0001 AVO Fundamental

AVO/AVA for Gas/Fluid Detection & Seis Seismi micc Lith Lithol olog ogy y Anal Analys ysis is

AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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1. Preface Amplitude Va Variation with Of Offset (AVO) or Am Amplitude Vari Variat atio ion n with with Angl Anglee (AVA (AVA)) bec becom omee pop popul ular ar in expl explor orat atio ion n indus industr try y since since intr introdu oduce ced d by Ostr Ostran ande derr (1984 (1984), ), Pichi Pichin n and and Mitche Mitchell ll (1991) (1991),, Mazzot Mazzotti ti and Mirri Mirri (1991) (1991).. Amplitude variation with offset (AVO) , , or often called as Amplitude Versus Offset first suggested by Ostrander in 1982 and 1984 to analyze seismic anomaly associated with gas-sand model.


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The gas-sand model used by Ostrander can give increasing reflection amplitude with the increasing offset or angle and the term of AVO/AVA comes from here. The rock physics basis for AVO/AVA analysis such as density, porosity, seismic wave velocity, etc., have been discussed in previous section . The discussion here will be concentrated on the mathematical basis and practical application of the method.


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The need of AVO is improving specially because of the ambiguity of amplitude anomaly to distinguish the anomaly from gas and the anomaly from : 1.

Low impedance sandstone

2.

Shale

3.

Coal

4.

Porous ca carbonate

5.

Other lithology effect


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2. Mathematical Foundation 2.1. 2.1. Zoeppr Zoeppritz itz Equati Equation on One of the basic assumption about seismic data is that the seismic wave strikes the rock layer at vertical incidence. In this case, the reflection coefficient is given as following equation (1) :

KRi

=

AI i +1 − AI i AI i +1 + AI i

(1)


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When the seismic wave strike the boundary at non zero incidence angles, the conversion of P to S wave will occur. As the consequence, the reflection coefficient becomes a function of the P-wave velocity, S-wave velocity and density of each of the layers. Indeed, there are now four curves that can be derived : reflected P-wave amplitude, transmitted P-wave amplitude, reflected S-wave amplitude, and transmitted S-wave amplitude, as shown in Figure 1. The variation of amplitude with offset will also affected by the Poisson’s Ratio.


6

B1

A 0

A 1

λ1 θ1

θ1

λ2 θ2

B2

A 2

Figure 1. Illustration of how the P-wave strike the boundary and split into 4 waves


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The formula for Poisson’s ratio is given by the following equation (2) :

−2 σ = 2(V p / V s ) 2 − 2 V p / V s ) 2

(2)

Theoretically the Poisson’s ratio can vary between 0 and 0.5 and is close to 0 for gas and is 0.5 for a liquid.


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From equation (2), it is obvious that when the Poisson’s ratio approaches 0.5, the Vp/Vs ratio goes to infinity. This is because the S-wave velocity is zero in a fluid. On the other hand, the Vo/Vs ratio = √2 when the Poisson’s ratio is 0. Schoenberg suggested that a parameter that can be used to simplify the transformation from velocity to Poisson’s ratio is γ = (Vp/Vs)2. In this case, we see that :


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As mentioned, the equations which determine the amplitude variations as a function of offset are dependent on P-wave velocity, Poisson’s ratio, and density. They were derived from the continuity of displacement and stress in both the normal and tangential directions across an interface between two layers by Zeoppritz. Equation Equation 3 gives gives the final form of of the Zeoppri Zeoppritz tz equations, equations, and and relates to the rays shown in Figure 1.


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 sin λ r − cos λ r   sin 2λ r    cos 2λ r 

cos φ r

sin λ r

sin φ r

cos λ t

α 1 B1 β 1 α 1

2

cos 2φ sin 2λ r

ρ 2 B2 α 1 2

sin 2 λ t

2

cos 2 φ

ρ 1 B1 α 2 − ρ 2 λ 2 ρ 1 B1 α 2

 − sin λ r   A − cos λ - sin φ t r   B - ρ 2 B2α 1  cos 2φ t    C  = sin 2λ r ρ 1 B1   - ρ 2 B2 sin 2φ   D  = − cos 2φ t  ρ 1 α 1 cos φ t

(3)


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2.2. Approxi Approximatio mation n to the the Zeopprit Zeoppritz’s z’s Equation Equation a. The Aki, Richard and Frasier Approximation The 4x4 series of linear equations shown in Figure (1) is a good way of deriving the exact amplitudes of a reflected P-wave as a function of angle. But it does not give an intuitive understanding of how these amplitudes relate to the various physical parameter. The Aki, Richards and Frasier approximation is appealing because it is written as three terms, the first involving density, the second involving Vp, and the third involving Vs. Their formula can be written as the following equation (4) : AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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R( θ) = a

α

where : a

α

+ b

ρ ρ

+c

 β β

(4)

= 1/(2 cos2 θ) = 1/2 + tan2 θ b = 0.5 –[(2β2/α2) sin 2 θ] c = -(4β2/ α 2) sin2 θ α = (α 1+ α 2)/2 β = (β1+ β2)/2 ρ = (ρ 1+ ρ 2)/2 ∆ α = α 2+ α 1 ∆ β = β2+ β1 ∆ ρ = ρ 2+ ρ 1 θ = (θi+ θt)/2 θt = arc sin [(α 2/ α1)sin θi] AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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b. The Smith/Gidlow Method Smith and Gidlow Gidlow (1987) rearranged rearranged Aki-Ri Aki-Richard’ chard’ss equation equation in the following way :

R (θ ) =

1  ∆α

 2  α

∆ ρ  β 2  ∆ β ∆ ρ  2 1 ∆α + + sin θ + tan 2 θ  − 2 2 2 ρ  α  β ρ  2 α (5)


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They then chose to remove the dependency on density by using Gardner’s equation :

ρ=cα 1

4

(6)

which can be differentiated to give :

ρ ρ

=

1 α 4 α

(7)

Substituting equations above, we can re-express Aki and Richard’s Richard’s equatio equation n as the the following following weighted weighted sum sum of PP- and SSwave velocity variations.


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R (θ ) = a

α α

where a = and b = - 4

+ b

∆ β β

2

5 β 1 2 2 - 2 sin θ + tan θ 8 α 2 β 2 α

2

2

sin θ

(8)


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Notice that once we have chosen a suitable β/α ratio, the coefficients a and b can then be calculated (the angular values can be found by ray-tracing), and used to solve for ∆ α/α and ∆ β/β using the amplitudes of the seismic gather. Once the P and S velocities have been extracted, they can be comb combin ined ed in in vari variou ouss way ways. s. The The firs firstt is is ter terme med d ‘ pseu pseudo do Poisson’s ratio’, and can be written :

σ σ

=

α  α β

(9)


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The next use is to consider the ‘fluid factor’ which based on the ‘mud ‘mudro rock ck equa equati tion on by by Cas Casta tagn gnaa :

α

= 1360 + 1.16 β

(10)

where α, β are in m/sec. The differential from equation above is ∆α = 1.16 ∆β which can be expressed in ratio form as : α α

= 1.16

β  β α β

(11)


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The equation only accurate in the case of wet non-productive reservoir. For an anomalous reservoir, we can define the ‘fluid factor’ error from the following equation :

∆F =

∆α α

- 1.16

∆ α β

(12)

In other words, if ∆F =0, the reservoir is non-prospective, but if | ∆F | = 0, the reservoir is prospective.


