geophysics · avo
Shuey AVO Approximation (2-Term / 3-Term)
R(θ) = R₀ + G·sin²θ + F(tan²θ − sin²θ)
click formula to derive ↑
Inputs
ft/s
ft/s
g/cc
ft/s
ft/s
g/cc
°
Description
Computes Shuey's (1985) re-expression of the Aki-Richards linearization as an intercept (R0) and gradient (G) pair, plus the 2-term and 3-term angle-dependent reflectivity built from them. R0/G are the canonical attributes behind AVO intercept-gradient crossplotting.
Variables
| Symbol | Unit | Description |
|---|---|---|
| R₀ | — | Intercept (Normal-Incidence R) |
| G | — | AVO Gradient |
| R₂(θ) | — | 2-Term R(θ) |
| R₃(θ) | — | 3-Term R(θ) |
| Vp₁ | ft/s | P-wave velocity of the layer above the interface. |
| Vs₁ | ft/s | S-wave velocity of the layer above the interface. |
| ρ₁ | g/cc | Bulk density of the layer above the interface. |
| Vp₂ | ft/s | P-wave velocity of the layer below the interface. |
| Vs₂ | ft/s | S-wave velocity of the layer below the interface. |
| ρ₂ | g/cc | Bulk density of the layer below the interface. |
| θ | ° | P-wave angle of incidence at which to evaluate the 2-term and 3-term approximations. |
Assumptions
- Same small-contrast, welded-interface assumptions as Aki-Richards — this is an algebraic re-expression, not a new physical model
- 2-term form additionally assumes interpretation only at near-to-intermediate angles (<~30°)
Limitations
- The 2-term form systematically underestimates far-angle amplitude for strong Vp/Vs contrasts — prefer the 3-term value beyond ~30°
- Like Aki-Richards, unreliable near and beyond the critical angle
- G alone is not a fluid indicator — always interpret R0 and G together (see avo_intercept_gradient_class)
Use Cases
- → AVO intercept-gradient attribute generation: Produce the classic (R0, G) pair used for crossplot analysis and hydrocarbon-indicator screening.
- → Gather-fitting QC: Compare a real seismic gather's fitted R0/G against a well-log-derived value at the same interface.
- → 3-term vs. 2-term decision: Check how much the two truncations diverge at a target's typical far-stack angle before choosing which to trust.
Related Calculations
Region Notes
Permian Basin
Wolfcamp shale-on-carbonate targets often show a strongly negative G with a small positive R0 (Class IIp-leaning) — the divergence between 2-term and 3-term grows quickly past 30° in these settings.
Gulf of Mexico
Classic Class III gas sands (R0<0, G<0) are well-approximated by the 2-term form across most practical angle-stack ranges.
Global
Always report which truncation (2-term or 3-term) was used alongside any published R0/G pair — the two are not interchangeable at far offset.
References
Primary source
Primary source
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