AVO: Amplitude Variation with Offset, Classes, and Direct Hydrocarbon Indicators

Key Takeaways

• Physical basis: Zoeppritz equations and the Shuey linearization: The full Zoeppritz equations express the P-wave reflection coefficient Rpp as a complex function of incidence angle θ and the elastic contrasts across the interface (Vp, Vs, and density of upper and lower media). Because the full equations are complex and difficult to interpret intuitively, Shuey's 1985 linearization separates the reflection coefficient into three angle-dependent terms: Rpp(θ) ≈ A + B sin²(θ) + C sin²(θ)tan²(θ), where A is the zero-offset reflectivity (acoustic impedance contrast only, the "intercept"), B is the gradient (controlling the slope of amplitude change from near to far offset), and C is the far-angle curvature term that is significant only at angles above 35-40 degrees. For typical AVO analysis on WCSB reflection data where usable offsets cover angles of 5-35 degrees, the two-term simplification Rpp(θ) ≈ A + B sin²(θ) is used. The A intercept is dominated by the P-wave impedance contrast; the B gradient is dominated by the contrast in Poisson's ratio across the interface. Gas sand has low Poisson's ratio (typically 0.10-0.15 for tight gas sand) versus brine sand or shale (typically 0.25-0.35), so the B gradient for a gas sand reflection is strongly negative: amplitude becomes more negative (or more positive, depending on polarity convention) with increasing offset. This systematic gradient is the primary AVO signature of gas-bearing rock and is the basis for all AVO DHI analysis.
• AVO classes and their geological context: AVO anomalies are classified into four classes based on the sign and magnitude of the intercept A and gradient B. Class I AVO applies to a sand that has higher acoustic impedance than the overlying shale (a "hard" event), typical of well-cemented, compacted sands at moderate to deep burial: the intercept is positive (hard kick), and the gradient is negative, so the amplitude decreases in magnitude with offset (a positive amplitude event that becomes less positive at far offsets). Class II AVO applies near-zero intercept reflections where the sand and shale have similar acoustic impedance; the gradient may be positive or negative, and these events are the most ambiguous AVO cases because the zero-offset amplitude alone gives little information. Class III AVO applies to sand with lower acoustic impedance than the overlying shale (a "soft" event), typical of young, unconsolidated gas sand at shallow depths: the intercept is negative, and the gradient is also negative, so the absolute amplitude increases with offset (a bright spot that becomes even brighter at far offsets). Class III is the most distinctive gas-sand AVO anomaly and the one most reliably identified as a DHI. Class IV AVO applies to soft sand events (negative intercept) where the gradient is positive, meaning amplitude decreases with offset; this is a more unusual pattern seen in some specific impedance configurations and is easier to miss on a simple far-minus-near amplitude map. The Montney Formation, being a moderately compacted siltstone, typically produces Class I-II AVO anomalies at the Top Montney reflection, while shallower unconventional plays like some Cretaceous gas sands produce Class III responses.
• AVO attributes: intercept, gradient, and fluid factor: From the two-term Shuey approximation, the intercept A and gradient B are extracted by least-squares fitting of the amplitude versus sin²(θ) relationship in the CMP gather, producing an A trace and a B trace at every location in the seismic dataset. These two attributes are the primary AVO outputs. Their combination produces additional diagnostic attributes: the near-stack approximates A + B/4 (for a 15-degree average near-angle), the far-stack approximates A + B/2 (for a 30-degree average far-angle), and the near-minus-far difference stack (also called the AVO difference or AVO product A×B) highlights anomalies where both A and B are negative (Class III gas sand). The fluid factor F, defined as F = A - (Vp/Vs)₀ × B / 2, where (Vp/Vs)₀ is the background Vp/Vs ratio for the local lithology (typically 1.9-2.1 for shale-dominated WCSB sections), subtracts the brine-sand background trend from the A-B relationship to isolate fluid-sensitive anomalies. Points on the fluid factor map that deviate significantly from zero are potential gas indicators. The (Vp + Vs) product or the P-wave reflectivity P = A + B, which equals approximately the reflection coefficient at 45-degree incidence, is also used as a simplified gas-sand indicator because gas sand produces strongly negative P for Class III events.
• AVO crossplot and background trend analysis: The AVO crossplot, a graph of intercept A versus gradient B for all picks on a given horizon in the seismic survey, provides a powerful visual tool for identifying anomalous reflections relative to the background lithology trend. Background shale-over-shale and brine-sand-over-shale reflections cluster along a trend with negative slope in A-B space (high acoustic impedance contrasts have positive A and negative B, and vice versa), which is called the "mudrock" or "brine" background trend. Gas sands that have negative Poisson's ratio contrast relative to the encasing shale plot below this background trend in A-B space: their B values are more negative than a brine sand with the same intercept A would predict. The deviation from the background trend is the AVO anomaly indicator, and the distance from the background trend in A-B space (perpendicular to the background trend direction) is approximately proportional to the Poisson's ratio contrast, which in turn correlates with the difference in gas saturation between the reservoir and the background brine. The crossplot is computed from all picks on a single horizon or from all samples in a time window, and the interpreter evaluates which clusters of points plot anomalously relative to the background trend and then maps those anomalous data points back to their spatial location on the 3D seismic grid to produce an AVO anomaly map.
• AVO extraction workflow and data requirements: Reliable AVO analysis requires seismic data that has been processed to preserve true amplitudes throughout the processing sequence, with no AGC applied (as discussed in the automatic-gain-control glossary article), careful surface-consistent amplitude corrections, spherical divergence compensation, and pre-stack noise attenuation that does not preferentially attenuate far-offset data. The data must be binned into partial-angle stacks (typically three to four angle classes: near 5-15 degrees, mid 15-25 degrees, far 25-35 degrees, and ultra-far 35-45 degrees where available), with the angle stack extraction guided by ray-traced offset-to-angle conversion using the average velocity model. Alternatively, AVO analysis is performed directly on offset-sorted CMP gathers using a least-squares A-B regression at each sample time. The reliability of AVO is highest when the data has a wide usable angular aperture (at least 25-30 degrees of offset angles), low noise level at far offsets (where AVO discriminating power is greatest), and careful multiples suppression (because interbed multiples contaminate the far-offset amplitude and create spurious AVO anomalies). Pre-stack simultaneous inversion, which inverts the full set of angle stacks jointly for Vp, Vs, and density using a model-based inversion framework, is the most quantitative AVO workflow and provides the most direct estimation of reservoir rock and fluid properties from the seismic data.