Question

10. A succession consists of alternating sandstones and shales, with the top layer being sandstone. Calculate how the amplitude diminishes for reflections from each of the top four interfaces (ignore spreading of the wavefront and absorp- tion), if the densities and velocities are as fol- lows: sandstone 2 Mg/m², 2.6 km/s; shale 2.3 Mg/m², 2.8 km/s.

Answer 1

Given for sandstone

density $\rho$ ₁ = 2 Mg/m³

velocityV₁ = 2.6 km/s

For shale

density $\rho$ ₂ = 2.3 Mg/m³

velocity V₂ = 2.8 km/s

Reflection coefficient (R) is the ratio between amplitude of the reflected wave and amplitude of the incident wave.

R = ($\rho$₂ V₂ -$\rho$₁V₁ ) _/ ($\rho$₂ V₂ + $\rho$ ₁V₁ )

R = (2.3 Mg/m^3* 2.8 km/s - 2 Mg/m³*2.6 km/s) / (2.3 Mg/m^3* 2.8 km/s + 2 Mg/m³*2.6 km/s)

R = 0.1065

The amplitude diminishes as 0.1065 for reflections from the top of interfaces.