^{1}One simple model of earthquake behavior is called the slider-block model. Essentially, a block of mass

*m*rests on a flat surface, and it is pulled horizontally by a spring. When the force exerted by the spring equals the frictional resistance, slip occurs. The model predicts the displacement

*δl*of the slider block (corresponding to the fault displacement) and the maximum slip velocity

*v*

_{m}on the fault as

^{2}

*f*

_{s}and

*f*

_{d}are the (dimensionless) coefficients of static and dynamic friction, respectively;

*ρ*is the rock density;

*g*is the local gravitational acceleration;

*h*is the mean fault depth; and

*A*is the rupture area.

** Question 1:** Given that

*A*≈ 400 km

^{2}, what are

*δl*and

*v*

_{m}? Assume that

*S*≈ 3 × 10

^{10}Pa,

*f*

_{s}≈ 0.05, and

*f*

_{d}≈ 0.045.

** Question 2:** Suppose that tremors from body waves

^{3}are recorded 20 s apart. The fastest such waves are primary waves with speed

*v*

_{p}≈ 5.5 km/s in rock; shear waves have a corresponding speed

*v*

_{s}≈ 3 km/s. How far away is the epicenter of the earthquake? (Assume that the waves travel in straight lines from the epicenter to the recording seismometer.)

** Solution to Question 1:** To estimate

*h*, we take the geometric mean of 1 km and 70 km, or ~8 km, and take

*ρ*≈ 2500 kg/m

^{3}. Hence,

*δl*≈ 4 × 0.05 × (2.5 × 10

^{3}kg/m

^{3}) × (10 m/s

^{2}) × (8 × 10

^{3}m) × (2 × 10

^{4}m) × 0.1 ÷ (3 × 10

^{10}kg · m

^{−1}· s

^{−2}) ≈ 1.3 m.

(Note that this is not meant to be an estimate of the width of the Icelandic rock fracture in the photograph, though it appears to be of the right order of magnitude.)

Similarly, *v*_{m} ≈ 0.05 × (10 m/s^{2}) × (8 × 10^{3} m) × [(2 × 2.5 × 10^{3} kg/m^{3}) ÷ (3 × 10^{10} kg · m^{−1} · s^{−2})]^{1/2} × 0.1 ≈ 0.16 m/s.

**The time interval Δ**

*Solution to Question 2:**t*= 20 s. The distance from the epicenter is therefore

*d*≈

*v*

_{p}×

*t*≈

*v*

_{s}× (

*t*+ Δ

*t*), so after a little algebra, it follows that

## REFERENCES

*TPT Online*at https://doi.org/10.1119/5.0165482, in the “Supplementary Material” section.