Slicing seismic arrays

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Scientific computing is largely made up of doing linear algebra on matrices, and then visualizing those matrices for their patterns and signals. It's a fundamental concept, and there is no better example than a 3D seismic volume.

Seeing in geoscience, literally

Digital seismic data is nothing but an array of numbers, decorated with header information, sorted and processed along different dimensions depending on the application.

In Python, you can index into any sequence, whether it be a string, list, or array of numbers. For example, we can index into the fourth character (counting from 0) of the word 'geoscience' to select the letter 's':

>>> word = 'geosciences'
>>> word[3]
's'

Or, we can slice the string with the syntax word[start:end:step] to produce a sub-sequence of characters. Note also how we can index backwards with negative numbers, or skip indices to use defaults:

>>> word[3:-1]  # From the 4th character to the penultimate character.
'science'
>>> word[3::2]  # Every other character from the 4th to the end.
'sine'

Seismic data is a matrix

In exactly the same way, we index into a multi-dimensional array in order to select a subset of elements. Slicing and indexing is a cinch using the numerical library NumPy for crunching numbers. Let's look at an example... if data is a 3D array of seismic amplitudes:

timeslice = data[:,:,122] # The 122nd element from the third dimension.
inline = data[30,:,:]     # The 30th element from the first dimension.
crossline = data[:,60,:]  # The 60th element from the second dimension.

Here we have sliced all of the inlines and crosslines at a specific travel time index, to yield a time slice (left). We have sliced all the crossline traces along an inline (middle), and we have sliced the inline traces along a single crossline (right). There's no reason for the slices to remain orthogonal however, and we could, if we wished, index through the multi-dimensional array and extract an arbitrary combination of all three.

Questions involving well logs (a 1D matrix), cross sections (2D), and geomodels (3D) can all be addressed with the rigours of linear algebra and digital signal processing. An essential step in working with your data is treating it as arrays.

View the notebook for this example, or get the get the notebook from GitHub and play with around with the code.

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If you want to practise slicing your data into bits, and other power tools you can make, the Agile Geocomputing course will be running twice in the UK this summer. Click one of the buttons below to buy a seat.

Eventbrite - Agile Geocomputing, Aberdeen

Eventbrite - Agile Geocomputing, London

More locations in North America for the fall. If you would like us to bring the course to your organization, get in touch.

Great geophysicists #11: Thomas Young

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Painting of Young by Sir Thomas LawrenceThomas Young was a British scientist, one of the great polymaths of the early 19th century, and one of the greatest scientists. One author has called him 'the last man who knew everything'¹. He was born in Somerset, England, on 13 June 1773, and died in London on 10 May 1829, at the age of only 55. 

Like his contemporary Joseph Fourier, Young was an early Egyptologist. With Jean-François Champollion he is credited with deciphering the Rosetta Stone, a famous lump of granodiorite. This is not very surprising considering that at the age of 14, Young knew Greek, Latin, French, Italian, Hebrew, Chaldean, Syriac, Samaritan, Arabic, Persian, Turkish and Amharic. And English, presumably. 

But we don't include Young in our list because of hieroglyphics. Nor  because he proved, by demonstrating diffraction and interference, that light is a wave — and a transverse wave at that. Nor because he wasn't a demented sociopath like Newton. No, he's here because of his modulus. 

Elasticity is the most fundamental principle of material science. First explored by Hooke, but largely ignored by the mathematically inclined French theorists of the day, Young took the next important steps in this more practical domain. Using an empirical approach, he discovered that when a body is put under pressure, the amount of deformation it experiences is proportional to a constant for that particular material — what we now call Young's modulus, or E:

This well-known quantity is one of the stars of the new geophysical pursuit of predicting brittleness from seismic data, and a renewed interested in geomechanics in general. We know that Young's modulus on its own is not enough information, because the mechanics of failure (as opposed to deformation) are highly nonlinear, but Young's disciplined approach to scientific understanding is the best model for figuring it out. 

