Seismic Reflection Coefficient Calculator
Compute seismic reflection coefficient using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Formula
R = (Z2 - Z1) / (Z2 + Z1) | Z = rho * V
The reflection coefficient R is the ratio of reflected to incident wave amplitude, determined by the acoustic impedance contrast between two layers. Z is acoustic impedance (density times velocity). T = 2Z1/(Z1+Z2) gives the transmission coefficient.
Worked Examples
Example 1: Sandstone over Limestone
Problem: Calculate the reflection coefficient at the boundary between sandstone (V=3000 m/s, rho=2300 kg/m^3) and limestone (V=5000 m/s, rho=2700 kg/m^3).
Solution: Z1 = 2300 * 3000 = 6.9e6\nZ2 = 2700 * 5000 = 1.35e7\nR = (1.35e7 - 6.9e6) / (1.35e7 + 6.9e6) = 6.6e6 / 2.04e7 = 0.3235\nCritical angle = arcsin(3000/5000) = 36.87 degrees
Result: R = 0.3235, Critical angle = 36.87 deg
Example 2: Shale over Gas Sand
Problem: Calculate R for shale (V=2500 m/s, rho=2350 kg/m^3) over gas sand (V=2000 m/s, rho=2100 kg/m^3).
Solution: Z1 = 2350 * 2500 = 5.875e6\nZ2 = 2100 * 2000 = 4.2e6\nR = (4.2e6 - 5.875e6) / (4.2e6 + 5.875e6) = -0.1664\nNegative R indicates polarity reversal (gas indicator)
Result: R = -0.1664 (negative polarity, potential gas indicator)
Frequently Asked Questions
What is a seismic reflection coefficient?
The seismic reflection coefficient describes the fraction of seismic wave amplitude that is reflected when the wave encounters a boundary between two rock layers with different acoustic properties. It ranges from -1 to +1, where positive values indicate the reflected wave has the same polarity as the incident wave, and negative values indicate a polarity reversal. The coefficient depends on the acoustic impedance contrast between the layers, which is the product of density and seismic velocity.
What is the critical angle in seismic reflection?
The critical angle occurs when a seismic wave traveling from a slower medium to a faster medium reaches an incidence angle where the refracted wave travels along the interface. It is calculated as arcsin(V1/V2), where V1 is the velocity in the upper layer and V2 in the lower. Beyond the critical angle, total internal reflection occurs and no energy is transmitted into the lower layer. The critical angle only exists when V2 is greater than V1. At the critical angle, head waves (refracted arrivals) are generated, which are used in seismic refraction surveys.
How does the reflection coefficient change with angle?
The reflection coefficient varies with the angle of incidence according to the Zoeppritz equations, which account for P-to-S wave conversions at the interface. The Shuey approximation simplifies this to R(theta) = R0 + G*sin^2(theta) + F*sin^2(theta)*tan^2(theta), where R0 is the normal incidence reflectivity and G is the AVO gradient. This angle-dependent behavior is the basis of AVO (Amplitude Versus Offset) analysis, a key technique in hydrocarbon exploration used to distinguish gas-bearing sands from other lithologies.
What formula does Seismic Reflection Coefficient Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
Is Seismic Reflection Coefficient Calculator free to use?
Yes, completely free with no sign-up required. All calculators on NovaCalculator are free to use without registration, subscription, or payment.
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