Six books about seismic analysis

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Last year, I did a round-up of six books about seismic interpretation. A raft of new geophysics books recently, mostly from Cambridge, prompts this look at six volumes on seismic analysis — the more quantitative side of interpretation. We seem to be a bit hopeless at full-blown book reviews, and I certainly haven't read all of these books from cover to cover, but I thought I could at least mention them, and give you my first impressions.

If you have read any of these books, I'd love to hear what you think of them! Please leave a comment. 

Observation: none of these volumes mention compressive sensing, borehole seismic, microseismic, tight gas, or source rock plays. So I guess we can look forward to another batch in a year or two, when Cambridge realizes that people will probably buy anything with 3 or more of those words in the title. Even at $75 a go.

Quantitative Seismic Interpretation

Per Avseth, Tapan Mukerji and Gary Mavko (2005). Cambridge University Press, 408 pages, ISBN 978-0-521-15135-1. List price USD 91, $81.90 at Amazon.com, £45.79 at Amazon.co.uk

You have this book, right?

Every seismic interpreter that's thinking about rock properties, AVO, inversion, or anything beyond pure basin-scale geological interpretation needs this book. And the MATLAB scripts.

Rock Physics Handbook

Gary Mavko, Tapan Mukerji & Jack Dvorkin (2009). Cambridge University Press, 511 pages, ISBN 978-0-521-19910-0. List price USD 100, $92.41 at Amazon.com, £40.50 at Amazon.co.uk

If QSI is the book for quantitative interpreters, this is the book for people helping those interpreters. It's the Aki & Richards of rock physics. So if you like sums, and QSI left you feeling unsatisifed, buy this too. It also has lots of MATLAB scripts.

Seismic Reflections of Rock Properties

Jack Dvorkin, Mario Gutierrez & Dario Grana (2014). Cambridge University Press, 365 pages, ISBN 978-0-521-89919-2. List price USD 75, $67.50 at Amazon.com, £40.50 at Amazon.co.uk

This book seems to be a companion to The Rock Physics Handbook. It feels quite academic, though it doesn't contain too much maths. Instead, it's more like a systematic catalog of log models — exploring the full range of seismic responses to rock properies.

Practical Seismic Data Analysis

Hua-Wei Zhou (2014). Cambridge University Press, 496 pages, ISBN 978-0-521-19910-0. List price USD 75, $67.50 at Amazon.com, £40.50 at Amazon.co.uk

Zhou is a professor at the University of Houston. His book leans towards imaging and velocity analysis — it's not really about interpretation. If you're into signal processing and tomography, this is the book for you. Mostly black and white, the book has lots of exercises (no solutions though).

Seismic Amplitude: An Interpreter's Handbook

Rob Simm & Mike Bacon (2014). Cambridge University Press, 279 pages, ISBN 978-1-107-01150-2 (hardback). List price USD 80, $72 at Amazon.com, £40.50 at Amazon.co.uk

Simm is a legend in quantitative interpretation and the similarly lauded Bacon is at Ikon, the pre-eminent rock physics company. These guys know their stuff, and they've filled this superbly illustrated book with the essentials. It belongs on every interpreter's desk.

Seismic Data Analysis Techniques...

Enwenode Onajite (2013). Elsevier. 256 pages, ISBN 978-0124200234. List price USD 130, $113.40 at Amazon.com. £74.91 at Amazon.co.uk.

This is the only book of the collection I don't have. From the preview I'd say it's aimed at undergraduates. It starts with a petroleum geology primer, then covers seismic acquisition, and seems to focus on processing, with a little on interpretation. The figures look rather weak, compared to the other books here. Not recommended, not at this price.

NOTE These prices are Amazon's discounted prices and are subject to change. The links contain a tag that gets us commission, but does not change the price to you. You can almost certainly buy these books elsewhere. 

