The main factor that controls when and where an earthquake occurs is the state of stress on the fault. Earthquakes occur when shear stresses around a fault which work towards rupturing it, overcome the force of static friction (due to normal or clamping stress) which prevents the fault from slipping.

For my PhD research I have looked at how stresses evolve with time (over 100's of years) on faults by modeling all the three major phases of the earthquake cycle i.e.,
  1. Long term interseismic deformation due to tectonic loading,
  2. Coseismic slip (or earthquakes) on neighboring fault segments or nearby faults, and
  3. Subsequent postseismic deformation due to relaxation of a viscous lower crust/upper mantle.
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 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) while decomposing them into their interseismic and postseismic (transient) components.
More information on these can be found in the publications listed below.

Recently I have been looking at Southcentral Alaska where the Pacific plate is subducting beneath the North American plate and has been the site of the world's second largest instrumentally recorded earthquake (1964, Prince William Sound) and the largest instrumentally recorded strike-slip earthquake (2002, Denali) in North America. Our objective has been to (i) decompose the GPS observations into postseismic transients and secular interseismic (~steady state) velocity-field using self consistent numerical[a] models and (ii) to calculate the evolution of stress on major active faults due to co-, post- and inter-seismic deformation over the past ~100 years. The results allow us to quantify seismic hazard (in terms of stress increase) for the region in the near future.

A picture of the discretized geometry which I used for some of the initial numerical experiments is shown below along with some results (for a simplified, 1964 type rupture):


Total elements: 188186; Total nodes: 35661
(Y is North and X is East)

Pattern of horizontal (arrows) and vertical (colors; red being uplift and blue subsidence) velocities over a 100 year period following the rupture (~3.2 Mb animated gif)


Map of Alaska showing GPS observations and the location of the 2D cross-section (B-B') plotted below. The southeast trending green arrows, observed in the GPS data (near the Bruin Bay Fault) can be attributed to the relaxing of the viscous lower crust/mantle


Model results compared to observations
(The interseismic velocity vectors are not shown)

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 (some results are shown here)

  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 coseismic, postsesimic and interseismic deformation, Geophys. J. Int., 174, p.904-918

  3. Manaker DM, Calais E, Freed AM, Ali ST et al., Plate coupling and strain partitioning in the Northeastern Caribbean, Geophys. J. Int., 174, p.889-903

  4. Ali ST and Freed AM, Contemporary deformation and stressing rates in Southern Alaska (submitted to Geophys. J. Int.)

My thesis is mostly made up of 1, 2 and 4 above.


Some other papers on regional stress evolution:
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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 (with special techniques such as split-nodes, cohesive elements (with Lagrange multipliers) etc. to handle/implement fault slip).

My broader interests include: using (mesh based) numerical methods to solve PDE's. In the near future I am also considering to use the extendend finite element method (X-FEM) for solving problems in crustal dynamics.