What is anisotropy?


Geophysicists often assume that the earth is isotropic. This word comes from 'iso', meaning same, and 'tropikos', meaning something to do with turning. The idea is that isotropic materials look the same in all directions — they have no orientation, and we can make measurements in any direction and get the same result. Note that this is different from homogeneous, which is the quality of uniformity of composition. You can think of anisotropy as a directional (not just spatial) variation in homogeneity. 

In the illustration, I may have cheated a bit. The lower-left image shows a material that is homogeneous but anisotropic. The thin lines are supposed to indicate microfractures, say, or the alignment of clay flakes, or even just stress. So although the material has uniform composition, at least at this scale, it has an orientation.

The recognition of the earth's anisotropy is a dominant theme among papers in our forthcoming 52 Things book on rock physics. It's not exactly a new thing — it was an emerging trend 10 years ago when Larry Lines at U of C reviewed Milo Backus's famous 'challenges' (Lines 2005). And even then, the spread of anisotropic processing and analysis had been underway for almost 20 years since Leon Thomsen's classic 1986 paper, Weak elastic anisotropy. This paper introduced three parameters that we need—alongside the usual \(V_\text{P}\), \(V_\text{S}\), and \(\rho\)—to describe anisotropy. They are \(\delta\) (delta), \(\epsilon\) (epsilon), and \(\gamma\) (gamma), collectively referred to as Thomsen's parameters

  • \(\delta\) or delta — the short offset effect — captures the relationship between the velocity required to flatten gathers (the NMO velocity) and the zero-offset average velocity as recorded by checkshots. It's easy to measure, but perhaps hard to understand in physical terms.
  • \(\epsilon\) or epsilon — the long offset effect — is, according to Thomsen himself:  "the fractional difference between vertical and horizontal P velocities; i.e., it is the parameter usually referred to as 'the' anisotropy of a rock". Unfortunately, the horizontal velocity is rather hard to measure. 
  • \(\gamma\) or gamma — the shear wave effect — relates, as rock physics meister Colin Sayers put it on Twitter, a horizontal shear wave with horizontal polarization to a vertical shear wave. He added, "\(\gamma\) can be determined in a single well using sonic. So the correlation with \(\epsilon\) and \(\delta\) is of great interest."

Sidenote to aspiring authors: Thomsen's seminal paper, which has been cited over 2800 times, is barely 13 pages long. Three and a half of those pages are taken up by... data! A huge table containing the elastic parameters of almost 60 samples. And this is from a corporate scientist at Amoco. So no more excuses: publish you data! </rant>

Vertical transverse what now?

The other bit of jargon you will come across is the concept of transverse isotropy, which is a slightly perverse (to me) way of expressing the orientation of the anisotropy effect. In vertical transverse isotropy, the horizontal velocity is different from the vertical velocity. Think of flat-lying shales with gravity dominating the stress field. Usually, the velocity is faster along the beds than it is across the beds. This manifests as nonhyperbolic moveout in the far offsets, in particular a pull-up or 'hockey stick' effect in the gathers — the arrivals are unexpectedly early at long offsets. Clearly, this will also affect AVO analysis

There's more jargon. If the rocks are dipping, we call it tilted transverse isotropy, or TTI. But if the anisotropies, so to speak, are oriented vertically — as with fractures, for example, or simply horizontal stress — then it's horizontal transverse isotropy, or HTI. This causes azimuthal (compass directional) travel-time variations. We can even venture into situations where we encounter orthorhombic anisotropy, as in the combined VTI/HTI model shown above. It's easy to imagine how these effects, if not accounted for in processing, can (and do!) result in suboptimal seismic images. Accounting for them is not easy though, and trying can do more harm than good.

If you have handy rules of thumb of ways of conceptualizing anisotropy, I'd love to hear about them. Some time soon I want to write about thin-layer anisotropy, which is where this post was going until I got sidetracked...


Lines, L (2005). Addressing Milo's challenges with 25 years of seismic advances. The Leading Edge 24 (1), 32–35. DOI 10.1190/1.2112389.

Thomsen, L (1986). Weak elastic anisotropy. Geophysics 51 (10), 1954–1966. DOI 10.1190/1.1442051.

Grand challenges, anisotropy, and diffractions

Some more highlights from the two final days of the SEG Annual Meeting in Houston.

