Software, stats, and tidal energy

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Today was the last day of the conference part of SciPy 2015 in Austin. Almost all the talks at this conference have been inspiring and/or enlightening. This makes it all the more wonderful that the organizers get the talks online within a couple of hours (!), so you can see everything (compared to about 5% maximum coverage at SEG).

Jake Vanderplas, a young astronomer and data scientist at UW's eScience Institute, gave the keynote this morning. He eloquently reviewed the history and state-of-the-art of the so-called SciPy stack, the collection of tools that Pythonistic scientists use to get their research done. If you're just getting started in this world, it's about the best intro you could ask for:

Chris Fonnesbeck treated the room to what might as well have been a second keynote, so well did he express his convictions. Beautiful slides, and a big message: statistics matters.

Kristen Thyng, an energetic contributor to the conference, gave a fantastic talk about tidal energy, her main field, as well as one about perceptual colourmaps, which is more of a hobby. The work includes some very nice visualizations of tidal currents in my home province...

Finally, I highly recommend watching the lightning talks. Apart from being filled with some mind-blowing ideas, many of them eliciting spontaneous applause (imagine that!), I doubt you will ever witness a more effective exercise in building a community of passionate professionals. It's remarkable. (If you don't have an hour these three are awesome.)

Next we'll be enjoying the 'sprints', a weekend of coding on open source projects. We'll be back to geophysics blogging next week :)

Geophysics at SciPy 2015

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Yesterday was the geoscience day at SciPy 2015 in Austin.

At lunchtime, Paige Bailey (Chevron) organized a Birds of a Feather on GIS. This was a much-needed meetup for anyone interested in spatial data. It was useful to hear about the tools the fifty-or-so participants  use every day, and a great chance to air some frustrations like Why is it so hard to install a geospatial stack? And questions like How do people make attractive maps with the toolset?

One way to make attractive maps is go beyond the screen and 3D print them. Almost any subsurface dataset could seem more tangible and believable as a 3D object, and Joe Kington (Chevron) showed us how to make data into objects. Just watch:

Matteus Ueckermann followed up with some virtual elevation models, showing how Python can process not just a few tiles of data, but can handle hydrology modeling for the entire world:

Nicola Creati (OGS, Trieste) showed us the PyGmod package, a new and fully parallel geodynamic simulation tool for HPC nuts. So now you can make more plate tectonic models before most people are out of bed!

We also heard from Lindsey Heagy and Gudnir Rosenkjaer from UBC, talking about various applications of Rowan Cockett's awesome SimPEG package to their work. As at the hackathon in Denver, it's very clear that this group's investment in and passion for a well-architected, integrated package is well worth the work, giving everyone who works with it superpowers. And, as we all know, superpowers are awesome. Especially geophysical ones.

Last up, I talked about striplog, a small package for handling interval and point data in logs, core, and other 1D datasets. It's still very immature, but almost ready for real-world users, so if you think you have a use case, I'd love to hear from you.

Today is the last day of the conference part, before we head into the coding sprints tomorrow. Stay tuned for more, or follow the #scipy2015 hashtag to keep up. See all the videos, which go up almost right after talks, on YouTube.

Attribute analysis and statistics

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Last week I wrote a basic introduction to attribute analysis. The post focused on the different ways of thinking about sampling and intervals, and on how instantaneous attributes have to be interpolated from the discrete data. This week, I want to look more closely at those interval attributes. We'd often like to summarize the attributes of an interval info a single number, perhaps to make a map.

Before thinking about amplitudes and seismic traces, it's worth reminding ourselves about different kinds of average. This table from SubSurfWiki might help... 

A peculiar feature of seismic data. from a statistical point of view, is the lack of the very low frequencies needed to give it a trend. Because of this, it oscillates around zero, so the average amplitude over a window tends to zero — seismic data has a mean value of zero. So not only do we have to think about interpolation issues when we extract attributes, we also have to think about statistics.

