(COMPUTER) Assume density-normalized elastic constants for elastic wave
propagation within an iron crystal. This crystal has cubic symmetry with 1111 =
2222 = 3333 = 29.64 km2 s−2, 1122 = 1133 = 2233 = 17.71 km2 s−2, and
2323 = 1313 = 1212 = 14.78 km2 s−2 (values from Musgrave, 1970).
(a) Using the symmetry relationships (11.19), fill in all 81 values of ijkl. Here is
a handy subroutine that does this:
(b) Compute and plot the slowness surfaces in the s1–s3 plane. Label the
qP and two qS waves. Note: You will need to construct the Mik matrix
at a range of slowness directions using equation (11.27) and then find
the eigenvalues of this matrix with an appropriate subroutine or software
package. Depending upon how the eigenvalues are sorted, you may find it
difficult to draw lines between the points without switching between the
different surfaces. If so, simply plot a symbol at each point and do not
attempt to connect the points.
(c) Compute and plot the wavefronts resulting from a point source after
1 s. You will need to use equation (11.29).
(d) Test your program by repeating steps (a)–(c) for the olivine model of
Figure 11.8, using the elastic constants listed in the figure caption and the
hexagonal symmetry conditions given in equations (11.33).