Permeability Anisotropy from Seismic Anisotropy and Other Holy Grails

Permeability anisotropy from seismic anisotropy is an exciting avenue to gain insights into the aligned flow conduits – the aligned connected porosity – which set up a form of seismic anisotropy.

The last SEG Annual Meeting (2002) had an entire session on the relationships between seismic anisotropy and permeability anisotropy. [Do you want to hear more? Come to the next SEG Annual Meeting!]

As discussed in a previous article, the method by which the data is acquired (narrow-azimuth 3D or full-azimuth 3D) governs the conclusions that the interpreters make about the earth. (“Where you sit governs what you see”)

The chance to study permeability anisotropy in a meaningful fashion is almost nil in a narrow azimuth PP 3D survey. One’s chances improve considerably with a 3D PP full-azimuth full-offset survey. A narrow azimuth 3D 3C is still better, but one’s chances get to (almost) a slam-dunk with a 3D 3C full-azimuth full-offset survey. Of course, I realize that that last sentence is inflammatory, but part of my job is to spread the word about what those fuzzball anisotropists are talking about these days. (I cheerfully admit to being one of Them, but I am also one of Us.)

In the full-azimuth full-offset 3D PP reflection survey, the good news is that all those wonderful PP reflectors are imaged (by azimuthal processing techniques) and then mapped, to see the fault, and synclines and anticlines, and reefs, and all those other earth-structures buried at depth. There is the Fast Velocity Direction (telling us about the maximum horizontal stress direction and/or the vertical aligned fractures), and the Slow Velocity Direction (telling us about the combination of Lithology and Fractures & Stress). And of course there are the azimuthal differences in the AVO gradient. But, with two AVO gradients, and two velocity fields, “Which one is true?”

They both are.

“Are they different?” Yes.

“Which one is right?” They both are.

There isn’t just “one” answer. If you want just one answer, you have to phrase your question very carefully, very mindfully, and very intently. And even then, don’t hold your breath til you get The One Answer.

So of course you are muttering, “Enough of the Zen! All I want is Structure, Lithology, Porosity, and Pore-Fluids!!!” (Perhaps you might also be thinking, “and if you throw in pore pressure and permeability, I’ll say, thank you very much, ma’am!”). So, of course, this list is beginning to sound like “A Holy Grail” for seismic reflectionists…. The definition of A Holy Grail is that which, if we have, then we have all that is, and all our sorrows and problems go away.

Structure is the true-depth attitudes of the rock layers. Lithology is the rock type with which we are dealing.

Porosity is All-That-Is-Not-Rock —that’s the empty holes that hold the fluids. To have a reservoir, we gotta have Not-Rock. The more not-rock, the better, as long as the not-rock is connected with large enough pore throats to flow the desired fluid. So here, finally we’re talking connected porosity. If the connected porosity is aligned, then you are looking at an azimuthally anisotropic earth, for one direction appears stiff and the orthogonal direction appears compliant. Aligned compliant members, smaller than a wavelength and embedded in a rock, cause azimuthal anisotropy.

Pore fluids are obviously either Brine, Oil, or Gas, and/or some mixture thereof.

The only reason that anybody fools with seismic data is that in the past, our industry has been pretty successful in getting structure (although complex structure areas are still challenging us); we have learned to estimate lithology; we do get porosity from PP amplitudes in most settings; and we do get pore fluid estimates (in some environments). However, everybody is convinced that We Can Do Better. That’s what humans always say. Being human is getting “We Can Do Better” done.

To do better in the 3D multicomponent multiazimuth world will go easier if one realizes that Aristotelian logic ain’t gonna cut it.

Aristotelian logic dealt with “A” and “Not-A”. The middle (partly A and partly Not A) was excluded. This excluded middle is a great flaw in a thinking process, for we humans live in the middle. We don’t live in an extreme (A or Not A), we experience the middle, with bits and pieces of A and Not A swirling all around. Our job is to separate out what we need and want, and hang on to it; while letting what we don’t need and don’t want get swirled away.

We geophysicists stack what we don’t want to see, and we preserve what we do want to see as 3D volumes of numbers. We stack amplitudes across offset, yet preserve a volume of AVO gradient and zero-offset intercept, for we know that the AVO gradient carries geologic meaning, like the contrast of the VP/VS ratio at a boundary for the given azimuth of the source-receiver raypath. If the far-offsets have a nonlinear AVO term, then this 3rd term ought to be estimated, kept, and interpreted (modeled).

We NMO correct prior to stack, yet preserve a volume of Vrms that described how the NMO was done, because we need that traveltime information, usually as converted to interval velocity information, in order to get a handle on lithology. It is also useful for going to depth: there is much merit in considering pre-stack depth migration using a tomographic approach that understands azimuthal anisotropy. Removing the first-order heterogeneity prior to estimating the azimuthal anisotropy is a step forward.

prior to estimating the azimuthal anisotropy is a step forward. We geophysicists stack across azimuth and offset, yet preserve the azimuthal variation in AVO gradient as volumes and the azimuthal variation in V_rms and/or V_int as volumes, because we know the azimuthal variations in our measurements are caused by the presence of vertical aligned fractures and/or unequal horizontal stress fields. With AVOA, there are at least four volumes of derived attributes: the large (most positive) AVO gradient, the azimuth of the large AVO gradient, the azimuthal difference in the AVO gradient, and the error in the fit between the model (an ellipse) and the field data.