The event that connects like the web

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Last week, Matt, Ben, and I attended SciPy 2014, the 13th annual scientific computing with Python conference. On a superficial level, it was just another conference. But there were other elements, brought forth by the organizers and participants (definitely not just attendees) and slowly revealed over the week. Together, the community created the conditions for a truly remarkable experience.

Immutable accessibility

By design, the experience starts before the event, and continues after it is over. Before each of the four half-day tutorials I attended, the instructors posted their teaching materials, code, and setup instructions. Most oral presentations did the same. Most code and content was served through GitHub or Bitbucket and instructions were posted using Mozilla's Etherpad. Ultimately the tools don't matter — it's the intention that is important. Instructors and speakers plan to connect.

Enhancing the being there

Beyond talks and posters, here are some examples of other events that were executed with engagement in mind:

  • Keynote presentations. If a keynote is truly key, design the schedule so that everyone can show up — they're a great way to start the day on a high note.
  • Birds of a Feather sessions are better than a panel discussion or Q&A. Run around with a microphone, and record notes in Etherpad.
  • Lightning talks at the end the day. Anyone can request 5 minutes on a show & tell. It was the first time I've heard applause erupt in the middle of a talk — and it happened several times.
  • Developer sprints take an hour to teach newbies how to become active members of your community or your project. Then spend two-days showing them how you work.

Record all the things

SciPy is not a conference, it's a hypermedia stream that connects networks across organizational boundaries. And it happens in real time — I overheard several people remarking in astonishment that the video of so-and-so's talk earlier that same morning was already posted online. My trained habit of frantic note-taking was redundant, freeing my concentration for more active listening. Instructors and presenters published their media online, and the majority of presenters pulled up interactive iPython notebooks in the browser and executed code on the fly. 

As an example of this, here's Karl Schleicher of Sergey Fomel's group at UT, talking about reproducing the results from a classic paper in The Leading Edge, Spitz (1999): 

We need this

On Friday evening Matt remarked to one of the sponsors, "This is the closest thing I have seen to what a conference should be". I think what he meant by that is that it should be about connecting. It should be about pushing our work out to the largest possible scope. It should be open by default, and designed to support ideas and conversations long after it is over. Just like all the things that the web is for as well.

Our question: Can we help SEG, AAPG, or EAGE deliver this to our community? Or do we have to go and build it? 

Geophysics at SciPy 2014

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Wednesday was geophysics day at SciPy 2014, the conference for scientific Python in Austin. We had a mini-symposium in the afternoon, with 4 talks and 2 lightning talks about posters.

All the talks

Here's what went on in the session...

The talks should all be online eventually. For now, you can watch my talk and Joe's (awesome) talk right here...

And also...

There have been so many other highlights at this amazing conference that I can't resist sharing a couple of the non-geophysical gems...

Last thing... If you use the scientific Python stack in your work, please consider giving as generously as you can to the NumFOCUS Foundation. Support open source!

SciPy will eat the world... in a good way

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We're at the SciPy 2014 conference in Austin, the big giant meetup for everyone into scientific Python.

One surprising thing so far is the breadth of science and computing in play, from astronomy to zoology, and from AI to zero-based indexing. It shouldn't have been surprising, as SciPy.org hints at the variety:

There's really nothing you can't do in the scientific Python ecosystem, but this isn't why SciPy will soon be everywhere in science, including geophysics and even geology. I think the reason is IPython Notebook, and new web-friendly ways to present data, directly from the computing environment to the web — where anyone can see it, share it, interact with it, and even build on it in their own work.

Teaching STEM

In Tuesday's keynote, Lorena Barba, an uber-prof of engineering at The George Washington University, called IPython Notebook the killer app for teaching in the STEM fields. She has built two amazing courses in Notebook: 12 Steps to Navier–Stokes and AeroPython (right), and more are on the way. Soon, perhaps through Jupyter CoLaboratory (launching in alpha today), perhaps with the help of tools like Bokeh or mpld3, the web versions of these notebooks will be live and interactive. Python is already the new star of teaching computer science, web-friendly super-powers will continue to push this.

