This document discusses Amplitude Variation with Offset (AVO) techniques and impedance inversion methods. It covers the basics of AVO modeling using the Zoeppritz, Aki-Richards, and Fatti equations. The key methods are described, including intercept-gradient analysis and modeling AVO classes. Examples are provided to illustrate modeling reflections from wet versus gas sands and comparing the different AVO modeling approaches.

1. AVO and Inversion - Part 2
A summary of AVO and Inversion Techniques
Dr. Brian Russell

2. Introduction
 The Amplitude Variations with Offset (AVO) technique has
grown to include a multitude of sub-techniques, each with its
own assumptions.
 AVO techniques can be subdivided as either:
 (1) seismic reflectivity or (2) impedance methods.
 Seismic reflectivity methods include: Near and Far stacks,
Intercept vs Gradient analysis and the fluid factor.
 Impedance methods include: P and S-impedance inversion,
Lambda-mu-rho, Elastic Impedance and Poisson
Impedance.
 The objective of this section is to make sense of all of these
methods and show how they are related.
 Let us start by looking at the different ways in which a
geologist and geophysicist look at data.

3. From Geology to Geophysics
For a layered earth, a well log measures a parameter P for each
layer and the seismic trace measures the interface reflectivity R.
Pi
Pi+1
Ri
Well Log Reflectivity
Layer i
Layer i+1

4. The reflectivity at each interface is
found by dividing the change in the
value of the parameter by twice its
average.
The reflectivity
Pi
Pi+1
Ri
Well Log Reflectivity
2
and
:where
,
2
1
1
1
1
ii
iiii
i
i
ii
ii
i
PP
PPPP
P
P
PP
PP
=R










As an equation, this is written:

5. One extra thing to observe is that the seismic trace is the
convolution of the reflectivity with a wavelet (S = W*R).
The convolutional model
Parameter Reflectivity
Wavelet
Seismic

6. Which parameter?
 But which parameter P are we interested in?
 To the geophysicist the choices usually are:
 P-wave velocity (VP)
 S-wave velocity (VS)
 Density (r)
 Transforms of velocity and density such as acoustic
impedance (rVP) and shear impedance (rVS).
 The geologist would add:
 Gamma ray
 Water saturation, etc…
 How many of these can we derive from the seismic?
 Let us now look at several seismic examples.

7. The zero-angle trace
can be modeled
using a well known
model, where the
trace is the
convolution of the
acoustic impedance
reflectivity with the
wavelet.
Note: the stack is
only approximately
zero-angle.
The zero-angle model
Acoustic
Impedance
Reflectivity
Wavelet
W
Seismic


AI
AI
=RAI
2
 PVAI r AIRWS *

8. Convolution
Convolution with the seismic wavelet, which can be written mathematically
as S = W*R, is illustrated pictorially below:
+ + + + =>
S = Seismic
Trace
R = Reflection
Coefficients
=*
W = Wavelet
8

9. A Seismic Example
The seismic
line is the
“stack” of a
series of CMP
gathers, as
shown here.
Here is a portion of a 2D
seismic line showing a
gas sand “bright-spot”.
The gas sand is
a typical Class 3
AVO anomaly.

10. The pre-stack gathers
• The traces in a seismic gather reflect from the subsurface at increasing
angles of incidence q, related to offset X.
• If the angle is greater than zero, notice that there is both a shear
component and a compressional component.
q1q2q3
Surface
Reflectorr1 VP1 VS1
r2 VP2 VS2
X1
X2
X3
Compression
Shear
q

11. Reflected
P-wave = RP(q1)
Reflected
SV-wave = RS(q1)
Transmitted
P-wave = TP(q1)
Incident
P-wave
Transmitted
SV-wave = TS(q1)
VP1 , VS1 , r1
VP2 , VS2 , r2
q1
1
q1
q2
2
More technically speaking, if q > 0°, an incident P-wave will produce
both P and SV reflected and transmitted waves. This is called mode
conversion.
Mode Conversion of an incident P-Wave
11

12. 12
The Zoeppritz Equations (1919)












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











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






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


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


1
1
1
1
1
2
11
22
2
11
22
1
1
1
1
22
11
122
2
2
2
11
1
2
22
1
1
1
1
2211
2211
1
1
1
1
2cos
2sin
cos
sin
2sin2cos2sin2cos
2cos2sin2cos2sin
sincossincos
cossincossin
)(
)(
)(
)(

q
q
q

r
r

r
r


r
r
q
r
r
q
qq
qq
q
q
q
q
P
S
P
P
P
S
S
PS
PS
PS
S
P
S
P
S
P
V
V
V
V
V
V
V
VV
VV
VV
V
V
T
T
R
R
 Karl 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.
 These equations should be used for modeling, but for
analysis we usually used the linearized equations
developed by Aki and Richards.

