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The article “Insights into Present-Day Crustal Motion in
Chapter 3, Problem 9SE(choose chapter or problem)
The article “Insights into Present-Day Crustal Motion in the Central Mediterranean Area from GPS Surveys” (M. Anzidei, P. Baldi, et al., Geophysical Journal International, 2001:98–100) reports that the components of velocity of the earth’s crust in Zimmerwald, Switzerland, are \(22.10 \pm 0.34\) mm/year in a northerly direction and \(14.3 \pm 0.32\) mm/year in an easterly direction.
a. Estimate the velocity of the earth’s crust, and find the uncertainty in the estimate.
b. Using your answer to part (a), estimate the number of years it will take for the crust to move 100 mm, and find the uncertainty in the estimate.
Equation Transcription:
Text Transcription:
22.10 pm 0.34
14.3 pm 0.32
Questions & Answers
QUESTION:
The article “Insights into Present-Day Crustal Motion in the Central Mediterranean Area from GPS Surveys” (M. Anzidei, P. Baldi, et al., Geophysical Journal International, 2001:98–100) reports that the components of velocity of the earth’s crust in Zimmerwald, Switzerland, are \(22.10 \pm 0.34\) mm/year in a northerly direction and \(14.3 \pm 0.32\) mm/year in an easterly direction.
a. Estimate the velocity of the earth’s crust, and find the uncertainty in the estimate.
b. Using your answer to part (a), estimate the number of years it will take for the crust to move 100 mm, and find the uncertainty in the estimate.
Equation Transcription:
Text Transcription:
22.10 pm 0.34
14.3 pm 0.32
ANSWER:Solution 9SE
Step1 of 3:
We have article that Insights into Present Day Crustal Motion in the Central Mediterranean Area from GPS Surveys reports that the components of velocity of the earth’s crust in Zimmerwald, Switzerland, are 22.100.34 mm/year in a northerly direction and 14.3
0.32 mm/year in an easterly direction.
That is and
Here our goal is:
a).We need to Estimate the velocity of the earth’s crust, and find the uncertainty in the estimate.
b).We need to estimate the number of years it will take for the crust to move 100 mm, and find the uncertainty in the estimate by using our answer to part (a).
Step2 of 3:
a).
Let us consider the measured northerly component of velocity is X and the measured easterly component of velocity is Y.
Now, the velocity of Earth’s crust is estimated by using the formula
From the given information we have X = 22.10 and Y = 14.3
Then
=
=
=
= 26.3229
Hence, 26.3229.
1).Differentiate with respect X then we get
Let us take u =
Apply chain rule to differentiate above equation we get
=
Hence, =
Substitute “u” value in above equation we get
=
=
=
Therefore, =
Consider