Shooting into the dark

Part of what makes uncertainty such a slippery subject is that it conflates several concepts that are better kept apart: precision, accuracy, and repeatability. People often mention the first two, less often the third.

It's clear that precision and accuracy are different things. If someone's shooting at you, for instance, it's better that they are inaccurate but precise so that every bullet whizzes exactly 1 metre over your head. But, though the idea of one-off repeatability is built in to the concept of multiple 'readings', scientists often repeat experiments and this wholesale repeatability also needs to be captured. Hence the third drawing. 

One of the things I really like in Peter Copeland's book Communicating Rocks is the accuracy-precision-repeatability figure (here's my review). He captured this concept very nicely, and gives a good description too. There are two weaknesses though, I think, in these classic target figures. First, they portray two dimensions (spatial, in this case), when really each measurement we make is on a single axis. So I tried re-drawing the figure, but on one axis:

The second thing that bothers me is that there is an implied 'correct answer'—the middle of the target. This seems reasonable: we are trying to measure some external reality, after all. The problem is that when we make our measurements, we do not know where the middle of the target is. We are blind.

If we don't know where the bullseye is, we cannot tell the difference between precise and imprecise. But if we don't know the size of the bullseye, we also do not know how accurate we are, or how repeatable our experiments are. Both of these things are entirely relative to the nature of the target. 

What can we do? Sound statistical methods can help us, but most of us don't know what we're doing with statistics (be honest). Do we just need more data? No. More expensive analysis equipment? No.

No, none of this will help. You cannot beat uncertainty. You just have to deal with it.

This is based on an article of mine in the February issue of the CSEG Recorder. Rather woolly, even for me, it's the beginning of a thought experiment about doing a better job dealing with uncertainty. See Hall, M (2012). Do you know what you think you know? CSEG Recorder, February 2012. Online in May. Figures are here. 

A mixing board for the seismic symphony

Seismic processing is busy chasing its tail. OK, maybe an over-generalization, but researchers in the field are very skilled at finding incremental—and sometimes great—improvements in imaging algorithms, geometric corrections, and fidelity. But I don't want any of these things. Or, to be more precise: I don't need any more. 

Reflection seismic data are infested with filters. We don't know what most of these filters look like, and we've trained ourselves to accept and ignore them. We filter out the filters with our intuition. And you know where intuition gets us.

If I don't want reverse-time, curved-ray migration, or 7-dimensional interpolation, what do I want? Easy: I want to see the filters. I want them perturbed and examined and exposed. Instead of soaking up whatever is left of Moore's Law with cluster-hogging precision, I would prefer to see more of the imprecise stuff. I think we've pushed the precision envelope to somewhere beyond the net uncertainty of our subsurface data, so that quality and sharpness of the seismic image is not, in most cases, the weak point of an integrated interpretation.

So I don't want any more processing products. I want a mixing board for seismic data.

To fully appreciate my point of view, you need to have experienced a large seismic processing project. It's hard enough to process seismic, but if there is enough at stake—traces, deadlines, decisions, or just money—then it is almost impossible to iterate the solution. This is rather ironic, and unfortunate. Every decision, from migration aperture to anisotropic parameters, is considered, tested, and made... and then left behind, never to be revisited.

But this linear model, in which each decision is cemented onto the ones before it, seems unlikely to land on the optimal solution. Our fateful string of choices may lead us to a lovely spot, with a picnic area and clean toilets, but the chances that it is the global maximum, which might lie in a distant corner of the solution space, seem slim. What if the spherical divergence was off? Perhaps we should have interpolated to a regularized geometry. Did we leave some ground roll in the data? 

Look, I don't know the answer. But I know what it would look like. Instead of spending three months generating the best-ever migration, we'd spend three months (maybe less) generating a universe of good-enough migrations. Then I could sit at my desk and—at least with first order precision—change the spherical divergence, or see if less aggressive noise attenuation helps. A different migration algorithm, perhaps. Maybe my multiples weren't gone after all: more radon!

Instead of looking along the tunnel of the processing flow, I want the bird's eye view of all the possiblities. 