13. The Aki-Richards equation
 The Aki-Richards equation is a linearized form of the
Zoeppritz equations which is written:
,)( DVSVP cRbRaRR q
 The Aki-Richards equation says that the reflectivity at angle
q is the weighted sum of the VP, VS and density reflectivities.
,
2
,
2
,
2
:where
r
r




 D
S
S
VS
P
P
VP R
V
V
R
V
V
R
.and,sin41,sin8,tan1
2
222







P
S
V
V
KKcKba qqq

14. 14
To understand the Aki-Richards equation, let us look at a picked
event at a given time on the 3 trace angle gather shown below:
Each pick at time t and angle q is equal to
the Aki-Richards reflectivity at that point
(after convolution with an angle-dependent
wavelet) given by the sum of the three
weighted reflectivities. If we assume that at
time t, (VS/VP)2
= 0.25, we see that:
Understanding Aki-Richards
 
 333.030tanand25.030sin:Note
2
750.0
2
500.0
2
333.1)30(
00tan0sin:Note
2
0
2
)0(
22












oo
S
S
P
Po
P
oo
P
Po
P
V
V
V
V
R
V
V
R
r
r
r
r
t
Constant Angle
600 ms
700 ms
Picks
15
o
0
o
30
o

15. 15
The Fatti et al. Equation
 To show the connection between the pre- and post-stack
formulations more clearly, Fatti et al. (1994) re-formulated the
Aki-Richards equation as:
,')( DSIAIP RcbRaRR q
 Notice that RP(0) = RAI, equal to the zero-angle model.
,,
2
where PDVPAI VAIRR
AI
AI
R r


,,
2
SDVSSI VSIRR
SI
SI
R r


.tansin4'and 22
qq  Kc

16. Smith and Gidlow
 Fatti et al. (1994) is a refinement of the original work of
Smith and Gidlow (1987).
 The key difference between the two papers is the Smith and
Gidlow use the original Aki-Richards equation and absorb
density into VP using Gardner’s equation.
 Both papers also define the Poisson’s Ratio reflectivity Rs
and the fluid factor F (which was derived from Castagna’s
mudrock line) as:
)/(16.1where,
and,
2
PSSIAI
SIAI
VVggRRF
RRR




s
s
s

17. 17
Modified from Castagna et al, (1985)
The Mudrock Line
In non-mathematical
terms, Fatti and
Smith define F as
the difference away
from the VP versus VS
line that defines wet
sands and shales.
These differences
should indicate fluid
anomalies.
F
VP(km/sec)
VS (km/sec)

18. The Intercept/Gradient method
 The most common approach to AVO is the Intercept/Gradient
method, which involves re-arranging the Aki-Richards
equation to:
:where,tansinsin)( 222
qqqq VPAIP RGRR 
 This is again a weighted reflectivity equation with weights
of a = 1, b = sin2q, c = sin2q tan2q.
 The three reflectivities are usually called A, B, and C (or:
intercept, gradient and curvature) but this obscures the
fact that only G is a new reflectivity compared with the
previous methods.
gradient.the48  DVSVP KRKRRG

19. Let us now see how to get from the geology to the seismic
using the second two forms of the Aki-Richards equation. We
will do this by using the two models shown below. Model A
consists of a wet, or brine, sand, and Model B consists of a
gas-saturated sand.
Wet and Gas Models
(a) Wet model (b) Gas model
VP1,VS1, r1
VP2,VS2, r2
VP1,VS1, r1
VP2,VS2, r2
19

20. In the section on rock physics, we computed values for wet and
gas sands using the Biot-Gassmann equations. Recall that the
computed values were:
Wet: VP2 = 2500 m/s, VS2= 1250 m/s, r2 = 2.11 g/cc, s2 = 0.33
Gas: VP2 = 2000 m/s, VS2 = 1310 m/s, r2 = 1.95 g/cc, s2 = 0.12
Values for a typical shale are:
Shale: VP1 = 2250 m/s, VS1 = 1125 m/s, r1 = 2.0 g/cc, s1 = 0.33
The next four figures will show the results of modeling with the
Intercept/Gradient and Fatti equations.
Model Values
20

