PROBLEM SET 2

 

 

1. Cox & Hart:  Problem 8-1.  Do sections a, b, d, and g.

 

2.  Using the Heirtzler et al. model of marine magnetic anomalies, compute the average rate of sea-floor spreading for (a) the South Atlantic, (b) the North Pacific, and (c) the South Pacific oceans.  [Note that the distance and time scales differ for each profile.]  Specify whether the spreading rate is full- or half-rate.  Do you think these spreading rates were constant through time?  Why or why not?

 

3.  Based on a model of oceanic lithosphere cooling and contracting as it migrates laterally from a spreading ridge, we can predict the variation of heat flow and bathymetry with age of the lithosphere.  A theoretical model presented by Turcotte and Schubert (1982) predicts the variation in surface heat flow and depth as a function of age:

 

,     where                   qs = heat flow (Wm-2)

                                                            k = thermal conductivity (Wm-1° K-1)

                                                            Tm = mantle temperature (° K)

                                                            Ts = surface temperature (° K)

                                                            k = thermal diffusivity (m2s-1)

                                                            t = time (s)

 

and

 

, where      d = seafloor depth (m, measured from top of the ridge crest)

                                                            rm = mantle density (kg m-3)

                                                            rw = water density (kg m-3)

                                                            av = coefficient of thermal expansion (° K-1)

 

Realistic values for the constants in these expressions are:

                                    k = 3.3 Wm-1° K-1

                                    Tm - Ts = 1300° K

                                    k = 1 mm2s-1 [hint:  watch your units!]

                                    rm =  3300 kg m-3

                                    rw = 1000 kg m-3

                                    av = 3 ´ 10-5° K-1

 

(a) Average heatflow values for several sites in the Pacific Ocean are given in Table 1.  Use the magnetic lineations map (Fig. 1) to determine the age for the sites using the magnetic polarity time scale from Larson & Pitman (1972; Fig. 2, attached).  Plot heat flow vs. age for the sites, showing uncertainties in both heat flow and age (for age, use the range of ages included in each sampling area as the uncertainty).

 

[Notes:  Zones b and c are in the magnetic 'quiet zone' of the central Pacific; determine their ages by extrapolating from the magnetic anomalies at the edge of the zone.  Zones f and g are groups of measurements taken at single points atop anomalies 4 and 3, respectively; Average measurements located north and south of the Galapagos Ridge are represented by Zones e and h, respectively.  Zones j and k are located adjacent to the Juan de Fuca Ridge.  A more detailed map of magnetic anomalies for this area is given in Figure 3.]

 

(b) Plot the theoretical heat flow-age relationship curve on the same graph.  Do the observations and theory agree?  What are the sources of disagreement?

 

(c) Because transform faults juxtapose oceanic lithosphere of different ages, there is a vertical offset on the fracture zones.  Assuming the theoretical depth/age relationship to be applicable, construct a graph of fracture zone scarp height as a function of distance from the ridge crest for a ridge offset of 100 km and a spreading rate of 5 cm/yr.  How might this relation be used?  [Hint:  Watch your units!!!]

 

(d)  Because of the cooling of the seafloor, it subsides relative to a continent as a passive continental margin.  Determine the instantaneous subsidence rate for a 20 million-year-old continental margin, and for a 100 million-year-old continental margin.