Question 1. Sketch all reflected and transmitted seismic rays (on the two sides only of the specified boundary), showing correct angular relationships for:
- upgoing S wave incident at the base of the crust, at 15° to the normal
- downgoing P wave incident from the mantle at the outer boundary of the core, at 30° to the normal
Assume Poisson-s ratio of 0.25
Question 2. Compute the deepest point reached in the Earth by a P wave which enters the top of the mantle at an angle of 60° from the normal. Tables of P-wave velocity may be found in Richter, Appendix, or in Bull. Seis. Soc. Amer., 1968, p. 1223
Question 3. Assume constant velocity for P in the mantle and core of 13.6 and 8.1 km/sec. Construct a cross section to scale through the Earth showing the core boundary. Draw raypaths from the surface through the core and back to the surface, for rays incident at the core boundary at angles of 0, 15, 30, 45, 60, 75 and 89 degrees, and just missing. Start from the same point at the surface to show where they emerge.
Question 4. Compute and graph the form of the travel-time curve along the surface of a uniform sphere of velocity V, from 0° to 180°, and compare with the shape of the same curve for a flat earth.
Question 5. Starting from the spherical earth formulation of the Wiechert-
Herglotz integral given in lectures, deduce an expression for the depth of maximum penetration in the case of a flat earth (i.e., ray penetration small relative to the Earth's radius) in which the velocity is an arbitrary function of depth. Compute the velocity depth-function corresponding to a travel-time graph of the form T = A sinh (bX).