Sources and bibliography

Footnote

¹ Thomas Young wrote a lot of entries in the 1818 edition of Encyclopædia Britannica, including pieces on bridges, colour, double refraction, Egypt, friction, hieroglyphics, hydraulics, languages, ships, sound, tides, and waves. Considering that lots of Wikipedia is from the out-of-copyright Encyclopædia Britannica 11th ed. (1911), I wonder if some of Wikipedia was written by the great polymath? I hope so.

The nonlinear ear

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Hearing, audition, or audioception, is one of the Famous Five of our twenty or so senses. Indeed, it is the most powerful sense, having about 100 dB of dynamic range, compared to about 90 dB for vision. Like vision, hearing — which is to say, the ear–brain system — has a nonlinear response to stimuli. This means that increasing the stimulus by, say, 10%, does not necessarily increase the response by 10%. Instead, it depends on the power and bandwidth of the signal, and on the response of the system itself.

What difference does it make if hearing is nonlinear? Well, nonlinear perception produces some interesting effects. Some of them are especially interesting to us because hearing is analogous to the detection of seismic signals — which are just very low frequency sounds, after all.

Stochastic resonance (Zeng et al, 2000)

One of the most unintuitive properties of nonlinear detection systems is that, under some circumstances, most importantly in the presence of a detection threshold, adding noise increases the signal-to-noise ratio.

I'll just let you read that last sentence again.

Add noise to increase S:N? It might seem bizarre, and downright wrong, but it's actually a fairly simple idea. If a signal is below the detection threshold, then adding a small Goldilocks amount of noise can make the signal 'peep' above the threshold, allowing it to be detected. Like this:

I have long wondered what sort of nonlinear detection system in geophysics might benefit from a small amount of noise. It also occurs to me that signal reconstruction methods like compressive sensing might help estimate that 'hidden' signal from the few semi-random samples that peep above the threshold. If you know of experiments in this, I'd love to hear about it.

Better than Heisenberg (Oppenheim & Magnasco, 2012)

Denis Gabor realized in 1946 that Heisenberg's uncertainty principle also applies to linear measures of a signal's time and frequency. That is, methods like the short-time Fourier transform (STFT) cannot provide the time and the frequency of a signal with arbitrary precision. Mathematically, the product of the uncertainties has some minimum, sometimes called the Fourier limit of the time–bandwidth product.

So far so good. But it turns out our hearing doesn't work like this. It turns out we can do better — about ten times better.

Oppenheim & Magnasco (2012) asked subjects to discriminate the timing and pitch of short sound pulses, overlapping in time and/or frequency. Most people were able to localize the pulses, especially in time, better than the Fourier limit. Unsurprisingly, musicians were especially sensitive, improving on the STFT by a factor of about 10. While seismic signals are not anything like pure tones, it's clear that human hearing does better than one of our workhorse algorithms.

Isolating weak signals (Gomez et al, 2014)

One of the most remarkable characteristics of biological systems is adaptation. It seems likely that the time–frequency localization ability most of us have is a long-term adaption. But it turns out our hearing system can also rapidly adapt itself to tune in to specific types of sound.

Listening to a voice in a noisy crowd, or a particular instrument in an orchestra, is often surprisingly easy. A group at the University of Zurich has figured out part of how we do this. Surprisingly, it's not high-level processing in the auditory cortex. It's not in the brain at all; it's in the ear itself.

That hearing is an active process was known. But the team modeled the cochlea (right, purple) with a feature called Hopf bifurcation, which helps describe certain types of nonlinear oscillator. They established a mechanism for the way the inner ear's tiny mechanoreceptive hairs engage in active sensing.

What does all this mean for geophysics?

I have yet to hear of any biomimetic geophysical research, but it's hard to believe that there are no leads here for us. Are there applications for stochastic resonance in acquisition systems? We strive to make receivers with linear responses, but maybe we shouldn't! Could our hearing do a better job of time-frequency localization than any spectral decomposition scheme? Could turning seismic into music help us detect weak signals in the geological noise?

All very intriguing, but of course no detection system is perfect... you can fool your ears too!

References

Zeng FG, Fu Q, Morse R (2000). Human hearing enhanced by noise. Brain Research 869, 251–255.

Oppenheim, J, and M Magnasco (2013). Human time-frequency acuity beats the Fourier uncertainty principle. Physical Review Letters. DOI 10.1103/PhysRevLett.110.044301 and in the arXiv.