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Figure 2a. The model parameter, dashed is the‘smooth’ function which used in weight computation


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Figure 2b. Synthetic CMP Gather resulting from application of Zeopritz’s equation in Figure 6.24a (Russel, 1998)


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Now we have four parameters that can be extracted from gather data by using suitable weights : ∆α / α, ∆β / β and ∆F The following following is the the illust illustratio ration n of Smith and Gidlow Gidlow method models. Figure 2a shows model parameter, while Figure 2b is the synthetic model.


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Figure 3 shows the effect of ray tracing through a smooth velocity model. Notice that the angular relationship increases with time and offset. Figure 4a, b, c, and d, respectively, show the calculated weights for the ∆α / α, ∆β / β, ∆σ / σ, and ∆F calculations. These weights are applied to the seismic gather and the resulting weighted amplitude values are summed together horizontally. Figure 6(a) and (b) show the final result of synthetic in Figure 2b, in synthetic form and also as exact reflection coefficient. Notice that ∆α / α and ∆β / β traces show the same magnitude and direction of velocity change as the input model in Figure 2a.


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The trace ∆α /α also show the same magnitude and direction of change as the Poisson’s ratio log. However, the most interesting result is the ∆F trace, which has zero amplitude for the nonanomalous parts of the log and larger amplitudes at the two anomalies (approximately 2.2 s and 2.5s).


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Russel Russel (1998) gave real data examples examples of of the case above for for a line crosses an existing well gas. Cross plots of the well values are shown in Figure 6 and 7. On cross plot between α vs. β, both wet sands and shales shales and and and also also the gas sands sands display display linear linear trend, but these trends are shifted relative to each other. Figure 7 is the cross plot between log ρ vs. log α. Seen that the gas- and non-gas non-gas sandstone sandstone can can not not be separated, separated, which which means the use of Gardner’s equation may be slightly in error.


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Figure 3. Example of ‘ray-tracing’ through a smooth velocity model to recover incidence angle of a CMP gather (Russel, 1998)


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Figure 4a. Example of weighting, if it’s applied before the stacking, we can extract the reflectivity of P-velocity (Russel, 1998)


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Figure 4b. Example of weighting, if applied before the stacking we can extract the reflectivity of P-velocity (Russel, 1998)


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Figure 4c. Example of weighting, if applied before the stacking we can extract the Poisson’ s Ratio reflectivity


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Figure 4d. Example of weighting , if applied before the stacking, will give the fluid factor value (Russel, 1998)


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Figure 5a). The result of weighted stack from model in Figure 2b. b). The reflection coefficient which extracted from model in Figure 2a (Russel, 1998)


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Figure 6. The cross plot between between P-velocity against S-velocity (Russel, 1998)


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Figure 7. The cross-plot between density log and P-velocity log of (Russel, 1998)


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Figure 8. P-wave display (Russel, 1998)


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Figure 9. S-velocity display (Russel, 1998)


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Figure 10. The pseudo-Poisson’s Ratio display (Russel, 1998)


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Figure 11. The fluid factor display (Russel, 1998)


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Figure 8-11 show various display types. Neither ∆α /α and ∆β/ ∆β/β displays in Figure 8-9 show the anomaly very clearly. In ∆α /α and ∆F the anomaly is starting to become clear. Equation 3 is certainly appealing from a physical parameter standpoint. However, on the seismic section we measure the amplitude of reflection coefficients. Therefore, it would be nice to get this Equation 3 arranged into a function of reflection coefficient, as follows :


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R (θ ) =

+

1 α 2 α

1  α

 2  α

(tan

2

 1 α β 2 +  +  -4 2 ρ   2 α α ρ 

θ − sin 2 θ

 β β

-2

β 2 ρ  α

2

ρ

 sin 2 θ 

)

(13)

Simplification is held by assuming that β/α = ½ (σ = ⅓) and ignore the third term(tan2θ ≈ sin2θ), which leads to ;

R (θ ) =

1  α

 + 2  α

ρ  ρ

 1 α ∆ β 1 ρ  2  +   sin θ   2 α β 2 ρ 

(14)


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With simplification as follows : ρ  +   2  α ρ  1   β ρ  Rs =  +  2  β ρ  Rp =

1  α

Thus the equation 6.32 can be rewrite as : R(θ) = Rp + (Rp – 2Rs) sin2θ R(θ) = Rp + G sin2 θ where G = Rp-Rs

(15) (16)


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c. Shuey’ Shuey’ss Approxi Approximat mation ion Shue Shuey y (198 (1985) 5) gave gave a clos closed ed form form appr approxi oxima mati tion on of Zeoppr Zeoppritz itz’s ’s equati equations ons,, as follows follows : R(θ( = R p

+ (R p A 0 +

σ

(1- σ)

2

)sin2θ + 1/2

α α

(tan2θ − sin 2θ)

the the

(17)

where σ = (σ (σ1+σ2)/2 A0

= B - 2(1+ B)

B=

1 - 2σ 1- σ

α/α α/α + ρ/ρ


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Figure 12. The comparison of Zeopprit’s Zeopprit’s equation and approximations (Russel, 1998)


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Figure 13. The error value from negative reflector as shown on Figure 6.34 (Russel, 1998)


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Figure 14. The illustration of a) AVO response and b) transformation from a into AVA response (Amplitude versus Angle) (Russel, 1998)


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Hiltermann simpli plified Sh Shuey’s equation eve even n fu further by by making the following assumptions : 1) Use Use only only the the fir first two two terms erms (sin (since ce tan2θ – sin2θ << sin2θ) 2) Set σ = 1/3, which mean that A0 = -1 Then, equation (6.35) simplifies to: R(θ R(θ) = Rp (1-sin2θ) + 9/4 ∆σ sin2θ

(18)

R(θ R(θ) = Rp cos2θ + 9/4 ∆σ sin2θ

(19)

Equations (18) and (19) suggest that the AVO response is dominated by R 0 at small angles and by ∆σ at large angles. Figure 12-13 give the comparison between Zeoppritz’s method result and others. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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3. Offset to Angle Transformation Both Both Zeop Zeoppri pritz’ tz’ss and Shuey’ Shuey’ss equati equations ons are depend dependent ent upon upon the the incidence angle of seismic wave. Since the seismic data was recorded as a function of offset, the data must be transformed from the offset domain to the angle domain, as shown in Figure 14. In Figure 14a is shown an offset gather, and in Figure 14b is shown the equivalent angle gather. At the top of each gather is shown a schematic of the ray path. Notice that the angle of incidence for a constant offset trace decreases with depth, whereas the angle remains constant with depth for a constant angle trace. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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To transform from constant offset to constant angle, we use the following equation :

tanθ =

X

(20)

2Z

where: θ = angle of incidence X = offset Z = depth If we know the velocity down to the layer of interest, the above equation can be rewritten as following equation (21) : Z

=

Vt 0 2

(21)

where : V = velocity (RMS or average) t0 = total zero offset travel time AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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Substituting equation (6.39) to (6.38) gives the following equations (6.40) and (6.41):

tan θ

=

X

(22)

Vt 0

or θ

= tan -1 X Vt  0 

(23)

By using those equations, the offset can be transformed to angle.


