Timeline

• By the end of April, 2004, I will verify that the principal-symbol variant method results in the same characteristic equation as the standard method of characteristics.
• During May, 2004 I will code a numerical solution of the characteristic (eikonal) equation. I will also learn more about FIO mathematics and extend my literature review on FIO applications. I may also submit an abstract to by May 31.
• From June to August, 2004 I will build on the principal-symbol work by applying the FIO method (which includes use of symbols) to the equations of motion. In late July 2004, I will meet with de Hoop (and Stolk if he is here) and other scientists visiting St. John's for the 11th IWSA conference.
• In 2004-2005 I will continue the application of FIO methods to the equations of motion and code up fully analytic solutions of simple cases and also numerical solution of a stage I anticipate FIO methods may reduce the equations of motion to, beyond which an analytic solution will not be possible except for such simple cases/approximations. This approach still should yield some advantages over full numerical solution of the equations of motion. In late stages I will also code up (or build on existing code of others) a full numerical solution, using finite element or finite difference method, to at least one test model for the equations of motion. I will also compare results, especially three-component displacement, to real data obtained above known geology. Ideally that would be the model used for the full numerical solution as well. Also, I hope to apply existing code, written by others, for solving the eikonal and transport equations to the same model. There would thus be comparisons for the same model of: (1) real data, (2) full numerical solution, (3) method of characteristics followed by numerical solution of the eikonal equation, (4) existing methods for solving the transport and eikonal equation, and (5) FIO methods with at least some analytic reduction of the equations of motion followed by, in complicated cases, probably some numerical work to get the final solution.
• The earliest date of completion is early September, 2005. This date is unlikely but possible if all goes well and if I put off submitting papers for publication until after thesis submission. If I submit a couple of primary publications during the course of the thesis, there are difficulties in the analytic math or numerical coding or if I follow a lead for a month or so and then it turns out not to pan out and I have to start a new course, then early September, 2006, four years after I started, is more likely. However, I would prefer to graduate by May 2006 convocation if I can.