Curved Ray Tomography Example
OBJECTIVE:
Solve Traveltime Tomography Ls=t by
s=[LTL]-1LTt.
except now use curved ray tracing code written by Ruiqing.
All matlab codes can be downloaded here, curved_ray.zip.
Ruiqing's codes are called "buildL.m", "lineT.m", "lineseg.m","ray1.m", and "tomo.m". He says that you have to type
"tomo" for an example.
Use exact matrix inverse to compute [LTL]-1.
BACKGROUND: Straight ray tomography does not take into
account ray bending so we use a curved ray method now.
You will recognize that the problem is non-linear so you need to update
the velocity model for more than one iteration (as opposed to straight rays
which is a linear problem and only one iteration is needed).
PROCEDURE:
-
Download the programs above.
Turn them into working tomography programs using
the same models as in the straight ray exercises.
The code "tomo.m" will run a 10 iteration example
for inverting data from a 2-layer model.
Repeat the same exercises as before, except include a few new models
that test the limits of inversion (e.g., slanted ray models)
In the covariance matrix case,
determine the variances in 2 different ways.
- Determine the variance values by a matrix inverse for the
final slowness model, as in the straight ray exercise.
- Try large damping parameter at first few iterations (5 %)
and then reduce to .01% by final iteration. Does this help
speed up convergence and get better answer?
- Try inverting models with 5% random time errors.
Compare results to data with perfect data. Is there much of an
error amplified into the estimated model?
- Do both covariance estimates agree in predicting areas of poor resolution?
- Comment on differences in results between straight ray and curved ray results.
Should straight ray model estimate be used as a starting model?
Make sure all results are displayed in a professional manner, and comapred to figures
in a consistent way with straight ray results.
- Comment on sensitivity of final result w/r to traveltime noise, starting models and damping
parameters.