21. This figure on the right
shows the AVO curves
computed using the
Zoeppritz equations
and the two and three
term ABC equation, for
the gas sand model.
Notice the strong
deviation for the two
term versus three term
sum.
Zoeppritz vs the ABC Method – Gas Sand
Zoeppritz
AB method
ABC method
21August 2014

22. This figure on the
right shows the AVO
curves computed
using the Zoeppritz
equations and the
two and three term
ABC equation, for
the wet sand model.
Again, notice the
strong deviation for
the two term versus
three term sum.
Zoeppritz vs the ABC Method – Wet Sand
Zoeppritz
AB method
ABC method
22August 2014

23. This figure on the
right shows the AVO
curves computed
using the Zoeppritz
equations and the
two and three term
Fatti equation, for
the gas sand model.
Notice there is less
deviation between
the two term and
three term sum than
with the ABC
approach.
Zoeppritz vs the Fatti Method – Gas Sand
Zoeppritz
Fatti method,
two term
Fatti method,
three term
23August 2014

24. Zoeppritz vs the Fatti Method – Wet Sand
Zoeppritz
Fatti method,
two term
Fatti method,
three term
24August 2014
This figure on the
right shows the AVO
curves computed
using the Zoeppritz
equations and the two
and three term Fatti
equation, for the wet
sand model.
As in the gas sand
case, there is less
deviation between the
two term and three
term sum than with
the ABC approach.

25. AVO Class 3
The model curves just shown for the gas case were for a Class 3 AVO
anomaly, of which the Colony sand we are considering is an example.
Here is a set of modeled well logs for a Class 3 sand, with the computed
synthetic (using all three terms in the A-B-C equation) on the right. Note that
the P-wave velocity and density (and thus the P-impedance) decrease in the
gas sand, the S-wave velocity increases, and the VP/VS ratio decreases. The
synthetic shows increasing amplitude versus offset for both the overlying
trough and underlying peak. The far angle is 45o
.
25

26. AVO Class 2
There are several other AVO classes, of which Class 1 and 2 are the most
often seen.
Here is a Class 2 example well log, where the P-impedance change is very
small and the amplitude change on the synthetic is very large. Note that the
VP/VS ratio is still decreasing to 1.5, as expected in a clean gas sand (recall
the discussion in the rock physics section).
26

27. AVO Class 1
27
Here is a Class 1 well log example, where the P-impedance change is now
an increase and the amplitudes on the synthetic are seen to change
polarity. Again, the VP/VS ratio is still decreasing to 1.5, as expected in a
clean gas sand.
The figure on the next slide compares all three classes and also shows the
picked amplitudes.

28. The three AVO Classes
28
A comparison of the
synthetic seismic
gathers from the three
classes, where the top
and base of the gas
sand have been picked.
The picks are shown at
the bottom of the
display and clearly
show the AVO effects.
These synthetics were
created at the same
time, but in practice
class 1 sands are deep,
class 2 sands are at
medium depths and
class 3 sands are at
shallow depths.
Class 1 Class 2 Class 3
time(ms)amplitude

29.  We are usually interested in modeling a lot more than one
or two layers.
 Multi-layer modeling consists first of creating a stack of N
layers, generally using well logs, and defining the
thickness, P-wave velocity, S-wave velocity, and density
for each layer, as shown below:
Multi-Layer AVO Modeling
29

30. You must then decide what effects are to be included in the model:
primaries only, converted waves, multiples, or some combination of these.
The full solution is with a technique called Wave Equation modeling.
Multi-Layer AVO Modeling
30

31. AVO Modeling in our gas sand
Based on AVO theory and the rock physics of the reservoir, we can perform
AVO modeling of our earlier example, as shown above. Note that the model
result is a fairly good match to the offset stack.
P-wave Density S-wave
Poisson’s
ratio
Synthetic Offset Stack
31

32. The angle gather
Using the P-wave velocity, we can
transform the offset gathers shown
earlier to angle gathers. There are
two ways in which AVO methods
extract reflectivity from angle gathers.
q1
time
angle
Or we can extract the reflectivity
function at a single angle q.
We can perform a least-squares fit to
the reflectivity at a given time for all
angles.
qN