Grand challenges

On Friday, I reported on Chevron's take on the unsolved problems in petroleum geoscience. It was largely about technology. Ken Tubman, VP of Geoscience and Reservoir Engineering at ConocoPhillips gave an equally compelling outlook on some different issue. He had five points:

  • Protect the base — Fighting the decline of current production is more challenging than growing production.
  • Deepwater — Recent advances in drilling are providing access to larger fields in deep water, and compressed sampling in seismic will make exploration more efficient.
  • Unconventionals — In regard to the shale gas frenzy, it is not yet obvious why these reservoirs produce the way that they do. Also, since resource plays are so massive, a big challenge will be shooting larger surveys on land.
  • Environment and safety — Containment assurance is more critical than pay-zone management, and geophysics will find an expanding role in preventing and diagnosing environmental and safety issues.
  • People — Corporations are concerned about maintaining world class people. Which will only become more difficult as the demographic bump of senior knowledge heads off into retirement.

The Calgary crowd that harvested the list of unsolved problems at our unsession in May touched on many of these points, and identified many others that went unmentioned in this session.

Driving anisotropic ideas

In the past, seismic imaging and wave propagation were almost exclusively driven by isotropic ideas. In the final talk of the technical program, Leon Thomsen asserted that the industry has been doing AVO wrong for 30 years, and doing geomechanics wrong for 5 years. Three take-aways:

  • Isotropy is no longer an acceptable approximation. It is conceptually flawed to relate Young's modulus (an elastic property), to brittleness (a mode of failure). 
  • Abolish the terms vertically transverse isotropy (VTI), and horizontally transverse isotropy (HTI) from our vocabulary; how confusing to have types of anisotropy with isotropy in the name! Use polar anisotropy (for VTI), and azimuthal anisotropy (for HTI) instead.
  • λ13 is a simple expression of P-wave modulus M, and Thomsen's polar anisotropy parameter δ, so it should be attainable with logs.

Bill Goodway, whose work with elasticity has been criticized by Thomsen, walked to the microphone and pointed out to both the speaker and audience, that the tractability of λ13 is what he has been saying all along. Colin Sayers then stood up to reiterate that geomechanics is the statistics of extremes. Anisotropic rock physics is uncontestable, but the challenge remains to find correlations with things we actually measure.

Thomas Young's sketch of 2-slit diffraction, which he showed to the Royal Society in 1803.

Imaging fractures using diffractions

Diffractions are fascinating physical phenomena that occur when the conditions of wave propagation change dramatically. They are a sort of grey zone between reflection and scattering, and can be used to resolve fractures in the subsufrace. The question is whether or not there is enough diffraction energy to detect the fractures; it can be 10× smaller than a specular reflection, so one needs very good data acquisition. Problem is, we must subtract reflections — which we deliberately optimized for — from the wavefield to get diffractions. Evgeny Landa, from Opera Geophysical, was terse, 'we must first study noise, in this case the noise is the reflections... We must study the enemy before we kill it.'

Prospecting with plate tectonics

The Santos, Campos, and Espirito Basins off the coast of Brazil contain prolific oil discoveries and, through the application of plate tectonics, explorers have been able to extend the play concepts to offshore western Africa. John Dribus, Geological Advisor at Schlumberger, described a number of discoveries as 'kissing cousins' on either side of the Atlantic, using fundamental concepts of continental margin systems and plate tectonics (read more here). He spoke passionately about big ideas, and acknowledged collaboration as a necessity: 'if we don't share our knowledge we re-invent the wheel, and we can't do that any longer'.

In the discussion session afterwards, I asked him to comment on offshore successes, which has historically hovered around 14–18%. He noted that a step change — up to about 35% — in success occured in 2009, and he gave 3 causes for it: 

  • Seismic imaging around 2005 started dealing with anisotropy appropriately, getting the images right.
  • Improved understanding of maturation and petroleum system elements that we didn’t have before.
  • Access to places we didn’t have access to before.

Although the workshop format isn't all that different from the relentless PowerPoint of the technical talks, it did have an entirely different feeling. Was it the ample discussion time, or the fact that the trade show, now packed neatly in plywood boxes, boosted the signal:noise? Did you see anything remarkable at a workshop last week? 

Submitting assumptions for meaningful answers

The best talk of the conference was Ran Bachrach's on seismics for unconventionals. He enthusiastically described the physics to his spectators with conviction and duty, and explained why they should care. Isotropic, VTI, and orthorhombic media anisotropy models are used not because they are right, but because they are simple. If the assumptions you bring to the problem are reasonable, the answers can be considered meaningful. If you haven't considered and tested your assumptions, you haven't subscribed to reason. In a sense, you haven't held up your end of the bargain, and there will never be agreement. This talk should be mandatory viewing for anyone working seismic for unconventionals. Advocacy for reason. Too bad it wasn't recorded.