If this sounds impossible, that's because it is impossible, with today's approach: process in full, then view. Why not just do this swath? Ray trace on the graphics card. Do everything in memory and make me buy 256GB of RAM. The Magic Earth mentality of 2001—remember that?

Am I wrong? Maybe we're not even close to good-enough, and we should continue honing, at all costs. But what if the gains to be made in exploring the solution space are bigger than whatever is left for image quality?

I think I can see another local maximum just over there...

Mixing board image: iStockphoto.

Bring it into time

A student competing in the AAPG's Imperial Barrel Award recently asked me how to take seismic data, and “bring it into depth”. How I read this was, “how do I take something that is outside my comfort zone, and make it fit with what is familiar?” Geologists fear the time domain. Geology is in depth, logs are in depth, drill pipe is in depth. Heck, even X and Y are in depth. Seismic data relates to none of those things; useless right? 

It is excusable for the under-initiated, but this concept of “bringing [time domain data] into depth” is an informal fallacy. Experienced geophysicists understand this because depth conversion, in all of its forms and derivatives, is a process that introduces a number of known unknowns. It is easier for others to be dismissive, or ignore these nuances. So early-onset discomfort with the travel-time domain ensues. It is easier to stick to a domain that doesn’t cause such mental backflips; a kind of temporal spatial comfort zone. 

Linear in time

However, the unconverted should find comfort in one property where the time domain is advantageous; it is linear. In contrast, many drillers and wireline engineers are quick to point that measured depth is not nessecarily linear. Perhaps time is an even more robust, more linear domain of measurement (if there is such a concept). And, as a convenient result, a world of possibilities emerge out of time-linearity: time-series analysis, digital signal processing, and computational mathematics. Repeatable and mechanical operations on data.

Boot camp in time

The depth domain isn’t exactly omnipotent. A colleague, who started her career as a wireline-engineer at Schlumberger, explained to me that her new-graduate training involved painfully long recitations and lecturing on the intricacies of depth. What is measured depth? What is true vertical depth? What is drill-pipe stretch? What is wireline stretch? And so on. Absolute depth is important, but even with seemingly rigid sections of solid steel drill pipe, it is still elusive. And if any measurement requires a correction, that measurement has error. So even working in the depth domain data has its peculiarities.

Few of us ever get the privilege of such rigorous training in the spread of depth measurements. Sitting on the back of the rhetorical wireline truck, watching the coax-cable unpeel into the wellhead. Few of us have lifted a 300 pound logging tool, to feel the force that it would impart on kilometres of cable. We are the recipients of measurements. Either it is a text file, or an image. It is what it is, and who are we to change it? What would an equvialent boot camp for travel-time look like? Is there one?

In the filtered earth, even the depth domain is plastic. Travel-time is the only absolute.

More than a blueprint

"This company used to function just fine without any modeling."

My brother, an architect, paraphrased his supervisor this way one day; perhaps you have heard something similar. "But the construction industry is shifting," he noted. "Now, my boss needs to see things in 3D in order to understand. Which is why we have so many last minute changes in our projects. 'I had no idea that ceiling was so low, that high, that color, had so many lights,' and so on."

The geological modeling process is often an investment with the same goal. I am convinced that many are seduced by the appeal of an elegantly crafted digital design, the wow factor of 3D visualization. Seeing is believing, but in the case of the subsurface, seeing can be misleading.

Not your child's sandbox! Photo: R Weller.Building a geological model is fundamentally different than building a blueprint, or at least it should be. First of all, a geomodel will never be as accurate as a blueprint, even after the last well has been drilled. The geomodel is more akin to the apparatus of an experiment; literally the sandbox and the sand. The real lure of a geomodel is to explore and evaluate uncertainty. I am ambivalent about compelling visualizations that drop out of geomodels, they partially stand in the way of this high potential. Perhaps they are too convincing.

