News of the month

Another month flies by, and it's time for our regular news round-up! News tips, anyone?

Knowledge sharing

At the start of the month, SPE launched PetroWiki. The wiki has been seeded with one part of the 7-volume Petroleum Engineering Handbook, a tome that normally costs over $600. They started with Volume 2, Drilling Engineering, which includes lots of hot topics, like fracking (right). Agile was involved in the early design of the wiki, which is being built by Knowledge Reservoir

Agile stuff

Our cheatsheets are consistenly some of the most popular things on our site. We love them too, so we've been doing a little gardening — there are new, updated editions of the rock physics and geophysics cheatsheets.

Thank you so much to the readers who've let us know about typos! 


Nothing else really hit the headlines this month — perhaps people are waiting for SEG. Here are some nibbles...

  • We just upgraded a machine from Windows to Linux, sadly losing Spotfire in the process. So we're on the lookout for another awesome analytics tool. VISAGE isn't quite what we need, but you might like these nice graphs for oil and gas.
  • Last month we missed the newly awarded exploration licenses in the inhospitable Beaufort Sea [link opens a PDF]. Franklin Petroleum of the UK might have been surprised by the fact that they don't seem to have been bidding against anyone, as they picked up all six blocks for little more than the minimum bid.
  • It's the SEG Annual Meeting next week... and Matt will be there. Look out for daily updates from the technical sessions and the exhibition floor. There's at least one cool new thing this year: an app!

This regular news feature is for information only. We aren't connected with any of these organizations, and don't necessarily endorse their products or services. 


N is for Nyquist

In yesterday's post, I covered a few ideas from Fourier analysis for synthesizing and processing information. It serves as a primer for the next letter in our A to Z blog series: N is for Nyquist.

In seismology, the goal is to propagate a broadband impulse into the subsurface, and measure the reflected wavetrain that returns from the series of rock boundaries. A question that concerns the seismic experiment is: What sample rate should I choose to adequately capture the information from all the sinusoids that comprise the waveform? Sampling is the capturing of discrete data points from the continuous analog signal — a necessary step in recording digital data. Oversample it, using too high a sample rate, and you might run out of disk space. Undersample it and your recording will suffer from aliasing.

What is aliasing?

Alaising is a phenomenon observed when the sample interval is not sufficiently brief to capture the higher range of frequencies in a signal. In order to avoid aliasing, each constituent frequency has to be sampled at least two times per wavelength. So the term Nyquist frequency is defined as half of the sampling frequency of a digital recording system. Nyquist has to be higher than all of the frequencies in the observed signal to allow perfect recontstruction of the signal from the samples.

Above Nyquist, the signal frequencies are not sampled twice per wavelength, and will experience a folding about Nyquist to low frequencies. So not obeying Nyquist gives a double blow, not only does it fail to record all the frequencies, the frequencies that you leave out actually destroy part of the frequencies you do record. Can you see this happening in the seismic reflection trace shown below? You may need to traverse back and forth between the time domain and frequency domain representation of this signal.

Seismic data is usually acquired with either a 4 millisecond sample interval (250 Hz sample rate) if you are offshore, or 2 millisecond sample interval (500 Hz) if you are on land. A recording system with a 250 Hz sample rate has a Nyquist frequency of 125 Hz. So information coming in above 150 Hz will wrap around or fold to 100 Hz, and so on. 

It's important to note that the sampling rate of the recording system has nothing to do the native frequencies being observed. It turns out that most seismic acquisition systems are safe with Nyquist at 125 Hz, because seismic sources such as Vibroseis and dynamite don't send high frequencies very far; the earth filters and attenuates them out before they arrive at the receiver.

Space alias

Aliasing can happen in space, as well as in time. When the pixels in this image are larger than half the width of the bricks, we see these beautiful curved artifacts. In this case, the aliasing patterns are created by the very subtle perspective warping of the curved bricks across a regularly sampled grid of pixels. It creates a powerful illusion, a wonderful distortion of reality. The observations were not sampled at a high enough rate to adequately capture the nature of reality. Watch for this kind of thing on seismic records and sections. Spatial alaising. 

Click for the full demonstration (or adjust your screen resolution).You may also have seen this dizzying illusion of an accelerating wheel that suddenly appears to change direction after it rotates faster than the sample rate of the video frames captured. The classic example is the wagon whel effect in old Western movies.

Aliasing is just one phenomenon to worry about when transmitting and processing geophysical signals. After-the-fact tricks like anti-aliasing filters are sometimes employed, but if you really care about recovering all the information that the earth is spitting out at you, you probably need to oversample. At least two times for the shortest wavelengths.


Hooray for Fourier!

The theory of truth is a series of truisms - J.L Austin

The mathematical notion that any periodic function, no matter how jagged or irregular, can be represented as a sum of sines — called a Fourier series — is one of the most extraordinarily useful ideas ever. Ever! It is responsible for the theory of transmitting and recovering information, and yes, is ubiquitious in geophysics. Strikingly, any signal can be decomposed into an ensemble of sine waves. They are two different representations of the same object, two equal representations of the same information. Fourier analysis is this act of sending waves through a mathematical prism, breaking up a function into the frequencies that compose it.

To build an arbitrary signal, the trick is to mulitply each of the sines by a coefficient (to change thier amplitude) and to shift them so that they either add together or cancel (changing the phase). From the respective coefficients and phases of the composite sinusoids, one can reconstruct the original curve: no information is lost in translating from one state to the other. 

