AVO Intercept-Gradient Calculator: Shuey Approximation and AVO Classification

Calculate AVO intercept and gradient from Vp, Vs, and density using Shuey’s two term approximation, model how reflection amplitude changes across an angle gather, or solve the crossover angle or the gradient a target amplitude requires. Everything updates live.

AVO Intercept and Gradient: The Foundation of Amplitude Versus Offset Analysis

AVO intercept and gradient compress an entire angle gather of reflection amplitudes into two numbers that describe how a reflection behaves with offset, the foundation of amplitude versus offset analysis and one of the most common seismic direct hydrocarbon indicator workflows. This tool covers a quick intercept and gradient calculation from Vp, Vs, and density, a full angle gather model showing amplitude at each angle, and a reverse solve for the crossover angle or the gradient a target amplitude requires.

Start with the quick convert tab for a single intercept and gradient calculation from an upper and lower layer’s Vp, Vs, and density. Build an angle gather model to see how reflection amplitude changes across a full range of incidence angles. Or solve backward, find the crossover angle where a reflection changes polarity, or the gradient a target amplitude at a specific angle would require.

Shuey’s Two Term Approximation

Shuey’s two term approximation writes the reflection coefficient as a function of incidence angle, R of theta equals intercept A plus gradient B times sine squared of theta. Intercept A is simply the normal incidence reflection coefficient, the same quantity a zero offset acoustic impedance contrast would produce. Gradient B captures everything about how that reflection changes as offset and angle increase, driven by the contrast in Vp, Vs, and density between the two layers, weighted so that shear wave contrast plays a larger role than in the intercept alone.

This two term form is an approximation to the full Zoeppritz equations, but it holds up well for the small to moderate angles, roughly up to 30 to 40 degrees, that most conventional AVO analysis relies on.

The Four AVO Classes

Rutherford and Williams’ AVO classification groups reflections by their intercept and gradient combination. Class 1 shows a positive intercept with a negative gradient, a high impedance contrast that dims with offset. Class 2 sits near a zero intercept and can show a polarity reversal at moderate angles even from a small impedance contrast. Class 3, the classic bright spot, shows both a negative intercept and a negative gradient, amplitude growing more negative with offset, common for gas sands encased in shale. Class 4 shows a negative intercept with a positive gradient, dimming with offset from an already negative starting point.

Knowing which class a target most resembles helps set expectations for what an angle gather or AVO crossplot should show, and deviations from the expected class for a given lithology and fluid combination are themselves often diagnostic.

Reading Crossover Angle and Angle Gather Behavior

When intercept and gradient have the same sign, the reflection coefficient only grows more extreme with angle and never crosses zero within a physically reachable range. When they have opposite signs, the reflection amplitude passes through zero at a specific crossover angle and flips polarity beyond it, a distinctive signature worth checking against real gather data. Modeling the full angle gather from intercept and gradient, rather than relying on the intercept and gradient values alone, makes this crossover behavior and the overall amplitude trend easy to see at a glance.

Common Mistakes

Applying Shuey’s two term approximation well beyond its valid angle range, since the two term form increasingly diverges from the full Zoeppritz solution past roughly 30 to 40 degrees, where a three term approximation or the full equations become more appropriate.

Classifying a reflection by intercept and gradient sign alone without checking the actual angle gather, since two very different amplitude versus angle trends can occasionally share the same intercept and gradient classification.

Ignoring that gradient is especially sensitive to the shear wave velocity contrast between layers, so gradient estimates from a Vs log built on a poor or assumed Vp/Vs relationship carry meaningfully more uncertainty than the intercept.

Treating a crossover angle calculation as exact without accounting for the approximation error inherent in the two term Shuey equation at the angles where crossover often occurs.

Who Uses This

Geophysicists computing AVO intercept and gradient as part of a direct hydrocarbon indicator or amplitude versus offset workflow.

Interpreters classifying a prospect’s expected AVO response against the four standard AVO classes before drilling.

Students and early career geoscientists learning how Shuey’s equation connects rock properties to angle dependent reflection amplitude.

Analysts checking whether an observed angle gather’s crossover behavior is consistent with a particular AVO class or fluid scenario.

Try It Above

Use the quick convert tab for a single intercept and gradient calculation from Vp, Vs, and density, move to the angle gather model tab to see reflection amplitude across a full range of angles, or use the solve crossover angle tab when you need the angle where polarity flips or the gradient a target amplitude requires.

Related Calculators and References

Continue building your workflow with the Poisson’s Ratio Calculator. For background on the formulas used above, see SEG Wiki: AVO intercept and gradient.