One thing that could happen is if the tri-axial horizontal stress field is tipped due to in situ stresses, the mode-conversions’ behaviour will also be tipped relative to that symmetry. And of course if there are dipping layers, the mode-conversions’ behaviour will also be set by that symmetry.

For those of us operating in the multicomponent world, we have PS amplitudes, PS velocities, S interval velocities, and PS AVO (a two-term number), so counting up those volumes, we need to be looking at: PS₁ amplitudes; PS₂ amplitudes; PS₁ velocities; PS₂ velocities; S₁ interval velocities; S₂ interval velocities; PS₁ AVO Prime and Secondary; PS₂ AVO Prime and Secondary. Here are ten 3D volumes.

Obviously we need to co-render these ten S volumes and six to eight PP volumes. We co-render first by either going to depth or taking PP to PS time or taking PS to PP time. If your PP data is all messed up with fluid effects, you really need to be taking your PP data to PS time. If your PP data is not all messed up with fluid effects, then you can take your PS data to PP time. However, a favorite usage of PS data is in gas chimneys where the PP times are perturbed by the gas, especially when the gas chimney is a fracture effect, so logically PS time is a pretty good time to work in. (Or depth, if you can cut straight to what we really want.)

So now, of course, we have somewhere between 6 to 18 volumes of 3D seismic data, that we wish to co-render and interpret. This is a high-dimensionality dataset. The physicists are talking about how their reality contains 11 dimensions. Non-scientific humans easily identify the 3 space dimensions and the time dimension, but sometimes are puzzled as to how any higher dimensionalities exist. That’s where we geophysicists have a leg up on other scientific disciplines, for we readily know we deal in a high dimensionality reality. Our 3D volume which on first look simply has an amplitude (a 3D volume of wiggle traces) is really a 3D volume filled with 6-18 dimensional numbers. It is straightforward to list the most important eleven dimensions that I suggest geophysicists work in – that’s the next article. So, higher dimensions, here we come!

Back to Aristotelian logic. Often we think, is this Signal or is it Noise? If it is signal, then we’ll keep it. If it is noise, we’ll throw it away. Let’s work in the included middle, where there are bits of signal and bits of noise swirling all around. First of all, whether something is labelled signal or called noise depends upon what you want to accomplish. Once upon a time, the azimuthal variation in travel times and amplitudes was called Noise and it vanished, stacked across, either coherently or incoherently. (Usually incoherently.) Now of course, azimuthal variations are Signal that some of us look for all the time, because we are unwilling to give up such diagnostic information.

The back-scattered incoherently reflected wavefield has often been the prime candidate for the label Noise. Yet, if we see a strong azimuthal dependence upon the back-scattered incoherent wave-field, and if there is a symmetry in the polar co-ordinate display of the 3D seismic gather, of course we are speaking one-fold data, prestack, then we can learn more about the earth. We will need to produce a map showing the magnitude and orientation of this phenomenon, and if it relates to the presence of a fault; or better production from a fractured reservoir, then we can ask the question, what set of fracture(s) could produce the observed azimuthally-different back-scattered wavefield ? The theoreticians have been talking about how the back-scattered field is azimuthally-dependent. …. Now, there are probably all sorts of reasons for why we have been observing an azimuthally-dependent Signal/Noise for decades, but in many areas of the world, it is well known that the S/N ratio depends upon the azimuth. Now folks, why don’t some of us just try to extract the geologic reason for this phenomenon?

Another issue is the azimuth-dependency upon the multiples (the pegleg multiples, the short travelpath interbed bounces). If we see an azimuth-dependent periodicity in the far offset trailing legs (the coda), then it is obvious that the velocity is azimuth-dependent. Well, folks, some of us have been talking about azimuthal velocity dependence for years… If we could pull the Signal out from the Noise, then we will have more Signal to work with. That is a Good Thing. Many geophysicists have allowed the multiples’ periodicity to change with offset: that’s another interesting thing to look at…. Sometimes our reservoirs are “too thin” to see meaningful traveltime variations in, with just “the primary”…but the pegleg bounce through the reservoir units has seen the reservoir twice or thrice or more, depending upon how you count these things….Wouldn’t you rather pull a small number out of something that’s seen what you’re looking for several times?

There are other types of As and Not As to talk about, but I’m sure you can see what the argument is. This argument particularly extends to being Serendipitous or Smart, wherein oil people have said for decades (centuries), “I’d rather be lucky than smart.” Non- Aristotelian logic says: “Let’s recognize the bits of both, let’s have lots of both, and live in the included middle.”