The Earthquake Deformation Cycle
An Introduction to the Concepts of Deformation Modeling
MODELING
In order for us to model earthquakes, there are several criteria that we must meet. These are best understood when we ask ourselves the following questions:
- Are the assumptions that we make realistic?
- What are the data constraints? How much data do we have?
- Is our model testable?
Deformation modeling is a three step procedure
- Specify the geometry of the problem
- Fault geometry
- Sense of shear
- Constituitive behavior
- Elastic vs. non-elastic
- Rigidity
- Boundary conditions (the initial state)
Obviously, the more complex the factors are, the more complex the model needs to be. Caution must be used since we want to create a realistic model. Ultimately, we need to ask ourselves if what we are modeling really exists.
We'll look at the case of dislocation models in an elastic half-space
Stress boundary conditions vs. displacement boundary conditions
The typical modeling process is a process of trial and error. Simply put, it is finding a model that best describes the data. Typically, we don't have a model prior to an earthquake, so we need to take the data obtained by geologist, seismologists, and geophysicist after an earthquake and let the data lead us to a model. This is called the Inverse Theory Procedure or backwards modeling.
Dislocation theory originates from the study of how crystals deform under stress. There are three types of dislocations that are recognized:
- Edge dislocations (displacement perpendicular to the bounding surface)
- Screw dislocations (displacement parallel to the bounding surface)
- Mixed dislocations (a combination of screw and edge dislocations)
We'll look at a screw dislocation, which is similar to what goes on with strike-slip faults like the San Andreas fault in California.
Example: Screw Dislocation
We'll define a vector b called the Burger's vector that is the actual slip vector of the dislocation. Now we'll establish some boundary conditions:
- Geometry - screw dislocation
- Constituitive material behavior - linearly elastic, homogeneous, isotropic solid (ie., Hookean solid)
- Boundary condition - displacement of vector b
Now applying what we know about stress and strain, we get:
which gives us a set of 6 linearly independent equations that relate stress and strain.
Anti-plane strain gives us displacement that is not in the plane of observation. Plane strain gives us displacement in the plane of observation.
The following figures shows our screw dislocation on a cylinder.
We now use the equilibrium equations.There must be a balance of forces in the static state, so body forces cancel out.
Now to measure the displacement of the screw disclocation
Measuring the displacement of our dislocation
The greater the locking depth, the wider the zone of deformation.
Accelerated strain following an earthquake.
We can model the deformation using thick or thin lithosphere models. Unfortunately the predicted displacements are the same. We therefore have to fall back on what we know about the lithosphere in the area to generate a realistic model.
Slip in narrow shear zones vs. Flow
There is a decay in shear strain after an earthquake. We therefore need data over a long period of time to understand the earthquake cycle on a particular fault.
Notes originally prepared by David Manaker
back to EPS 216 mainpage