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Equation (22) also allows the mapping of amplitudes on an offset gather to amplitudes on an angle gather. Figure 15 shows curves of angle which related to the offset correspondence. Notice that these curves increase to larger offsets at deeper time. This means that a constant angle seismic trace would contain amplitudes collected from longer offsets on the AVO gather as time increases.


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The preceding equations are strictly valid only for a single layer. An approximation that can be used for the multi layer case involves using the ray parameter P and total travel time t : P = sin θ/ VINT

(24)

and t2 = t02 + X2/ VRMS2

(25)

where VINT = interval velocity for a particular layer VRMS= velocity down to the layer Note also that P and t are related by the the equation:

dt dx

=

P

(26)


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This can be seen in Figure 16. By substituting equation (6.43) to (6.44), we get :

P

X

=

t VRMS

(27)

2

By substituting equation (6.42) to (6.43), we get : sin θ

=

X VINT t VRMS

2

(28)


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To see that equation (6.46) reduces to equation (6.38) for the single layer case, refer to Figure 16, notice that : t0 = t cos θ

(29)

Thus, by substituting equation (6.47) to (6.46), and noting that VRMS = VINT = V for a single layer, we see that :

sinθ sinθ cosθ cosθ

= tan θ =

x Vto

(30)


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Figure 15. Angle curves superimposed on the corresponding offsets (Russel, 1998)


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Figure 16. The τ-p analysis of NMO curve


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Figure 17. The schema of relationship between depth and offset.


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Figure 18. Example of the plot of amplitude versus sin2 θ


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(a)

(b)

(c)

Figure 19. Display of P (b) and S -wave (c) (c) stacks which derived from CMP CMP stack input in figure (a) (Russel, 1998)


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Once we have transformed from offset to angle, we can use the Shuey’s Shuey’s approximati approximation, on, which which were written written : R(θ R(θ) = Rp + G sin 2θ

(31)

where R(θ R(θ) = change of reflection coefficient with angle θ Rp

= P-w P-wav avee ref refle lect ctio ion n coe coeff ffic icie ient nt at norm normal al inci incide denc ncee

G

= gradient term depending on change of Poisson’s ratio

A. example of this curve plot is shown in Figure 18.


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Using the values of P and G derived from the plot in Figure 18, a P-wave stack and an S-wave stack can be derived from the seismic seismic data. data. This was done done using using Gelfand’s Gelfand’s approximatio approximation n for G: G = Rp – 2 Rs

(32)

where Rs Rs = normal incidence incidence S-wave S-wave reflecti reflection on coefficien coefficientt Therefore ; Rs = (Rp - G)/ 2

(33)

Figure 19 shows a seismic section and the derived P and S-wave stacks. A bright anomaly at about 1.25 seconds indicates the possible presence of a gas sand. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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4. The Prediction of AVO Response In previous discussion, we saw that, for the case of angles less than 30º, 30º, the Zeopprit Zeoppritz’s z’s equation equation may be simplif simplified ied into into : R(θ R(θ) = Rp Rp + G sin2 θ The equation shows that reflectivity is roughly parabolic as a function of angle and that its relative change depends on the sign of the Poisson’s ratio change. That is, the curve will increase for a positive change in Poisson’s ratio, and will decrease for a negative change (Figure 20).


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Next, let us consider the sign of the reflection coefficient (i.e. the direction of change of acoustic impedance). If we consider the case of a significant change in Poisson’s ratio (i.e. in the order of + or or – 0.2), the relati relative ve change change will will still still be be the same, same, increasing for an increase in Poisson’s ratio, and decreasing for a decrease in Poisson’s ratio. However, we are more interested in absolute amplitude change than the relative change. Thus, a relative decrease for a negative reflection coefficient will produce an increase in absolute amplitude. Likewise, an increase in relative amplitude will produce a decrease in absolute amplitude. This is shown in Figure 21. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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Figure 20. The summary of AVO effects due to Poisson’s Ratio and AI changes (Russel, 1998)


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Figure 21. AVO model model showing the effect of increasing Poisson’s Ratio Ratio and AI (Russel, 1998)


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Figure 22. AVO model showing the effect of increasing AI and decreasing Poisson’s Ratio (Russel, 1998)


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Figure 23. AVO model model showing decreasing AI and increasing Poisson’s Ratio (Russel, 1998)


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Figure 24. AVO model showing decreasing AI and Poisson’s Ratio (Russel, 1998)


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Figure 25. The summary of AVO response due to the AI and Poisson’s Ratio changes (Russel, 1998)


67

To illustrate the phenomena above, followings are the illustration of four possible cases for increasing and decreasing AI and Poisson’s ratio (Figure 21-24) . Figure 21 shows the situation in which both Poisson’s ratio and AI increase, Figure 22 shows increasing AI and decreasing Poisson’s ratio. Figure 23 the situation is reversed, decreasing AI and increasing Poisson’s ratio. Figure 24 summarizes all the possible combination.


68

5. AVO Modeling 5.1. Ostrander’s Model Figure 26 the tree-layered gas-sandstone model with typical parameter of young geology age and shallow. In here, the gas-sandstone with Poisson’s ratio = 0.1 located under the shale with Poisson’s ratio = 0.4. In this model, P-seismic wave velocity is reduced from shale to gas-sandstone in amount of 20 %, that is from 10,000 ft/sec to 8,00 ft/sec, and density decrease in amount of 10 % from 2.40 g/cm3 to 2.16 g/cm3. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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The wave reflection coefficient (RC) change as a function of angle as shown in Figure 27. Two solid curves are reflection coefficient resulted from the gas-sandstone model parameters which shown in Figure 26. The horizontal line is the seismic wave angle of incidence on gas-sandstone top. Because of refraction, the angle of incidence on top gassandstone is only presented up to 40º, angle of incidence on base gas-sandstone is only presented up to 31º. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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From Figure 27 we can see that the reflection coefficient of top sandstone changes from –0.16 to –0.28, while the reflection coefficient of base sandstone base changes from +0.16 to +0.26. Thus, the seismic wave amplitude can increase in the amount of 70 % in rang rangee of 40º incide incidence nce.. The dashed curve in Figure 27 shows what will happen on reflection coefficient if the Poisson’s ratio of gas-sandstone change into 0.4.


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Figure 26. The model of hypothetic three-lapped t hree-lapped gas-sandstone (Ostrander, 1984)


72

Figure 27. Plot of P-wave reflection coefficient against the incidence angl e for three-lapped gas-sandstone model (Ostrander, 1984)


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Figure 28. The stacked-seismic stacked-seismic section for line SV-1 SV-1 (Ostrander, 1984)


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Figure 28 shows 24-fold CDP seismic section passing thru the Sacramento Valley gas field. The sandstone reservoir is located in depth about 6.700 ft which associated with seismic amplitude anomaly in 1.75 seconds. This reservoir is the sea fan deposit in Cretaceous which has maximum net pay up to 95 ft. The existing existing traps traps are the the structure structure and and stratigraphy stratigraphy traps. Faults Faults exist in SP 95, wedging reservoir is in SP 75.


75

Seismic wave velocity and density in gas-sandstone are lower than the seal-shale, which give strong seismic reflection on top and base of gas-sandstone. In 1.8 s between SP 115 and SP 135, we see the flat spot phenomena. This phenomena is also seen in SP 75 to SP 130.


