of the Tongan
slab in the vicinity of the Samoan plume.
Rheologic Controls on Subduction Dynamics
Billen, M. I. and G. Hirth. Rheologic Controls on Slab Dynamics, Geochemistry, Geophysics,
Geosystems (G3), 8, Q08012, doi:101029/2007GC001597, 2007.
Billen, M. I. and G. Hirth, Newtonian versus Non-Newtonian Upper Mantle Viscosity:
Implications for Subduction Initiation, Geophysical Research Letters, 32(19), L19304,
doi:10.1029/2005GL023457, 2005.
In my current research, I am working to make more realistic models of subduction in order to
understand how the viscosity and thermal structure evolve in time. In these
models, subduction is driven by velocity boundary conditions on the surface, but
flow within the mantle evolves dynamically. This allows us to study both how the
viscosity structure affects the evolution of the slab and its thermal structure
and how this couples to the flow and thermal structure of the mantle wedge.
The rheologic law we use is a combination of diffusion creep (in the lower mantle
and warm, low strain-rate regions), dislocation creep (in warm, high strain-rate
regions) and a yield stress criterion at low temperatures.
Evolution a slab at three time-steps. The combination of
a strong slab, non-newtonian viscosity, sufficient resolution (2.5 km)
and a large enough box (6000 x 2890 km) makes it possible to
reproduce the observed dips of slab between 30 and 90 degrees.
Once we understand how the viscosity structure influences the deformation, we will use
both geophysical observations (topography, geoid, stress) and geochemical observations
(pressure and temperature of melting beneath island-arcs) to constrain which viscosity
structure is most consistent with these observations in different subduction zones.
This is a just completed project, funded my the NSF-MARGINS program in collaboration with Drs.
Greg Hirth of the Woods Hole Oceanographic
Institution and Peter Kelemen of the Lamont-Doherty Earth Observatory.
Geodynamic Framework for the Tectonic Trigger of Late Neogene Deformation in
Southern Alaska (Margarete Jadamec
PhD Thesis Project)
Jadamec, M., M. I. Billen and O. Kreylos. Slab Geometry and Plate Boundary Deformation:
3D Numerical Models of the Plate Boundary Corner in Southern Alaska. Subduction Zone
Geodynamics Conference, Montpellier, France, 2007.
Jadamec, M., and M. I. Billen. Influence of Slab Geometry on Diffuse Plate Boundary Deforma-
tion: 3D Numerical Models of the Plate Boundary Corner in Southern Alaska. Eos Trans.
AGU, 87(52), Fall Meet. Suppl., Abstract T23B-0491, 2006.
This project, funded by the NSF-EAR-Tectonics program, is directed at understanding
the cause of recent uplift of the Central Alaska Range located more than 500
kilometers from the active subduction zone in southern Alaska. The approach is to
build geodynamic models that incorporate the observed 3D structure of the subducting
slab and overriding continental plate, and then to test various hypothesis for how
the convergence is transferred to the region of the Central Alaska Range. These
models use a realistic rheology including Newtonian, non-Newtonian and yielding
behavior, and model the plate boundary as a low viscosity shear zone.
Creating smooth, continuous input data from the complex 3D structure of Alaska and
analyzing the 3D flow field has posed several computing challenges. These challenges
have been overcome, in part, through collaboration with computer scientists with
expertise in scientific visualization through the KeckCAVES
collaboration.
Color slices of the 3D viscosity structure of the southern Alaska Slab viewed
using the Visualizer
software developed by KeckCaves. The 3D structure of the
slab is determined from slab seismicity and tomography, while the overriding
plate structure depends on the age (lithospheric thickness) of accreted terranes.
Deformation in the overriding plate depends on coupling between the subducting plate
and the overall viscosity structure.
Dynamics of Slab Detachment (Erin Andrews,
PhD Thesis Project)
Andrews, E. and M. I. Billen. Rheologic Controls on Slab Detachment, Tectonophysics Special
Volume on Slab Detachment, in revision, 2007
Andrews, E. R., and M. I. Billen. Numerical Models of the Dynamics of Slab Detachment. Eos
Trans. AGU, 87(52), Fall Meet. Suppl., Abstract T11B-0441, 2006.
Slab detachment (or break-off) may
occur in subduction zones following an event such as continent or
ridge collision with the trench, which prevents the existing slab
from effectively pulling the unsubducted lithosphere into the
mantle. However, even the most basic aspects of deformation
accompanying slab detachment are not understood; for example, does
the location detachment initiates in the slab (top or bottom
surface) influence the resulting deformation? The proposed
research is the first to explore slab detachment using
fully-dynamic, numerical models of thermal convection, (in 2-D and
3-D spherical geometry), capable of treating both the process of
detachment and its geological expression.
Cartoon Illustrating Two Simple Detachment Scenarios:
(A) Case 1: possible mantle flow following slab
detachment initiated at the base of the slab. (B) Case 2: possible
mantle flow following slab detachment initiated along the top of
the slab. Star indicates location of detachment initiation.
Our aim is to characterize the dependence of slab detachment
dynamics on the rheologic structure of the lithosphere, slab and
upper mantle, including the importance of lateral changes in
lithospheric/slab structure due to age, composition, subduction
velocity and geometry. Existing geological and geophysical
observations will provide the constraints on the numerical models,
which are necessary to infer the thermal and viscosity structure
active during slab detachment. We will then design 3-D models
including the observed, past plate geometry and plate motions for
southern Baja California in the late Miocene, in order to test
whether the observed deformation and magmatism following
ridge-trench collision is consistent with the proposed mechanism
of shallow slab detachment and to constrain the viscosity
structure. Geological observations on the timing of
deformation in this region, provide unique constraints on the slab
detachment process.
The results of two preliminary models, included in the proposal,
demonstrate the influence of rheology on the detachment process.
Based on these exploratory models and the results of previous
research, we expect to find that: (1) slab detachment will occur
for a range of model parameters, but the location, timing and mode
of detachment will depend strongly on the choice of rheology,
pre-existing viscosity variations (weak zones), surface plate
motion, and geometry; (2) for a subset of these models, the
resulting mantle flow will lead to geologically observable changes
in deformation and thermal structure; and (3) for the Baja
California/western Mexico region, there are two competing
time-scales, a detachment induced flow time-scale versus a
plate-boundary force time-scale, which determine the relative
contribution of slab detachment to the observed deformation.
Results from preliminary slab detachment model,
demonstrating the numerical methods and ability to model the
detachment processes and resulting deformation and thermal
structure. (A-B) Cross section of model results for case 1 at time
t1 and t2: viscosity (shading) and thermal structure
(contours every 200 deg C) and velocity vectors. (C-D) Model
results for case 2 at t1 and t2. (E) Dynamic topography
profiles at t1 (solid) and t2 (dashed) for case 1
(black) and case 2 (gray). (F) Stress-state, given by
maximum horizontal compression stress as a function of time from detachment
initiation for case 1 (black) and case 2 (gray).
Placing constraints on the upper mantle viscosity structure, is
essential to understanding the rheologic controls on mantle
convection and plate tectonics. The viscosity structure in
subduction zones plays a vital role in regulating plate velocities
and may be an important controlling factor on efficiency of mantle
convection. Developing a fuller understanding of slab detachment
dynamics provides a unique opportunity to constrain upper mantle
viscosity structure by integrating analysis of geological
observations with numerical modelling.
If I'm doing what I'm suppose to be doing, this page will
forever be under construction.
Last update September, 2007.