33. 33
Angle
Time
(ms)
600
650
t
1 NTo estimate the reflectivities
in the Fatti method, the
amplitudes at each time t in
an N-trace angle gather are
picked as shown here.
We can solve for the
reflectivities at each time
sample using least-squares:
Estimating RAI and RSI


























 
)(
)( 11
NP
P
D
SI
AI
R
R
matrix
weight
R
R
R
q
q

Reflectivities
Generalized inverse of
weight matrix
Observations

34. Smith and Gidlow’s results
Here are the
Rs and F
sections from
an offshore
field in South
Africa. Note
that the fluid
factor F
shows the fluid
anomaly the
best.
Rs section F section
Smith and Gidlow
(1987)

35. Fatti et al. (1994)
A comparison of a seismic amplitude map and a fluid factor
map for a gas sand play. Note the correlation of high F
values with the gas wells.
Fatti et al.’s results
F MapSeismic Amplitude Map

36. 36
Offset
+RAI
+G
- G
sin2q
Time
Regression curves are
calculated to give RAI and G
values for each time sample.
For the intercept/gradient
method, we can visualize the fit
like this:
-RAI
The Intercept/Gradient method

37. 37
The result of this
calculation is to
produce 2 basic
attribute volumes
Intercept: RAI
Gradient: G
The Intercept/Gradient method

38. 38
Intercept/Gradient combinations
The AVO product shows a positive response at the top and base of the reservoir:
Top
Base
Top
Base
The AVO difference shows pseudo-shear reflectivity:
Top
Base
The AVO sum shows pseudo-Poisson’s ratio:

39. 39
Intercept / Gradient Cross-Plots
Here is the cross-plot of Gradient
and Intercept zones, where:
- Red = Top of Gas
- Yellow = Base of Gas
- Blue = Hard streak
- Ellipse = Mudrock trend
Below, the zones are plotted back
on the seismic section.

40. 40
Impedance Methods
 The second group of AVO methods, impedance methods,
are based on the inversion of the reflectivity estimates to
give impedance.
 The simplest set of methods use the reflectivity estimates
from the Fatti et al. equation to invert for acoustic and
shear impedance, and possibly density. That is:
(Density)
Impedance)(Shear
Impedance)(Acoustic
r
r
r



D
SSI
PAI
R
VSIR
VAIR
 The inversion can be done independently (separately for
each term) or using simultaneous inversion.

41. 41
Impedance Reflectivity
Inverse
Wavelet
Seismic
Seismic Inversion reverses the forward procedure:
Seismic inversion
In principle, inversion is done as shown above, but in practice,
the procedure is as shown in the next slide.

42. Model-based inversion
(1) Optimally process the seismic data (2) Build model from picks and impedances
(3) Iteratively update
model until output
synthetic matches
original seismic data.
S=W*RAI M=AI=rVP
AI=rVP
In acoustic impedance
inversion the seismic,
model and output are
as shown here.
S=W*RSI M=SI=rVS
SI=rVS
In shear impedance
inversion the seismic,
model and output are
as shown here.

43. 43
P-wave and S-wave Inversions
Here is the P-wave
inversion result.
The low acoustic
impedance below
Horizon 2
represents the gas
sand.
AI = rVP
SI = rVSHere is the S-wave
inversion result.
The gas sand is
now an increase,
since S-waves
respond to the
matrix.

44. 44
AI/SI = rVP/rVS = VP/VS
Vp/Vs Ratio
Here is the ratio of P to S impedance, which is equal to the
ratio of P to S velocity. Notice the low ratio at the gas sand.

45. 45
Cross-plot
When we crossplot
VP/VS ratio against P-
impedance, the zone of
low values of each
parameter should
correspond to gas, as
shown.
This zone should
correspond to gas:

46. 46
 Other AVO impedance methods combine the P and S-
impedance volumes in new ways.
22
2
2SIAI
SI


r
r
Lambda-mu-rho (LMR)
 The interpretation of this approach is that r gives the
matrix value of the rock and r the fluid value.
 Russell et al. (2003) derived a more general approach
based on Biot-Gassmann theory in which the factor 2 is
replaced with c = (VP/VS)dry
2, allowing empirical calibration to
find a best value.
 For example, Goodway et al. (1997) proposed the Lambda-
Mu-Rho (LMR) method which utilized the Lamé parameters
 and , and density, where it can be shown that:

47. 47
The r and r
sections derived
from the AI and SI
inverted sections
shown earlier.
Note the decrease
in r and the
increase in r at
the gas sand zone.
r and r example
r (lambda-rho)
r (mu-rho)

