Reflection coefficient

The reflection coefficient or reflectivity is the proportion of seismic wave amplitude reflected from an interface to the wave amplitude incident upon it. If 10% of the amplitude is returned, then the reflection coefficient is 0.10.

Impedance

The reflection coefficient depends on the impedance of a rock layer. For P-waves, this is defined as the product of bulk density ρ_B and P-wave velocity V_P:

$Z_{\mathrm {P} }=\rho _{\mathrm {B} }V_{\mathrm {P} }\$

The normal incidence (vertical) reflection coefficient between a lower layer 1 and an upper layer 2 is given by

$R_{i}={\frac {Z_{1}-Z_{2}}{Z_{1}+Z_{2}}}$

Dependence on angle of incidence

The reflection coefficient also depends on the angle of incidence. The reflectivity in this case is given by the Zoeppritz equation. There are also various simplifications of this exact solution, including:

• Aki-Richards equation
• Shuey equation
• Fatti equation
• Bortfeld equation

Dependence on Q

Lines and Vasheghani showed that the reflection coefficient also depends on quality factor Q:

$R={\frac {\rho _{1}V_{1}\left[1+{\frac {\mathrm {i} }{2Q_{1}}}\right]-\rho _{2}V_{2}\left[1+{\frac {\mathrm {i} }{2Q_{2}}}\right]}{\rho _{1}V_{1}\left[1+{\frac {\mathrm {i} }{2Q_{1}}}\right]+\rho _{2}V_{2}\left[1+{\frac {\mathrm {i} }{2Q_{2}}}\right]}}$

If there is no absorption, then Q₁ = Q₂ and we are reduced to the 'standard' equation shown earlier in this article.

On the other hand, if there is no acoustic impedance contrast, and only a Q contrast, we can still get a reflection coefficient:

$R={\frac {\mathrm {i} \left[{\frac {1}{Q_{1}}}-{\frac {1}{Q_{2}}}\right]}{2\left[2+{\frac {\mathrm {i} }{2}}\left[{\frac {1}{Q_{1}}}+{\frac {1}{Q_{2}}}\right]\right]}}$

References

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