### Introduction

Amplitude variations with offset (AVO) have been used for over a quarter of a century in the hunt for gas and oil. The first public disclosure of the technique was made by Bill Ostrander, at the 1982 SEG convention in Dallas. At the time, Bill was reporting on a seasoned technology - having been used for a decade within Chevron. A seasoned technique, perhaps, but certainly not mature.

The first year of public AVO was a mad scramble characterized by wild claims, outrageous prices ($5000 per CMP) for incredible products (Poisson’s ratio to three decimal places with resolution to match) - a snake oil bonanza. Some relief came from the SEG continuing education course, Seismic Lithology - AVO, first offered in 1983 (and still going strong, with constant upgrades and repairs), but only through the concerted efforts of industrial and academic research teams did reason supplant panic in the ever expanding and myth-filled field.

In 1992, a watershed event took place: the SEG AVO Symposium in Big Sky, Montana. This seismic epiphany was the beginning of an era of enlightenment. Within a year, the Magnus Opus of editors John Castagna and Milo Backus, Offset-Dependent Reflectivity - Theory and Practice of AVO Analysis, began populating the offices of the geophysical world. The number sessions at the international meeting of the SEG devoted to AVO and related topics had to be expanded - repeatedly. Hardly an issue of Geophysics, The Leading Edge, Geophysical Prospecting, or First Break appears without at least one AVO paper. That interest in this topic has not waned is evidenced by the SRO attendance at Fred Hilterman’s SEG DISC, Seismic Amplitude Interpretation.

So what has happened in the last 10 years? Let’s take a retrolook and see if it points the way to the future of AVO.

### Rock Physics and Forward Modeling

The work of Castagna, Batzle, Wang, Han, and many, many others, in relating rock properties to lithology and pore fluid, has facilitated realistic modeling of both P-wave and S-wave reflectivities. Castagna’s 1985 “mudrock line” (MRL), relating shear and p-wave velocities, has been augmented by numerous field and lab trend curves extending the clastic-silicate model to include many different and mixed lithologies. Density-velocity relationships for various lithologies and pore fluids have been added. The effects of pressure, temperature, clay content, fluid mixtures, and porosity have led to methods for predicting elastic properties necessary for implementing the venerable Gassmann equations. Krief, Greenberg and Castagna, and Xu and White have published methods extending and complementing the work of Gassmann. Their techniques estimate, for example, shear velocity, from commonly available field measurements. This allows for prediction of reasonable rock parameters under fluid substitution or porosity perturbation. An excellent and up-to-date summary of these results and much more may be found in The Rock Physics Handbook by Mavko, Mukerji, and Dvorkin (1998).

As the trend toward longer offsets continues, the modeling techniques have kept pace. Accounting for such aggravating factors as post-critical complex reflectivity, anisotropy, and Q, has led to a better understanding of the tenuous relationship between Zoeppritz and hard reality. The fundamental nonuniqueness of AVO is under attack, with a goal of at least limiting the interpretations to a reasonable few.

### Crossplotting

This technique has been in popular use since the early 1990’s. Most often, it takes the form of a horizon-related crossplots of AVO-derived parameters such as intercept (A) vs slope (B), defined by the so-called two term approximation, **R() = A + Bsin2()**. Now, virtually any AVO attributes or derived parameters (e.g., EI, elastic impedance) may be crossplotted in n-dimensions in the search for trends or clusters which may aid in the interpretation. Color-coded visualization techniques, as well as the discriminating axis rotations and scaling methods, have added much to this popular procedure.

### Classifications

In 1997, Castagna added a much needed classification to the three reservoir-top AVO categories of Rutherford and Williams. His Class IV AVOmaly represents a low impedance reservoir whose reflectivity shows a diminishing magnitude with offset. This type of amplitude behavior dramatically pointed out the necessity to evaluate AVO against the background trend of wet rocks. The “Fluid Factor” method of Smith and Gidlow (1987) typified this type of analysis.