76

CDP gather from three location, A, B, and C, are shown in Figure 29, 30, 30, respectively. Both single-fold and 10-fold refer to location A and B, and only 10-fold refers to location C. Shot to the offset group for all gather increases from right to the left. On objective objective gas-sands gas-sandstone, tone, the the near-offs near-offset et related related to 5º angle of incidence, incidence, while while far-offse far-offsett related related to 35º angle of incidenc incidence. e.


77

Figure 29 and 30 show a strong amplitude which increase with the offset gather increasing in location A and B. CDP gather in location C is shown in Figure 31 and shows that there is no amplitude increase with the offset increasing. It is shown by the absence of gas in location C.


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Figure 29. CDP gathers for location A on line SV-1 (Ostrander, 1984)


79

Figure 30. CDP gathers for location B on line SV-1(Ostrander, 1984)


80

Figure 31. CDP gathers for location C on line SV-1 (Ostrander, 1984)


81

Figure 32. The stacked seismic section for line GM-1(Ostrander, 1984)


82

Figure 33. CDP gather for location A on line GM-1 (Ostrander, 1984)


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Figure 34. CDP gathers for location B on line GM-1 (Ostrander, 1984)


84

Figure 32 shows the anomaly of seismic wave amplitude which related to gas in GM-1 seismic line, in Gulf of Mexico. The first anomaly is located on the left of seismic section at the time about 0.65 seconds. The second anomaly is a deeper anomaly located to the center of seismic section at the time about 1.35 seconds.


85

Summed CDP gather is presented on Figure 33 for location A on shallow anomaly and on Figure 34 for location B on deep anomaly. Both anomalies show that the reflection amplitude increases with the offset increasing. On the shallower anomaly case on location A, the array attenuation effect and NMO stretching on trace offset 5 is obvious.


86

Figure 35 is the 24-fold CDP stack seismic line in Nevada basin. A well is located in this line, on A SP 127 (location A) down to the depth under 2.0 s. Anomaly of seismic amplitude is shown on seismic data at the time about 1.6 s. What happened here, that the bright spot phenomena did not show the presence of gas in sediment rock.


87

6. AVO AVO Classi Classific ficati ation on Rutherford and Williams in 1989 said that there are three classes of gas-sandstone reservoirs, i.e : Class 1 : high impedance gas-sandstones Class 2 : near zero impedance contrast gas-sandstones Class 3 : low impedance gas-sandstones


88

Figure35. The stacked seismic section for line FB-1 (Ostrander, 1984)


89

Figure 36. CDP gathers for location A on line FB-1 (Ostrander, 1984)


90

Figure 37. The reflection coefficient of flat wave on each gas-sandstone top of Rutherford and Williams classification (1989)


91

Figure 37 shows a set of AVO reflection coefficient curves on the interface between shale and gas-sandstone which computed in reflection coefficient range on normal incidence of RC0. The curves in Figure 37 are computed based on the Poisson’s ratio of shale and gas-sandstone, 0.38 and 0.15, respectively, and the density of shale and gas-sandstone, respectively, 2.4 and 2.0 g/cm3.


92

6.1. Anomaly Class 1: High Acoustic Impedance Sandstone Sandstone Class 1 has relatively high impedance than its seal layer, which usually is shale. Interface between shale and this sandstone will result relative high positive coefficient reflection (R 0). The top curve on Figure 37 showing anomaly curve for sandstone class 1, usually this sandstone is found in coastal exploration area. This sandstone is a mature sandstone which have moderately to highly compacted.


93

Coefficient reflection of high acoustic impedance sandstone is positive on zero offset and began with amplitude magnitude decrease as the offset increases. Magnitude of amplitude change to offset (usually known as the term ‘gradient’) for sandstone class 1 usually is bigger than gradient of sandstone class 2 or 3. The gradient depends on the RC0, generally, gradient will decrease as the RC0 and Poisson’s ratio decreases.


94

Reflectivity magnitude of sandstone class 1 initially will decrease as the offset increasing and may have polarity change on certain angle, and then the amplitude increase will happened again as the offset increases with the oppositely polarity of the initial polarity. Therefore, on a good case, synthetic seismogram with normal incidence can not accurately predict a reflection amplitude response of sandstone class 1on stacked data.


95

6.2. Anomaly Class 2 : Near-Zero Acoustic Impedance Contras Sandstone Sandstone Sandstone class class 2 has almost almost the same same Acoustic Acoustic Impedance Impedance as the seal rock. This sandstone is a compacted and moderately consolidated sandstone. Gradient of sandstone class 2 usually has big magnitude, but generally it’s smaller than the magnitude of sandstone class 1. Reflectivity of sandstone class 2 on small offset is zero. This is often blurred due to the presence of noise on our data seismic. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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The reflectivity suddenly emerge on bigger offset, that is when the reflection amplitude is located on a higher level than the noise. Polarity change happen if the RC0 is positive, but usually it’s undetected, because it happen on the near offset where the signal level is under the noise. Sandstone class 2 might and might not be related to amplitude anomaly on stack data. If the angular range is available, so the amplitude will rise as the offset increasing, it is the amplitude anomaly on stacked data.


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6.3. Anomaly Class 3 : Low Acoustic Impedance Sandstone Sandstone class 3 has lower acoustic impedance than the seal rock. Usually this sandstone is the less compacted and unconsolidated sandstone. On seismic stack data, sandstone class 3 has big amplitude anomaly and reflectivity in the whole offset. Usually, the gradient is significant enough but it has lower magnitude than the sandstone class 1and 2 during the RC’s normal incidence angle is always negative.


98

In some conditions, relatively small change of amplitude to offset can cause detection difficulties because the presence of tuning thickness, attenuation, recording array, and decreasing of signal-to-noise to the offset ratio. Sandstone class 3 sometime has high amplitude response which relatively flat along with the offset.


99

7. The Examples of AVO Anomaly 7.1. Example of Sandstone Class 1 Figure 38 showing an example of AVO anomaly class 1 in Hartsh Hartshorn orn channel channel area. area. The The mode modelin ling g of normal normal incide incidence nce angle doesn’t show the dim out phenomena. Figure 39c showing the synthetic CMP gather which computed by using the well data log that penetrate the Hartshorn sandstone channel.


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The first trace on the left of Figure 39c is the trace of normal incidence. The second trace shows trace on 50 m offset, and the rest are the traces on each 134 m offset increasing. Sonic Sonic log on Figu Figure re 39a showing showing that that Hart Hartshor shorn n sandst sandstone one packet is a sandstone class 1, which is high acoustic impedance sandstone. Figure 40 showing three CMP gathers which related to the dim out area in Figure 38. Notice that the polarity change happen on middle of offset interval. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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7.2. Example of Sandstone Class 2 Example for AVO anomaly of sandstone class 2 is a mid-ag mid-aged ed Mioc Miocene ene sandst sandstone one in Braz Brazos os area, area, Gulf Gulf of Mexico. Figure 41 is the stack section which shows the reflection of thin gas-sandstone. Figure 43 is the seismic synthetic section from Figure 42 model model which which comput computed ed by the Zeoppr Zeoppritz’s itz’s equation. equation. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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First 10 traces on the left of each figure are identical and computed from log well which through the mid Miocene gassandstone reflector as shown on Figure 39. Last 10 traces on the right of each figure are identical and computed from the same log well from water saturated sandstone model. Mid-offset (1524 m) and far-offset (3048 m) synthetic sections show that AVO effect which related to gas-sandstone is obvious. Gas-sandstone anomaly characters of data stack on Figure 39 are caused by big far-trace amplitude.