I am both privileged and obliged to celebrate such nuggets of awesomeness. That's a big reason why I blog. And on the contrary, we should call out crappy talks when we see them to raise the bar. Indeed, to quote Zen Faulkes, "...we should start creating more of an expectation that scientific talks will be reviewed and critiqued. And names will be named."

The talk from HEF Petrophysical entitled, Towards modelling three-dimensional oil sands permeability distribution using borehole image logs, drew me in. I was curious enough to show up. But as the talk unfolded, my curiosity was left unsatisfied. A potentially interesting workflow of transforming high-resolution resistivity measurements into flow permeability was obfuscated with a pointless upscaling step. The meat of anything like this is in the transform itself, but it was missing. It's also the most trivial bit; just cross-plot one property with another and show people. So I am guessing they didn't have any permeability data. If that was the case, how can you stand up and talk about permeability? It was a sandwich without the filling. The essential thing that defines a piece of work is the creativity. The thing you add that wasn't there before. I was disappointed. Disappointed that it was accepted, and that no one else piped up. 

I will paraphrase a conversation I had with Ran at the coffee break: Some are not aware, some choose to ignore, and some forget that works of geoscience are problems of extreme complexity. In fact, the only way we can cope with complexity is to make certain assumptions that make our problem solvable. If all you do is say "here is my solution", you suck. But if instead you ask, "Have I convinced you that my assumptions are reasonable?", it entirely changes the conversation. It entirely changes the specialist's role. Only when you understand your assumptions can we talk about whether the results are reasonable. 

Have you ever felt conflicted on whether or not you should say something?

Resolution, anisotropy, and brains

Day 1 of the SEG Annual Meeting continued with the start of the regular program — 96 talks and 71 posters, not to mention the 323 booths on the exhibition floor. Instead of deciding where to start, I wandered around the bookstore and bought Don Herron's nice-looking new book, First Steps in Seismic Interpretation, which we will review some time soon.

Here are my highlights from the rest of the day.

Chuck Ursenbach, Arcis

Calgary is the home of seismic geophysics. There's a deep tradition of signal processing, and getting the basics right. Sometimes there's snake oil too, but mostly it's good, honest science. And mathematics. So when Jim Gaiser suggested last year at SEG that PS data might offer as good resolution as SS or PP — as good, and possibly better — you know someone in Calgary will jump on it with MATLAB. Ursenbach, Cary, and Perz [PDF] did some jumping, and conclude: PP-to-PS mapping can indeed increase bandwidth, but the resolution is unchanged, because the wavelength is unchanged — 'conservation of resolution', as Ursenbach put it. Resolution isn't everything. 

Gabriel Chao, Total E&P

Chao showed a real-world case study starting with a PreSTM gather with a decent Class 2p AVO anomaly at the top of the reservoir interval (TTI Kirchhoff with 450–4350 m offset). There was residual NMO in the gather, as Leon Thomsen himself later forced Chao to admit, but there did seem to be a phase reversal at about 25°. The authors compared the gather with three synthetics: isotropic convolutional, anisotropic convolutional, and full waveform. The isotropic model was fair, but the phase reversal was out at 33°. The anisotropic convolutional model matched well right up to about 42°, beyond which only the full waveform model was close (right). Anisotropy made a similar difference to wavelet extraction, especially beyond about 25°.

Canada prevails

With no hockey to divert them, Canadians are focusing on geophysical contests this year. With the Canadian champions Keneth Silva and Abdolnaser Yousetz Zadeh denied the chance to go for the world title by circumstances beyond their control, Canada fielded a scratch team of Adrian Smith (U of C) and Darragh O'Connor (Dalhousie). So much depth is there in the boreal Americas that the pair stormed home with the trophy, the cash, and the glory.

The Challenge Bowl event was a delight — live music, semi-raucous cheering, and who can resist MC Peter Duncan's cheesy jests? If you weren't there, promise yourself you'll go next year. 

The image from Chao is copyright of SEG, from the 2012 Annual Meeting proceedings, and used here in accordance with their permissions guidelines. The image of Herron's book is also copyright of SEG; its use here is proposed to be fair use.