Natural Science Forum / Physics / Acoustics / April 2004

I'm currently editing my geophysics/applied math Ph.D. proposal
and would like comments back, preferably to my campus e-mail
address n06drd@mun.ca (where that is zero and not Oh) on its
potential originality and on any literature review references
I may have missed.

Now the possible disadvantage of my posting it here is that
someone might steal my ideas but I judge that unlikely,
along the lines of my presenting a poster paper in July and
then someone immediately writing a journal paper based
on it without referencing me.    But if someone does build
on my ideas they can reference the google groups URL of
this post and the web page PDF copy of my proposal.

The advantage of posting is that I might learn of new
references or possible duplication by me of an approach
of someone else such that I should shift my focus
slightly to ensure origiality.   Also comments I
get, while they may not be in time for me to edit
the proposal before probable April 20 1800 UTC
submission to the examining committee, might
help me prepare for questions during the April 27 defense.

If you do comment, in exchange I could proofread a
paper of yours at a later date (after the end of April)
and I am a very good proofreader of other people's
material but not quite as good at proofreading
my own material.

OK, yesterday's draft of the proposal in PDF form
is at  
http://www.nfld.com/~dalton/proposal/proposal.pdf   .

And the title for now is

"Seismic wave and ray theory in elastic media:
Solution of equations of motion by method of characteristics,
principal symbols, and Fourier integral operators,with
comparison to numerical results and real data."

and the abstract for now is

"My proposed research will focus on the mathematics of seismic wave
theory in elastic media.  In particular I will solve the three coupled
Cauchy's equations of motion in anisotropic inhomogeneous media using
the standard method of characteristics, a variant based on principal
symbol analysis, Fourier-integral operator (FIO) theory, and numerical
analysis.  I have begun and will continue to apply the method of
characteristics to the equations of motion.  I have also begun to
apply Principal Symbol theory, related to Fourier Integral Operators,
to the equations of motion and from that should also get the same
characteristics.  This would also put the equations in a framework
amenable to application of Fourier-integral operators.  In parallel
with that I will try to apply Fourier-integral operator theory to
simple cases so that solutions can be tested against known solutions.
Then I will extend that theory to the inhomogeneous anisotropic case
and ideally show that it extends the results of ray theory.  However
to handle the general case I expect the FIO theory will reduce the
equations somewhat but some numerical solution will still be required
to complete the solution but less than for full numerical solution of
the equations.  All that will involve some computer implementation,
and comparison to real data over well known geology.  The FIO
modelling results for the inhomogeneous anisotropic case could be
checked by e.g. inserting the isotropic elasticity matrix into the
algorithm and checking that the solution reduces to that for the
isotropic case.  I will also check it against a full numerical
solution for at least one test case."

Followups set to sci.physics .

David
http://www.nfld.com/~dalton