Fortunately, once we understand the issue it's easy to come up with ways around it. Look at the trace (black line) below:

The mean is, as expected, close to zero. So I've applied some other statistics to represent the amplitude values, shown as black dots, in the window (the length of the plot):

  • Average absolute amplitude (light green) — treat all values as positive and take the mean.
  • Root-mean-square amplitude (dark green) — tends to emphasize large values, so it's a bit higher.
  • Average energy (magenta) — the mean of the magnitude of the complex trace, or the envelope, shown in grey.
  • Maximum amplitude (blue) — the absolute maximum value encountered, which is higher than the actual sample values (which are all integers in this fake dataset) because of interpolation.
  • Maximum energy (purple) — the maximum value of the envelope, which is higher still because it is phase independent.

There are other statistics besides these, of course. We could compute the median average, or some other mean. We could take the strongest trough, or the maximum derivative (steepest slope). The options are really only limited by your imagination, and the physical relationship with geology that you expect.

We'll return to this series over the summer, asking questions like How do you know what to expect? and Does a physically realistic relationship even matter? 

To view and run the code that I used in creating the figures for this post, grab the iPython/Jupyter Notebook.

An attribute analysis primer

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A question on Stack Exchange the other day reminded me of the black magic feeling I used to have about attribute analysis. It was all very meta: statistics of combinations of attributes, with shifted windows and crazy colourbars. I realized I haven't written much about the subject, despite the fact that many of us spend a lot of time trying to make sense of attributes.

Time slices, horizon slices, and windows

One of the first questions a new attribute-analyser has is, "Where should the window be?" Like most things in geoscience: it depends. There are lots of ways of doing it, so think about what you're after...

  • Timeslice. Often the most basic top-down view is a timeslice, because they are so easy to make. This is often where attribute analysis begins, but since timeslices cut across stratigraphy, not usually where it ends.
  • Horizon. If you're interested in the properties of a strong reflector, such as a hard, karsted unconformity, maybe you just want the instantaneous attribute from the horizon itself.
  • Zone. If the horizon was hard to interpret, or is known to be a gradual facies transition, you may want to gather statistics from a zone around it. Or perhaps you couldn't interpret the thing you really wanted, but only that nice strong reflection right above it... maybe you can bootstrap yourself from there. 
  • Interval. If you're interested in a stratigraphic interval, you can bookend it with existing horizons, perhaps with a constant shift on one or both of them.
  • Proportional. If seismic geomorphology is your game, then you might get the most reasonable inter-horizon slices from proportionally slicing in between stratigraphic surface. Most volume interpretation software supports this. 

There are some caveats to simply choosing the stratigraphic interval you are after. Beware of choosing an interval that strong reflectors come into and out of. They may have an unduly large effect on most statistics, and could look 'geological'. And if you're after spectral attributes, do remember that the Fourier transform needs time! The only way to get good frequency resolution is to provide long windows: a 100 ms window gives you frequency information every 10 Hz.

Extraction depends on sample interpolation

When you extract an attribute, say amplitude, from a trace, it's easy to forget that the software has to do some approximation to give you an answer. This is because seismic traces are not continuous curves, but discrete series, with samples typically every 1, 2, or 4 milliseconds. Asking for the amplitude at some arbitrary time, like the point at which a horizon crosses a trace, means the software has to interpolate between samples somehow. Different software do this in different ways (linear, spline, polynomial, etc), and the methods give quite different results in some parts of the trace. Here are some samples interpolated with a spline (black curve) and linearly (blue). The nearest sample gives the 'no interpolation' result.

As well as deciding how to handle non-sampled parts of the trace, we have to decide how to represent attributes operating over many samples. In a future post, we'll give some guidance for using statistics to extract information about the entire window. What options are available and how do we choose? Do we take the average? The maximum? Something else?

There's a lot more to come!

As I wrote this post, I realized that this is a massive subject. Here are some aspects I have not covered today:

  • Calibration is a gaping void in many published workflows. How can we move past "that red blob looks like a point bar so I drew a line around it in PowerPoint" to "there's a 70% chance of finding reservoir quality sand at that location"?
  • This article was about  single-trace attributes at single instants or over static windows. Multi-trace and volume attributes, like semblance, curvature, and spectral decomposition, need a post of their own.
  • There are a million attributes (though only a few that count, just ask Art Barnes) so choosing which ones to use can be a challenge. Criteria range from what software licenses you have to what is physically reasonable.
  • Because there are a million attributes, the art of combining attributes with statistical methods like principal component analysis or multi-linear regression needs a look. This gets into seismic inversion.