So the wiggle trace we plot of the seismic waveform has bits of information partitioned across each of its individual sinusoids. The more frequencies it has, the more information carrying capacity it has. Think of it as being able to paint with a full color palette. The degree of richess or range is known as bandwidth. In making this example, I was surprised how few sine waves (only ten) it took to make a signal that actually looks like a bonafide seismic trace. 

In 52 Things You Should Know About Geophysics, Mostafa Nagizadeh wrote an essay on the magic of Fourier; it's applications for geophysics data analysis. And he should know. In tomorrow's post, I will elaborate on the practical and economical issues we encounter making discrete measurements of continuous (analog) phenomena.


The blind geoscientist

Last time I wrote about using randomized, blind, controlled tests in geoscience. Today, I want to look a bit closer at what such a test or experiment might look like. But before we do anything else, it's worth taking 20 minutes, or at least 4, to watch Ben Goldacre's talk on the subject at Strata in London recently:

How would blind testing work?

It doesn't have to be complicated, or much different from what you already do. Here’s how it could work for the biostrat study I mentioned last time:

  1. Collect the samples as normal. There is plenty of nuance here too: do you sample regularly, or do you target ‘interesting’ zones? Only regular sampling is free from bias, but it’s expensive.
  2. Label the samples with unique identifiers, perhaps well name and depth.
  3. Give the samples to a disinterested, competent person. They repackage the samples and assign different identifiers randomly to the samples.
  4. Send the samples for analysis. Provide no other data. Ask for the most objective analysis possible, without guesswork about sample identification or origin. The samples should all be treated in the same way.
  5. When you get the results, analyse the data for quality issues. Perform any analysis that does not depend on depth or well location — for example, cluster analysis.
  6. If you want to be really thorough, the disinterested party to provide depths only, allowing you to sort by well and by depth but without knowing which wells are which. Perform any analysis that doesn’t depend on spatial location.
  7. Finally, ask for the key that reveals well names. Hopefully, any problems with the data have already revealed themselves. At this point, if something doesn’t fit your expectations, maybe your expectations need adjusting!

Where else could we apply these ideas?

  1. Random selection of some locations in a drilling program, perhaps in contraindicated locations
  2. Blinded, randomized inspection of gathers, for example with different processing parameters
  3. Random selection of wells as blind control for a seismic inversion or attribute analysis
  4. Random selection of realizations from geomodel simulation, for example for flow simulation
  5. Blinded inspection of the results of a 'turkey shoot' or vendor competition (e.g. Hayles et al, 2011)

It strikes me that we often see some of this — one or two wells held back for blind testing, or one well in a program that targets a non-optimal location. But I bet they are rarely selected randomly (more like grudgingly), and blind samples are often peeked at ('just to be sure'). It's easy to argue that "this is a business, not a science experiment", but that's fallacious. It's because it's a business that we must get the science right. Scientific rigour serves the business.

I'm sure there are dozens of other ways to push in this direction. Think about the science you're doing right now. How could you make it a little less prone to bias? How can you make it a shade less likely that you'll pull the wool over your own eyes?


Experimental good practice

Like hitting piñatas, scientific experiments need blindfolds. Image: Juergen. CC-BY.I once sent some samples to a biostratigrapher, who immediately asked for the logs to go with the well. 'Fair enough,' I thought, 'he wants to see where the samples are from'. Later, when we went over the results, I asked about a particular organism. I was surprised it was completely absent from one of the samples. He said, 'oh, it’s in there, it’s just not important in that facies, so I don’t count it.' I was stunned. The data had been interpreted before it had even been collected.

I made up my mind to do a blind test next time, but moved to another project before I got the chance. I haven’t ordered lab analyses since, so haven't put my plan into action. To find out if others already do it, I asked my Twitter friends:

Randomized, blinded, controlled testing should be standard practice in geoscience. I mean, if you can randomize trials of government policy, then rocks should be no problem. If there are multiple experimenters involved, like me and the biostrat guy in the story above, perhaps there’s an argument for double-blinding too.

Designing a good experiment

What should we be doing to make geoscience experiments, and the reported results, less prone to bias and error? I'm no expert on lab procedure, but for what it's worth, here are my seven Rs:

  • Randomized blinding or double-blinding. Look for opportunities to fight confirmation bias. There’s some anecdotal evidence that geochronologists do this, at least informally — can you do it too, or can you do more?
  • Regular instrument calibration, per manufacturer instructions. You should be doing this more often than you think you need to do it.
  • Repeatability tests. Does your method give you the same answer today as yesterday? Does an almost identical sample give you the same answer? Of course it does! Right? Right??
  • Report errors. Error estimates should be based on known problems with the method or the instrument, and on the outcomes of calibration and repeatability tests. What is the expected variance in your result?
  • Report all the data. Unless you know there was an operational problem that invalidated an experiment, report all your data. Don’t weed it, report it. 
  • Report precedents. How do your results compare to others’ work on the same stuff? Most academics do this well, but industrial scientists should report this rigorously too. If your results disagree, why is this? Can you prove it?
  • Release your data. Follow Hjalmar Gislason's advice — use CSV and earn at least 3 Berners-Lee stars. And state the license clearly, preferably a copyfree one. Open data is not altruistic — it's scientific.

Why go to all this trouble? Listen to Richard Feynman:

The first principle is that you must not fool yourself, and you are the easiest person to fool.

Thank you to @ToriHerridge@mammathus@volcan01010 and @ZeticaLtd for the stories about blinded experiments in geoscience. There are at least a few out there. Do you know of others? Have you tried blinding? We'd love to hear from you in the comments!