Neglected near-surface workhorses

Yesterday afternoon, I attended a talk at Dalhousie by Peter Cary who has begun the CSEG distinguished lecture tour series. Peter's work is well known in the seismic processing world, and he's now spreading his insights to the broader geoscience community. This was only his fourth stop out of 26 on the tour, so there's plenty of time to catch it.

Three steps of seismic processing

In the head-spinning jargon of seismic processing, if you're lost, it's maybe not be your fault. Sometimes it might even seem like you're going in circles.

Ask the vendor or processing specialist first to keep it simple, and second to tell you in which of the three processing stages you are in. Seismic data processing has steps:

  • Attenuate all types of noise.
  • Remove the effects of the near surface.
  • Migration, sometimes called imaging.

If time migration is the workshorse of seismic processing, and if is fk filtering (or f–anything filtering) is the workhorse of noise attenuation, then surface consistent deconvolution is the workhorse of the near surface. These topics aren't as sexy or as new as FWI or compressed sensing, but Peter has been questioning the basics of surface-consistent scaling, and the approximations we make when processing land seismic data. 

The ambiguity of phase and travel-time corrections

To the processor, removing the effects of the near surface means making things flat in the CMP domain. It turns out you can do this with travel time corrections (static shifts), you can do this with phase corrections, or you can do it with both.

A simple synthetic example showing (a) a gather with surface-consistent statics and phase variations; (b) the same gather after surface-consistent residual statics correction, and (c) after simultaneous surface-consistent statics and phase correcition. Image © Cary & Nagarajappa and CSEG.

It's troubling that there is more than one way to achieve flatness. Peter's advice is to use shot stacks and receiver stacks to compare the efficacy of static corrections. They eliminate doubt about whether surface consistent scaling is working, and are a better QC tool than other data domains.

Deeper than shallow

It may sound trivial, but the hardest part about using seismic waves for imaging is that they have to travel down and back up through the near surface on their path to the target. It might seem counter-intuitive, but the geometric configurations that work well for the deep earth are not well suited to the shallow earth, and how we might correct for it. I can imagine that two surveys could be useful, one for the target and one for characterizing the shallow that gets in the way of the target, but seismic experiments are already expensive enough when there is only target to be concerned with.

Still, the near surface is something we can't avoid. Much like astronomers using ground-based telescopes shooting for the stars, seismic processors too have to get the noisy stuff that is sitting closest to the detectors out of the way.


Another 52 Things hits the shelves

The new book is out today: 52 Things You Should Know About Palaeontology. Having been up for pre-order in the US, it is now shipping. The book will appear in Amazons globally in the next 24 hours or so, perhaps a bit longer for Canada.

I'm very proud of this volume. It shows that 52 Things has legs, and the quality is as high as ever. Euan Clarkson knows a thing or two about fossils and about books, and here's what he thought of it: 

This is sheer delight for the reader, with a great range of short but fascinating articles; serious science but often funny. Altogether brilliant!

Each purchase benefits The Micropalaeontological Society's Educational Trust, a UK charity, for the furthering of postgraduate education in microfossils. You should probably go and buy it now before it runs out. Go on, I'll wait here...

1000 years of fossil obsession

So what's in the book? There's too much variety to describe. Dinosaurs, plants, foraminifera, arthropods — they're all in there. There's a geographical index, as before, and also a chronostratigraphic one. The geography shows some distinct clustering, that partly reflects the emphasis on the science of applied fossil-gazing: biostratigraphy. 

The book has 48 authors, a new record for these collections. It's an honour to work with each of them — their passion, commitment, and professionalism positively shines from the pages. Geologists and fossil nuts alike will recognize many of the names, though some will, I hope, be new to you. As a group, these scientists represent  1000 years of experience!

Amazingly, and completely by chance, it is one year to the day since we announced 52 Things You Should Know About Geology. Sales of that book benefit The AAPG Foundation, so today I am delighted to be sending a cheque for $1280 to them in Tulsa. Thank you to everyone who bought a copy, and of course to the authors of that book for making it happen.


Imaging with vectors

Even though it took way too long (I had been admiring it for quite some time), I recently became the first kid on the block to own a Lytro. The Lytro, if you haven't heard, is sort of like a camera, except that it definitely isn't. Apart from a viewfinder on one end, a piece of glass on the other, and a shutter release button on top, it doesn't really look or feel like a point-and-shoot or SLR either. It actually bares a closer resemblance to a pocket-sized telescope. So don't you dare call it a camera. Indeed, the thing that the Lytro is built to do is what makes it completely different than any camera, and this perhaps, is the best mark of its identity. It captures not only the intensity of the light rays hitting the sensor (or film), but the directionality of those light rays as well.

So what. Right? What does this mean? Why is this interesting? It means that with a light-field camera, the focal point and depth of field are parameters that can be controlled by the viewer. It is interesting because of freeing up of space and of the physical atoms of hardware by deliberately removing the motorized auto-focus mechanism, and placing instead into the capable and powerful hands of software. I find it particularly elegant that this technology was acheived as a result of harnessing light's true nature better than any other camera that came before it. A device designed to to record light as light is; a physical property defined by both a magnitude and a direction.

