# All the time freaks

/Thursday was our last day at the SEG Annual Meeting. Evan and I took in the Recent developments in time-frequency analysis workshop, organized by Mirko van der Baan, Sergey Fomel, and Jean-Baptiste Tary (Vienna). The workshop came out of an excellent paper I reviewed this summer, which was published online a couple of weeks ago:

Tary, JB, RH Herrera, J Han, and M van der Baan (2014), Spectral estimation—What is new? What is next?, *Rev. Geophys.* **52**. doi:10.1002/2014RG000461.

The paper compares the results of several time–frequency transforms on a suite of 'benchmark' signals. The idea of the workshop was to invite further investigation or other transforms. The organizers did a nice job of inviting contributors with diverse interests and backgrounds. The following people gave talks, several of them sharing their code (*):

**John Castagna**(Lumina) with a review of the applications of spectral decomposition for seismic analysis.**Steven Lin**(NCU, Taiwan) on empirical methods and the Hilbert–Huang transform.**Hau-Tieng Wu**(Toronto) on the application of transforms to monitoring respiratory patterns in animals.***Marcílio Matos**(SISMO) gave an entertaining, talk about various aspects of the problem.**Haizhou Yang**(Standford) on synchrosqueezing transforms applied to problems in anatomy.***Sergey Fomel**(UT Austin) on Prony's method... and how things don't always work out.***Me**, talking about the fidelity of time–frequency transforms, and some 'unsolved problems' (for me).***Mirko van der Baan**(Alberta) on the results from the Tary et al. paper.

Some interesting discussion came up in the two or three unstructured parts of the session, organized as mini-panel discussions with groups of authors. Indeed, it felt like the session could have lasted longer, because I don't think we got very close to resolving anything. Some of the points I took away from the discussion:

- My observation: there is no existing survey of the performance of spectral decomposition (or AVO) — these would be great risking tools.
- Castagna's assertion: there is no model that predicts the low-frequency 'shadow' effect (confusingly it's a bright thing, not a shadow).
- There is no agreement on whether the so-called 'Gabor limit' of time–frequency localization is a lower-bound on spectral decomposition. I will write more about this in the coming weeks.
- Should we even be attempting to use reassignment, or other 'sharpening' tools, on broadband signals? To put it another way: does instantaneous frequency mean anything in seismic signals?
- What statistical measures might help us understand the amount of reassignment, or the precision of time–frequency decompositions in general?

### The fidelity of time–frequency transforms

My own talk was one of the hardest I've ever done, mainly because I don't think about these problems very often. I'm not much of a mathematician, so when I do think about them, I tend to have more questions than insights, so I made my talk into a series of questions for the audience. I'm not sure I got much closer to any answers, but I have a better idea of my questions now... which is a kind of progress I suppose.

**Here's my talk (latest slides — GitHub repo). Comments and feedback are, as always, welcome.**