AVO, 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 data.
The basics of the AVO method will
be explained here using the two geological models shown in Figure
1a shows a brine-filled sand pinchout encased in shale.
1b displays the same sand saturated with gas.
Wells have been drilled into each
P- and S-Waves
To understand the AVO effects of
these two models, we must first discuss seismic waves and the recording
of seismic data.
Traditional seismic data are recorded
using compressional waves, or P-waves, which move through the earth
by alternately compressing and expanding the rocks in their direction
However, there is a second type of
wave called a shear wave, or S-wave, which travels by shearing the rocks
at right angles to its direction of propagation. This is illustrated
in Figure 2.
There are several important differences
between P- and S-waves:
the velocity of the S-wave is slower than the velocity of the P-wave
for a given geological formation.
S-waves are less sensitive to the presence of gas in a reservoir than
P-waves, since the high compressibility of gas has more of an effect
on the P-wave velocity.
third important physical parameter
is the density that is strongly affected by the presence of gas.
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.
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 synthetic
seismic traces shown at the far right of both figures.
The P and S synthetics for the wet
model are almost identical, but for the gas model the S-wave synthetic
is the reverse of the P-wave synthetic and has lower amplitudes
The high amplitude reflections seen
on the P-wave response of the gas model are called "bright-spots," and
can be effective in the Gulf Coast and other areas in the search for
gas sands. Figure 5 shows such a bright-spot
reflection from a shallow Cretaceous play in Alberta at 640 msec.
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 needs to be supplemented
with an S-wave recording. Unfortunately, S-wave recording is not that
This leads us to the AVO method,
which allows us to derive a similar result without actually recording
an S-wave section.
The AVO Method
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 data. Ostrander (1984)
showed that, for the simple model of Figure
1b, the amplitudes on a prestack gather would increase with offset
This is shown in Figure
7, in which the reflections from the gathers (seismic traces from
one point displayed side by side) over the shallow gas sand of Figure
6 are seen quite clearly to increase.
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
Intercept = the P-wave reflection
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
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 data. Figure
11 shows the sum of intercept and gradient, or pseudo-Poisson's
ratio computed over the top of a channel sand in Alberta.
The negative values on this plot
indicate the possible presence of gas in the channel sand.
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
Applied to 3-D seismic data, the
AVO technique gives us a robust and inexpensive method for identifying
potential reservoirs, and is a technique that adds an extra dimension
to studies done only with stacked seismic data.