AVO classes and the intercept-gradient crossplot

Anatomy of the crossplot

The (R₀, G) plane is divided into four natural quadrants by the R₀ = 0 and G = 0 axes. Each quadrant corresponds to a distinct AVO class:

• Bottom-right (R₀ > 0, G < 0) — Class I. High-impedance reservoir; bright peak that dims at far offsets. Carbonates atop shales, tight gas sands.
• Bottom-left (R₀ < 0, G < 0) — Class III. Bright trough that brightens further with angle. The textbook gas-sand DHI signature; the most-targeted region of the crossplot.
• Top-left (R₀ < 0, G > 0) — Class IV. Trough that dims at far offsets. Low-impedance soft sands and shaley reservoirs.
• Top-right (R₀ > 0, G > 0) — Class I+. Unusual peak that brightens with angle. Rare in clastic settings; sometimes carbonates with high Vp/Vs above shales.
• Near the origin with strongly negative G — Class II / IIp. Subtle anomalies that the stack barely registers but AVO catches.

The widget below visualizes this for the rock library. Pick a top rock; see how all 12 candidate bottoms scatter across the four classes.

The brine background trend

Brine-saturated clastics in a typical sedimentary basin do NOT scatter randomly across the crossplot. They cluster along an approximately linear trend with slope close to −1.3 (Castagna, Swan & Foster 1998):

$G \approx -1.3 , R_0$

This is the brine background trend. It has a physical origin: in a brine-saturated clastic sequence, the rocks broadly follow Castagna’s mudrock line in (Vp, Vs) space (§5.2), and the Aki-Richards algebra of two such rocks produces this approximately-linear (R₀, G) relation. Any rock pair that is brine-saturated and clastic falls near this trend.

The interpretive consequence: departures from the background trend are diagnostic. A point that sits on the trend is "ordinary" — a normal brine-saturated boundary. A point well below the trend (more negative G than the trend predicts) suggests a non-brine fluid (oil or gas) or a non-clastic lithology. The greater the departure, the more anomalous the response.

This is the workflow: compute (R₀, G) for every voxel, plot them, identify the cluster that follows the brine trend, then HIGHLIGHT the voxels that deviate — those are the candidate prospects.

Exercise — read the crossplot

• The widget defaults to medium shale as the top rock. Look at where each bottom rock plots. Notice the three sandstones (brine, oil, gas) sit at progressively more negative R₀ and G — the fluid-substitution trajectory moving from the upper-right (brine) through Class II (oil) into Class III (gas). This trajectory is what AVO uses to detect fluid changes.
• Find the limestone and dolomite points. They sit far to the lower right — large positive R₀ (high-impedance carbonate atop softer shale) and large negative G. Class I behaviour: bright peak that dims at far offsets.
• Find the salt point. Large positive R₀ and slightly negative G — also Class I, but with a smaller AVO swing. Salt is acoustically very hard but its Vp/Vs is similar to other clastics, giving a subdued gradient.
• Switch the top rock to limestone. Now most points migrate toward the lower-LEFT (the carbonate is the high-Z layer; sands and shales below it produce R₀ < 0). The (R₀, G) landscape shifts; Class III and Class IV become the dominant regions.
• Switch the top to salt. Similar story — negative R₀ for almost everything, because halite is one of the highest-impedance rocks in the library. AVO interpretation under salt is harder for exactly this reason: the impedance contrast across the salt boundary dominates the AVO and obscures fluid signals beneath.
• Notice the dashed background trend line throughout. Points that sit ON the line are well-behaved background; points far OFF the line in the lower-left are AVO anomalies worth chasing. The visual eye scan for "outliers below the trend" is exactly the workflow real interpreters use on crossplot displays of full survey data.

How interpreters use the crossplot in practice

A typical AVO crossplot workflow on real seismic data:

• Compute R₀ and G volumes from pre-stack seismic via angle-stack regression (or full inversion).
• Crossplot the (R₀, G) values for a target depth interval. The result is a "data cloud" — typically a tight cluster along the brine-background trend with a tail of outliers.
• Identify the brine background trend in the actual data (it may not be exactly G = −1.3 R₀ — the slope and intercept depend on the basin). Fit a line through the cloud.
• Define an "anomaly polygon" in the (R₀, G) plane around the candidate Class III region: large negative R₀ with G well below the brine trend.
• Highlight back to 3D: every voxel whose (R₀, G) falls inside the anomaly polygon gets coloured on the seismic display. The result is a "DHI map" showing only the voxels with anomalous AVO.
• Compare with structural maps and well control to confirm the candidate prospects align with reasonable trap geometries.

This polygon-based highlighting is one of the most powerful screening tools in modern interpretation. A multi-million-trace volume condenses to a scatter that the eye reads in seconds; the candidate prospects then get the detailed treatment described in Part 6 (multi-attribute interpretation, RGB blending, reservoir gating).

Beyond R₀ and G: the LMR and Mu-Rho space

(R₀, G) is the most accessible AVO parameterization but not the only one. Goodway, Chen & Downton (1997) showed that the Aki-Richards form can be re-expressed in terms of λ·ρ ("lambda-rho") and μ·ρ ("mu-rho"):

• μ·ρ: the rock’s shear modulus times density. Sensitive primarily to LITHOLOGY (sands cluster differently from shales).
• λ·ρ: the Lamé first-parameter times density. Sensitive primarily to FLUID (gas drops λ dramatically; brine doesn’t).

The (μ·ρ, λ·ρ) crossplot — often called the LMR crossplot — separates lithology and fluid effects more cleanly than (R₀, G). Modern QI workflows often present both crossplots to capture different aspects of the same data. We don’t build the LMR widget here, but it operates on exactly the same Aki-Richards inputs (Vp, Vs, ρ for both layers); the math is a re-parameterization, not new physics.

Common crossplot pitfalls

• The background trend is basin-specific. G = −1.3 R₀ is the global average; specific basins can have slopes from −0.8 to −1.6 depending on the Vp/Vs structure of their typical clastics. Always fit the trend to the local data, don’t assume the textbook value.
• Far-offset noise tilts the cloud. Real (R₀, G) volumes from seismic suffer from the noise gradient that grows with offset. The cloud often shifts upward (more positive G) than the rock physics predicts because the far-offset measurements are noisier than the near-offset measurements; the regression bias produces an apparent G shift. Calibrate carefully.
• Anomaly polygons can be overdrawn. An interpreter who wants to find prospects can draw a generous polygon around any deviation. Discipline: define the anomaly polygon BEFORE looking at the data, based on a rock-physics model and well control. Don’t fit the polygon to the prospects.
• (R₀, G) is post-stack-flavored. The crossplot uses information that’s embedded in the angle-stack regression, which is essentially a post-stack-style reduction. Full pre-stack elastic inversion gives more separable lithology/fluid information (the LMR space, or full Vp/Vs/ρ volumes). Use (R₀, G) as a screening tool, full inversion as the deeper analysis.
• Crossplot density does not equal subsurface area. A tight cluster in the crossplot represents many voxels; an isolated point represents one or a few voxels. The interpreter should always check how MUCH 3D volume each region represents, especially for "anomalies" that may be just a handful of voxels in noise.