23.3. Mechanics of Elastic Rebound

The relationship between stress and strain in rocks follows an initially linear (elastic) path:

• Elastic region: Stress and strain are proportional.
• Yield point: Beyond this, plastic deformation begins.
• Fracture point: Rupture occurs, marking fault slip initiation.

In the mechanics of elastic rebound, the stress and strain in rocks can be visualized through a stress-strain curve. Initially, when stress is applied to the rock, it deforms elastically, meaning that it can return to its original shape once the stress is removed. This is the 'elastic region' of the graph, where stress (force applied) and strain (deformation) are directly proportional. As stress continues to increase, the material eventually reaches a 'yield point,' where it starts to deform permanently, known as plastic deformation. If the stress surpasses the yield point, the rock eventually fractures, leading to a rupture that initiates the fault slip. This process is crucial in understanding how energy is stored in the earth's crust and released during an earthquake.

Think of a rubber band: When you pull it lightly, it stretches and returns to its original shape when released. This is like the elastic region. If you pull it too far, it will be permanently stretched or even break, analogous to the yield and fracture points in rocks. This helps us understand the behavior of rocks under tectonic stresses.

• Displacement is greatest at the fault and decreases with distance.
• The amount of fault slip correlates with the amount of elastic strain previously accumulated.

Fault displacement refers to the distance that rocks on either side of a fault move past each other when a rupture occurs. The displacement is maximum at the fault line itself and diminishes with increasing distance from the fault. This means that if you are standing right at the fault, you would experience the largest movement, but as you move away, the displacement becomes less noticeable. Furthermore, this displacement is directly related to the elastic strain that has built up over time. The more strain that accumulates as tectonic forces act on the rocks, the greater the potential slip once the fault ruptures.

Imagine a stretched out slinky: if you pull on both ends (building up tension), the point where you release it will snap back furthest, while the ends may not move as much. Similarly, this concept helps visualize how fault slip works, highlighting the relationship between strain accumulation and actual fault displacement.

• Elastic potential energy per unit volume = 1σϵ where σ = stress and ϵ = strain.
• Energy builds up over years or centuries and is released in seconds during an earthquake.

Elastic energy storage involves the accumulation of energy in rocks due to applied stress. The formula given shows that the elastic potential energy stored in a rock is proportional to both the stress applied to it and the strain it experiences. Over long periods, as tectonic forces continuously act on the rocks, this energy builds up significantly. However, when a fault finally slips, this stored energy is released almost instantaneously in the form of seismic waves during an earthquake, highlighting the rapid transition from a slow accumulation of energy to a sudden release.

Think of a compressed spring: when you gradually compress it, energy builds up in the spring. If you suddenly release the spring, that energy is released all at once, causing it to expand rapidly. This analogy is similar to the way energy is stored in the Earth's crust and then released in an earthquake.

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