Rheology L curve analysis for regularization

lkaluzi

I'm trying to perform an L curve analysis similar to the one in Morlighem et al. 2013 in order to pick out the best Tikhanov parameter for the Rheology gradient cost function (I'm interpreting this to be the same as the weighting value). I believe I need the misfit between the model and observations (is this the value of the cost function at the end of the run?) and the regularization term (is this the value of the contribution of the 502 term at the end of the run?).
Thanks!

mathieumorlighem

Hi Lynn,

we recently made a tutorial here: trunk/examples/LcurveAnalysis take a look and let me know if you have questions
Best
Mathieu

lkaluzi

Thanks Mathieu,
The tutorial works well. How exactly did you choose the Tikhanov parameter based on the Lcurve though? For the tutorial you chose 4e-17 which looks like it was chosen minimize the cost function, but in your 2013 paper you chose a value that didn't quite minimize the cost function.

lkaluzi

Oh wait I see, when I rescale the axes it's a bit more clear. It's not minimizing the cost function, but at an inflection point between the regularization term and cost function. I'm not sure if I quite understand the significance though. This is the location where you have the best fit without giving too much weight to your regularization term?

lkaluzi

One more question for an L curve analysis for the friction coefficient. How should I initialize my 101 and 103 terms before performing the analysis?