103

Figure 39. A stacked seismic section on Hartshorn field. The productive interval corresponds to the dim out phenomena which which highlighted in the figure. The dim out is caused by a change in polarity to with offset of the Hartshorn reflection (Rutherford and Williams, 1989)


104

Figure 40. The CMP gather modeling. (a) P-wave sonic log through the Hartshorn interval. (b) estimated S-wave sonic log (c) the computed CMP gather (d) stack stack of the traces in (c). (c). (Rutherford & Williams, 1989)


105

Figure 41. Three CMP gathers show the change in polarity which which associated to Hartshorn gas-sandstone. The last trace on each gather of far offset were distorted by NMO stretching (Rutherford & Williams, 1989)


106

Figure 42. Migrated-stacked section on Miocene gas-sandstone in Brazos Gulf of Mexico. The reflector of interest is at about 2.1 s on the section. (Rutherford & Williams, 1989)


107

Figure 43. Diagram of Brazos gas-sandstone (Rutherford & Williams, 1989)


108

Figure 44. Synthetic model section section on Figure 42 which computed by using the log from Miosen sandstone sandstone well as shown on Figure 40. First three sections related to 0 m, 1524 m and 3048 m offsets. The last sections s ections (right-down) produced by stacking range offset from data on Figure 6.62 (Rutherford & Williams, 1989 )


109

Figure 45. Panel display of constant reflection angle sections corresponding to Figure 40. The angles posted on the right side of figure refer to the centers of the angle ranges in each panel. Each 1.0 s panel displays 1.6 s to 2.4 s data (Rutherford & Williams, 1989)


110

Figure 46. Migrated, stacked seismic section on Pliocene gas-sandstone in High Island Gulf of Mexico. The reflector of interest is between 2.3 s and 2.5 s (Rutherford & Williams, 1989)


111

Stack section on Figure 44 predicts the anomaly response for the same gas-sandstone as appeared on Figure 42. Figure 45 is a display of constant reflection angle panels. Each panel on Figure 45 showing the data from Figure 42 with different reflection angles. Gas-sandstone reflectivity on small angle is is zero as the charact character er of gasgas- sandstone sandstone class class 2 . The gradient is obvious and showing high reflection amplitude on bigger reflection angle.


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7.3. Example of Sandstone class 3 Example for gas-sandstone class 3 is a AVO anomaly on High Island area of the gulf of Mexico. Figure 46 showing seismic section which through the gas-sandstone. Gas-sandstone associated to the bright spot phenomena. AVO characteristic of gas-sandstone class 3 is visible on Figure 47 as panel of constant incidence angle reflection.


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8. AVO Anomaly Class 4 In fact, the forth class of gas-sandstone is the anomaly with the reflection coefficient becoming positive along as offset increases, but the magnitude decreased as the offset increases. Sandstone class 4 often emerged when the porous sandstone, which is restricted by the lithology, has high seismic wave velocity, such as hard shale (e.g : siliceous or calcareous), siltstone, tightly cemented sand, or carbonate.


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Sandstone class 4, which fall in quadrant II (Figure 48), has big negative Intercept (A) and positive Gradient (B). Sandstone class 4 is the bright spot, but the reflection magnitude decreased as the offset increases. It is described on Figure 49 for low acoustic impedance brine sand which drops on background trend. Shuey’s Shuey’s (1985) approximati approximation on of two terms terms is good good enough enough on incidence angle about 300. For smaller angle, B is positive for brine and gas sands, and the magnitude decreased as the offset increases. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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Figure 47. Panel display of constant reflection angle sections corresponding to the section on Figure 6.23. The angles posted on the right side of the figure refer to the centers of of the reflection angle ranges in each panel. Each 1.0 s panel displays 2.0 s and 2,8 s of live data (Rutherford & Williams, 1989)


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Figure 48. Cross plot of AVO intercept (A) against gradient gradient (B) shows 4 possibilities of quadrant. For limited time window, brinesaturated sandstones and shale it present all along the background trend. Top reflection of gas-sandstone drops below the background trend, bottom reflection of gas-sandstone drops on the trend. Rutherford & Williams gas-sandstone classification (1989) is used as a reference reference (Castagna (Castagna et.al, 1998)


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Figure 49. Reflection coefficient of flat wave against the incident angle for top gas- sandstone class IV (quadrant (quadrant II), and related brine-sand reflection. The model parameters are : shale-VP = 3.24 km/s, VS = 1.62 km/s, ρ = 2.34 gm/cm3; brine sand-VP = 2.59 km/s, VS = 1.06 km/s, ρ = 2.21 gm/cm3; gas-sand-VP = 1.65 km/s, VS = 1.09 km/s, ρ = 2.07 gm/cm3


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Figure 50. Class II (dash) and IIp (solid) schematic showing the effective amplitudes of the far-range far-range stack and the near-range stack defined by incident angle. Separation of θn and θ f away from the angle of phase reversal (θ ( θ p) typically increases the dynamic range of the FN attribute. Here, an and a f are the average average amplitudes of the near- and far-ranges, respectively.


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Table 6.2. Reflection coefficient of gas-sandstone top against the offset for 4 classes of AVO anomaly.

Class

Relative Impedance

Quadrant

A

B

Note

I

Higher than the seal layer

IV

+

−

Coefficient Reflection (and magnitude) decreased as the offset increases

II

Almost the same with the seal layer

III or IV

±

−

Reflection Magnitude decreased or increased to offset and the polarity reversing can happen

III

Lower than the seal layer

III

−

−

Reflection Magnitude increases to offset

IV

Lower than the seal layer

II

−

+

Reflection Magnitude decreases to offset


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Figure 51. The cross plot of reflection coefficient of zero-offset (A) against AVO gradient (B) by assuming that the VP/VS is constant and Gardner’s relationship. The The background rotates oppositely to the clock and inline with the Vp/Vs Vp/Vs increase (Castagna (Castagna et.al, 1998)


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9. Nonbright-spot AVO Anomaly Analyzing the nonbright-spot seismic with AVO will have : 1) Inab Inabil ilit ity y to det detec ectt the the gas gas rese reserv rvoi oirr beca becaus usee aco acous usti ticc impedance contras between gas-sandstone and its seal rock is nearly zero. 2) Resu Result ltin ing g the the wron wrong g AVO AVO prod produc uctt (ne (nega gati tive ve)) if if the the incidence angle and the gradient value have the contrary sign. Certain contras of seismic wave velocity, density and Poisson’s Ratio can result anomaly class II or II p response (Figure 50). AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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10. Relationship of AVO Gradient and AVO Intercept The The para param meter eter Vp, Vp, Vs, and and ρ are often close related. This relationship caused varied relationship between angular coefficient reflection of A (Intercept) and B (Gradient). The background trend tilt is only depend on the (Vp)/(Vs) ratio. Figure 51 showing that as the (Vp)/(Vs) increasing, the background trend tilt become more positive (the trend rotates oppositely to the clock for Intercept (A) which plotted along the axis x).