I reckon most managers, drillers, completions folks, and many geoscientists are really only interested in a better blueprint. If that is the case, they are essentially behaving only as designers. That mindset drives a conflict any time the geomodel fails to predict future observations. A blueprint does not have space for uncertainty, it's not defined that way. A model, however, should have uncertainty and simplifying assumptions built right in.

Why are the narrow geological assumptions of the designer so widely accepted and in particular, so enthusiastically embraced by the industry? The neglect of science keeping up with technology is one factor. Our preference for simple and quickly understood explanations is another. Geology, in its wondrous complexity, does not conform to such easy reductions.

Despite popular belief, this is not a blueprint.We gravitate towards a single solution precisely because we are scared of the unknown. Treating uncertainty is more difficult that omitting it, and a range of solutions is somehow less marketable than precision (accuracy and precision are not the same thing). It is easier because if you have a blueprint, rigid, with tight constraints, you have relieved yourself from asking what if?

• What if the fault throw was 20 m instead of 10 m?
• What if the reservoir was oil instead of water?
• What if the pore pressure increases downdip?

The geomodelling process should be undertaken for the promise of invoking questions. Subsurface geoscience is riddled with inherent uncertainties, uncertainties that we aren't even aware of. Maybe our software should have a steel-blue background turned on as default, instead of the traditional black, white, or gray. It might be a subconscious reminder that unless you are capturing uncertainty and iterating, you are only designing a blueprint.

If you have been involved with building a geologic model, was it a one-time rigid design, or an experimental sandbox of iteration?

The photograph of the extensional sandbox experiment is used with permission from Roger Weller of Cochise College. Image of geocellular model from the MATLAB Reservoir Simulation Toolbox (MRST) from SINTEF applied mathematics, which has been recently release under the terms of the GNU General public license!

The filtered earth

Ground-based image (top left) vs Hubble's image. Click for a larger view. One of the reasons for launching the Hubble Space Telescope in 1990 was to eliminate the filter of the atmosphere that affects earth-bound observations of the night sky. The results speak for themselves: more than 10 000 peer-reviewed papers using Hubble data, around 98% of which have citations (only 70% of all astronomy papers are cited). There are plenty of other filters at work on Hubble's data: the optical system, the electronics of image capture and communication, space weather, and even the experience and perceptive power of the human observer. But it's clear: eliminating one filter changed the way we see the cosmos.

What is a filter? Mathematically, it's a subset of a larger set. In optics, it's a wavelength-selection device. In general, it's a thing or process which removes part of the input, leaving some output which may or may not be useful. For example, in seismic processing we apply filters which we hope remove noise, leaving signal for the interpreter. But if the filters are not under our control, if we don't even know what they are, then the relationship between output and input is not clear.

Imagine you fit a green filter to your petrographic microscope. You can't tell the difference between the scene on the left and the one on the right—they have the same amount and distribution of green. Indeed, without the benefit of geological knowledge, the range of possible inputs is infinite. If you could only see a monochrome view, and you didn't know what the filter was, or even if there was one, it's easy to see that the situation would be even worse. 

Like astronomy, the goal of geoscience is to glimpse the objective reality via our subjective observations. All we can do is collect, analyse and interpret filtered data, the sifted ghost of the reality we tried to observe. This is the best we can do. 

What do our filters look like? In the case of seismic reflection data, the filters are mostly familiar: 

• the design determines the spatial and temporal resolution you can achieve
• the source system and near-surface conditions determine the wavelet
• the boundaries and interval properties of the earth filter the wavelet
• the recording system and conditions affect the image resolution and fidelity
• the processing flow can destroy or enhance every aspect of the data
• the data loading process can be a filter, though it should not be
• the display and interpretation methods control what the interpreter sees
• the experience and insight of the interpreter decides what comes out of the entire process

Every other piece of data you touch, from wireline logs to point-count analyses, and from pressure plots to production volumes, is a filtered expression of the earth. Do you know your filters? Try making a list—it might surprise you how long it is. Then ask yourself if you can do anything about any of them, and imagine what you might see if you could. 

Hubble image is public domain. Photomicrograph from Flickr user Nagem R., licensed CC-BY-NC-SA.