Question

1. (i) Sketch the relationship between isotherms and heat flow vectors.
(ii) The magnitude of the heat flow vector is proportional to the temperature gradient. Use this to show why a steady-state geotherm must be a straight line in the absence of heat production. 7. Why is it that P waves can convert to SV, but not SH, at a horizontal interface? Explain.

2. The stress and strain tensors are symmetric; that is, _ij = _ji and _ij = _ji . Explain why this is true for the stress tensor.

3. Explain why the following moment tensor is not consistent with an earthquake. What else could have produced it?

M = AI, where A being constant
10. The ray parameter (in a flat Earth) is given by p_x = sin  / c. Use this to find the bottoming depth for a ray in a medium with the linearly increasing velocity profile c = c₀ + kz.

4. A sinusoidal temperature variation at the surface has a characteristic depth of penetration into a half-space z_c = ,for which the temperature as a function of time and depth is T (z,t) = A₀ e^i(t-z/z_c⁾e^-z/z_c. For a rockwith thermal diffusivity of 5×10^-6 m²/s, at what depth will the temperature have its daily maximum when the surface temperature has its daily minimum?

5. A simple-shear displacement field is written as u = x  Show that it contains both strain and rotation components.

Answer 1