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Earthquake data from a subduction zone are shown in the following table. What is the slope of the subducting plate in m/km?
Distance from Trench (km) |
Earthquake Depth (km) |
|
1 |
12.1 |
4.2 |
2 |
25.4 |
9.1 |
3 |
33.2 |
11.8 |
4 |
48.6 |
17.6 |
5 |
75.7 |
28.4 |
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The slope of the subduction zone in m/km.
Answer to Problem 14PEB
Solution:
The average slope of the subduction zone is
Explanation of Solution
Given data:
The following data has been provided:
Distance from Trench (km) |
Earthquake Depth (km) |
|
1 |
12.1 |
4.2 |
2 |
25.4 |
9.1 |
3 |
33.2 |
11.8 |
4 |
48.6 |
17.6 |
5 |
75.7 |
28.4 |
Formula used:
Write the expression for slope.
Here,
Write the expression for the average slope.
Here,
Explanation:
The upper surface of the subduction plate is delineated by the earthquake foci and thus the distance of the earthquake from the trench and the depth can be used to determine the slope of the subducting plate. Consider the depth of earthquake on the
Case 1: Convert
Here,
Calculate the slope when the earthquake depth is
Substitute
Consider case
Case 2: Convert
Calculate the slope when the earthquake depth is
Substitute
Consider case
Case 3: Convert
Calculate the slope when the earthquake depth is
Substitute
Consider case
Case 4: Convert
Calculate the slope when the earthquake depth is
Substitute
Consider case
Case 5: Convert
Calculate the slope when the earthquake depth is
Substitute
Now, calculate the average slope of the subducting plate.
Substitute
Conclusion:
The average slope of the subduction zone is
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