Further Study: Oil and Gas

The next obvious step is to look at the AVO response with the sand saturated with oil and gas to see how the AVO changes with depth and with different fluids. Gassmann's Relations Gassmann (1951) are used to transform the data.  

$$\frac{K_2}{K_{min}-K_2}-\frac{K_{fl2}}{\phi(K_{min}-K_{fl2})}= \frac{K_1}{K_{min}-K_1}-\frac{K_{fl1}}{\phi(K_{min}-K_{fl1})}$$ (5)

and  

$$\mu_2=\mu_1$$ (6)

where K_min is the bulk modulus of the mineral, K_fl is the bulk moduli of the fluid, K₁ is the bulk modulus of the rock saturated with the original fluid (water in this case), K₂ is the bulk modulus of the rock with fluid substitution, $\phi$ is porosity, and $\mu$ is the shear modulus. To find the new moduli, recompute the velocities with the equations:  

$$V_p=\sqrt{\frac{K_2+\frac{4}{3}\mu_2}{\rho_2}}$$ (7)

 

$$V_s=\sqrt{\frac{\mu_2}{\rho_2}}$$ (8)

From the preliminary look at the AVO response, it was difficult, if not impossible, to detect any changes in the amplitude as a function of offset. The AVO of the same depths with gas and oil as the saturating fluid were almost identical to the water saturated images. This aspect of the project will, therefore, need to be studied further before any conclusive results can be stated.