Let's be extra clear: if you are teaching geophysics using a proprietary tool like MATLAB, you are doing your students a disservice if you don't at least think hard about moving to Python. (There's a parallel argument for OpedTect over Petrel, but let's not get into that now.)

Reproducible and presentable

Can you imagine a day when geoscientists wield these data analysis tools with the same facility that they wield other interpretation software? With the same facility that scientists in other disciplines are already wielding them? I can, and I get excited thinking about how much easier it will be to collaborate with colleagues, document our workflows (for others and for our future selves), and write presentations and papers for others to read, interact with, and adapt for their own work.

To whet your appetite, here's the sort of thing I mean (not interactive, but here's the code)...

If you agree that it's needed, I want to ask: What traditions or skill gaps are in the way of this happening? How can our community of scientists and engineers drive this change? If you disagree, I'd love to hear why.

Well tie calculus

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As Matt wrote in March, he is editing a regular Tutorial column in SEG's The Leading Edge. I contributed the June edition, entitled Well-tie calculus. This is a brief synopsis only; if you have any questions about the workflow, or how to get started in Python, get in touch or come to my course.

Synthetic seismograms can be created by doing basic calculus on traveltime functions. Integrating slowness (the reciprocal of velocity) yields a time-depth relationship. Differentiating acoustic impedance (velocity times density) yields a reflectivity function along the borehole. In effect, the integral tells us where a rock interface is positioned in the time domain, whereas the derivative tells us how the seismic wavelet will be scaled.

This tutorial starts from nothing more than sonic and density well logs, and some seismic trace data (from the #opendata Penobscot dataset in dGB's awesome Open Seismic Repository). It steps through a simple well-tie workflow, showing every step in an IPython Notebook:

  1. Loading data with the brilliant LASReader
  2. Dealing with incomplete, noisy logs
  3. Computing the time-to-depth relationship
  4. Computing acoustic impedance and reflection coefficients
  5. Converting the logs to 2-way travel time
  6. Creating a Ricker wavelet
  7. Convolving the reflection coefficients with the wavelet to get a synthetic
  8. Making an awesome plot, like so...

Final thoughts

If you find yourself stretching or squeezing a time-depth relationship to make synthetic events align better with seismic events, take the time to compute the implied corrections to the well logs. Differentiate the new time-depth curve. How much have the interval velocities changed? Are the rock properties still reasonable? Synthetic seismograms should adhere to the simple laws of calculus — and not imply unphysical versions of the earth.

Matt is looking for tutorial ideas and offers to write them. Here are the author instructions. If you have an idea for something, please drop him a line.

Patents are slowing us down

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I visited a geoscience consulting company in Houston recently. Various patent awards were proudly commemorated on the walls on little plaques. It's understandable: patents are difficult and expensive to get, and can be valuable to own. But recently I've started to think that patents are one of the big reasons why innovation in our industry happens at a snail's pace, in the words of Paul de Groot in our little book about geophysics. 

Have you ever read a patent? Go and have a read of US Patent 8670288, by Børre Bjerkholt of Schlumberger. I'll wait here.

What are they for?

It is more or less totally unreadable. And Google's rendering, even the garbled math, is much nicer than the USPTO's horror show. Either way, I think it's safe to assume that almost no-one will ever read it. Apart from anything else, it's written in lawyerspeak, and who wants to read that stuff?

Clearly patents aren't there to inform. So why are they there?

  • To defend against claims of infringement by others? This seems to be one of the main reasons technology companies are doing it.
  • To intimidate others into not trying to innovate or commercialize an innovation? With the possible unintended consequence of forcing competitors to avoid trouble by being more inventive.
  • To say to Wall Street (or whoever), "we mean business"? Patents are valuable: the median per-patent price paid in corporate acquisitions in 2012 was $221k.
  • To formalize the relationship between the inventor (a human, given that only humans have the requisite inventive genius) and the intellectual property owner (usually a corporation, given that it costs about $40k in lawyer's fees to apply for a patent successfully)?
  • Because all the cool kids are doing it? Take a look at that table. You don't want to get left behind do you?

