Reflection coefficient

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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 ρB and P-wave velocity VP:

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:

Dependence on Q

Lines and Vasheghani[1] 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

  1. Lines, L & F Vasheghani (2008). Reflections on Q. CREWES Research Report.


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