We'll return to these ideas over the next few weeks. If you have specific questions or workflows to share, please leave a comment below, or get in touch by email or Twitter.

To view and run the code that I used in creating the figures for this post, grab the iPython/Jupyter Notebook.

Corendering more attributes

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My recent post on multi-attribute data visualization painted two seismic attributes from on a timeslice. Let's look now at corendering attributes extracted on a seismic horizon. I'll reproduce the example Matt gave in his post on colouring maps.

Although colour choices come down to personal preference, there are some points to keep in mind:

  • Data that varies relatively gradually across the canvas — e.g. elevation here — should use a colour scale that varies monotonically in hue and luminance, e.g. CubeHelix or Matteo Niccoli's colourmaps.
  • Data that varies relatively quickly across the canvas — e.g. my similarity data, (a member of the family that includes coherence, semblance, and so on) — should use a monochromatic colour scale, e.g. black–white. 
  • If we've chosen our colourmaps wisely, there should be some unused hues for rendering other additional attributes. In this case, there are no red hues in the elevation colourmap, so we can map redness to instantaneous amplitude.

Adding a light source

Without wanting to get too gimmicky, we can sometimes enliven the appearance of an attribute, accentuating its texture, by simulating a bumpy surface and shining a virtual light onto it. This isn't the same as casting a light source on the composite display. We can make our light source act on only one of our attributes and leave the others unchanged. 

Similarity attribute Displayed using a Greyscale Colourbar (left). Bump mapping of similarity attribute using a lightsource positioned at azimuth 350 degrees, inclination 20 degrees. 

The technique is called hill-shading. The terrain doesn't have to be a physical surface; it can be a slice. And unlike physical bumps, we're not actually making a new surface with relief, we are merely modifying the surface's luminance from an artificial light source. The result is a more pronounced texture.

One view, two dimensions, three attributes

Constructing this display takes a bit of trial an error. It wasn't immediately clear where to position the light source to get the most pronounced view. Furthermore, the amplitude extraction looked quite noisy, so I softened it a little bit using a Gaussian filter. Plus, I wanted to show only the brightest of the bright spots, so that all took a bit of fiddling.

Even though 3D data visualization is relatively common, my assertion is that it is much harder to get 3D visualization right, than for 2D. Looking at the 3 colour-bars that I've placed in the legend. I'm reminded of this difficulty of adding a third dimension; it's much harder to produce a colour-cube in the legend than a series of colour-bars. Maybe the best we can achieve is a colour-square like last time, with a colour-bar for the overlay on the side.

Check out the IPython notebook for the code used to create these figures.

Pick This again

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Since I last wrote about it, Pick This! has matured. We have continued to improve the tool, which is a collaboration between Agile and the 100% awesome Steve Purves at Euclidity.

Here's some of the new stuff we've added:

  • Multiple lines and polygons for each interpretation. This was a big limitation; now we can pick multiple fault sticks, say.
  • 'Preshows', to show the interpreter some text or an image before they interpret. In beta, talk to us if you want to try it.
  • Interpreter cohorts, with randomized selection, so we can conduct blind trials.  In beta, again, talk to us.
  • Complete picking history, so we can replay the entire act of interpretation. Coming soon: new visualizations of results that use this data.

Some of this, such as replaying the entire picking event, is of interest to researchers who want to know how experts interpret images. Remotely sensed images — whether in geophysics, radiology, astronomy, or forensics — are almost always ambiguous. Look at these faults, for example. How many are there? Where are they exactly? Where are their tips?  

A seismic line from the Browse Basin, offshore western Australia. Data courtesy of CGG and the Virtual Seismic Atlas

A seismic line from the Browse Basin, offshore western Australia. Data courtesy of CGG and the Virtual Seismic Atlas

Most of the challenges on the site are just fun challenges, but some — like the Browse Basin challenge, above — are part of an experiment by researchers Juan Alcalde and Clare Bond at the University of Aberdeen. Please help them with their research by taking part and making an interpretation! It would also be super if you could fill out your profile page — that will help Juan and Clare understand the results. 

If you're at the AAPG conference in Denver then you can win bonus points by stopping by Booth 404 to visit Juan and Clare. Ask them all about their fascinating research, and say hello from us!

While you're on the site, check out some of the other images — or upload one yourself! This one was a real eye-opener: time-lapse seismic reflections from the water column, revealing dynamic thermohaline stratification. Can you pick this?

