AVO/AVA can physically explain presence of hydrocarbon in the reservoirs and the thickness, porosity, density, velocity, lithology and fluid content of the reservoir of the rock can be estimated.

1. By Haseeb Ahmed
M.Phil Geophysics
Institute of Geology, University of the Punjab
AVO ANALYSIS

2.  Amplitude versus offset (AVO) is primarily
the variation in seismic reflection
amplitude with change in distance
between shot point and the receiver
 Its another name is AVA (amplitude
variation with angle)
 AVO analysis is conducted on CMP data

3. FIG. SHOWING AVO (A) & (B)

4. AVO INTRODUCTION
 It can physically explain presence of
hydrocarbon in the reservoirs and the
thickness, porosity, density, velocity,
lithology and fluid content of the
reservoir of the rock can be estimated.

5. THE ZOEPPRITZ EQUATIONS
 Zoeppritz derived the amplitudes of the reflected
and transmitted waves using the conservation of
stress and displacement across the layer
boundary
 which gives four equations with four unknowns.
 Inverting the matrix form of the Zoeppritz
equations gives us the exact amplitudes as a
function of angle

6. THE ZOEPPRITZ EQUATIONS















































1
1
1
1
1
2
1P1
2S2
2
1P1
2P2
1
1P
1S
1
22
1S1
1P2S2
1
2P
2
1S1
1P
2
2S2
1
1S
1P
1
2211
2211
S
P
S
P
2cos
2sin
cos
sin
2sin
V
V
2cos
V
V
2sin
V
V
2cos
2cos
V
VV
2cos
VV
VV
2cos
V
V
2sin
sincossincos
cossincossin
T
T
R
R





















7. THE AKI-RICHARDS EQUATION
 The Aki-Richards equation is a linearized
approximation to the Zoeppritz equations.
 The initial form (Richards and Frasier, 1976)
separated the velocity and density terms:
S
S
P
P
V
V
cb
V
V
aR








 )(

8. THE AKI-RICHARDS EQUATION
 Where;
,sin4
,sin25.0
,
cos2
1
2
2
2
2
2


























P
S
P
S
V
V
c
V
V
b
a
.
2
,,
2
,,
2
,,
2
12
12
12
12
12
12
ti
SSS
SS
S
PPP
PP
P
and
VVV
VV
V
VVV
VV
V

















9. WIGGINS’ VERSION OF THE
AKI-RICHARDS EQUATION
 A more intuitive, but totally equivalent, form was
derived by Wiggins.
 He separated the equation into three reflection
terms, each weaker than the previous term:
 222
sintanCsinBA)(R 

10. WHERE ?
p
P
2
P
S
S
S
2
P
S
p
P
p
P
V
V
2
1
C
V
V
2
V
V
V
V
4
V
V
2
1
B
V
V
2
1
A





























11. INTERPRETING THE AKI-RICHARDS EQUATION
 The first term, A, is a linearized version of the zero
offset reflection coefficient and is thus a function of
only density and P-wave velocity.
 The second term, B, is a gradient multiplied by sin2,
and has the biggest effect on amplitude change as a
function of offset. It is dependent on changes in P-
wave velocity, S-wave velocity, and density.
 The third term, C, is called the curvature term and is
dependent on changes in P-wave velocity only. It is
multiplied by tan2*sin2 and thus contributes very little
to the amplitude effects below angles of 30 degrees.
(Note: Prove to yourself that tan2*sin2 = tan2 -
sin2, since the equation is often written in this form.)

12. OSTRANDER’S GAS SAND MODEL
 Ostrander (1984) was one of the first to write about
AVO effects in gas sands and proposed a simple
two-layer model which encased a low impedance,
low Poisson’s ratio sand, between two higher
impedance, higher Poisson’s ratio shales.
(This model is shown in the next slide).
 Ostrander’s model worked well in the Sacramento
valley gas fields. However, it represents only one
type of AVO anomaly (Class 3) and the others will
be discussed in the next section.

13. * Note : The model consists of a low acoustic impedance and Poisson’s ratio gas
sand encased between two shales.

14. SYNTHETIC FROM OSTRANDER’S MODEL
 (a) Well log responses
for the model.
 (b) Synthetic seismic.

15. WET AND GAS MODELS
 Wet Sand Model  Gas Saturated Model

16. AVO MODELS
 In the next two slides, we are going to compute the top and base
event responses from Models A and B, using the following values,
where the Wet and Gas cases were computed using the Biot-
Gassmann equations:
Wet: VP= 2500 m/s, VS= 1250 m/s,  = 2.11 g/cc, s = 0.33
Gas: VP= 2000 m/s, VS= 1310 m/s,  = 1.95 g/cc, s = 0.12
Shale: VP= 2250 m/s, VS= 1125 m/s,  = 2.0 g/cc, s = 0.33
 We will consider the AVO effects with and without the third term in
the Aki-Richards equation.

17. AVO WET MODEL
AVO - Wet Sand (Model A) Top
0.000
0.020
0.040
0.060
0.080
0.100
0 5 10 15 20 25 30 35 40 45
Angle (degrees)
Amplitude
R (All three terms) R (First two terms)
AVO - Wet Sand (Model A) Base
-0.100
-0.080
-0.060
-0.040
-0.020
0.000
0 5 10 15 20 25 30 35 40 45
Angle (degrees)
Amplitude
R (All three terms) R (First two terms)
 These figures show the AVO responses from the (a) top and (b) base
of the wet sand. Notice the decrease of amplitude, and also the fact
that the two-term approximation is only valid out to 30 degrees.

