For more details on these completed projects please see the publications
list for each projects.
Estimating Friction on Reactivated Abyssal-hill Faults in Subduction Zones
Billen, M. I., E. Cowgill, and E. Buer. Determination of Fault Friction from Reactivation of
Abyssal-Hill Faults in Subduction Zones, Geology, 35(9), 819-822, doi:10.1130/G23847A,
2007.
This was a fun and different project for me which used 3D failure analysis and
basic continuum mechanics to place constraints on the lower bound of friction
on abyssal-hill faults in subduction zones. The key to study is the observation
that only abyssal-hill faults that are oriented within 25 degrees from trench-parallel
when they approach the trench are reactivated; in all other cases, new faults
form sub-parallel to the trench (or bending axis). This observation, with a
few other reasonable assumptions about the stress-state allows you to constrain
the minimum friction on the faults to be only about 30% weaker than the
surrounding rock. If the faults were weaker than this, then they would be
reactivated at higher angles.
Sketch illustrating the orientation of reactivated abyssal-hill faults and
the orientation of new faults within the outer-trench wall of a subduction zone.
Results of 3D failure analysis displayed on a Mohr Circle diagram. Red squares
indicate the orientation of new faults, which always form parallel to the trench
(in the x1-x3 plane). Green circles and blue triangles are abyssal hill faults
that are reactivated or are not reactivated, respectively. Each observation is
plotted three times, assuming fault dips of 30, 45 or 60 degrees. The lines labeled
0.3 through 0.85 are frictional failure envelopes. The point at which a line
crosses the transition from not-reactivated to reactivated abyssal-hill faults
indicates the minimum friction required to match the observations: if the
faults dip 45 degrees, this occurs for friction of 0.6.
Lithospheric Instabilities in Oblique Convergent Margins
Billen, M. I. and G. A. Houseman, Lithospheric Instability in
Obliquely Convergent Margins: San Gabriel Mountains, southern California ,
Journal of Geophysical Research, 109(B1), B01404 10.1029/2003JB002605, 10 January 2004.
This is a completed a project from my time as a post-doc at the University of Leeds
working with Dr. Greg Houseman.
This research focused on the role of weak zones in modifying the deformation of g
ravitationally unstable dense continental lithosphere in convergent margins.
This research is aimed at characterizing the signature of lithospheric instabilities
in observations of surface velocity and topography and will form the groundwork for
using these observations to constrain the importance of lithospheric instabilities in
continental convergent margins such as the Southern California Transverse Ranges
and the Southern Alps of New Zealand.
Final Model for Deformation across the San Gabriel Mountains
By running a series of models to investigate the response of topography and
convergence velocity to changes in the lithosphere viscosity, crust-mantle
viscosity ratio and weak zone viscosity and width, we found that only a small
subset of these models could explain the observed deformation and timing of
deformation in the San Gabriel Mountains along the San Andreas Fault in
southern California. The weak zone in these models is postulated to be due
to weakening of the lithosphere though non-linear response to large strike-parallel
strain-rate. The weak zone, then acts to localize strike-perpendicular deformation,
causing a steep, narrow region of uplift.
Dynamic Models of Subduction Zones
Billen, M. I., M. Gurnis and M. Simons, Multiscale Dynamic Models of the Tonga-Kermadec
Subduction Zone, Geophysical Journal International, 153, 359-388, 2003.
Billen, M. I. and M. Gurnis, A Comparison of Dynamic Models in the Aleutian and
Tonga-Kermadec Subduction Zones, Geochemistry, Geophysics
and Geosystems, 4(4), 1035, doi:10.1029/2001GC000295, 2003.
Billen, M. I. and M. Gurnis, A Low Viscosity Wedge in Subduction
Zones , Earth and Planetary Science Letters, 193, 227-236, 2001.
In modelling the dynamics of the Tonga-Kermadec subduction zone using
finite element analysis, I have worked with Mike Gurnis to improve the modelling
techniques to include realistic 3-D geometry of the subduction zone and
sinking slab (based on earthquake locations and tomography
images) in spherical coordinates, faults between major plate boundaries
and to use various geophysical observations as constraints on the physical
models. Together, observations of the geoid, gravity, dynamic topography,
stress field and strain rates reduce the number of plausible models and begin
to allow interpretation of surface observables, on short to long
length-scales, in terms of specific features of the models: radial variations
in viscosity versus lateral heterogeneities, response to crustal fault geometry
versus viscously controlled deformation, depth and location of driving
forces.
Cross section of temperature (bottom) and Viscosity (top) with a low viscosity wedge
Cross section showing change in back-arc and fore-bulge topography due to a low viscosity wedge
Marine Geophysics and Tectonics
Billen, M. I. and M. Gurnis, Constraints on Subducting Plate Strength
within the Kermadec Trench, Journal of Geophysical Research, 110, B05407,
doi:10.1029/2004JB003308, 2005.
Billen, M. I. and J. Stock, Origin and Morphology of the Osbourn Trough,
Journal of Geophysical Research, 105(B6), 13481-13490, June 2000.
Since I was first introduced to tectonic studies and marine geophysics, I have
participated in one expedition and two data collection transits, one of which
offered me the opportunity to oversee a survey of the inner trench wall of
the Tonga-Kermadec subduction zone (TKSZ) and the Osbourn Trough. The survey
of the TKSZ was motivated by the need for a better understanding of the
evolution of the strength of oceanic plates as they turn
into the mantle. Following this cruise several other trench-parallel lines
of bathymetry were collected and analysed using topography-gravity admittance
to determine how the strength of the plate changes in the outer rise of the
trench. We found that the effective elastic plate thickness dropped from around
50 km seaward of the outer rise to less than 5 km at the trench axis.
Swath bathymetry along the inner trench wall of the Kermadec Trench
The survey of the Osbourn Trough had two motivations. The first
was to discover the origin of the trough. Small and Abbott (1999)
suggested that this trough, visible in the gravity field, could be a recent
crack in the Pacific Plate caused by subduction of
the Osbourn Seamount at the intersection of the Tonga and Kermadec trenches,
rather than an extinct spreading center as suggested by Lonsdale (1997).
The second motivation was to constrain the age of this trough, if it was a
spreading center, thus contributing to the data available for tectonic studies
in this region. A short three line survey perpendicular to the trough
collected swath bathymetry, gravity, magnetic and echo sounder data.
Morphologic studies of the bathymetry image revealed that this trough is
an extinct spreading center and together with modeling of the gravity data
constrained the shape and depth extent of the trough and the spreading rate.
Modeling of the magnetic data provided the first constraint on the age of the
oceanic crust in this region to the end of the Cretaceaous Quiet zone (72 Ma).
3-D perspective view of swath bathymetry map across the Osbourn Trough