Pick This challenge showing time-lapse frames from a marine 3D. The seabed is shown in blue at the bottom of the images.

Pick This challenge showing time-lapse frames from a marine 3D. The seabed is shown in blue at the bottom of the images.

May linkfest

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The pick of the links from the last couple of months. We look for the awesome, so you don't have to :)

ICYMI on Pi Day, pimeariver.com wants to check how close river sinuosity comes to pi. (TL;DR — not very.)

If you're into statistics, someone at Imperial College London recently released a nice little app for stochastic simulations of simple calculations. Here's a back-of-the-envelope volumetric calculation by way of example. Good inspiration for our Volume* app.

I love it when people solve problems together on the web. A few days ago Chris Jackson (also at Imperial) posted a question about converting projected coordinates...

I responded with a code snippet that people quickly improved. Chris got several answers to his question, and I learned something about the pyproj library. Open source wins again!

In answering that question, I also discovered that Github now renders most IPython Notebooks. Sweet!

Speaking of notebooks, Beaker looks interesting: individual code blocks support different programming languages within the same notebook and allow you to pass data from one cell to another. For instance, you could do your basic stuff in Python, computationally expensive stuff in Julia, then render a visualization with JavaScript. Here's a simple example from their site.

Python is the language for science, but JavaScript certainly rules the visual side of the web. Taking after JavaScript data-artists like Bret Victor and Mike Bostock, Jack Schaedler has built a fantastic website called Seeing circles, sines, and signals containing visual explanations of signal processing concepts.

If that's not enough for you, there's loads more where that came from: Gallery of Concept Visualization. You're welcome.

My recent notebook about finding small things with 2D seismic grids sparked some chatter on Twitter. People had some great ideas about modeling non-random distributions, like clustered or anisotropic populations. Lots to think about!

Getting help quickly is perhaps social media's most potent capability — though some people do insist on spoiling everything by sharing U might be a genius if u can solve this! posts (gah, stop it!). Earth Science Stack Exchange is still far from being the tool is can be, but there have been some relevant questions on geophysics lately:

A fun thread came up on Reddit too recently: Geophysics software you wish existed. Perfect for inspiring people at hackathons! I'm keeping a list of hacky projects for the next one, by the way.

Not much to say about 3D models in Sketchfab, other than: they're wicked! I mean, check out this annotated anticline. And here's one by R Mahon based on sedimentological experiments by John Shaw and others...

Corendering attributes and 2D colourmaps

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The reason we use colourmaps is to facilitate the human eye in interpreting the morphology of the data. There are no hard and fast rules when it comes to choosing a good colourmap, but a poorly chosen colourmap can make you see features in your data that don't actually exist. 

Colourmaps are typically implemented in visualization software as 1D lookup tables. Given a value, what colour should I plot it? But most spatial data is multi-dimensional, and it's useful to look at more than one aspect of the data at one time. Previously, Matt asked, "how many attributes can a seismic interpreter show with colour on a single display?" He did this by stacking up a series of semi-opaque layers, each one assigned its own 1D colourbar. 

Another way to add more dimensions to the display is corendering. This effectively adds another dimension to the colourmap itself: instead of a 1D colour line for a single attribute, for two attributes we're defining a colour square; for 3 attributes, a colour cube, and so on.

Let's illustrate this by looking at a time-slice through a portion of the F3 seismic volume. A simple way of displaying two attributes is to decrease the opacity of one, and lay it on top of the other. In the figure below, I'm setting the opacity of the continuity to 75% in the third panel. At first glance, this looks pretty good; you can see both attributes, and because they have different hues, they complement each other without competing for visual bandwidth. But the approach is flawed. The vividness of each dataset is diminished; we don't see the same range of colours as we do in the colour palette shown above.

Overlaying one map on top of the other is one way to look at multiple attributes within a scene. It's not ideal however.

Overlaying one map on top of the other is one way to look at multiple attributes within a scene. It's not ideal however.

Instead of overlaying maps, we can improve the result by modulating the lightness of the amplitude image according to the magnitude of the continuity attribute. This time the corendered result is one image, instead of two. I prefer it, because it preserves the original colours we see in the amplitude image. If anything, it seems to deepen the contrast:

The lightness value of the seismic amplitude time slice has been modulated by the continuity attribute. 