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Figure Figure 52 showing showing that that when when the Vp decreased, decreased, the the background background trend tilt become more positive (the rotation is oppositely to the clock). This figure uses an assumption that the tilt of trend shale mud rock m is equal to 1.16 and the Intercept c is equal to 1.36 km/s, as given by Castagna et al. (1985). Notice that the background trend tilt changes dramatically for smaller velocity than 2.5 km/s.


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Deviat Deviation ion of of petrop petrophyca hycall relati relations onship hip back backgro ground und is is result resulted ed from brine substitution on pore space. The mechanical gas substitution to brine cause the (Vp)/(Vs) decrease and make the ∆VP and ∆ρ become more negative. Figure 53 showing computed AVO intercept and gradient for the reflector pair shale/gas sand and shale/brine sand. Figure 54 showing the connecting line of brine sand-gas sand for 25 sets of of sonic log insitu insitu measurement measurement on brine brine sands, sands, gas sand sands, s, and and shal shales es (Cas (Casta tagn gnaa & Smit Smith, h, 1994 1994). ).


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Figure 52. The cross plot of zero offset reflection coefficient (A) (A) against the AVO gradient (B) by assuming the VP trend linear to VS (m = 1.16; c = 1.36 km/s) and Gardner’s relationship. The background trend rotate oppositely to the clock and in line with the VP decrease decrease (Castagna (Castagna et.al, 1998) 1998)


126

Figure 53. The connecting line of brine sand-gas sand for shale which restrict the brine-sand reflection with P-wave average velocity of 3 km/s and which fill the Gardner Gardner curve trend and mud mud rock petrophysics (g = 0.25; m = 1.16; c = 1.36 km/s) km/s) and Gessmann’s equation equation (Castagna (Castagna et.al, 1998) 1998)


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Figure 54. AVO reflection coefficient movement due to the gas elimination o n sanded layer below the shale for 25 sets of velocity and shale density, brine-sand, and gas-sand (Castagna et.al, 1998)


128

Figure 55. Classes of AVO and AVO cross plots (Simm et.al, 2000)


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11. AVO Crossplot AVO AVO cros crossp splo lott is a sim simple ple way way to to show show the the AVO AVO data data.. Amplitude variation to the offset for reflection boundary is shown as single point on intercept and gradient crossplot. The advantag advantagee of this this crossplo crossplott is it can show show information information from a data which can not appeared by standard offset appearance. Figure 55 showing intercept (R 0) to gra gradi dien entt (G) (G) cros crossp splo lott and and also the gas sandstone classes that described before.


130

11.1. Signal and Noise Effects on AVO Crossplot Figure 56 showing single point on down right quadrant of crossplot. This point is resulted from AVO attribute (differentiated from least square regression) which related to single zero phase reflection of non-noise synthetic gather. This point shows the response of AVO anomaly class 1 from brine-filled consolidated sand top which adjacent to the seal shale, in here the amplitude decreased to offset.


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If the random noise is uniformly added to CMP gather (S/N decreased as the offset increases), crossplot response will be an oval distribution around the real location (Figure 57). It is caused by gradient sensitivity to noise. Hendrickson called this as ‘noise ellipse’. This noise is visible on real data by plotting the limited sample on the same horizon. Parallel spreading pattern to the gradient shows the decrease of S/N. On real data, noise trend usually has tilt about 50 or more. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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11.2. Porosity and Shale Content Effects to AVO Crossplot Porosity increase has two effects i.e : first, decreases the AVO gradient (such as : contras of Poisson Ratio and seal shale decreased), and second, decreases the intercept (as the impact of acoustic impedance contras decrease). Porosity change on sandstone causes the presence of an ellipse line as shown on Figure 58.


133

Figure 56. Anatomy of AVO cross plot, single class 1 reflection (Simm et.al, 2000)


134

Figure 57. The noise which associated with the gradient measurement on some gathers (Simm et.al, 2000)


135

Lithol Lithology ogy change change as as the shal shalee conten contentt increa increase se on sand sandsto stone ne cause the intercept and gradient decreasing, but the trend tilt is steeper than the trend porosity. On the case which the shale component in sandstone is different from the shale seal (as can found in sequence boundary), so ‘lithologi ‘lithologicc trend’ trend’ will have have intercept intercept non non zero value. value.


136

11.3. The Gas Presence Effect on AVO Crossplot Figure 59 showing fluids/gas substitution effect on sandstone with porosity variation. From the figure appeared the drifting phenomena to the down left of background trend as the result of gas presence in pored sandstone. From this figure we can obviously see the gas effect to intercept and gradient that moved to negative.


137

11.4. Time Window Crossplot The examples of time window are combined in a crossplot, horizon points sample, together with the reflection of sandstone base, involved in an ellipse points which concentrated on its origin place (Figure 60). Figure 61 and 62 are the time window window crosspl crossplot ot applying applying on real real data.


138

12. AVO Attributes AVO attributes are quite useful in interpretation increase, reservoir evaluation, understand the relationship between rock and fluids natures, and play role in hydrocarbon delineation. The AVO attributes are :      

Normal Incident P-Wave (A) Gradient (B) Product Gradient (A*B) Fluid Factor (F) Lambda Mu Reflectivity Amplitude Envelope (Far-Near)Far (Far-Near)Far AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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Figure 58. Porosity Porosity effect on AVO cross plot (Simm et.al, 2000)


140

Figure 59. Gas effect effect on AVO cross plot (Simm et.al, 2000)


141

Figure 60. Time Time window cross cross plot (Simm et.al, 2000)


142

Figure 61. The example of real data. (a) Stacking section describes bright spot with picked sandstone top in green. (b) Time window cross plot which produced produced from 40-ms 40-ms window around the top sand sand (Simm et.al, 2000)


143

Figure 62. Horizon cross plot. (a) R0/G cross plot for pick which shown on Figure 63 and illustrates the different between trend which associated with bright spot and background reflectivity. (b) Near/Far cross plot illustrates that the background trend on R0/G cross plot related related to noise, not to lithology (Simm et.al, 2000)


144

Figure 63. P-wave normal incident section (A) (source : www.vsl.com)


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12.1. Normal Incident P-wave (A) Normal Incident P-wave (A) is known kno wn as Intercept, this attribute is the acoustic impedance function and resulted from extrap extrapola olatio tion n of presta prestack ck AVO gradi gradient ent trend trend data data on zero zero offset. Normal incident P-wave (A) is the first digit on Shuey’s equation :

 σ  2 RC(θ ) = RC p + R p A 0 + sin θ + .... 2 (1 − σ )   Normal Incident P-Wave P-Wave (A)


146

12.2. Gradient (B) This section is resulted from AVO inversion equation where gradient is the characteristic of amplitude versus offset from a pre-stack seismic data. Gradient Gradient (B) is is the second second term on on following following Shuey’s Shuey’s equation: equation:

 σ  2 RC(θ ) = RC p + RC p A 0 + sin θ + .... 2 (1 − σ )   Gradient (B)


147

12.3. Product Gradient (A*B) Product gradient is resulted from multiplication between normal incidence and gradient. This product is used as the key to identify the bright spot of AVO anomaly class 3 and choose the amplitude anomaly of dim out class 2 if the positive value on product gradient showing positive AVO.


