Due: 3/28/02

Geodynamics

Problem Set 4

1. Temperatures at the interfaces between sedimentary layers of different rock types as determined from a well log are given below. The measured thermal conductivity of each layer is also given. Determine the heat flow through each layer.

Depth (m) Temp (°C) Rock Type k (W/m-°K)
380 18.362 Sandstone 3.2
402 18.871 Shale 1.7
412 19.330 Sandstone 5.3
465 20.446 Salt 6.1
475 20.580 Sandstone 3.4
510 21.331 Shale 1.9
515 21.510

2. Assume that the radioactive elements in the earth are uniformly distributed through a near-surface layer. The surface heat flow is 70 mW/m2, and there is no heat flow into the base of the layer. If k = 4 W/m-°K, Ts = 0 °C, and the temperature at the base of the layer is 1200 °C, determine the thickness of the layer and the volumetric heat production.

3. Assume that the yearly temperature variation is periodic. What is the skin depth? At what depth is the temperature 180° out of phase with the surface variation? Assume that k = 1 mm2/s.

4. The ocean ridges are made up of a series of parallel segments connected by transform faults, as shown below. Because of the difference of age there is a vertical offset on the fracture zones. What is the vertical offset (a) at the ridge crest and (b) 100 km from the ridge crest. (rm = 3300 kg/m3, k = 1 mm2/s, a = 3x10-5, Tm-To = 1300 °K, u = 50 mm/yr).

5. If petroleum formation requires temperatures between 100 °C and 150 °C, how deep would you drill in a sedimentary basin 20 Myr old? Assume To = 10 °C, Tm = 1300 °C, km = 1 mm2/s, ks = 2 W/m-°K, and km = 3.3 W/m-°K.