My previous work

So far I have, as outlined in subsection 2.2 below, applied the method of characteristics to the equations of motion to get a long determinantal eikonal equation. In the case of isotropy this equation reduces to the eikonal equations for P and S waves. This result is promising, but I will have to use numerical methods to solve the long form eikonal equation. I have also, as described in subsection 2.3 below, found a principal-symbol matrix determinant eikonal equation that is one-fifth the length of the first one. This equation also reduces to the eikonal equations for P and S waves for the case of isotropy. I plan to review my work for possible errors that, when corrected, would result in the first one and second one being identical.

As well, in the last year-and-a-half I have done some course study and literature review related to those courses and to my thesis research. The four courses are:

• a lecture course on seismic waves and rays (based on Slawinski, 2003), EASC6177;
• a reading/lecture course on differential geometry (based on Arnold, 1989), EASC6172;
• a reading/lecture course on differential geometry (based on Schutz, 1980), EASC6913;
• a reading/lecture course on functional analysis, Sobolev spaces, partial differential equations, pseudo-differential operators and Fourier-integral operators, and method of characteristics, EASC 6912.