Curved Ray Tomography Example

OBJECTIVE: Solve Traveltime Tomography Ls=t by s=[L^TL]^-1L^Tt. 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 [L^TL]^-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.