Problem 1
If the area of the oceanic crust is \(3.2 \times 10^{8} \mathrm{~km}^{2}\) and new seafloor is now being created at the rate of \(2.8 \mathrm{~km}^{2} \mathrm{yr}^{-1}\), what is the mean age of the oceanic crust? Assume that the rate of seafloor creation has been constant in the past.
Problem 2
At what depth will ascending mantle rock with a temperature of \(1600 \mathrm{~K}\) melt if the equation for the solidus temperature \(T\) is $$ T(K)=1500+0.12 p(\mathrm{MPa}) $$ Assume \(\rho=3300 \mathrm{~kg} \mathrm{~m}^{-3}, g=10 \mathrm{~m} \mathrm{~s}^{-2},\) and the mantle rock ascends at constant temperature.
Problem 3
If we assume that the current rate of subduction, \(0.09 \mathrm{~m}^{2} \mathrm{~s}^{-1}\), has been applicable in the past, what thickness of sediments would have to have been subducted in the last 3 Gyr if the mass of subducted sediments is equal to one-half the present mass of the continents? Assume the density of the continents \(\rho_{c}\) is \(2700 \mathrm{~kg} \mathrm{~m}^{-3},\) the density of the sediments \(\rho_{s}\) is \(2400 \mathrm{~kg} \mathrm{~m}^{-3},\) the continental area \(A_{c}\) is \(1.9 \times 10^{8} \mathrm{~km}^{2},\) and the mean continental thickness \(h_{c}\) is \(35 \mathrm{~km}\). A MATLAB code for the solution of this problem is provided in Appendix \(D\). An introduction to the use of MATLAB is given in Section 11.2 .
Problem 5
Assume that the Earth's magnetic field is a dipole. At what distance above the Earth's surface is the magnitude of the field one-half of its value at the surface?
Problem 6
The measured declination and inclination of the paleomagnetic field in Upper Triassic rocks at \(41.5^{\circ} \mathrm{N}\) and \(72.7^{\circ} \mathrm{W}\) are \(D=18^{\circ}\) and \(I=12^{\circ} .\) Deter- mine the paleomagnetic pole position. A MATLAB code for solving this problem is given in Appendix \(D\).
Problem 7
The measured declination and inclination of the paleomagnetic field in Oligocene rocks at \(51^{\circ} \mathrm{N}\) and \(14.7^{\circ} \mathrm{E}\) are \(D=200^{\circ}\) and \(I=-63^{\circ} .\) Determine the paleomagnetic pole position. A MATLAB code for solving this problem is given in Appendix \(D\).
Problem 18
What is the relative plate velocity between the Nazca and South American plates at Lima, Peru \(\left(12^{\circ} \mathrm{S},\right.\) \(\left.77^{\circ} \mathrm{W}\right) ?\) A MATLAB code for solving this problem is given in Appendix \(D\).
