1. (i) Sketch the relationship between isotherms and heat flowvectors.
(ii) The magnitude of the heat flow vector is proportional to thetemperature gradient. Use this to show why a steady-state geothermmust be a straight line in the absence of heat production. 7. Whyis it that P waves can convert to SV, but not SH, at a horizontalinterface? 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 consistentwith an earthquake. What else could have produced it?

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

4. A sinusoidal temperature variation at the surface has acharacteristic depth of penetration into a half-space z_c= ,for which the temperature as a function of time and depth is T(z,t) = A₀e^i(t-z/z_c⁾e^-z/z_c.For a rockwith thermal diffusivity of 5×10^-6m²/s, at what depth will the temperature have its dailymaximum when the surface temperature has its daily minimum?

5. A simple-shear displacement field is written asu = x  Show that it contains both strainand rotation components.