Gomez, F, V Saase, N Buchheim, and R Stoop (2014). How the ear tunes in to sounds: A physics approach. Physics Review Applied 1, 014003. DOI 10.1103/PhysRevApplied.1.014003.

The stochastic resonance figure is original, inspired by Simonotto et al (1997), Physical Review Letters 78 (6). The figure from Oppenheim & Magnasco is copyright of the authors. The ear image is licensed CC-BY by Bruce Blaus. 

Saving time with code

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A year or so ago I wrote that...

...every team should have a coder. Not to build software, not exactly. But to help build quick, thin solutions to everyday problems — in a smart way. Developers are special people. They are good at solving problems in flexible, reusable, scalable ways.

Since writing that, I've written more code than ever. I'm not ready to say that my starry-eyed vision of a perfect world of techs-cum-coders, but now I see that the path to nimble teams is probably paved with long cycle times, and never-ending iterations of fixing bugs and writing documentation.

So potentially we replace the time saved, three times over, with a tool that now needs documenting, maintaining, and enhancing. This may not be a problem if it scales to lots of users with the same problem, but of course having lots of users just adds to the maintaining. And if you want to get paid, you can add 'selling' and 'marketing' to the list. Pfff, it's a wonder anybody ever makes anthing!

At least xkcd has some advice on how long we should spend on this sort of thing...

All of the comics in this post were drawn by and are copyright of the nonpareil of geek cartoonery, Randall Munroe, aka xkcd. You should subscribe to his comics and his What If series. All his work is licensed under the terms of Creative Commons Attribution Noncommercial.

Lusi's 8th birthday

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Lusi is the nickname of Lumpur Sidoarjo — 'the mud of Sidoarjo' — the giant mud volcano in the city of Sidoarjo, East Java, Indonesia. This week, Lusi is eight years old.

Google MapsBefore you read on, I recommend taking a look at it in Google Maps. Actually, Google Earth is even better — especially with the historical imagery. 

The mud flow was [may have been; see comments below — edit, 26 June 2014] triggered by the Banjar Panji 1 exploration well, operated by Lapindo Brantas, though the conditions may have been set up by a deadly earthquake. Mud loss events started in the early hours of 27 May 2006, seven minutes after the 6.2 Mw Yogyakarta earthquake that killed about 6,000 people. About 24 hours later, a large kick was killed and the blow-out preventer activated. Another 22 hours after this, while fishing in the killed well, mud, steam, and natural gas erupted from a fissure about 200 m southwest of the well. A few weeks after that, it was venting 180,000 m³ every day — enough mud to fill 72 Olympic swimming pools.

Thousands of years

In the slow-motion disaster that followed, as hot water from Miocene carbonates mobilized volcanic mud from Pleistocene mudstones, at least 15,000 people — and maybe as many as 50,000 people — were displaced from their homes. Davies et al. (2011) estimated that the main eruption may last 26 years, though recent sources suggest it is easing quickly. Still, during this time, we might expect 95–475 m of subsidence. And in the long term? 

By analogy with natural mud volcanoes it can be expected to continue to flow at lower rates for thousands of years. — Davies et al. (2011)

So we're only 8 years into a thousand-year man-made eruption. And there's already enough mud thrown up from the depths to cover downtown Calgary...

References and further reading

Quite a bit has been written about LUSI. The Hot Mud Flow blog tracks a lot of it. The National University of Singapore has a lot of satellite photographs, besides those you'll find in Google Earth. The Wikipedia article links to a lot of information, as you'd expect. The Interweb has a few others, including this article by Tayvis Dunnahoe in E&P Magazine. 

