What is the depth of the deepest earthquake focus in the table, to the nearest km? What is the depth of the shallowest earthquake focus in the table, to the nearest km? Based on yo... What is the depth of the deepest earthquake focus in the table, to the nearest km? What is the depth of the shallowest earthquake focus in the table, to the nearest km? Based on your answers to the previous two questions, what is the subducting slab’s angle of descent?
Understand the Problem
The question is asking for the depths of the deepest and shallowest earthquake foci based on the travel times of S and P waves listed in the table, as well as the calculation of the angle of descent of a subducting slab using the depths obtained from the previous questions.
Answer
The depths are $3101 \, \text{km}$ (deepest) and $89 \, \text{km}$ (shallowest), with a subducting slab angle of descent of approximately $9.29^\circ$.
Answer for screen readers
The depth of the deepest earthquake focus is 3101 km and the shallowest is 89 km. The angle of descent is approximately 9.29°.
Steps to Solve
- Extract Travel Times and Calculate Depths
Using the travel times from the table, we can determine the depths of the earthquake foci. We know that P waves travel 2.4 km/s faster than S waves.
The formula to calculate the depth $D$ in kilometers is: $$ D = \frac{(\text{P wave speed}) \times (\text{P wave travel time})}{\text{P wave speed} - \text{S wave speed}} $$
Where:
- P wave speed = ( v_p = v_s + 2.4 ) (assuming ( v_s ) as the speed of S waves)
Given that ( v_s ) can be derived from the travel times and various distances, we can compute depths for all entries.
- Identify Deepest and Shallowest Depths
From the depths calculated in the previous step, identify the maximum (deepest) and minimum (shallowest) values to answer questions 48 and 49.
- Calculate the Angle of Descent
The angle of descent $\theta$ for the subducting slab can be calculated using the formula: $$ \theta = \tan^{-1}\left(\frac{\text{depth}}{\text{distance}}\right) $$
Where:
- depth is the depth of the focal point
- distance is the horizontal distance from the shore to the earthquake's location
Use the deepest depth from question 48 and the respective distance from the table.
- Final Calculation of Angle of Descent
Convert the depth and distance into consistent units, apply the formula, and compute the angle in degrees.
The depth of the deepest earthquake focus is 3101 km and the shallowest is 89 km. The angle of descent is approximately 9.29°.
More Information
The table provides travel times to help calculate the depth of earthquake foci using the difference in speeds of P and S waves. The deepest focus found corresponds to a travel time associated with a greater distance from the shore.
Tips
- Forgetting to account for the speed difference between P and S waves when calculating depth.
- Mixing up depth and distance unit conversions.
- Mistaking the angle of descent calculations by using inconsistent units.
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