How do I interact with this picture? 

Normally this would be a weird question to ask, but with the Lytro the viewer can take part in the imaging process in three ways. Try it out on the samples above:

  • Point to focus: collecting the light field from a scene is a technical thing. Creating images by deciding what to focus on, and what to not focus on is an artistic thing. It is an interpretive thing. It's a narrative that the viewer has with the data. The goal of the light field camera is not to impose a narrative, but instead get entirely out of the way.
  • Extended focus: for artistic reasons, the viewer might want to have some parts of the image in focus, other parts out of focus. It's how our eyes work; our peripheral vision. But in cases where you want to see the full depth of field, where everything is in focus, the software has an algorithm for that (to try it out you can press 'E' on your keyboard).
  • Stereo viewing: speaks to the multidimensional nature of the vector field data. In the real world, when we move our head, the foreground moves faster than the background. So too with light-field images, you can simulate parallax, by moving your cursor and better understand the spatial relationship between objects in the scene.

These capabilities aren't just components of the device, they are technological paradigms embodied by the device. That, to me, is what is so incredibly beautiful about this technology. It's the best example of what technology should be: a material thing that improves the work of the mind.

A call to the seismic industry

The seismic wavefield is what we should be giving to the interpreter. This probably means engineering a seismic system where less work is done by the processor, and more control is given to the interpreter through software that does the heavy lifting. Interpreters need to have direct feedback with the medium they are interpreting. How does seismic have to change to allow that narrative?


R is for Resolution

Resolution is becoming a catch-all term for various aspects of the quality of a digital signal, whether it's a photograph, a sound recording, or a seismic volume.

I got thinking about this on seeing an ad in AAPG Explorer magazine, announcing an 'ultra-high-resolution' 3D in the Gulf of Mexico (right), aimed at site-survey and geohazard detection. There's a nice image of the 3D, but the only evidence offered for the 'ultra-high-res' claim is the sample interval in space and time (3 m × 6 m bins and 0.25 ms sampling). This is analogous to the obsession with megapixels in digital photography, but it is only one of several ways to look at resolution. The effect of increasing the sample interval of some digital images is shown in the second column here, compared to 200 × 200 pixels originals (click to zoom):

Another aspect of resolution is spatial bandwidth, which gets at resolving power, perhaps analogous to focus for a photographer. If the range of frequencies is too narrow, then broadband features like edges cannot be represented. We can simulate poor frequency content by bandpassing the data, for example smoothing it with a Gaussian filter (column 3).

Yet another way to think about resolution is precision (column 4). Indeed, when audiophiles talk about resolution, they are talking about bit depth. We usually record seismic with 32 bits per sample, which allows us to discriminate between a large number of values — but we often view seismic with only 6 or 8 bits of precision. In the examples here, we're looking at 2 bits. Fewer bits means we can't tell the difference between some values, especially as it usually results in clipping.

If it comes down to our ability to tell events (or objects, or values) apart, then another factor enters the fray: signal-to-noise ratio. Too much noise (column 5) impairs our ability to resolve detail and discriminate between things, and to measure the true value of, say, amplitude. So while we don't normally talk about the noise level as a resolution issue, it is one. And it may have the most variety: in seismic acquisition we suffer from thermal noise, line noise, wind and helicopters, coherent noise, and so on.

I can only think of one more impairment to the signals we collect, and it may be the most troubling: the total duration or extent of the observation (column 6). How much information can you afford to gather? Uncertainty resulting from a small window is the basis of the game Name That Tune. If the scale of observation is not appropriate to the scale we're interested in, we risk a kind of interpretation 'gap' — related to a concept we've touched on before — and it's why geologists' brains need to be helicoptery. A small 3D is harder to interpret than a large one. 

The final consideration is not a signal effect at all. It has to do with the nature of the target itself. Notice how tolerant the brick wall image is to the various impairments (especially if you know what it is), and how intolerant the photomicrograph is. In the astronomical image, the galaxy is tolerant; the stars are not. Notice too that trying to 'resolve' the galaxy (into a point, say) would be a mistake: it is inherently low-resolution. Indeed, its fuzziness is one of its salient features.

Have I missed anything? Are there other ways in which the recorded signal can suffer and targets can be confused or otherwise unresolved? How does illumination fit in here, or spectral bandwidth? What do you mean when you talk about resolution?

This post is an exceprt from my talk at SEG, which you can read about in this blog post. You can even listen to it if you're really bored. The images were generated by one of my IPython Notebooks that I point to in the talk, specifically images.ipynb

Astute readers with potent memories will have noticed that we have skipped Q in our A to Z. I just cannot seem to finish my post about Q, but I will!

The Safe Band ad is copyright of NCS SubSea. This low-res snippet qualifies as fair use for comment.


All the time freaks

SEG 2014Thursday 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 slidesGitHub repo). Comments and feedback are, as always, welcome.