### Pressure Predictions and Applications

The effect of pressure on rock properties is becoming usefully clear. Carcione (2001) noted that consideration of pore pressure above and below a reservoir seal, along with the seal thickness, may lead to a Class III AVOmaly exhibiting a Class IV persona. This work is substantiated by the findings of Lindsay and Towner (2001) that pore pressure has a much greater effect on shales than sandstones. This disproportionate influence may lead to wildly variable AVO results for the same sand under different pressure conditions. It suggests that pressure-perturbed modeling may be called for. Independent of the search for hydrocarbons, AVO is becoming a popular validation method in the very important field of geopressure prediction.

### Geostatistics

The recognition of the inevitable ambiguity of AVO inversions has led to the use of probabilistic assessments. Probability density functions (likelihood of gas, for example), superimposed on crossplots, provide the interpreter with meaningful risk analysis. Of course, quantitative reliance on such information is, itself, a risky proposition. The uncertainties in seismic data do not lend themselves to easy quantification, but the statistical approach has much merit. This was nicely illustrated by Mukerji, et al. (2001).

### Long Offsets

The acquisition and use of data in which offset-to-depth ratio (O/D) exceeds two is becoming the norm, both in land and marine exploration. With such data, subtle AVOmalies may be transformed into the obvious. Such was the observation of Hilterman, et al. (2000) in a Gulf of Mexico example in which a risky Class I reflection was moved into the Class II category by the enlightened use of offsets in the 9000 m range. Of course, one does not just apply standard (O/D < 1) procedures to such data. There is much to consider in the land of nonhyperbolic NMO and waveform variations due to complex reflection coefficients. There is also much to be gained.

### Fizz Water Discrimination

The first thing to ponder about this popular scapegoat for the “noncommercial” production is just exactly what does it mean? When one says, “30% gas saturation,” does that mean 30% free gas volume in tiny-bubble, homogeneous suspension with 70% brine? Is each pore occupied by 30% gas? What keeps it from migrating to the reservoir top (where it might become a respectable, albeit thin, 85% saturation)? (If the rock lacks the permeability, what kind of reservoir is it?) Han, Batzle, and Gibson, at the SEG Symposium on Reservoir Resolution (2001), provided answers and insights into this very important - but ill-defined - issue. The effect of dissolved gas, or even exsolving bubbles, under high pressure conditions (>3000 psi), on fluid properties, is negligible. Gas, under high in situ pressure and temperature conditions, behaves much like a light oil. The in situ distribution of gas - perhaps “patchy” - is a key element in the modeling and understanding of the “fizz water” phenomenon.

Zhu, et al., (2000), using multicomponent seismic data and AVO techniques, report a method capable of distinguishing low saturation reservoir from the commercial through certain P-wave and PS wave parameters. Kelly, et al. (2001) and Skidmore, et al. (2001) promote a method utilizing the 3-term approximation to the Zoeppritz equations. In theory, an AVO curve with 3 well estimated parameters would allow separation of the density, and both P- and S-wave velocity contrasts. This, in turn, might yield sufficient information to distinguish lithologic and saturation effects.

### Pore Fluid and Lithologic Discriminators

There is no lack of proposed indicators in the direct detection world. Beyond the A - B crossplots, and the approximation parameters suggested by Hilterman and Verm (NI and PR, normal incidence and Poisson reflectivity, respectively) there are numerous others derivable from 2- and 3-term AVO curve fitting procedures. A few of the more popular or newer ones are noted below.

**The Fluid Factor** (Smith and Gidlow, 1987)

**ΔF(t) = Rp(t) – gRs(t)**

Rp(t) and Rs(t) represent the P and S normal incident reflectivity sections respectively. The g term represents the average ratio, (Rp/Rs), for wet rocks - a background parameter. For nongaseous rocks, ΔF ≈ 0. It has been noted that the Fluid Factor and Poisson reflectivity are essentially equivalent when Vp/Vs =2.