I'm pretty sure most patents in our industry are a waste of money, and an unecessary impediment to innovation in our industry. If this is true then, as you see from the trend in the data, we have something to worry about.

A dangerous euphemism

That phrase, intellectual property, what exactly does that mean? I like what Cory Doctorow — one of Canada's greatest intellects — had to say about intellectual property in 2008:

the phrase "intellectual property" is, at root, a dangerous euphemism that leads us to all sorts of faulty reasoning about knowledge.

He goes on to discuss that intellectual property is another way of saying 'ideas and knowledge', but can those things really be 'property'? They certainly aren't like things that definitely are property: if I steal your Vibroseis truck, you can't use it any more. If I take your knowledge, you still have it... and so do I. If it was useful knowlege, then now it's twice as useful.

This goes some way to explaining why 2 weeks ago, the electric car manufacturer Telsa relinquished its right to sue patent infringers. The irrepressible Elon Musk explained::

Yesterday [11 June], there was a wall of Tesla patents in the lobby of our Palo Alto headquarters. That is no longer the case. They have been removed, in the spirit of the open source movement, for the advancement of electric vehicle technology.

This is bold, but smart — Tesla knows that its best chance of dominating a large electric vehicle industry depends on there being a large electric vehicle industry. And they've just made that about 10 times more likely.

What will we choose?

I think one of the greatest questions facing our industry, and our profession, is: How can we give ourselves the best chance of maintaining the ability to find and extract petroleum in a smart, safe, ethical way, for as long as humanity needs it? By seeking to stop others from applying a slightly new velocity model building algorithm? By locking up over 2000 other possibly game-changing ideas a year? Will society thank us for that?

Cross sections into seismic sections

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We've added to the core functionality of modelr. Instead of creating an arbitrarily shaped wedge (which is plenty useful in its own right), users can now create a synthetic seismogram out of any geology they can think of, or extract from their data.

Turn a geologic-section into an earth model

We implemented a color picker within an image processing scheme, so that each unique colour gets mapped to an editable rock type. Users can create and manage their own rock property catalog, and save models as templates to share and re-use. You can use as many or as few colours as you like, and you'll never run out of rocks.

To give an example, let's use the stratigraphic diagram that Bruce Hart used in making synthetic seismic forward models in his recent Whither seismic stratigraphy article. There are 7 unique colours, so we can generate an earth model by assigning a rock to each of the colours in the image.

If you can imagine it, you can draw it. If you can draw it, you can model it.

Modeling as an interactive experience

We've exposed parameters in the interface and so you can interact with the multidimensional seismic data space. Why is this important? Well, modeling shouldn't be a one-shot deal. It's an iterative process. A feedback cycle where you turn knobs, pull levers, and learn about the behaviour of a physical system; in this case it is the interplay between geologic units and seismic waves. 

A model isn't just a single image, but a swath of possibilities teased out by varying a multitude of inputs. With modelr, the seismic experiment can be manipulated, so that the gamut of geologic variability can be explored. That process is how we train our ability to see geology in seismic.

Hart's paper doesn't specifically mention the rock properties used, so it's difficult to match amplitudes, but you can see here how modelr stands up next to Hart's images for high (75 Hz) and low (25 Hz) frequency Ricker wavelets.

There are some cosmetic differences too... I've used fewer wiggle traces to make it easier to see the seismic waveforms. And I think Bruce forgot the blue strata on his 25 Hz model. But I like this display, with the earth model in the background, and the wiggle traces on top — geology and seismic blended in the same graphical space, as they are in the real world, albeit briefly.

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Seismic models: Hart, BS (2013). Whither seismic stratigraphy? Interpretation, volume 1 (1). The image is copyright of SEG and AAPG.

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.

Sign up!

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

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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.