148

12.4. Fluids Factor (F) Fluid factor section has been known for years as Direct Hydrocarbon Indicator (DHI) section that shows low amplitudes for reflecti reflection on related related to clastic clastic sediment sediment sequence, sequence, the the rock with with low amplitude trend ‘mud rock line’ including the sandstone contained hydrocarbon, carbonate, and igneous rock. Fluid factor section is generated by using AVO inversion equation which explained by Smith and Gidlow.


149

Figure 64. The gradient section (B) (source : www.vsl.com)


150

Figure 65. The gradient product (A*B) section (source : www.vsl.com)


151

Figure 66. The fluid factor (F) section (source : www.vsl.com)


152

Figure 67. The lambda reflectivity section (source : www.vsl.com)


153

Anomaly trend (such : hydrocarbon-bearing reservoirs) is shown as high amplitude reflector on fluid factor section. Fluid factor section is an ideal attribute for recognition in area which has few well control.


154

Exercise L-1 The construction construction of Poisson Poisson’s ’s ratio ratio vs P-wave P-wave velocity velocity (Vp) cross plot using empiric measurement. Objective Unders Understan tand d the use of of Poisson Poisson’s ’s rati ratio o vs. Vp Vp cross cross plot plot to predict the rock physical characters. Material 1. Poro Porosi sity ty,, Vp, Vp, and and Poi Poiss sson on’s ’s rati ratio o dat dataa on on Tab Table le L6-1 L6-1-1 -1 to Table L6-1-6 2. Graphic block of Figure L6-1-1


155

Questions: 1.

By usin using g dat dataa in in Tab Table le L6-1 L6-1-1 -1 to L6-1 L6-1-6 -6,, mak makee a cros crosss plo plott of Vp Vp agains againstt Pois Poisson son’s ’s ratio ratio (PR) (PR) on on avai availab lable le block block (Figure L6-1-1). 2. Plot Plot thes thesee two two foll follow owin ing g san sands dsto tone ne samp sample less on on the the cros crosss plot that you have made. Sandst Sandstone one A : Vp = 2400 2400 m/sec m/sec;; σ = 0.16 Sandst Sandstone one B : Vp Vp = 2700 2700 m/se m/sec; c; σ = 0.36 3. Refe Referr rrin ing g to to Fig Figur uree 6.1 6.16, 6, what what type type are are the the sand sandst ston onee A and B? 4. How How much much is the the app appro roxi xima mate te valu valuee of the the sand sandst ston onee A and B porosities? AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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Table L1-1 : Φ, Vp Vp and and σ on measurement I

Porositas Porositas (%) (%) 0 10 20 30 40 50 60 70 80 90 100

Vp(m/s p(m/sec) ec) 5984 3573 2911 2571 2368 2236 2157 2110 2093 2103 2142

Poiss Poisson Ratio 0 .1 2 0 .2 9 0 .3 2 0 .3 3 0 .3 3 0 .3 4 0 .3 4 0 .3 4 0 .3 4 0 .3 4 0 .3 4

Table L1-2 : Φ, Vp Vp and and σ on measurement II

P or o ro sit as as ( %) 0 10 20 30 40 50 60 70 80 90 100

Vp ( m /sec) 5964 3621 2400 2132 2004 1959 1983 2001 2296 2762 4264

P oi oisso n Rat io io 0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 2


157

Table L1-3 : Φ, Vp Vp and and σ on measurement III

Table L1-4 : Φ, Vp Vp and and σ on measurement IV

Po rositas rositas (%) (%)

Vp(m/sec p(m/sec))

Po iss isson Ratio

Porosi Porosit as (%) (%)

Vp(m/s p(m/sec) ec)

Poiss Poisson Ratio atio

5 5 5 5 5 5 5 5 5 5

3753 3750 3748 3746 3744 3743 3744 3747 3758 3786

0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 2 0 .1 3 0 .1 3 0 .1 3 0 .1 3 0 .1 5

15

2641

0 .1 2

15

2633

0 .1 2

15

2626

0 .1 3

15

2619

0 .1 3

15

2612

0 .1 3

15

2607

0 .1 3

15

2602

0 .1 3

15

2600

0 .1 3

15

2604

0 .1 4

15

2629

0 .1 5

5

4248

0 .2 5

15

3117

0 .3 1


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Table L1-5 : Φ, Vp Vp and σ on measurement V

Table L1-6 : Φ, Vp Vp and and σ on measurement VI

Po rositas rositas (%) (%) 33 33 33 33 33 33 33 33 33 33

Vp(m/sec p(m/sec)) 2091 2074 2057 2040 2025 2010 1997 1986 1980 1993

Po iss isson Ratio 0 .1 2 0 .1 2 0 .1 3 0 .1 3 0 .1 3 0 .1 3 0 .1 3 0 .1 3 0 .1 4 0 .1 6

Porosi Porositas (%) (%)

Vp(m/s p(m/sec) ec)

Poiss Poisson Ratio atio

50

1977

0 .1 2

50

1943

0 .1 3

50

1911

0 .1 3

50 50

1881 1853

0 .1 3 0 .1 3

50

1826

0 .1 3

50

1802

0 .1 3

50

1781

0 .1 3

50

1765

0 .1 4

50

1767

0 .1 6

33

2500

0 .3 3

50

2238

0 .3 4


159

0.5 o i t a R s ’ n o s s i o P

0.4 0.3 0.2 0.1 0

0

1

2

3

4

5

6

7

V P (km/sec)

Figure L1-1. L1-1. The section section of Vp versus Poisson’s Poisson’s Ratio Ratio cross plot AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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Exercise L2 : Computation of amplitude response to angle of incidence (offset) based on the sonic log and density data. Purpose: The student able to do the forward modeling of AVO response base on the sonic and density log, also able to analyze the AVO class anomaly. Material: Figure L2-1 ; work sheet ; graphic block AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

161

Questions: 1.

Comp Comput utee the the refl reflec ecti tion on ampl amplit itud udee aga again inst st the the ang angle le of incidence by using the Zeoppritz’s approximation : R(θ R(θ) = (Rp – 2Rs)sin2 θ, for θ = 0º, 10º, 20º, 30º.

2.

Plot Plot the the amp ampli litu tude de to the the ang angle le in the the ava avail ilab able le grap graphi hic. c. What type of gas sandstone is that?


162

Vp = 10.000 ft/s ; ρ = 2.6 g/cc ; Vs = 5000 50 00 ft/s

Vp = 12.000 12.000 ft/s ft/s ; ρ = 2.2 g/cc ; Vs = 7.500 ft/s

Figure L2-1. Curves log of Sonic P, Sonic S, and Log density resulting from measurement in Well ‘S’ of field X


163

Table L2-1. Table of amplitude computation

Litologi Shale Batupasir

Vp Vs ρ 10000 000 5000 2.6 12000 000 7500 2.2

Zp

Zs

Rp

sin (θ) sin^2( n^2(θ)

θ

Rs 2Rs Rp-2Rs

R(θ)

0 10 20 30 AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

164

Amplitude-Incident Angle 0.02 0.015 0.01 0.005 0 -0.005 0

5

10

15

20

25

30

35

-0.01

e d -0.015 u t i l -0.02 p m-0.025 A -0.03 -0.035 -0.04 -0.045 -0.05 -0.055 -0.06

Incident Angle Figure L2-2. Diagram of amplitude-incident angle cross plot


165

Exercise L3 Delineation of top and bottom of gas-sandstone reservoir in CDP gather.