There are also some scholarly articles. These two are worth tracking down:

Davies, R, S Mathias, R Swarbrick and M Tingay (2011). Probabilistic longevity estimate for the LUSI mud volcano, East Java. Journal of the Geological Society 168, 517–523. DOI 10.1144/0016-76492010-129

Sawolo, N, E Sutriono, B Istadi, A Darmoyo (2009). The LUSI mud volcano triggering controversy: was it caused by drilling? Marine & Petroleum Geology 26 (9), 1766–1784. DOI 10.1016/j.marpetgeo.2009.04.002

The satellite images in this post are © DigitalGlobe and Google, captured from Google Earth, and are used here in accordance with their terms of use. The maps are © OpenStreetMap and licensed ODbL. The seismic section is from Davies et al. 2011 and © The Geological Society of London and is used here in accordance with their terms of use. The text of this post is © Agile Geoscience and openly licensed under the terms of CC-BY, as always!

Are we alright?

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GeoConvention_2014_logo.png

This year's Canada GeoConvention tried a few new things. There was the Openness Unsession, Jen Russel Houston's Best of 2013 PechaKutcha session, and the On Belay careers session. Attendance at the unsession was a bit thin; the others were well attended. Hats off to the organizers for getting out of a rut.

I went to the afternoon of the On Belay session. It featured several applied geoscientists with less than 5 years of experience in the industry. I gather the conference asked them for a candid 'insider' view, with career tips for people like them. I heard 2 talks, and the experience left me literally shaking, prompting Ben Cowie to ask me if I was alright.

I was alright, but I'm not sure about us. Our community — or this industry — has a problem.

Don't be yourself

Marc Enter gave a talk entitled Breaking into Calgary's oil and gas industry, an Aussie's perspective.

Marc narrated the arc of his career: well site geology in a trailer in the outback, re-location to Calgary, being laid-off, stumbling into consultancy (what a person does when they can't find a real job), and so on. On this journey, Marc racked up hundreds of hours of interview experience searching for work in Calgary. Here are some of his learnings, paraphrased but I think they are accurate:

  • Being yourself is impossible in a unfamiliar place. So don't be yourself.
  • Interview experience is crucial to being comfortable, so apply for jobs you have no interest in, just for the experience.
  • If the job description doesn’t sound exactly right to you, apply anyway. It's experience.
  • Confidence is everything. HR people are sniffer dogs for confidence. If you don't have it, invent it.
  • On confidence: it is easier to find a job when you have a job.

What on earth are we teaching these young professionals about working in this industry? This is awful.

How to survive the workday 

Jesse Shoengut gave a talk entitled One man’s tips and tricks for surviving your early professional career. 

Surviving. That's the word he chose. Might as well have been enduring. Tolerating. TGIF mindset. Like Marc, Jesse spoke about a haphazard transition from university into the working world. If you can't find a job after you finish your undergrad, you can always have a go at grad school. That's one way to get work experience, if all else fails.

Fine, finding work can be hard, and not all jobs are awesome. But with statements like, "Here are some things that keep me sane at work, and help get me through the day," I started to react a bit. C'mon, is that really what people in the audience deserve to hear? Is that really what work is like? It's depressing.

A broken promise

Listening to these talks, I felt embarrassed for our profession. They felt like a candid celebration of mediocrity, where confidence compensates for complacency. I don't blame these young professionals — students have been groomed, through summer internships and hyper-conventional careers events, to get their resumes in order, fit in, and follow instructions. We in industry have built this trap we're mired in. And we are continually seduced. Seduced by the bait of more-then-decent pay and plenty of other rewards. 

I talked to one fellow afterwards. He said, "Yeah, well, a lot of people are finding it hard to find a job right now." If these cynical, jaded young professionals are representative, I'm not surprised.

Were you at this session? Did you see other talks, or walk away with a different impression? I'd love to hear your viewpoints... am I being unfair? Leave a comment.

Mining innovation

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by Jelena Markov and Tom Horrocks

Jelena is a postgraduate student and Tom is a research assistant at the University of Western Australia, Perth. They competed in the recent RIIT Unearthed hackathon, and kindly offered to tell us all about it. Thank you, Jelena and Tom!

Two weeks ago Perth coworking space Spacecubed hosted a unique 54-hour-long hackathon focused on the mining industry. Most innovations in the mining industry are the result of long-term strategic planning in big mining companies, or collaboration with university groups. In contrast, the Unearthed hackathon provided different perspectives on problems in the mining domain by giving 'outsiders' a chance to work on industry problems.

