AVO Theory

Basic AVO theory is well understood because it is widely used as a tool in hydrocarbon detection Smith (1987). We will highlight a few of the most important ideas to keep in mind when doing AVA analysis. Figure 1 shows the theoretical energy partition at an interface. This figure illustrates an important point that accounts for AVA phenomena: the conversion of P-wave energy to S-wave energy. Though the majority of seismic data is recorded simply as a single component pressure wave, the fact that the Earth is elastic causes amplitudes of P-wave arrivals to be a function of S-wave properties of the rocks. In theory, the best AVA attribute would be one that included the S-wave reflection coefficient (R_s) Castagna and Smith (1994). In practice, R_s is tricky to obtain and the P-wave reflection coefficient (R_p) is what we have in the vast majority of cases Smith and Sutherland (1996).

Classification of AVO sands was first done by Rutherford and Williams (1989). Though a greater number of AVO signatures have now been classified, we will focus on only the typical Gulf of Mexico bright spot (Class III). This anomaly is caused by a relatively low impedance oil or gas bearing sand that shows up as a high amplitude anomaly on far offset sections. Figure 2 shows the cause of this: a high negative reflection coefficient (intercept, A) and a negative gradient, B. In the cases of deeper targets or on-shore facies, the hydrocarbon bearing sands might be high impedance, and thus the dim spot associated with Class I AVO sands would be of interest Mavko (2000).

The formulas for A and B up to a 30^o incidence angle are described by Shuey (1985) as approximations of the Zoeppritz equations:

$$R(\theta) \; \approx \; A + B\sin^2\theta \;$$ (1)

with

$$A \; = \; \left( \frac{\Delta Vp}{Vp} + \frac{\Delta \rho}{\rho} \right) / 2 \;$$ (2)

and

$$B \; = \; -2\frac{{V_s}^2}{{V_p}^2}\frac{\Delta \rho}{\rho} ... ...V_p}{2V_p} - 4\frac{{V_s}^2}{{V_p}^2}\frac{\Delta V_s}{V_s} \;,$$ (3)

where $V_p, V_s, \rho$ are the average across an interface, that is $\frac{X_1 + X_2}{2}$, and $\Delta V_p, \Delta V_s, \Delta \rho$ are the difference across an interface, that is X₂ - X₁.

Past 30^o these approximations break down, and thus we must be careful to limit our maximum offset ray parameter to the value corresponding to an incidence angle of 30^o.