48. 48
A cross-plot of the r and r sections, with the corresponding
seismic section. Two zones are shown, where red = gas (low
r values) and blue = non-gas.
Colony Sand – cross-plot
r (lambda-rho)
r(mu-rho)

49. Last updated: June 2008 49
One AVO reflectivity
method we did not
discuss was near
and far angle stacks,
as shown here.
Note the amplitude
of the “bright-spot”
event is stronger on
the far-angle stack
than it is on the
near-angle stack.
But what does this
mean?
Near and far trace stacks
Near angle (0-15o) stack
Far angle (15-30o) stack

50. 50
Elastic Impedance
 The equivalent impedance method to near and far angle
stacking is Elastic Impedance, or EI (Connolly,1999).
 To understand EI, recall the Aki-Richards equation:
.sin21and,sin8,tan1
:where,
222
)(
222
qqq
r
r
q
KcKba
c
V
V
b
V
V
aR
S
S
P
P
P







cb
S
a
PEI VVEIEI
EI
EI
R rqq
q
q
q 

 )(where,)(ln
2
1
)(
)(
2
1
)(
 Connolly postulated that associated with this equation is
an underlying elastic impedance, written (where I have re-
named the reflectivity to match the EI concept):

51. 51
Elastic
Impedance (EI)
= VP
aVS
brc
Aki-Richards
reflectivity at q
RP(q)
Wavelet
Seismic trace
at angle q
S(q)
Analogous to AI, the model that forms the basis for EI is:
The elastic impedance model

52. 52
Elastic
Impedance (EI)
= VP
aVS
brc
Aki-Richards
reflectivity at q
RP(q)
Wavelet
Seismic trace
at angle q
S(q)
The elastic impedance model
Inverse
Wavelet
Elastic impedance inversion reverses the forward EI model:

53. Elastic impedance inversion
(1) Optimally process the seismic data (2) Build model from picks and impedances
(3) Iteratively update
model until output
synthetic matches
original seismic data.
In elastic impedance
inversion the seismic,
model and output are
as shown here.
SEI(q)=W(q)*REI(q)
cb
S
a
P VVEIM rq  )(
cb
S
a
P VVEI rq )(

54. 54
Here is the
comparison
between the EI
inversions of the
near-angle stack
and far-angle
stack.
Notice the
decrease in the
elastic impedance
value on the far-
angle stack.
Gas sand case study
EI(7.5o)
EI(22.5o)

55. The figures show the (a) crossplot between near and far EI logs, and (b) the
zones on the logs. Notice the clear indication of the gas sand (yellow).
EI from logs
(a) (b)
EI_Near EI_Far

56. 56
Gas sand case study
This figure shows a crossplot
between EI at 7.5o and EI at 22.5o.
The background trend is the grey
ellipse, and the anomaly is the yellow
ellipse. As shown below, the yellow
zone corresponds to the known gas
sand.
EI at 7.5o
EIat22.5o

57. 57
 Since EI values do not scale correctly for different angles,
Whitcombe et al. (2002) created a new method (EEI) that
did scale correctly, and was extended to predict other rock
physics and fluid parameters (using the c factor).
Extended Elastic Impedance (EEI)
 I will not go into
the details today,
but here is an
example of
predicting Vp/Vs
ratio using our
previous example,
where the units are
Elastic Impedance.

58. 58
 Finally, Quackenbush et al. (2006) proposed the Poisson
Impedance (PI) attribute, given by:
2where,  ccSIAIPI
Poisson Impedance (PI)
 The authors show that Poisson Impedance is like a
scaled version of the product of Poisson’s ratio and
density.
 We can think of this method as an impedance version of
Poisson Reflectivity, defined by Smith and Gidlow.
 Also note the relationship with r:
    PISIPISIAISIAISIAI 22222 22
r

59. 59
Above, notice that PI can be thought
of as a rotation in AI/SI space.
Poisson Impedance (PI)
On the right is a comparison of PI
with other impedance attributes.
Quackenbush et al. (2006)
Quackenbush et al. (2006)

60. VP(0o)
VP(45o)
VP(90o)
 We will consider the cases of Transverse Isotropy with a
vertical symmetry axis, or VTI, and Transverse Isotropy
with a Horizontal symmetry axis, or HTI.
 Let us finish with a discussion of anisotropic effects.
 In an isotropic earth P and S-wave velocities are
independent of angle.
 In an anisotropic earth, velocities and other parameters
are dependent on direction, as shown below.
Anisotropic effects
60

