AVO Is Not What You Think

Amplitude Versus Offset (AVO) was born in the late 1970s and early 1980s. The first major step came in 1979, when Aki and Richards proposed a linearized version of the Zoeppritz equations. Their aim was modest: distill elastic physics into a form interpreters could actually use.

Then Shuey arrived in 1985. His two-term approximation was elegant, intuitive, and immediately became the common language of AVO. In 1994, Fatti et al. reframed the same physics into impedance contrasts, nudging AVO toward quantitative inversion.

Three models, three decades, one underlying truth: they are all approximations of a deeper elastic reality. Forty years later, we still treat these approximations as if they were laws of nature.

The Temptation of the Simple Equation

Shuey’s expression:

R(θ) ≈ A + B sin²θ

is popular not because it is universally correct, but because it is easily interpretable. A is the zero-angle reflectivity, mostly ΔI_p. B is the gradient, influenced by ΔI_s and density.

From this came the AVO Classes; a tidy typology that looks scientific, feels predictive, and is easy to memorize.

The AVO Classes were never meant to be universal laws. They are simply patterns that emerge from the signs of A and B:

• Class I: A positive, B negative; hard over soft; amplitude decreases with angle.
• Class II: A near zero, B negative; the “zero-crossing” family.
• Class III: A negative, B strongly negative; the classic brightening gas sand.
• Class IV: A negative, B positive; amplitude becomes less negative with angle.

They are not different “rock types”. They are different combinations of signs inside a two-term approximation. Nothing in geology guarantees that a real reflector will behave according to these four idealized curves.

But real geology does not respect typologies. Lithology changes. Fluids mix. Anisotropy bends rays. Thin beds tune. Angles distort. The Earth is not required to behave like a two-term polynomial.

These models were created for weak contrasts, small to moderate angles, and simple layerings. When we use them outside that domain, we are not “interpreting”; we are projecting the Earth into a mathematical box that makes us comfortable.

The approximation is not the problem.
The forgetting is the problem.

Aki Richards: Adding Back the Lost Dimensions

Aki and Richards introduced the three-term expansion:

R(θ) ≈ A₀ + A₁ sin²θ + A₂ tan²θ

The third term, A₂, captures far-angle behaviour and is highly sensitive to ΔV_s  , the dimension most interpreters quietly ignore because shear sensitivity refuses to fit tidy typologies.

What this model really reveals is that AVO is not a one-dimensional trend you can summarize with a single gradient. The elastic response is multi-directional: different contrasts push reflections in different directions across angle space. A₀, A₁, and A₂ form a small vector describing how the reflector distributes its physics.

Reducing this richness back into “Class III” versus “Class IIp” collapses a multidimensional phenomenon into a binary label. It should make us uneasy, because the Earth is not obligated to align itself with our preferred simplifications.

Fatti: The Shift Toward Impedance

Fatti reframed AVO by solving directly for:

ΔI_p/I_p , ΔI_s/I_s

This is not a cosmetic reformulation. It is a conceptual pivot. The analysis moves from amplitude space to impedance space; from the outward appearance of reflections to the inward structure of the rock. Instead of asking “How does the waveform behave with angle?”, we begin asking, “What elastic contrasts must exist in the subsurface for this behaviour to appear at all?”

In that sense, Fatti marks the moment when AVO stopped being a qualitative classifier and became a doorway to inversion. It invites the interpreter to think in terms of causes rather than symptoms, physics rather than patterns. The Earth ceases to be a cartoon curve on an angle plot and becomes a set of contrasts struggling to express themselves through a limited and noisy channel.

And yet many workflows still interpret Fatti results using Shuey-style heuristics: negative means gas, brightening means pay, a dot in one quadrant means fluid. We slip between frameworks without noticing we are mixing languages. Amplitude coefficients and impedance contrasts do not live in the same conceptual space; treating them as interchangeable is not interpretation; it is wishful translation.

Fatti reminds us that what we call “AVO” is not a fixed doctrine but a family of related approximations, each with its own geometry, logic, and blind spots. To think with AVO is to hold these spaces in tension; to understand what each reveals and what each hides. Interpretation begins when we recognize that the map is not the territory, and our tools are not the truth but instruments through which truth may occasionally appear.

A Question the Community Rarely Asks

Why do we treat ΔI_p and ΔI_s as if they lived on separate axes when the Earth rarely does?

Why do we call an anomaly “gas” when its behaviour collapses under the faintest change in angle, noise, or wavelet?

Why do we trust the classification more than the physics that produced it?

We have forgotten that AVO is a sensitivity analysis with a pulse, not a fortune-teller with an answer key. Amplitude does not reveal the fluid; it reveals how contrasts distribute themselves across angle. It opens a small window into multiple possible subsurface worlds. Interpretation begins when we learn to inhabit that plurality instead of rushing to collapse it.

Most anomalies have more than one explanation.
That is not a flaw. That is a signal: the Earth is deeper, stranger, and less obedient than the diagrams we draw of it.

AVO Needs Fewer Recipes and More Thinking

The industry loves certainty packaged as slogans:

Class I means one thing, Class III means another, brightness means fluid, a flat gather means victory.

But slogans are not interpretations; they are the shadows of interpretations.

AVO becomes meaningful only when we confront what refuses to fit:

• the reflector that shifts with noise,
• the anomaly that vanishes when V_P/V_S moves half a step,
• the bed that changes character when it thins by a few metres,
• the response that sounds like Shuey but is speaking a different dialect.

These tensions are not obstacles. They are the raw material of interpretation. AVO is not a classification machine; it is the stress field we apply to our own hypotheses to see which ones survive.

When we stop thinking, AVO becomes ritual. When we think, it becomes exploration.

Why We Build Tools Like the AVO Sandbox

Equations give structure, but intuition grows only through disturbance and play. When you twist depth, stretch angle range, scramble lithologies, inject noise, or nudge contrasts, the behaviour of the reflector begins to reveal its invariants; the features that resist change, the ones that fracture instantly, the quiet patterns that appear only under tension.

This is when AVO stops being a checklist and becomes a conversation. Not “What class is it?” But “What is this reflector trying to say, and under what conditions does its voice change?”

The Mark We Leave

Exploration geophysics has always lived between what we know and what we wish we knew. Our task is not to eliminate uncertainty with a formula, but to understand how the Earth speaks through imperfect data; filtered by approximations, shaped by noise, and interpreted through our limitations.

AVO remains powerful not because Shuey, Aki Richards, or Fatti were right for all time, but because each offers a different angle of truth; a different way the Earth becomes visible.

If we meet these models with humility, if we allow their contradictions to sharpen us, if we learn to dwell in the tension between frameworks instead of fleeing to the nearest label, then interpretation becomes something closer to science, and something closer to art.

And perhaps that is the real mark exploration leaves on us: not certainty, but a deeper kind of attention.