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 man- tle 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 \(35 \mathrm{~km}\)
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 8
The measured declination and inclination of the paleomagnetic field in Lower Cretaceous rocks at \(45.5^{\circ} \mathrm{N}\) and \(73^{\circ} \mathrm{W}\) are \(D=154^{\circ}\) and \(I=-58^{\circ}\). Determine the paleomagnetic pole position.
Problem 11
Determine the declination and inclination of the Earth's magnetic field at Boston \(\left(\phi=42.5^{\circ}, \psi=-71^{\circ}\right)\). Use the dipole approximation to the field, but do not assume that the geographic and magnetic poles coincide.
Problem 20
Consider an RRR triple junction of plates \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C}\). The ridge between plates \(\mathrm{A}\) and \(\mathrm{B}\) lies in a north-south direction (an azimuth of \(0^{\circ}\) with respect to the triple junction) and has a relative velocity of \(60 \mathrm{~mm} \mathrm{yr}^{-1}\). The ridge between plates \(\mathrm{B}\) and C has an azimuth of \(120^{\circ}\) with respect to the triple junction, and the ridge between plates \(\mathrm{A}\) and \(\mathrm{C}\) has an azimuth of \(270^{\circ}\) with respect to the triple junction. Determine the azimuths and magnitudes of the relative velocities between plates \(\mathrm{B}\) and \(\mathrm{C}\) and \(\mathrm{C}\) and \(\mathrm{A}\).
Problem 21
Show that a triple junction of three transform faults cannot exist.
Problem 22
Consider the TTT triple junction illustrated in Figure \(1-38 .\) This triple junction is acceptable because the relative velocity between plates \(\mathrm{C}\) and \(\mathrm{A}, \mathbf{u}_{\mathrm{CA}},\) is parallel to the trench in which plate \(\mathrm{B}\) is being subducted beneath plate \(\mathrm{C}\). The trench between plates \(\mathrm{C}\) and \(\mathrm{B}\) has an azimuth of \(180^{\circ}\) so that \(\mathbf{u}_{\mathrm{CA}}\) has an azimuth of \(0^{\circ}\); assume that \(u_{\mathrm{CA}}=\) \(50 \mathrm{~mm} \mathrm{yr}^{-1}\). Also assume that the azimuth and magnitude of \(\mathbf{u}_{B A}\) are \(315^{\circ}\) and \(60 \mathrm{~mm} \mathrm{yr}^{-1} .\) Determine the azimuth and magnitude of \(\mathbf{u}_{B C}\).