Objective Understand how to delineate the top and bottom of gassandstone reservoir on CDP gather, based on the amplitude character against offset.


166

Material : Figure L3-1 is one off the CDP gather in North Paria gas field Venezuela. The gas-sandstone reservoir has relative high acoustic impedance than the seal rock. (note: we using the wavelet porosity of NORMAL SEG). Question: 1.

From From the the fig figur ure, e, do the the top top and and bot botto tom m del delin inea eati tion on of thre threee sandstone reservoirs.


167

Figure L3-1. The CDP gather of Paria gas filed, North Venezuela (Regueiro, 1996)


168

Exercise L4 Compute the amplitude of reflection wave based on the Shuey’s approximati approximation on and the error error to to the Zeoppritz Zeoppritz amplitude. amplitude. Objective: Understand the basic concept of amplitude computation by using using the the Shuey Shuey’s ’s approx approxima imatio tion n based based on the the rock rock physi physical cal parameter and ray path geometry. Material: Figure L4-1 shows the Ostrander sandstone and its physical characters. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

169

Questions: 1.

How How muc much h is is the the ampl amplit itud udee of of ref refle lect cted ed wave wave base based d on on the the Shuey’s Shuey’s approximatio approximation n in angle angle of of incidence incidence 26.6 º?

2.

How much uch is is the the appr approx oxiimate mated d err error or agai agains nstt the the comput computati ation on using using Zeop Zeoppri pritz’ tz’ss equati equation, on, if if we know know the the amplitude based on the Zeoppritz’s equation in angle of incide incidence nce 26.6 26.6 º is –0.2196 –0.2196??


170

Figure L4-1 : 3 layers Ostrander model which the first first layer is the shale with Vp = 10000 ft/s, ρ = 2.40 g/cc, and σ = 0.4 ; the second layer is gas gas sand with Vp Vp = 8000 ft/s, ft/s, ρ = 2.41 g/cc, σ = 0.1 ; the third layer is the shale with the same character as the first one (Ostrander, 1984)


171

Work Sheet of Exercise L4 :

Vp1

= 10000

ρ1= 2.4

σ1 = 0,4

θ1 = 26.6º

Vp2

= 8000

ρ2= 2.14

σ2 = 0,1

θ2 = ……

∆ Vp = ……

∆ρ = …… ∆σ = ……

θ = ……

Vp

ρ = ……

sin2θ = …..

=……..

∆Vp/Vp =……

σ = ……

∆ρ/ρ =……

tan2θ = ……


172

Rp = ½(∆Vp/Vp + ∆ρ/ρ) = ……….. (RpTRUE = -0.1673) B = (∆Vp/Vp) / (∆Vp/Vp + ∆ρ/ρ) = ………… A0 = B – 2 (1 + B) ((1 - 2σ) / (1-σ)) =……….. G = Rp A0 + ∆σ / (1 – σ)2 = ……….. c = ½ (∆Vp/Vp) (tan2θ –sin2θ) = ……… R (26 (26.6 .6)) = Rp + G sin sin2θ + c = ………. Error Error = -0.219 -0.2196 6 – R(26.6 R(26.6)) = ……… ………..


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Exercise L5 : Classification of gas-sandstone reservoir based on the seismic attribute section and AVO cross plot Purpose : The student able to analyze type of gas-sandstone based on the characteristic of complex attribute Instantaneous Frequency and Acoustic Impedance, also cross plot of AVO Intercept vs. Gradient. Material : Figure L5-1, the Instantaneous Frequency section (left-down), Acoustic Impedance (right-down), and AVO cross plot (top)


174

Questions : 1.

Deter etermi mine ne type type of gasgas-sa sand ndst ston onee whi which ch is high highli ligh ghte ted d bas based ed on the classification of Rutherford and Williams !

2.

Deli elinea neate the the top top and and bot botttom of the gas gas-san -sands dsto tone ne on the Instantaneous Frequency and Acoustic Impedance sections!


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Figure L5-1. The Instantaneous Frequency (left-down), Acoustic Impedance (right-down) and AVO cross plot (top).


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Exercise L6 Analysis of Intercept vs. Gradient cross plot Purpose: The student able to do the classification of AVO anomaly based on the cross plot of Intercept vs. Gradient Material: Figure L6-1 and Figure L6-2.


177

Questions: 1.

Do the the clas classi sifi fica cati tion on of AVO AVO anom anomal aly y fr from om AVO AVO cros crosss plot in Figure L6-1 and Figure L6-2.

2.

How How doe doess the the rela relati tion onsh ship ip betw betwee een n the the AVO AVO ano anoma maly ly and and its background attribute ?


178

Well #1

Figure L6-1 : Some Intercept versus Gradient cross plots with background of Instantaneous Frequency section (Abdulah, 2001)


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Figure L6-2. Some Intercept versus Gradient cross plots with background of P*G section (Abdulah, 2001)


180

Exercise L7 Delineation of horizon and structure based on the AVO attribute of Far-offset and Near-offset. Purpose: The student understands the use of AVO attribute Far-offset and Near-offset for horizon and structure delineation. Material & Question Figure L7-1 shows the AVO Far-offset and Near-offset sections of study area. Delineate the anomaly area. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

181

Exercise L8 Delineation of top and bottom gas-sandstone from the attribute section P*G. Purpose: The stude student nt unders understan tands ds the use use of attribu attribute te PxG (Inter (Intercep ceptt x Gradient) for reservoir delineation. Material & Question: Figure Figure L8-1 shows the the PxG attribute, attribute, determine determine the the top-bottom top-bottom gas sand class III. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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Exercise L9 Delineation of top and bottom gas-sandstone from the attribute section PxG. Purpose: The stude student nt unders understan tands ds the use use of attribu attribute te PxG (Inter (Intercep ceptt x Gradient) for reservoir delineation. Material & Question: Figure L9-1 and L9-2 show the near-far offset attribute and also PxG. Determine the anomaly area and top-bottom gas sand class III. AVO/AVA for Gas/Fluid Gas/Fluid Detection & Seismic Seismic Lithology Analysis

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Figure L7-1 : NearNear- (left) & Far-offset Far-offset (right) sections of line X. Anomaly area delineation.


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Figure L8-1. Display of PRODUCT Ro x G and Ro vs. G cross plot on previous figure. Determine Determine the top and bottom of gas sand. The red indicates that the product is positive while blue is negative. The wiggle display is the Intercept on zero angle with normal polarity.


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Figure Figure L9-1. ANGLEANGLE-STAC STACK K NEAR-TRA NEAR-TRACE CE (left, (left, 1º - 9 º) and FAR-TRACE FAR-TRACE (right (right,, 17 º - 25 º). Determine Determine the the anomaly anomaly of gassandstone class III.


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Figure L9-2. Figure L6-8-1. Display of PRODUCT PRODUCT Ro x G and and Ro vs. G cross plot on previous figure. Determine the top and bottom of gas sand. The red indicates that the product is positive while blue is negative. The wiggle display is the Intercept on zero angle with normal polarity.


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0001 AVO Fundamental

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