23.9. Mathematical Modeling of Elastic Rebound

Try these first

1. 1.

   What is the purpose of mathematical modeling in elastic rebound?

   Hint

   Think about what scientists need to understand about earthquakes.

2. 2.

   Define surface displacement in the context of earthquakes.

   Hint

   What happens to the land when a fault slips?

3. 3.

   What does the variable D in the equation $u(x) = \frac{D}{\pi(x^2 + h^2)}$ represent?

   • Depth of the fault
   • Slip on the fault
   • Surface displacement

   Hint

   Think about what this variable measures.

4. 4.

   True or False: The Okada equations only apply to vertical fault movements.

   • True
   • False

   Hint

   Consider the nature of fault movements.

5. 5.

   Given a fault slip of 1 meter at a depth of 5 meters, calculate the surface displacement at a distance of 10 meters from the fault using the equation $u(x) = \frac{D}{\pi(x^2 + h^2)}$.

   Hint

   Don’t forget to square the distances when inserting them into the equation!

6. 6.

   Discuss how changing the fault depth affects the calculated surface displacement and provide an example calculation for a depth of 10 meters.

   Hint

   Reflect on how the equation’s parameters interact and affect the output.