61. VTI – AVO Effects
61
qq

q

q
22
2
tansin
2
sin
2
)(





 






 

C
BARVTI

The VTI model consists of horizontal
layers and can be extrinsic, caused by
fine layering of the earth, or intrinsic,
caused by particle alignment as in a
shale. It can be modeled as follows,
where  and  are the change in
Thomsen’s first two anisotropic
parameters across a boundary:
A VTI shale over an isotropic wet sand
can create the appearance of a gas
sandstone anomaly, as shown here:
Class 1
Class 2
Class 3
Isotropic
--- Anisotropic
 = -0.15
 = -0.3
Adapted from Blangy (1997)

62. In this display, the synthetic responses for a shallow gas sand in
Alberta are shown. Note the difference due to anisotropy.
(a) Isotropic (b) Anisotropic (a) – (b)
Anisotropic AVO Synthetics
62

63. HTI effects on AVO
63
Next, we will discuss AVO
and HTI anisotropy, as
shown in the figure on the
left. This shows a set of
fractures, with the
symmetry axis orthogonal
to the fractures, and the
isotropy plane parallel to
the fractures.
In addition to the raypath angle q, we
now introduce an azimuth angle ,
which is defined with respect to the
symmetry-axis plane. Note that the
azimuth angle  is equal to 0 degrees
along the symmetry-axis plane and
90 degrees along the isotropy plane.
q
From Ruger, Geophysics, May-June 1998

64. Modeling HTI
64
 
 
 .sin
2
1
,8
2
1
:where
tansincos
sincos
)(2)(
2
)(
222
22
VV
HTI
P
SV
HTI
HTI
HTIHTI
C
V
V
B
CC
BBAR


qq
q



















HTI anisotropy can be modeled with
the following equation, where  is
Thomsen’s third anisotropic
parameter and (V) indicates with
respect to vertical. When  = 0, along
the isotropy plane, we get the
isotropic equation, as expected:
The reflection coefficients for a
model where only  changes, as
a function of incidence angle for
0, 30, 60 and 90 degrees azimuth.
Isotropy plane:
Symmetry-axis
plane:

65. Fracture Interpretation
Edge
Effects
Orientation
of Fault
Direction of Line is
estimated fault strike,
length of line and color
is estimated crack
density
AVO Fracture Analysis
measures fracture
volume from differences
in AVO response with
Azimuth. Fracture strike
is determined where this
difference is a maximum.
Interpreted Faults
Fractures abutting
the fault
Fractures curling
into the fault
Oil Well
Courtesy: Dave Gray, CGGVeritas65

66. Summary of AVO methods
AVO
Methods
Seismic
Reflectivity
Impedance
Methods
Near and
Far Stack
Intercept
Gradient
Fluid
Factor
Acoustic
and Shear
Impedance
Elastic
Impedance
LMR
EEI
PI

67. 67
Seismic reflectivity methods
 The advantages of AVO methods based on seismic
reflectivity are that:
 They are robust and easy to derive.
 They allow the data to “speak for itself” since
their interpretation relies on detecting deviations
away from a background trend.
 The disadvantage of AVO methods based on
seismic reflectivity is that:
 They do not give geologists what they really
want, which is some physical parameter with a
trend.

68. 68
Impedance methods
 The advantages of AVO and inversion methods based on
impedance are that:
 They give geologists what they want: a physical
parameter with a trend.
 They can be transformed to reservoir properties.
 The disadvantages of AVO and inversion methods based
on impedance are as follows:
 The original data has to be transformed from its
natural reflectivity form.
 Care must be taken to derive a good quality
inversion.

69. Conclusions
 This presentation has been a brief overview of the various
methods used in Amplitude Variations with Offset (AVO)
and pre-stack inversion.
 I showed that all of these methods are based of the Aki-
Richards approximation to the Zoeppritz equations.
 I then subdivided these techniques as either:
 (1) seismic reflectivity or (2) impedance methods.
 Seismic reflectivity methods are straightforward to derive
and to interpret but do not give us physical parameters.
 Impedance methods are more difficult to derive but give us
physical parameters including reservoir properties.
 In the final analysis, there is no single “best” method for
solving all your exploration objectives. Pick the method that
works best in your area.