The event attracted web-designers, software developers, data gurus, and few geology and geophysics geeks, all of whom worked together on data — both open and proprietary from the Western Australian Government and industry respectively — to deliver time-constrained solutions to problems in the mining domain. There were around 100 competitors divided into 18 teams, but just one underlying question: can web-designers and software developers create solutions that compete, on an innovative level, with those from the R&D divisions of mining companies? Well, according to panel of mining executives and entrepreneurs, they can.

Safe, seamless shutdown

The majority of the teams chose to work on logistic problems in mining production. For example, the Stockphiles worked on a Rio Tinto problem about how to efficiently and safely shut down equipment without majorly disturbing the overall system. Their solution used Directed Acyclic Graphs as the basis for an interactive web-based interface that visualised the impacted parts of the system. Outside of the mining production domain, however, two teams tackled problems focused on geology and geophysics...

Geoscience hacking

The team Ultramafia used augmented reality and cloud-based analysis to visualize geological mapping, with the underlying theme of the smartphone replacing the geological hammer, and also the boring task of joint logging!

The other team in this domain — and the team we were part of — was 50 Grades of Shale...

The team consisted of three PhD students and three staff members from the Centre for Exploration Targeting at the UWA. We created an app for real-time downhole petrophysical data analysis — dubbed Wireline Spelunker — that automatically classifies lithology types from wireline logs and correlates user-selected log segments across the drill holes. We used some public libraries for machine learning and signal analysis algorithms, and within 54 hours the team had implemented a workflow and interface, using data from the government database.

The boulder detection problem

The first prize, a 1 oz gold medal, was awarded to Applied Mathematics, who came up with an extraordinary use of accelerometers. They worked on Rio Tinto's 'boulder detection' problem — early detection of a large rocks loaded into mining trucks in order to prevent crusher malfunctions later in the process, which could ultimately cost $250,000 per hour in lost revenue. The team's solution was to detect large boulders by measuring the truck's vibrations during loading.

Second and third prizes went to Pit IQ and The Froys respectively. Both teams worked on data visualization problems on the mine site, and came up with interactive mobile dashboards.

A new role for Perth?

Besides having a chance to tackle problems that are costing the mining industry millions of dollars a year, this event has demonstrated that Perth is not just a mining hub but also has potential for something else.

This potential is recognized by event organizers Resources Innovation through Information Technology — Zane, Justin, Paul, and Kevin. They see potential in Perth as a centre for tech start-ups focused on the resource industry. Evidently, the potential is huge.

Follow Jelena on Twitter

Fibre optic seismology at #GeoCon14

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We've been so busy this week, it's hard to take time to write. But for the record, here are two talks I liked yesterday at the Canada GeoConvention. Short version — Geophysics is awesome!

DAS good

Todd Bown from OptaSense gave an overview of the emerging applications for distributed acoustic sensing (DAS) technology. DAS works by shining laser pulses down a fibre optic cable, and measuring the amount of backscatter from impurities in the cable. Tiny variations in strain on the cable induced by a passing seismic wave, say, are detected as subtle time delays between light pulses. Amazing.

Fibre optic cables aren't as sensitive as standard geophone systems (yet?), but compared to conventional instrumentation, DAS systems have several advantages:

  • Deployment is easy: fibre is strapped to the outside of casing, and left in place for years.
  • You don't have to re-enter and interupt well operations to collect data.
  • You can build ultra-long receiver arrays — as long as your spool of fibre.
  • They are sensitive to a very broad band of signals, from DC to kilohertz.

Strain fronts

Later in the same session, Paul Webster (Shell) showed results from an experiment that used DAS as a fracture diagnosis tool. That means you can record for minutes, hours, even days; if you can cope with all that data. Shell has accumulated over 300 TB of records from a handful of projects, and seems to be a leader in this area.

By placing a cable in one horizontal well in order to listen to the frac treatment from another, the cable can effectively designed to record data similar to a conventional shot gather, except with a time axis of 30 minutes. On the gathers he drew attention to slow-moving arcuate events that he called strain fronts. He hypothesized a number of mechanisms that might cause these curious signals: the flood of fracking fluids finding their way into the wellbore, the settling and closing creep of rock around proppant, and so on. This work is novel and important because it offers insight into the mechanical behavoir of engineered reservoirs, not just during the treatment, but long after.

