Research



The main factor which controls when and where an earthquake occurs is the state of stress. Earthquakes occur when shear stress around a fault which work towards rupturing it, overcomes the normal (or clamping) stress which prevents the fault from slipping.

For my PhD research I have looked at how stresses evolve with time (over 0-100's of years) on faults by numerically modeling[a] all the three major phases of the earthquake cycle i.e.,
  1. Long term interseismic deformation due to tectonic loading,
  2. Coseismic slip on neighboring fault segments or nearby faults and
  3. Subsequent postseismic deformation due to relaxation of a (warmer) viscous lower crust/upper mantle[b].
Specifically I have worked on tectonically active regions such as Southern California and the Northeastern Caribbean, and have used numerical results to:
  1. Estimate the current state of stress (or seismic hazard) on major faults and fault segments in the region,
  2. Explain (i) possible triggering of historic earthquakes due to stress transfer, (ii) earthquake sequences, and
  3. Explain the observed crustal velocities (measured by highly accurate GPS receivers; ~1 mm/yr) and decomposing them into their interseismic and postseismic (transient) components.
More information on these can be found in my journal publications listed below.

Currently I am looking at Central/Southern Alaska where the Pacific plate is subducting beneath the North American plate and has been the site of the world's third largest instrumentally recorded earthquake (1964, Prince William Sound) and the largest instrumentally recorded strike-slip earthquake (2002, Denali) in North America. Our objective is to first decompose the postseismic transients from GPS observations to obtain the interseismic (~steady state) velocity field (or deformation rate) which when combined with co- and postseismic deformation resulting due to large earthquakes in the past ~100 years would allow us to track the stress change since then, on major active faults. The results will allow us to quantify (in terms of stress) the seismic hazard for the region in the near future.

Some pictures of the (crudely resolved) FE mesh which I used for some of the initial numerical experiments are shown below:

        

Part of the megathrust that ruptures (as an example) is highlighted in the second figure (Y is North; X is East)



Surface velocities (0-100 years) following the rupture (3.3Mb animated gif; looped)

Advisor: Dr. Andy Freed

Journal Publications:
  1. Freed AM, Ali ST and Burgmann R, Evolution of stress in Southern California for the past 200 years from coseismic, postseismic and interseismic stress changes (Geophys. J. Int., 169, p.1164-1179)

  2. Ali ST, Freed AM, Calais E, Manaker DM and McCann WR, Coulomb stress evolution in Northeastern Caribbean over the past 250 years due to oblique subduction (Geophys. J. Int., in press)

  3. Manaker DM, Calais E, Freed AM, Ali ST et al., Plate coupling and strain partitioning in the Northeastern Caribbean (Geophys. J. Int., in press)

  4. Ali ST and Freed AM, Contemporary strain and stressing rates in Central and Southern Alaska through the earthquake cycle[c] (in preparation)

My PhD thesis is mostly made up of 1, 2 and 4 (above) which are fairly large papers.

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[a] In numerical terms the problem can be thought of as an initial boundary value problem in which the elastostatic equilibrium equation (i.e., the momentum equation minus the unsteady term in a Lagrangian reference frame) is solved along with time dependent constitutive relations (for quasi-static viscoelasticity) and loading, using, for example, the Finite element method
[b] Mantle, although it transmits shear waves on human timescales behaves as a viscous fluid over geological time scales
[c] Working title from the NSF proposal written by my advisor Dr. Freed

My general interests include (mesh based) numerical methods for PDE's (though recently I have been doing some introductory reading on particle based methods such as SPH and DEM) and parallel numerical algorithms for solving sparse linear systems. At some point in the future I might also consider working on problems involving large deformation and high strain rates such as those observed during hypervelocity impacts (for example during asteroid collision) and are modeled using shock codes (also called hydrocodes) that simulate compressible dynamics usually in an arbitrary (or a coupled) Eulerian-Lagrangian frame.

On and off I also like to read literature on turbulence modeling, problems involving fluid structure interaction and multiphase flow in porous media (the latter in the context of reservoir engineering).