Reflection Coefficient Calculator: Impedance Contrast to Seismic Amplitude

Calculate the normal incidence reflection coefficient from two layers’ velocity and density, model reflection strength and polarity across a full set of boundaries, or solve for the lower layer impedance needed to hit a target reflection coefficient. Everything updates live.

Acoustic impedance only becomes useful once it is compared across a boundary. The reflection coefficient is that comparison, a single number between minus one and one that tells you how strong a seismic reflection will be and which way its polarity points. This tool builds it directly from velocity and density on either side of an interface.

Start with a single boundary to get the reflection coefficient and reflected energy in seconds. Build a multi boundary model to see how reflection strength and polarity vary across a set of lithology contacts, using presets for common rock pairs. Or solve backward, enter a target reflection coefficient and the upper layer properties, and find the lower layer impedance required to produce it.

The Reflection Coefficient Equation

Normal incidence reflection coefficient is defined as the lower layer impedance minus the upper layer impedance, divided by their sum, R equals (Z2 minus Z1) divided by (Z2 plus Z1). Impedance itself is simply velocity multiplied by density, so the reflection coefficient depends on both properties at once rather than either one alone.

The sign of R carries real meaning. A positive R means the lower layer has higher impedance than the layer above it, producing a reflection with the same polarity as the source wavelet, often called a hard kick. A negative R means the lower layer has lower impedance, producing a polarity reversal, a soft kick. Reflected energy is R squared, so a reflection coefficient of 0.2 reflects four percent of incident energy regardless of whether R is positive or negative.

Reflection Strength Across Multiple Boundaries

Real sections stack many boundaries with very different reflection strengths. A shale over sandstone contact typically produces a modest positive reflection coefficient. A shale over limestone contact usually produces a much larger positive coefficient, since carbonates carry a substantially higher impedance. A wet sand over gas sand contact is the classic negative reflection coefficient case, gas charging drops both velocity and density in the lower layer, flipping polarity and often producing the bright, reversed amplitude anomaly interpreters use as a direct hydrocarbon indicator.

Building even a simple multi boundary model this way makes it easy to see which contacts in a stratigraphic column should generate the strongest events on a seismic section, and which reflections should carry a polarity reversal rather than a hard kick.

Solving for a Target Reflection Coefficient

Sometimes the question runs in reverse, an interpreter sees an amplitude anomaly of a certain strength and wants to know what impedance contrast could produce it. Since the reflection coefficient equation is a simple ratio, it can be solved directly for the unknown impedance without any iteration, Z2 equals Z1 times (1 plus R) divided by (1 minus R).

This is useful for sanity checking whether a proposed lithology or fluid change downhole is even capable of producing an observed amplitude, or for estimating the density and velocity change a fluid substitution would need to cause to explain a given anomaly.

Common Mistakes

Treating reflection amplitude as proportional to velocity contrast alone, when it is impedance contrast, velocity times density together, that actually controls reflection strength.

Forgetting that reflected energy scales with R squared, not R, so doubling the reflection coefficient quadruples the reflected energy rather than doubling it.

Ignoring the sign of R and therefore missing a polarity reversal, which on a real section can make a soft kick look like it belongs to the wrong reflector entirely if the polarity convention is not tracked carefully.

Assuming a strong amplitude anomaly always indicates a fluid effect, when a purely lithological contrast, such as a shale to tight carbonate transition, can produce an equally strong reflection.

Who Uses This

Seismic interpreters relating amplitude strength and polarity on a section back to the impedance contrasts that generate them.

Petrophysicists and rock physicists checking whether a proposed lithology or fluid scenario is consistent with an observed amplitude anomaly.

AVO and seismic inversion analysts using normal incidence reflection coefficient as the starting point before extending to offset dependent behavior.

Students and early career geoscientists building intuition for how velocity, density, and their contrast combine into reflection strength and polarity.

Try It Above

Use the quick convert tab for a single boundary check, move to the boundary model to compare reflection strength and polarity across several lithology contacts, or use the solve target R tab when you know the upper layer and the amplitude you need to explain.

Related Calculators and References

Continue building your workflow with the Acoustic Impedance Calculator. For background on the formulas used above, see Wikipedia: Reflection coefficient.