The lightness value of the seismic amplitude time slice has been modulated by the continuity attribute. 

Such a composite display needs a two-dimensional colormap for a legend. Just as a 1D colourbar, it's also a lookup table; each position in the scene corresponds to a unique pair of values in the colourmap plane.

We can go one step further. Say we want to emphasize only the largest discontinuities in the data. We can modulate the opacity with a non-linear function. In this example, I'm using a sigmoid function:

In order to achieve this effect in most conventional software, you usually have to copy the attribute, colour it black, apply an opacity curve, then position it just above the base amplitude layer. Software companies call this workaround a 'workflow'. 

Are there data visualizations you want to create, but you're stuck with software limitations? In a future post, I'll recreate some cool co-rendering effects; like bump-mapping, and hill-shading.

To view and run the code that I used in creating the images for this post, grab the iPython/Jupyter Notebook.

You can do it too!

If you're in Calgary, Houston, New Orleans, or Stavanger, listen up!

If you'd like to gear up on coding skills and explore the benefits of scientific computing, we're going to be running the 2-day version of the Geocomputing Course several times this fall in select cities. To buy tickets or for more information about our courses, check out the courses page.

None of these times or locations good for you? Consider rounding up your colleagues for an in-house training option. We'll come to your turf, we can spend more than 2 days, and customize the content to suit your team's needs. Get in touch.

The curse of hunting rare things

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What are the chances of intersecting features with a grid of cross-sections? I often wonder about this when interpreting 2D seismic data, but I think it also applies to outcrops, or any other transects. I want to know:

  1. If there are only a few of these features, how many should I see?
  2. What's the probability of the lines missing them all? 
  3. Conversely, if I interpret x of them, then how many are there really?
  4. How is the detectability affected by the reliability of the data or my skills?

I used to have a spreadsheet for computing all this stuff, but spreadsheets are dead to me so here's an IPython Notebook :)

An example

I'm interpreting seep locations on 2D data at the moment. So I'm looking for subvertical pipes and chimneys, mud volcanos, seafloor pockmarks and pingos, that sort of thing (see Løseth et al., 2009 for a great overview). Here are some similar features from the Norwegian continental shelf from Hustoft et al., 2010:

Figure 3 from hustoft et al. (2010) showing the 3D expression of some hydrocarbon leakage features in Norway. © The Authors.

As Hustoft et al. show, these can be rather small features — most pockmarks are in the 100–800 m diameter range, so let's call it 500 m. The dataset I have is an orthogonal grid of decent quality 2D lines with a 3 km spacing. The area is about 120,000 km². For the sake of argument (and a forward model), let's imagine there are 120 features I'm interested in — one per 1000 km². Here's a zoomed-in view showing a subset of the problem:

Zoomed-in view of part of my example. A grid of 2D seismic lines, 3 km apart, and randomly distributed features, each 500 m in diameter. If a feature's centre falls inside a grey square, then the feature is not intersected by the data. The grey squa…

Zoomed-in view of part of my example. A grid of 2D seismic lines, 3 km apart, and randomly distributed features, each 500 m in diameter. If a feature's centre falls inside a grey square, then the feature is not intersected by the data. The grey squares are 2.5 km across.

According to my calculations...

  1. Of the 120 features in the area, we expect 37 to be intersected by the data. Of course, some of those intersections might be very subtle, if they are right at the edge of the feature.
  2. The probability of intersecting a given feature is 0.31. There are 120 features, so the probability of the whole dataset intersecting at least one is essentially 1 (certain). That's good! Conversely, the probability of missing them all is effectively 0. (If there were only 5 features, then there'd be about a 16% chance of missing them all.)
  3. Clearly, if I interpret 37 features, there are about 120 in total (that was my a priori). It's a linear relationship, so if I interpret 10 features, I can expect there to be about 33 altogether, and if I see 100 then I can expect that there are almost 330 in total. (I think the probability distribution would be log-normal, but would appreciate others' insights here.)
  4. Reliability? That sounds like a job for Bayes' theorem...

It's far from certain that I will interpret everything the data intersects, for all sorts of reasons:

  • I am human and therefore inconsistent, biased, and fallible.
  • The feature may be cryptic in the section , because of how it was intersected.
  • The data may be poor quality at that point, or everywhere.

