New Paper Published On Full Wave Inversion

Case Study On What Good Algorithms Can Accomplish

Posted by Joseph Young on Thu, Jul 17, 2014
In Reports under Inversion, Optizelle, History

I posted a new paper in our reports section that I collaborated on called Full Wave Inversion Using a Spectral-Element Discontinuous Galerkin Method. I contributed to this paper during my last stint with Sandia between 2010 and 2013.

The results for this paper were generated using an interesting, powerful DG solver called DGM and PEOpt, which I eventually spun off into Optizelle. These results offer a glimpse of what an optimization solver like Optizelle has to offer on real world problems. Namely, the software and algorithms, including second-order methods, work well on large-scale PDE-constrained optimization problems as well as on full wave inversion problems. In addition, our framework integrates easily computationally necessary heuristics such as the encoded simultaneous source method. Specifically, using a StateManipulator, we can insert the appropriate code after we take a step, but before we compute the gradient.

If anyone is interested in the mathematical underpinnings of encoded, simultaneous sources, it’s related to random projection. I published a paper with Denis Ridzal detailing this method in An Application of Random Projection to Parameter Estimation in Partial Differential Equations, which we published in SIAM. As it happens, an oil company cites our paper in their patent Simultaneous source inversion for marine streamer data with cross-correlation objective function. It turns out there are lots of interesting ways to encode sources that don’t violate their patent. And, frankly, these methods are critical for any sort of large-scale full wave inversion solver. If anyone is interested, pass by a note; I do consult and could write you and your company a wonderful piece of software that accomplishes this.

In any case, I often hear at oil and gas conferences that finite elements combined with second-order optimization methods don’t work on real world full wave inversion problems. This is false and the paper above demonstrates that these algorithms work well. In addition, I’m glad to see that Sandia cooperated with an outside oil company on an interesting paper.