Lecture-12 1 Lecture #12- Elastic Rebound

Lecture-12 2 Stress and Strain F Two of the key physical concepts used to understand earthquakes and seismic waves are: –Stress –Strain

Lecture-12 3 Stress F Stress is a force per unit area: stress = force / area where force = mass x acceleration F Thus, units for stress are: [(kg)(m/s 2 )](1/m 2 ) = N/m 2 = Pa (pascal)

Lecture-12 4 Stress F An example of stress is pressure. F At what depth in the Earth is the pressure the largest? F Why are deep sea vehicles (Alvin) small ??

Lecture-12 5 Stress When a material is stressed it can respond in different ways: Fdeform (change shape or volume) – this is often elastic behavior and the material returns to its former shape when the stress is eliminated. (In plastic deformation that material does not return to its original state). Fflow - this would be viscous (fluid) behavior. The material does not return to its former shape when the stress is elimated. This is ductile behavior. Ffracture – this is brittle behavior, and can only occur in solids. The material does not return to its former state when the stress is eliminated.

Lecture-12 6 Stress F Tall buildings are designed so that they sway back and forth at the top. F Is this a good idea? Why? F Yes! If the buildings did not accommodate stresses (from winds) by deforming elastically they would have to accommodate them by fracturing …

Lecture-12 7 Strain F Strain is the deformation in a solid that has been induced by an applied stress. F Strain has no units, it is dimensionless.

Lecture-12 8 Strain F Example: If I take a rubber band that is 5 cm long and I stretch it so that it becomes 6 cm long the strain is: F Strain = 1 cm / 5 cm = 0.20 or 20% F There are no units for strain.

Lecture-12 9 Strain F Some materials will strain a lot from a tiny stress while others will strain very little from a large stress F The relationship between stress and strain is thus a material property (like density) F This stress-strain relationship is known as the rheology of the material.

Lecture Strain F Even though strain is the result of an applied stress, it can itself be a source of a new stress. This new stress can then cause a strain itself: stress -> strain -> stress -> stress … chicken -> egg -> chicken -> egg …

Lecture Elastic Energy F When you strain an elastic material, it stores the energy that you used to deform it. F When given an opportunity, an elastic material can release the stored energy.

Lecture Earthquakes & Strain F An earthquake is the catastrophic release of strain energy stored in the rocks around a fault. F Where does the energy come from? –Moving plates which are driven by gravity and heat from Earth’s interior.

Lecture A “Creeping” Fault

Lecture Fault Friction F Friction is a stress that resists motion. As plates slide past one another along a fault, the friction on the fault holds the plates together. F The moving plates store elastic strain energy in the rocks surrounding the fault. The strained rocks exert a stress on the fault.

Lecture A Locked Fault This is a “snapshot” of the strain surrounding a fault at an instant of time.

Lecture Earthquake Energy F During an earthquake, most of the strain energy is converted to heat, only a few percent is converted to seismic waves. F But that’s still enough to generate the powerful shaking that topples structures.

Lecture Reid’s Elastic Rebound Model F Soon after the 1906 San Francisco earthquake, H. F. Reid proposed a hypothesis to explain earthquake occurrence. F Reid’s elastic rebound model includes earthquakes in a cycle of strain build-up and strain release.

Lecture The Elastic Rebound Model

Lecture Reid’s Earthquake Cycle

Lecture Earthquakes F Stress is applied to a locked fault by the relative motion of the tectonic plates. F The material near the fault deforms in response to these stresses and is strained. F When the stress becomes too large the fault fractures and relieves (drops) the stress. This is an earthquake.

Lecture Earthquakes F As the material near the fault releases the elastic energy it has stored up it “snaps” back into place. F The fault does not snap perfectly back into place and the new configuration increases the stress in certain patches of the fault. F These new, smaller, stresses cause strains which are often released in more “snaps” (aftershocks), which cause smaller aftershocks themselves in a cascade of earthquakes.

Lecture Earthquakes Are More Complex F Earthquakes do not follow the simplest form of the elastic rebound theory. F A number of complications make the deformation cycle difficult to predict. For example: u Variations in fault strength and structure u Fault interactions F Unraveling these is difficult because our observations are so short.