Let's assume that if a feature has been intersected by the data, then I have a 75% chance of actually interpreting it. Bayes' theorem tells us how to update the prior probability of 0.31 (for a given feature; point 2 above) to get a posterior probability. Here's the table:

Interpreted Not interpreted
Intersected by a 2D line 28 9
Not intersected by any lines 21 63

What do the numbers mean?

  • Of the 37 intersected features, I interpret 28.
  • I fail to interpret 9 features that are intersected by the data. These are Type II errors, false negatives.
  • I interpret another 21 features which are not real! These are Type I errors: false positives. 
  • Therefore I interpret 48 features, of which only 57% are real. This seems like a lot, but it's a function of my imperfect reliability (75%) and the poor sampling, resulting in a large number of 'missed' features.

Interestingly, my 75% reliability translates into a 57% chance of being right about the existence of a feature. We've seen this effect before — it's the curse of hunting rare things: with imperfect knowledge, we are often wrong. 

References

Hustoft, S, S Bünz, and J Mienart (2010). Three-dimensional seismic analysis of the morphology and spatial distribution of chimneys beneath the Nyegga pockmark field, offshore mid-Norway. Basin Research 22, 465–480. DOI 10.1111/j.1365-2117.2010.00486.x 

Løseth, H, M Gading, and L Wensaas (2009). Hydrocarbon leakage interpreted on seismic data. Marine & Petroleum Geology 26, 1304–1319. DOI 10.1016/j.marpetgeo.2008.09.008 

Six comic books about science

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Ever since reading my dad's old Tintin books late into the night as a kid, I've loved comics and graphic novels. I've never been into the usual Marvel and DC stuff — superheroes aren't my thing. But I often re-read Tintin, I think I've read every Astérix, and since moving to Canada I've been a big fan of Seth and Chester Brown.

Last year in France I bought an album of Léonard, an amusing imagining of da Vinci's exploits as an inventor... Almost but not quite about science. These six books, on the other hand, show meticulous research and a love of natural philosophy. Enjoy!

The Thrilling Adventures of Lovelace and Babbage

Sydney Padua, 2015. New York, USA: Pantheon. List price USD 28.95.

I just finished devouring this terrific book by Padua, a young Canadian animator. It's an amazing mish-mash of writing and drawing, science and story, computing and history, fiction and non-fiction. This book has gone straight into my top 10 favourite books ever. It's really, really good.

Author — Amazon — Google — Pantheon

T-Minus: The Race to the Moon

Jim Ottaviani, Zander Cannon, Kevin Cannon, 2009. GT Labs. List price USD 15.99.

Who doesn't love books about space exploration? This is a relatively short exposition, aimed primarily at kids, but is thoroughly researched and suspenseful enough for anyone. The black and white artwork bounces between the USA and USSR, visualizing this unique time in history.

Amazon — Google — GT Labs

Feynman

Jim Ottaviani, Leland Myrick, 2011. First Second Books. List price USD 19.99.

A 248-page colour biography of the great physicist, whose personality was almost as remarkable as his work. The book covers the period 1923 to 1986 — almost birth to death — and is neither overly critical of Feynman's flaws, nor hero-worshipping. Just well-researched, and skillfully told.

Amazon — Google — First Second.

A Wrinkle in Time

Hope Larson, Madeleine L'Engle, 2012. New York, USA: Farrar, Straus & Giroux. List price USD 19.99

A graphic adaptation of L'Engle's young adult novel, first published in 1963. The story is pretty wacky, and the science is far from literal, so perhaps not for all tastes — but if you or your kids enjoy Doctor Who and Red Dwarf, then I predict you'll enjoy this. Warning: sentimental in places.

Amazon — Macmillan — Author 

Destination Moon and Explorers on the Moon

Hergé, 1953, 1954. Tournai, Belgium: Casterman (English: 1959, Methuen). List price USD 24.95.

These remarkable books show what Hergé was capable of imagining — and drawing — at his peak. The iconic ligne claire artwork depicts space travel and lunar exploration over a decade before Apollo. There is the usual espionage subplot and Thom(p)son-based humour, but it's the story that thrills.

Amazon — Google

What about you? Have you read anything good lately?