The LMR Parameters (Goodway, et al., 1997) The L, M, and R represent (Englishly) λ, μ, and ρ, respectively. λ is the Lame constant; μ the shear modulus or coefficient of rigidity; and ρ, the density. λ = k - (2/3)μ, where k = bulk modulus. The various combinations of λ, μ, and ρ, e.g., λρ, μρ, show good separation of varying pore-fluid zones, in crossplots. λρ may also be plotted in trace form, as a seismic section or volume, highlighting those areas of most likely reservoir potential. The extraction and use of these parameters seems particularly well suited for the hard-rock reservoirs of Canada. Hilterman (2001) demonstrates that λρ is equivalent to Gassmann’s fluid discriminator, the pore-fluid bulk modulus effect - essentially the difference between the dry rock bulk modulus and the saturated rock bulk modulus: **ΔK = Ksat - Kdry**. Water, gas, and oil have distinct bulk moduli, so an accurate estimate of ΔK may provide a direct evaluation of pore fluid.

**(K - μ )** This fluid indicator was proposed by Batzle, Han, and Hofman (2001). It provides a direct look at the effect of pore fluid on the bulk modulus, and as such is quite similar to the λρ (above), and therefore, to the Gassmann fluid indicator described by Hilterman. It has the potential for serving best in a sandstone regime where the clay content may vary from negligible to significant.

**Elastic Impedance** Connolly (TLE, 1999) defines this parameter as,

**EI(θ) = V ^{ (1 + tan2 (θ))}. ^{W –8γ2sin2 (θ)}. ρ^{(1–4γ2sin2 (θ))}**

W is the S-wave velocity, and γ = average (W/V). EI plays the same role for angle-dependent reflectivity that acoustic impedance (AI) does for incident angle θ = 0. Note that EI(0) = Vρ = AI. The computation of elastic reflectivity is analogous to P-wave reflectivity:

**RE(θ) = [E2(θ)- E1(θ] / [ E2(θ) + E1(θ)]**

Crossplots of EI vs AI are quite similar to Poisson’s ratio vs AI in their ability to separate into distinguishable clusters the gas sands of Class II AVOmalies. Wet sands and shales align separately in different trends. Connolly (1999) provides an excellent tutorial on this murky subject.

Recently, Duffaut, et alia (2000) extended the concept of elastic impedance to include shear-wave elastic impedance for use on converted wave data. Both methods may derive estimated parameters from partial (angle) stack inversion techniques.

### AVO Processing Considerations

There have always been problems associated with the proper prestack processing protocol, and the robust determination of AVO attributes. These problems are still with us, and have become more critical with the acquisition of 3D data and the growing use of long offset recordings. Below, we highlight a few of the issues facing the processor and interpreter with seismic data of today.

#### 3D Land Acquisition Problems (also applies to OBC data):

- Most land data is acquired without the benefit of proper spatial anti-aliasing (the arrays are pitifully inadequate). This would lead to 3-alarm aliasing of coherent noise, but the concept of aliasing is somewhat blurred by the fact that the spatial
**sampling in offset space is not uniform**. The essence of the problem is that the data is in very poor condition (compared to the old 2D data) when it arrives in the processing center; and because of the nonuniform sampling, the usual arsenal of weaponry is unavailable: no FK, no Radon, no anything which counts on a spatial FFT for efficacy. Were it not for the power of migration and stacking, 3D data would be overwhelmingly incapacitated by noise. **Azimuth: friend and foe**. Azimuthal AVO is the life blood of such applications as fracture detection (see below), but acts as an evil twin for purposes of velocity analysis. With or without intrinsic anisotropy, the structural conditions alone may provide the unwary velocity picker with a befuddling choice of equally incorrect NMO curves for any given CMP gather. Unless the processor is blessed with enough fold to do azimuthal velocity analysis, he is in deep difficulty.**Acquisition footprints**. In addition to variable fold, the offset distribution is rarely close to uniform, and the prestack migration aperture is commonly inadequate.

#### Long offsets

Even ignoring the azimuthal factors noted above, the long offsets bring screaming to into focus something we all knew, but would rather not think about: the **NMO curve** never was a hyperbola. We were able to get away with standard hyperbolic analysis techniques as long as the O/D < 1 (and we muted away all evidence to the contrary). Not anymore: the dreaded “hockey stick” NMO patterns at the far offsets require new procedures. We may also expect severe waveform variations, both “legitimate,” i.e., due to complex reflectivity variations post critical, where θ > θc, and pathologic, e.g., as a result of Q, or perhaps array effects. The processor merely needs to differentiate the problem sources – and then eliminate the bad guys without obliterating the reflectivity information.