18. AVO GAS MODEL
AVO - Gas Sand (Model B) Top
-0.250
-0.200
-0.150
-0.100
-0.050
0.000
0 5 10 15 20 25 30 35 40 45
Angle (degrees)
Amplitude
R (All three terms) R (First two terms)
AVO - Gas Sand (Model B) Base
0.000
0.050
0.100
0.150
0.200
0.250
0 5 10 15 20 25 30 35 40 45
Angle (degrees)
Amplitude
R (All three terms) R (First two terms)
 The above figures show the AVO responses from the (a) top and (b) base
of the gas sand. Notice the increase of amplitude, and again the fact that
the two-term approximation is only valid out to 30 degrees.

19. SHUEY’S EQUATION
 Shuey (1985) rewrote the Aki-Richards equation using VP, , and s.
Only the gradient is different than in the Aki-Richards expression
2
)1(1
21
)D1(2DAB
s
s
s
s










12
12
2
,
//
/
:
sss
ss
s







PP
PP
VV
VV
Dwhere

20. THIS FIGURE SHOWS A COMPARISON BETWEEN THE TWO FORMS OF THE AKI-
RICHARDS EQUATION FOR THE GAS SAND CONSIDERED EARLIER.
-0.250
-0.200
-0.150
-0.100
-0.050
0.000
0.050
0.100
0.150
0.200
0.250
0 5 10 15 20 25 30 35 40 45
Amplitude
Angle (degrees)
Gas Sand Model
Aki-Richards vs Shuey
A-R Top Shuey Top
A-R Base Shuey Base

21. AVO EFFECTS
 (a) Gas sandstone case:
Note that the effect of d
and e is to increase the
AVO effects
 b) Wet sandstone case:
Note that the effect of d
and e is to create apparent
AVO decreases.
Class 1
Class 2
Class 3
Class 1
Class 2
Class 3

22. BACK-TREND AVO
 For brine-saturated clastic
rocks over a limited depth
range in a particular locality,
there may be a well-defined
relationship between the AVO
intercept (A) and the AVO
gradient (B). linear A versus B
trends, all of which pass
through the origin (B = 0 when
A = 0).
 Thus, in a given time window,
non-hydrocarbon-bearing
clastic rocks often exhibit a
well-defined back- ground
trend; deviations from this
background are indicative of
hydrocarbons or unusual
litholo- gies.

23. POSSIBLE DEVIATION B/W GAS AND BRINE
 Deviations from the
background petro- physical
trends, as would be caused
by hydrocarbons or unusual
litholo- gies, cause
deviations from the
background A versus B
trend. This figure shows
brine sand-gas sand tie
lines for shale over brine-
sand reflections falling
along a given background
trend

24. GENERAL CLASSIFICATION
 Rutherford and Williams
(Geophysics, 1989) for Class
I (high impedance) and Class
II (small impedance contrast)
sands. However, we differ
from Rutherford and Williams
in that we subdivide their
Class III sands (low
impedance) into two classes
(III and IV).

25. AMPLITUDE VS ANGLE

26. CLASS 1 (DIM OUT)
 Amplitude decreases with increasing angle, and may
reverse phase on the far angle stack
 Amplitude on the full stack is smaller for the
hydrocarbon zone than for an equivalent wet
saturated zone.
 Wavelet character is peak-trough on near angle stack
 Wavelet character may or may not be peak-trough on
the far angle stack.

27. CLASS 2 (PHASE REVERSAL)
 There is little indication of the gas sand on the near angle
stack.
 The gas sand event increases amplitude with increasing
angle. This attribute is more pronounced than anticipated
because of the amplitude decrease of the shale- upon-
shale reflections.
 The gas sand event may or may not be evident on the full
stack, depending on the far angle amplitude contribution
to the stack.
 Wavelet character on the stack may or may not be
trough-peak for a hydrocarbon charged thin bed.

28. CLASS 2 (PHASE REVERSAL)
 Wavelet character is trough-peak on the far
angle stack.
 Inferences about lithology are contained in the
amplitude variation with incident angle.
 AVO alone, unless carefully calibrated, cannot
unambiguously distinguish a clean wet sand
from a gas sand, because both have similar
(increasing ) behavior with offset.

29. CLASS 3 (BRIGHT SPOT)
 Hydrocarbon zones are bright on the stack section
and on all angle limited stacks.
 The hydrocarbon reflection amplitude, with respect to
the background reflection amplitude, is constant or
increases slightly with incident angle range.
 Even though the amplitude of the hydrocarbon event
can decrease with angle, as suggested for the Class
4 AVO anomalies, the surrounding shale-upon-shale
reflections normally decrease in amplitude with angle
at a faster rate.

30. CLASS 3 (BRIGHT SPOT)
 Wavelet character is trough-peak on all angle
stacks. This assumes that the dominant
phase of the seismic wavelet is zero and the
reservoir is below tuning thickness
 Hydrocarbon prediction is possible from the
stack section.

31. CONT…

32. BEHAVIOR OF THE VARIOUS GAS SAND CLASSES.

33. Thank you