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An AVO Primer
By
Brian Russell1
Search and Discovery Article #40051 (2002)
*Adapted for online presentation from an article by the same author in AAPG Explorer (June, 1999), entitled “AVO Adds Flavor to Seismic Soup.” Appreciation is expressed to the author and to M. Ray Thomasson, former Chairman of the AAPG Geophysical Integration Committee, and Larry Nation, AAPG Communications Director, for their support of this online version.
1Hampson-Russell Software Services Ltd., Calgary, Canada (www.hampson-russell.com; [email protected]); past president of the Society of Exploration Geophysicists.
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General StatementAVO, which stands for Amplitude Variations
with Offset--or, more simply, Amplitude Versus Offset--is a seismic
technique that looks for direct hydrocarbon indicators using the
amplitudes of prestack seismic
Wells have been drilled into each sand. To
understand the AVO effects of these two models, we must first discuss
seismic waves and the recording of seismic There are several important differences between P- and S-waves:
Figures 3 and 4 show the P-wave velocity, S-wave velocity and density logs for the two models of Figure 1. Notice that both the P-wave velocity and the density are lower in the gas sand than in the wet sand, but the S-wave velocity is the same in both cases. To understand how this is related to the recorded seismic trace, note that the seismic recording measures two things: the time that it takes to travel down to a particular geological interface, and the reflection amplitude.
Figures
3 and 4
also show how the amplitudes are created. First, we multiply the
velocity times the density to get the P or S impedance. Then, we
calculate the difference between the impedances divided by their sum,
which gives us a reflection coefficient (reflectivity) at each
interface. Finally, we superimpose the seismic response, or wavelet, on
the reflection coefficients to get the The
P and S synthetics for the wet model are almost identical, but for the
gas model the S-wave However, there are other geological situations that create 'bright-spots," such as coal seams or hard streaks. From this discussion, it is obvious that the P-wave response does not reveal the presence of gas unambiguously, and it needs to be supplemented with an S-wave recording. Unfortunately, S-wave recording is not that common. This leads us to the AVO method, which allows us to derive a similar result without actually recording an S-wave section. Return to top.
The AVO Method
Figure
6, which shows a typical prestack seismic raypath, records that the
incident wave displays both compressional and shear effects, since it
strikes the interface at an angle a. The reflected wave thus contains
the effects of both P- and S-waves. Although the mathematics of this
process has been known since the nineteenth century, it was only very
recently that we have recognized it on our seismic Not all gas sands show increasing AVO effects, since the result is dependent on the nature of the acoustic impedance change. The different types of AVO anomalies have been classified as classes 1, 2 and 3 by Rutherford and Williams (1989} In the present paper we are looking at a Class 3 example, in which the impedance of the sand is lower than the encasing shale. If we measure the amplitude of each reflection amplitude as a function of offset, and plot them on a graph as a function of the sine of angle of incidence squared, we observe a straight line. For any line, the intercept and gradient can be measured. By linearizing the complicated mathematics behind the AVO technique, Richards and Frasier (1976) and Wiggins et al. (1986) gave us the following physical interpretation of the intercept and gradient: Intercept = the P-wave reflection amplitude. Gradient = the P-wave reflection amplitude minus twice the S-wave reflection amplitude. To illustrate this point, the amplitudes from a small portion of one of the gathers in Figure 7 are shown in Figure 8, with a straight line fit superimposed. Notice that the top of the sand has a negative intercept (a trough) and a negative gradient, and the base of the sand has a positive intercept (peak) and a positive gradient. When we perform this analysis at every sample, on every gather, we create two sections, or volumes. The intercept section is similar to the conventional stack--except that it represents a better estimate of the vertical P-wave reflections. The gradient contains information about both the P and S-wave reflections. There are many ways of displaying this information. As well as displaying the intercept and gradient on their own, it is common to display the difference and sum of the intercept and gradient. From the above explanation it is obvious that the difference, after scaling, is the approximate S-wave reflectivity. The sum of the intercept and the gradient can be shown to represent the approximate Poisson's ratio change, where Poisson's ratio is related to the square of the P-wave to S-wave velocity ratio. A negative Poisson's ratio change is associated with the top of a gas zone, whereas a positive change is associated with the base. These displays are shown in Figures 9 and 10 for our real example. Notice that the intercept (P-wave) shows a strong "bright-spot," whereas the pseudo-S-wave (intercept minus gradient) does not show a "bright-spot," indicating the presence of a gas sand. As
one final example, let us consider an example of the AVO technique
applied to 3-D This tutorial has reviewed the basic principles behind the AVO technique. We have concentrated on a single type of anomaly, the Class 3, in which the acoustic impedance of the gas sand drops with respect to the encasing shales. For a discussion of other types of anomalies refer to the papers by Rutherford and Williams (1989), Ross and Kinman (1995). and Verm and Hilterman (1995). The
key thing to remember about the AVO method is that the AVO gradient
responds to both P- and S-wave reflections from an interface, and this
behavior can be used to locate gas charged reservoirs. Applied to 3-D
seismic ReferencesOstrander, W.J., 1984, Plane-wave reflection coefficients for gas sands at nonnormal angles of incidence: Geophysics, v. 49, p. 1637-1648. Richards, P.G., and Frasier, C.W., 1976, Scattering of eleastic waves from depth-dependent inhomogeneities: Geophysics, v. 41, p. 441-458. Ross, C.P., and Kinman, D.L., 1995, Nonbright-spot AVO; two examples: Geophysics, v. 60, p. 1398-1408. Rutherford, S.R., and Williams, R.H., 1989, Amplitude-versus-offset variations in gas sands: Geophysics, v. 54, p. 680-688. Verm, R., and Hilterman, F., 1995, Lithology, color-coded siesmic sections; the calibration of AVO crossplotting to rock properties: Leading Edge, v. 14, p. 847-853.
Wiggins, W.,
Ng, P., and Manzur, A., 1986, The relation between the |