Ocean 540
Winter 2000
Problem Set #2

Due Wednesday, February 7, 2001

1. Consider the system An-Fo-Di at 1 atmosphere as a model for crystallization of the oceanic crust. (The phase diagram can be found in the notes for Lecture 6). For a liquid of the composition at point A, sketch semi-quantitatively the progression of liquid composition and solid composition as a function of fraction of liquid remaining and of temperature for closed, equilibrium conditions.
2. Suppose the rate of seafloor spreading is 10 cm/y and that sediment accumulates on this lithospheric plate at a rate of 3 cm/ky. What is the temperature at the base of this sediment layer as a function of the age of the lithosphere? What is the history of convection within the sediment if the permeability of the sediment is 10^-12 cm², 10^-11cm²?
3. In Lecture 14 there is a link to the Matlab script tidebuild.m. Use this script to generate the time series tide. Use both brute force (H=fft(h), etc) and the toolbox command psd to confirm the ~12 and ~24 periodicities present in tide. (Note: you will have difficulty resolving the two semidiurnal and two diurnal components separately, especially with the default parameters of psd; this is why tidal analysis is done via harmonic analysis). Apply a bandpass filter to separte out the two frequency paths in the time domain (You will want to use the Matlab command 'filtfilt' rather than 'filter' as used in the lecture example. This is because filtfilt is designed so as to not introduce a phase shift). Compute the comparable synthetic records and compare to your extract records. How large are the residuals?
4. Simplify equations 11-7 and 11-8 of Lecture 10 for application to upward flow and vertical conduction in a 1-dimensional sediment column. Solve this equation and apply the solution to infer the upward velocity from this profile of temperature vs depth on a ridge flank site:

   

   If the flow is driven by the buoyancy of the fluid, how permeable is the sediment?