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By Haseeb Ahmed
M.Phil Geophysics
Institute of Geology, University of the Punjab
AVO ANALYSIS
 Amplitude versus offset (AVO) is primarily
the variation in seismic reflection
amplitude with change in distance
between...
FIG. SHOWING AVO (A) & (B)
AVO INTRODUCTION
 It can physically explain presence of
hydrocarbon in the reservoirs and the
thickness, porosity, densit...
THE ZOEPPRITZ EQUATIONS
 Zoeppritz derived the amplitudes of the reflected
and transmitted waves using the conservation o...
THE ZOEPPRITZ EQUATIONS















































1...
THE AKI-RICHARDS EQUATION
 The Aki-Richards equation is a linearized
approximation to the Zoeppritz equations.
 The init...
THE AKI-RICHARDS EQUATION
 Where;
,sin4
,sin25.0
,
cos2
1
2
2
2
2
2
























...
WIGGINS’ VERSION OF THE
AKI-RICHARDS EQUATION
 A more intuitive, but totally equivalent, form was
derived by Wiggins.
 H...
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

















...
INTERPRETING THE AKI-RICHARDS EQUATION
 The first term, A, is a linearized version of the zero
offset reflection coeffici...
OSTRANDER’S GAS SAND MODEL
 Ostrander (1984) was one of the first to write about
AVO effects in gas sands and proposed a ...
* Note : The model consists of a low acoustic impedance and Poisson’s ratio gas
sand encased between two shales.
SYNTHETIC FROM OSTRANDER’S MODEL
 (a) Well log responses
for the model.
 (b) Synthetic seismic.
WET AND GAS MODELS
 Wet Sand Model  Gas Saturated Model
AVO MODELS
 In the next two slides, we are going to compute the top and base
event responses from Models A and B, using t...
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)...
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 (deg...
SHUEY’S EQUATION
 Shuey (1985) rewrote the Aki-Richards equation using VP, , and s.
Only the gradient is different than ...
THIS FIGURE SHOWS A COMPARISON BETWEEN THE TWO FORMS OF THE AKI-
RICHARDS EQUATION FOR THE GAS SAND CONSIDERED EARLIER.
-0...
AVO EFFECTS
 (a) Gas sandstone case:
Note that the effect of d
and e is to increase the
AVO effects
 b) Wet sandstone ...
BACK-TREND AVO
 For brine-saturated clastic
rocks over a limited depth
range in a particular locality,
there may be a wel...
POSSIBLE DEVIATION B/W GAS AND BRINE
 Deviations from the
background petro- physical
trends, as would be caused
by hydroc...
GENERAL CLASSIFICATION
 Rutherford and Williams
(Geophysics, 1989) for Class
I (high impedance) and Class
II (small imped...
AMPLITUDE VS ANGLE
CLASS 1 (DIM OUT)
 Amplitude decreases with increasing angle, and may
reverse phase on the far angle stack
 Amplitude on...
CLASS 2 (PHASE REVERSAL)
 There is little indication of the gas sand on the near angle
stack.
 The gas sand event increa...
CLASS 2 (PHASE REVERSAL)
 Wavelet character is trough-peak on the far
angle stack.
 Inferences about lithology are conta...
CLASS 3 (BRIGHT SPOT)
 Hydrocarbon zones are bright on the stack section
and on all angle limited stacks.
 The hydrocarb...
CLASS 3 (BRIGHT SPOT)
 Wavelet character is trough-peak on all angle
stacks. This assumes that the dominant
phase of the ...
CONT…
BEHAVIOR OF THE VARIOUS GAS SAND CLASSES.
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Avo ppt (Amplitude Variation with Offset)

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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.

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Avo ppt (Amplitude Variation with Offset)

  1. 1. By Haseeb Ahmed M.Phil Geophysics Institute of Geology, University of the Punjab AVO ANALYSIS
  2. 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. 3. FIG. SHOWING AVO (A) & (B)
  4. 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. 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. 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. 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. 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. 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. 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. 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. 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. 13. * Note : The model consists of a low acoustic impedance and Poisson’s ratio gas sand encased between two shales.
  14. 14. SYNTHETIC FROM OSTRANDER’S MODEL  (a) Well log responses for the model.  (b) Synthetic seismic.
  15. 15. WET AND GAS MODELS  Wet Sand Model  Gas Saturated Model
  16. 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. 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. 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. 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. 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. 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. 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. 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. 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. 25. AMPLITUDE VS ANGLE
  26. 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. 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. 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. 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. 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. 31. CONT…
  32. 32. BEHAVIOR OF THE VARIOUS GAS SAND CLASSES.
  33. 33. Thank you

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