#### Processing artifacts

**Residual NMO**– this is a fatal flaw if one is doing constant time, sample-by-sample attribute estimation of gradient and intercept of the AVO curve. The intercept is relatively insensitive to RNMO, but the gradient suffers exquisitely at the hands of even the slightest residual. Rock properties extracted from such flawed attributes are meaningless, if not dangerous.**Stretch**– a waveform variation rendering both intercept (Ro) and gradient (G) useless.**Amplitude balancing**– a necessary but ill-defined process in which the usual deterministic (model-based) procedures will not suffice. Invariably, a statistical, data dependent method must be invoked in order to prepare the migrated gathers for AVO attribute analysis. Precautions must be taken to protect the “AVOmalies” in the data, but the correct implementation of this policy is not always obvious to the weekend processor.**Wavelet processing**– the object here is equalization of those reflection wavelet shapes whose differences are as a result of factors independent of reflectivity itself. Such factors would include Q (inelastic attenuation), which causes phase and amplitude variations in time and offset, short-path interbed multiples (much like Q in its impact), and array effects. Any of these factors may cause irreparable damage to the derived attributes. Luh (1993) suggests prestack Q-compensation may well be necessary.**Noise suppression**– should be done provided the method attacks the noise and not the signal. This is not always an easy condition to satisfy – especially on land 3D data.

#### Cambois’ Caveat

Cambois (2000) posed the question, “Can P-wave AVO be quantitative?” After due consideration of various resistant factors, his answer may be paraphrased as, “Not right now – maybe later.” Cambois demonstrates that in most real data sets, the gradient and intercept are statistically correlated as a result of seismic “noise,” be it from wavelet variation (RNMO, stretch) or random noise. This negative correlation trend manifests itself as a negative slope on crossplotted data. That it is nongeologic in origin is demonstrated by a crossplot of gradient against ordinary mean stack.

The disheartening conclusion is that noise – particularly the wavelet variation type – renders some of the industry’s most treasured attributes (e.g., the Fluid Factor) essentially meaningless. Much work remains to be done in this area.

### 4D – Multicomponent AVO

The time-lapse comparison of AVO parameters may be much larger than predicted by simple Biot-Gassmann theory due to changes in rock frame moduli resulting from effective stress variations, microfracturing, reservoir consolidation, etc. In light of some of the difficulties cited above, this comes as welcome news, and will be pursued. Multicomponent recording (3-C in many land surveys, 3-C plus a hydrophone for OBC data) continues to gain popularity as the interpretive use of P-S waves becomes familiar.

### Anisotropy and Fracture Detection

Ruger and Tsvankin (1997) modify the Shuey approximation for P-wave reflectivity to show the influence of the Thompsen anisotropy parameters as a function of incident angle and azimuth with respect to the symmetry axis (perpendicular to the fracturing strike). P-wave AVO inversion, coupled with azimuthally varying short-spread velocity analysis, has the potential for discriminating between gas- and liquid-filled crack system, as well as fracture orientation, and the contrast of anisotropic model types at the reflecting interface. Contrasts in the anisotropic parameters are shown to have a first order effect on AVO gradients.

Gray and Head (2000) study 3D AVAZ (azimuthally varying AVO) for a fractured carbonate reservoir. The fracture-induced variations in rigidity lead to AVO responses sensitive to fracture orientation and crack density.

### AVO Attributes in Log Prediction

Hampson, et al. (2001) report on the use of multiattribute linear regression and probabilistic neural networks to predict log properties from seismic data. The input comprises a multitude of complex trace attributes, inversions, velocity and analyses, Q estimations, nonlinear transformations, and AVO attributes, as well as logs from selected training sites. This work was extended (e.g., Graul, SEG AVO Continuing Education course) to include a wider variety of AVO attributes, some of which are nonlinearly related to the common 2- and 3-term fit parameters.

The indications are clear that there is much work to do in the area of AVO. It is equally apparent that the rewards may well justify the effort.

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