Why is geophysics awesome? We can measure sound with light. A mile underground. That's all.

Free the (seismic) data!

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Yesterday afternoon Evan and I hosted the second unsession at the GeoConvention in Calgary. After last year exposing 'Free the data' as one of the unsolved problems in subsurface geoscience, we elected to explore this idea further. And we're addicted to this kind of guided, recorded conversation.

Attendance was a little thin, but those who came spent the afternoon deep in conversation about open data, open software, and greater industry transparency. And we unearthed an exciting and potentially epic conclusion that I hope leads to a small revolution.

What happened?

Rather than leaving the floor completely open, we again brought some structure to the proceedings. I'll post the full version to the wiki page, but here's the overview:

  1. Group seismic interpretation: 5 interpreters in 5 minutes.
  2. Stories about openness: which of 26 short stories resonate with you most?
  3. Open/closed, accessible/inaccessible: a scorecard for petroleum geoscience.
  4. Where are the opportunities? What should we move from closed to open?

As you might expect, the last part was the real point. We wanted to find some high-value areas to poke, or at least gather evidence around. And one area—one data type—was identified as being (a) closed and inaccessible in Canada and (b) much more impactful if it were open and accessible. I gave the punchline away in the title, but that data type is seismic data.

Open, public seismic data is much too juicy a topic to do justice to in this post, so stay tuned for a review of some the specifics of how that conversation went. Meanwhile, imagine a world with free, public seismic data...

Reflections on the 2nd edition

The afternoon went well, and the outcome was intriguing, but we were definitely disappointed by the turnout. We have multiple working hypotheses about it...

  • There may not be a strong appetite for this sort of session, especially on a 'soft' topic. Next time: seismic resolution?
  • The first day might not be the best time for it, because people are still in the mood for talks. Next time: Wednesday morning?
  • The programme maybe didn't reflect what the unsession was about, and the time was unclear. Next time: More visibility.
  • Three hours may be too much to ask from people, though you could say the same about any other session here.

We'd love to hear your thoughts too... Are we barking up completely the wrong tree? Does our community even want to have these conversations? Should we try again in 2015?

Looking forward to #GeoCon14

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Agile is off to Calgary on Sunday. We have three things on our List of Thing To Do: 

  1. We're hosting another Unsession on Monday... If you're in Calgary, please come along! It's just like any other session at the conference, only a bit more awesome.
  2. We'll be blogging from GeoConvention 2014. If there's a talk you'd like to send us to, we take requests! Just drop us a line or tweet at us!
  3. Evan is teaching his Creative Geocomputing class. Interested? There are still places. A transformative experience, or your money back.

What's hot at GeoCon14

Here's a run-down of what we're looking forward to catching:

  • Monday: Maybe it's just me, but I always find seismic acquisition talks stimulating. In the afternoon, the Unsession is the place to be. Not Marco Perez's probably awesome talk about brittleness and stress. Definitely not. 
  • Tuesday: If it wasn't for the fear of thrombosis, it'd be tempting to go to Glen 206 and stay in Log Analysis sessions all day. In the afternoon, the conference is trying something new and interesting — Jen Russel-Houston (a bright spark if ever there was one) is hosting a PechaKucha — lightning versions of the best of GeoConvention 2013. 
  • Wednesday: This year's conference is unusually promising, because there is yet another session being given over to 'something different' — two actually. A career-focused track will run all day in Macleod D, called (slightly weirdly) ‘On Belay’: FOCUSing on the Climb that is a Career in Geoscience. Outside of that, I'd head for the Core Analysis sessions.
  • Friday: We won't be there this year, but the Core Conference is always worth going to. I haven't been to anything like it at any other conference. It's open on Thursday too, but go on the Friday for the barbeque (tix required).

The GeoConvention is always a good conference. It surprises me how few geoscientists come from outside of Canada to this event. Adventurous geophysicists especially should consider trying it one year — Calgary is really the epicentre of seismic geophysics, and perhaps of petrophysics too.

And the ski hills are still open.